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Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

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CATEGORY:
Questioning the Foundations Essay Contest (2012)
[back]

TOPIC: Misinterpreting Reality: Confusing Mathematics for Physics by Robert H McEachern [refresh]

TOPIC: Misinterpreting Reality: Confusing Mathematics for Physics by Robert H McEachern [refresh]

In one of the great scientific tragedies of the past century, “Modern Physics” was developed long before the development of Information Theory. Consequently, the early search for the “meaning” of the equations of mathematical physics, especially quantum physics, was based on several critical assumptions about the nature of information, which have subsequently been shown to be untrue. Unfortunately, none of the physicists, at the time, (and apparently even today) recognized these assumptions, as such. Hence, the misunderstandings engendered by those assumptions have become unquestioned dogma. Equations contain very little information. This fact is what makes it possible to symbolically represent them, in a computer memory, by a very small number of bits. As a direct result of this fact, we can conclude, contrary to the fervent belief of most physicists, that equations cannot describe anything other than the most trivial physical phenomenon; those nearly devoid of all information. For complex phenomenon, it is the vast information content of the initial conditions (like the content of an observer's memory) rather than the tiny information content of equations, that really matters. Indeed, observations become “quantized” if and only if the information content of the observations is small. It is not small physical size, but small information content, that is the cause of “quantization.” More importantly, since the information content of the “meaning” of the equations is usually much greater than the information content of the equations themselves, the “meaning” cannot possibly be contained within the equations; the “meaning” has simply been made-up and slapped-on. The controversies and paradoxes surrounding non-locality, superposition, entanglement, and the uncertainty principle are all examples of this problem; the equations accurately describe the observations, it is only the slapped-on “meaning”, that causes of all the difficulties in understanding.

Robert H. McEachern was educated as an AstroPhysicist. He then worked for several years as a Geophysicist, during which time he became interested in signal processing theory. He then spent the rest of his career developing signal processing algorithms for application to communications systems, and sensor systems. He is now retired.

I have just begun to read your essay but feel overanxious to welcome your essay:

"More importantly, since the information content of the “meaning” of the equations is usually much greater than the information content of the equations themselves, the “meaning” cannot possibly be contained within the equations; the “meaning” has simply been made-up and slapped-on. The controversies and paradoxes surrounding non-locality, superposition, entanglement, and the uncertainty principle are all examples of this problem; the equations accurately describe the observations, it is only the slapped-on “meaning”, that causes of all the difficulties in understanding."

James

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"More importantly, since the information content of the “meaning” of the equations is usually much greater than the information content of the equations themselves, the “meaning” cannot possibly be contained within the equations; the “meaning” has simply been made-up and slapped-on. The controversies and paradoxes surrounding non-locality, superposition, entanglement, and the uncertainty principle are all examples of this problem; the equations accurately describe the observations, it is only the slapped-on “meaning”, that causes of all the difficulties in understanding."

James

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Dear Robert H. McEachern,

You are addressing some interesting aspects of signal processing in a refreshing manner. I would like to suggest you reading not just my current essay but also the earlier one in order to crosscheck our ideas. In turn I would be interested in hints to your earlier work on signal processing. Unfortunately, you did not list any reference. I do not see Einstein's 1905 paper on relativity a good example.

Regards,

Eckard

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You are addressing some interesting aspects of signal processing in a refreshing manner. I would like to suggest you reading not just my current essay but also the earlier one in order to crosscheck our ideas. In turn I would be interested in hints to your earlier work on signal processing. Unfortunately, you did not list any reference. I do not see Einstein's 1905 paper on relativity a good example.

Regards,

Eckard

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Robert,

The "slapped-on meaning" seems to be the rule rather than the exception. You stated, "Here we only seek to illuminate an underlying bad assumption at the heart of the issue; namely that the number of components that exist in the mathematical description of an observation must necessarily equal the number of components that actually exist in the entity being observed."

A mathematical symbol and its associated descriptor(s) should contain all the entity's components such there is no confusion as to the meaning. Consider the symbol "c" for the speed of light. Does everyone understand that this is a measured value made in a vacuum some place on the Earth's surface at some unspecified position in the Earth's orbit around the Sun? When c is used, shouldn't it be noted it is being used as a theoretical value or a measured value? To avoid confusion, c_{t} would represent theoretical and c_{me} would represent measured on the Earth. There are more components to c than just length per unit time.

A pure mathematical derivation of the value for the speed of light is contained in the July/August 2011 IEEE Potentials article titled, "A methodology to define physical constants using mathematical constants".

IEEE Methodology

or for those without IEEE membership,

Postprint Methodology

The NASA/JPL web site for the Curiosity lander has a question and answer process, ask Dr.C. I submitted a question, before it landed, "What is the measured permittivity on the surface of Mars?" I am still waiting for a response.

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The "slapped-on meaning" seems to be the rule rather than the exception. You stated, "Here we only seek to illuminate an underlying bad assumption at the heart of the issue; namely that the number of components that exist in the mathematical description of an observation must necessarily equal the number of components that actually exist in the entity being observed."

A mathematical symbol and its associated descriptor(s) should contain all the entity's components such there is no confusion as to the meaning. Consider the symbol "c" for the speed of light. Does everyone understand that this is a measured value made in a vacuum some place on the Earth's surface at some unspecified position in the Earth's orbit around the Sun? When c is used, shouldn't it be noted it is being used as a theoretical value or a measured value? To avoid confusion, c

A pure mathematical derivation of the value for the speed of light is contained in the July/August 2011 IEEE Potentials article titled, "A methodology to define physical constants using mathematical constants".

IEEE Methodology

or for those without IEEE membership,

Postprint Methodology

The NASA/JPL web site for the Curiosity lander has a question and answer process, ask Dr.C. I submitted a question, before it landed, "What is the measured permittivity on the surface of Mars?" I am still waiting for a response.

report post as inappropriate

Dear Robert H McEachern,

You've spent some time thinking about this. I've seen it pointed out before how little information is in equations, but no one has ever painted the consequences as well as you.

Thanks for your analysis of Bell's Theorem, although the Bell Believers may come looking for you with pitchforks. They have a lot riding on that horse.

Thanks also for your short lesson on Fourier analysis. I've claimed the same thing in my essay, The Nature of the Wave Function, [which I very much hope you will read and comment on] but you do so in such dispassionate manner, and so clearly.

Your discussion of the two-slit experiment was masterful. I had forgotten, if I ever knew, that the 2 slit response is a Sinc-function, not Gaussian. [I should have known--I took Fourier Optics from Joseph Goodman.]

Every paragraph of your wonderful essay is loaded with insight and information. It's too early to know what other great essays will yet be submitted, but todate yours may be the best.

Congratulations,

Edwin Eugene Klingman

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You've spent some time thinking about this. I've seen it pointed out before how little information is in equations, but no one has ever painted the consequences as well as you.

Thanks for your analysis of Bell's Theorem, although the Bell Believers may come looking for you with pitchforks. They have a lot riding on that horse.

Thanks also for your short lesson on Fourier analysis. I've claimed the same thing in my essay, The Nature of the Wave Function, [which I very much hope you will read and comment on] but you do so in such dispassionate manner, and so clearly.

Your discussion of the two-slit experiment was masterful. I had forgotten, if I ever knew, that the 2 slit response is a Sinc-function, not Gaussian. [I should have known--I took Fourier Optics from Joseph Goodman.]

Every paragraph of your wonderful essay is loaded with insight and information. It's too early to know what other great essays will yet be submitted, but todate yours may be the best.

Congratulations,

Edwin Eugene Klingman

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Dear Robert McEachern,

I have read your very well written and interesting essay. Its very relevant to the essay question. You have given me a lot that I would like to think about. Well done.

You might enjoy George Ellis' and Dan Bruiger's entries. Different from your own interesting analysis of the problems of physics but some overlapping of ideas.

Good luck in the competition.

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I have read your very well written and interesting essay. Its very relevant to the essay question. You have given me a lot that I would like to think about. Well done.

You might enjoy George Ellis' and Dan Bruiger's entries. Different from your own interesting analysis of the problems of physics but some overlapping of ideas.

Good luck in the competition.

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Dear Robert,

Yes, yes, yes, I totally agree with you when you say: "It is important to remember that nothing we have said alters any of the equations or predictions of the physical theories. We merely point out that the slapped-on misinterpretations of the 'meaning' and 'significance' of the equations is the source of all the 'weirdness'."

I have studied astronomy and computing as well as simulation modelling at MSc level. I would be very pleased if you would consider looking at a potential discovery I have made. Professor Iain Nicolson of Bayfordbury Observatory and the University of Hertfordshire advised me to solve the Ice Age Problem if I wanted to solve the t.o.e.

Newtons Isotropy and Equivalence Is Simplicity That Has Led to Modern Day Mass Misconceptions of Reality

Kind regards,

Alan

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Yes, yes, yes, I totally agree with you when you say: "It is important to remember that nothing we have said alters any of the equations or predictions of the physical theories. We merely point out that the slapped-on misinterpretations of the 'meaning' and 'significance' of the equations is the source of all the 'weirdness'."

I have studied astronomy and computing as well as simulation modelling at MSc level. I would be very pleased if you would consider looking at a potential discovery I have made. Professor Iain Nicolson of Bayfordbury Observatory and the University of Hertfordshire advised me to solve the Ice Age Problem if I wanted to solve the t.o.e.

Newtons Isotropy and Equivalence Is Simplicity That Has Led to Modern Day Mass Misconceptions of Reality

Kind regards,

Alan

report post as inappropriate

Dear Geophysicist Robert H. McEachern,

For me to describe your brilliantly written essay as being anything less than truly inspirational would be an insulting mean spirited disservice to you. There is a problem with your statement: “physicists seek to predict how physical substances behave.” As I carefully pointed out in my essay Sequence Consequence, no two real snowflakes of the trillions that have fallen have ever scientifically been found to be identical. There is a real “Stop” sign on my corner. It is my contention that that “Stop” sign not only modifies the behavior of the real cars in my neighborhood, it affects all of the real cars presently on the planet and the real vehicle that has just been landed on Mars. Not only that, this insignificant “Stop” sign will alter the actual braking capability of every real car put into operation anywhere in the future. It has to. One real Universe can only be eternally occurring in one dimension once. Each and every real and imagined event taking place in that one real Universe has to be unique. Abstract equations do not a real thing make.

report post as inappropriate

For me to describe your brilliantly written essay as being anything less than truly inspirational would be an insulting mean spirited disservice to you. There is a problem with your statement: “physicists seek to predict how physical substances behave.” As I carefully pointed out in my essay Sequence Consequence, no two real snowflakes of the trillions that have fallen have ever scientifically been found to be identical. There is a real “Stop” sign on my corner. It is my contention that that “Stop” sign not only modifies the behavior of the real cars in my neighborhood, it affects all of the real cars presently on the planet and the real vehicle that has just been landed on Mars. Not only that, this insignificant “Stop” sign will alter the actual braking capability of every real car put into operation anywhere in the future. It has to. One real Universe can only be eternally occurring in one dimension once. Each and every real and imagined event taking place in that one real Universe has to be unique. Abstract equations do not a real thing make.

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Joe, Robert,

Quote from Joe, "Abstract equations do not a real thing make." Robert stated in his essay, "A mathematical symbol and its associated descriptor(s) should contain all the entity's components such there is no confusion as to the meaning."

A mathematical equation can be compared to a "paint by number picture" of a real picture. If enough "number parameters" with the correct descriptors, "color, shape, etc.," are applied to the paint by number algorithm, you can get a close approximation of the real thing. New forms of mathematical methods have been developed to help fill in previously ill-defined characteristics, which allows an abstract equation to provide a more accurate description of how "we think" the real thing should be described.

Then there is the possibility that existing mathematical processes were not properly applied to describing a problem. I did not create the physical law or the mathematical processes described in the IEEE paper cited in my essay, 1294, I applied them in a different way. Postprint below.

Postprint Methodology

A quote from Roberts essay abstract, "Consequently, the early search for the 'meaning' of the equations of mathematical physics, especially quantum physics, was based on several critical assumptions about the nature of information, which have subsequently been shown to be untrue. Unfortunately, none of the physicists, at the time, (and apparently even today) recognized these assumptions, as such. "

Ultimately, when the decisions are made on which essay(s) deserve recognition, we will be able to determine if those individuals that make the decision have or have not managed to push aside decades of acceptance of untrue assumptions. You can get radically different peer review comments from reviewers that are from the academic community as compared to those outside of academics.

Monet's art became radically different after cataract surgery, no lens replacement back then, he painted what he saw. Same thing with scientific assumptions, once they have been implanted into impressionable minds, the individuals see the universe painted with these assumptions.

report post as inappropriate

Quote from Joe, "Abstract equations do not a real thing make." Robert stated in his essay, "A mathematical symbol and its associated descriptor(s) should contain all the entity's components such there is no confusion as to the meaning."

A mathematical equation can be compared to a "paint by number picture" of a real picture. If enough "number parameters" with the correct descriptors, "color, shape, etc.," are applied to the paint by number algorithm, you can get a close approximation of the real thing. New forms of mathematical methods have been developed to help fill in previously ill-defined characteristics, which allows an abstract equation to provide a more accurate description of how "we think" the real thing should be described.

Then there is the possibility that existing mathematical processes were not properly applied to describing a problem. I did not create the physical law or the mathematical processes described in the IEEE paper cited in my essay, 1294, I applied them in a different way. Postprint below.

Postprint Methodology

A quote from Roberts essay abstract, "Consequently, the early search for the 'meaning' of the equations of mathematical physics, especially quantum physics, was based on several critical assumptions about the nature of information, which have subsequently been shown to be untrue. Unfortunately, none of the physicists, at the time, (and apparently even today) recognized these assumptions, as such. "

Ultimately, when the decisions are made on which essay(s) deserve recognition, we will be able to determine if those individuals that make the decision have or have not managed to push aside decades of acceptance of untrue assumptions. You can get radically different peer review comments from reviewers that are from the academic community as compared to those outside of academics.

Monet's art became radically different after cataract surgery, no lens replacement back then, he painted what he saw. Same thing with scientific assumptions, once they have been implanted into impressionable minds, the individuals see the universe painted with these assumptions.

report post as inappropriate

Dear Mr. Makinson,

While I admire your appreciation for anyone being able to produce a real copy of a picture by using paint by numbers methodology I cannot help noticing that real artists produce real art without resorting to such a clever stratagem. I thought mathematics was supposed to be a science. Let us take your definition of mathematical applicability and apply it to Albert Einstein’s unrealistic equation e=mc². Let us take a 10” by 10” canvas and place a 1” diameter circle with a number 1 in its center somewhere on the canvas. This circle represents abstract energy. Of course we know that real energy does not have a shape or a fixed color which is one of the reasons I believe that an equation does not make a real thing, but I could be wrong. We now have to pick a shape and a color for abstract mass. This is not as easy as it sounds. We can draw a triangle numbered 2 around the circle implying that abstract energy operates internally on abstract mass, or we could place a smaller triangle numbered 2 inside of the circle denoting that abstract energy is an external force. Perhaps we should draw both triangles and number the internal one 2 and the external one 3. Thankfully, the constant speed of abstract light can easily be depicted on our canvas because it is a square. All we have to do is make sure the area of the numbered 4 square plus the area of the numbered 2 triangle plus the area of the numbered 3 triangle equals the area of the circle numbered 1.

report post as inappropriate

While I admire your appreciation for anyone being able to produce a real copy of a picture by using paint by numbers methodology I cannot help noticing that real artists produce real art without resorting to such a clever stratagem. I thought mathematics was supposed to be a science. Let us take your definition of mathematical applicability and apply it to Albert Einstein’s unrealistic equation e=mc². Let us take a 10” by 10” canvas and place a 1” diameter circle with a number 1 in its center somewhere on the canvas. This circle represents abstract energy. Of course we know that real energy does not have a shape or a fixed color which is one of the reasons I believe that an equation does not make a real thing, but I could be wrong. We now have to pick a shape and a color for abstract mass. This is not as easy as it sounds. We can draw a triangle numbered 2 around the circle implying that abstract energy operates internally on abstract mass, or we could place a smaller triangle numbered 2 inside of the circle denoting that abstract energy is an external force. Perhaps we should draw both triangles and number the internal one 2 and the external one 3. Thankfully, the constant speed of abstract light can easily be depicted on our canvas because it is a square. All we have to do is make sure the area of the numbered 4 square plus the area of the numbered 2 triangle plus the area of the numbered 3 triangle equals the area of the circle numbered 1.

report post as inappropriate

Robert,

You provide a noteworthy addition to the various entries here by seasoned professionals with jaundiced views on the current state of theoretical physics, based on lifetimes of professional experience that provide very deep understanding of the physical processes at work, which are not reflected in the forefront of the discipline. I, for one, hope some larger effort can grow out of this contest's call to "Question the Foundations."

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You provide a noteworthy addition to the various entries here by seasoned professionals with jaundiced views on the current state of theoretical physics, based on lifetimes of professional experience that provide very deep understanding of the physical processes at work, which are not reflected in the forefront of the discipline. I, for one, hope some larger effort can grow out of this contest's call to "Question the Foundations."

report post as inappropriate

Joe,

You are violating one of the axioms presented in Robert's essay, "A mathematical symbol and its associated descriptor(s) should contain all the entity's components such there is no confusion as to the meaning." Geometry is a specific type of mathematical abstraction, and when used properly, it can provide a basis for describing physical law characteristics. You are using a geometric plane shape to represent some physical law concept with no supporting evidence except by definition, "a circle denoting abstract energy." You can get away with that slight-of-hand if you are an artist, as an artist does not have represent anything that is actually real. The paint-by-number process is attempting to replicate something that is real.

A physical characteristics of the universe is something entirely different, with a equation attempting to describe it in the abstract language of mathematics, which can use actual numeric values with their descriptors and/or symbols to represent numeric values and their descriptors. If you read the IEEE article cited in my essay, 1294, you will find that I used identical geometric shapes, each with proper dimensional descriptors, to describe two physical law characteristics, space (length) and a time dependent action (frequency). Note that the duration of time did not have to be defined, it became a function of the angle of the triangle. I did not have to know the size of the dimensions ahead of time.

Postprint Methodology

You utilized different geometric shapes to represent different physical law characteristics with no dimensional descriptors. You then concluded that a proper resultant could be achieved just by having all the shapes inside the circle equaling the area of the circle.

This essay contest is the result of the "physics fiction" created by the professionals, where they are using assumptions that everyone is supposed to accept without question. Would an intelligent species continue to use the meter as a scientific unit of measure when it has been demonstrated an "intrinsic length" can be mathematically defined?

Robert's essay exposes the sloppiness of the so-called scientific method as being practiced. I noted in an earlier comment how the symbol c, representing the speed of EM emissions, is supposed to be accepted without specifying whether it is a theoretical value or measured value. There is a difference.

report post as inappropriate

You are violating one of the axioms presented in Robert's essay, "A mathematical symbol and its associated descriptor(s) should contain all the entity's components such there is no confusion as to the meaning." Geometry is a specific type of mathematical abstraction, and when used properly, it can provide a basis for describing physical law characteristics. You are using a geometric plane shape to represent some physical law concept with no supporting evidence except by definition, "a circle denoting abstract energy." You can get away with that slight-of-hand if you are an artist, as an artist does not have represent anything that is actually real. The paint-by-number process is attempting to replicate something that is real.

A physical characteristics of the universe is something entirely different, with a equation attempting to describe it in the abstract language of mathematics, which can use actual numeric values with their descriptors and/or symbols to represent numeric values and their descriptors. If you read the IEEE article cited in my essay, 1294, you will find that I used identical geometric shapes, each with proper dimensional descriptors, to describe two physical law characteristics, space (length) and a time dependent action (frequency). Note that the duration of time did not have to be defined, it became a function of the angle of the triangle. I did not have to know the size of the dimensions ahead of time.

Postprint Methodology

You utilized different geometric shapes to represent different physical law characteristics with no dimensional descriptors. You then concluded that a proper resultant could be achieved just by having all the shapes inside the circle equaling the area of the circle.

This essay contest is the result of the "physics fiction" created by the professionals, where they are using assumptions that everyone is supposed to accept without question. Would an intelligent species continue to use the meter as a scientific unit of measure when it has been demonstrated an "intrinsic length" can be mathematically defined?

Robert's essay exposes the sloppiness of the so-called scientific method as being practiced. I noted in an earlier comment how the symbol c, representing the speed of EM emissions, is supposed to be accepted without specifying whether it is a theoretical value or measured value. There is a difference.

report post as inappropriate

Dear Mr. Makinson,

Do forgive me for violating whatever it was I violated. I misunderstood your assessment that abstract mathematical equations can be compared to the production of a real paint by numbers picture. Now you assert that abstract mathematical equations can only be considered to be accurate providing they incorporate numbers that have real numeric values. That seems reasonable. The number 1 must have a real numeric value of 1. What is the real numeric value of 11? Do the first and second number 1s in the eleven have the same real numeric value as the first number 1 I typed? See, real things do not have a real numeric value, but they do constantly change. Is the number 11, eleven real numeric times the real numeric value of first 1? What is the real numeric value of the real space between the two 1’s? Can the real numeric value of the space around the two ones equal the real numeric value of the space between the two ones? Does the real numeric value of space increase or decrease with its extensiveness? Does the real numeric value of the 1 depend on the size of its representation? I think it ought to. I think that there should be an official standard for number representation as there is for the measurement of the speed of light. Otherwise, it gets kind of Orwellian with tall 1’s really equaling short 1’s, and real big chasms equaling real narrow gaps.

Rather than reading your IEEE tract 1294 where you claim to use “identical geometric shapes” to prove something or other about reality, why do you not read my essay, Sequence Consequence where I prove conclusively to the complete satisfaction of anybody with a scrap of common sense that real identical states have never existed and real identical states will never exist. I am not saying that scientifically propounded abstract theorems which all use imaginary identical numbers and identical shapes and identical imaginary observation are wrong. I am saying they are all unrealistic. As I understood this essay contest, authors were asked to comment on “questioning the foundations, “and that is what I tried my best to do.

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Do forgive me for violating whatever it was I violated. I misunderstood your assessment that abstract mathematical equations can be compared to the production of a real paint by numbers picture. Now you assert that abstract mathematical equations can only be considered to be accurate providing they incorporate numbers that have real numeric values. That seems reasonable. The number 1 must have a real numeric value of 1. What is the real numeric value of 11? Do the first and second number 1s in the eleven have the same real numeric value as the first number 1 I typed? See, real things do not have a real numeric value, but they do constantly change. Is the number 11, eleven real numeric times the real numeric value of first 1? What is the real numeric value of the real space between the two 1’s? Can the real numeric value of the space around the two ones equal the real numeric value of the space between the two ones? Does the real numeric value of space increase or decrease with its extensiveness? Does the real numeric value of the 1 depend on the size of its representation? I think it ought to. I think that there should be an official standard for number representation as there is for the measurement of the speed of light. Otherwise, it gets kind of Orwellian with tall 1’s really equaling short 1’s, and real big chasms equaling real narrow gaps.

Rather than reading your IEEE tract 1294 where you claim to use “identical geometric shapes” to prove something or other about reality, why do you not read my essay, Sequence Consequence where I prove conclusively to the complete satisfaction of anybody with a scrap of common sense that real identical states have never existed and real identical states will never exist. I am not saying that scientifically propounded abstract theorems which all use imaginary identical numbers and identical shapes and identical imaginary observation are wrong. I am saying they are all unrealistic. As I understood this essay contest, authors were asked to comment on “questioning the foundations, “and that is what I tried my best to do.

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Robert, thanks for your essay. It is important to expose some of the much publicized weirdness and confusion. It emphasized to me the importance of keeping context in our pursuit of understanding. Context can be thought of as the set of initial conditions lost when we use relationships to distill observations. From an information theory standpoint, context is the denominator in a probability that makes the probability meaningful. It is a large pertinent denominator that makes one observation interesting (not devoid of information…I like your definition). In my essay “A top-down approach to fundamental forces”, I use a count of the total number of particles (WMAP) as a denominator in probabilities that I believe nature uses to present its information. Once the pertinent denominator is determined, it is maintained throughout the analysis since this allows extraction of meaningful information. Information can be operated on to create subsets that represent different things to us. For example in my work, I show that the logarithm 90 is divided into four parts we call dimensions and the result 22.5 represents the Higgs particle. Meaning is not lost since after the division by 4 we can say “In a universe that has exp(180) particles and four dimensions, one particle is the Higgs particle”. If we just discover the Higgs particle we don’t understand its context.

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Hi Robert H. McEachern,

The essays in this contest have shown me that not everyone has TV commerical logic instilled in their brains. Your essay is brilliant and shows thinking that has been long thought through. Congradulations.

Jim Akerlund

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The essays in this contest have shown me that not everyone has TV commerical logic instilled in their brains. Your essay is brilliant and shows thinking that has been long thought through. Congradulations.

Jim Akerlund

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Hello, Robert

It seems we are on a parallel track. Your analysis of quantum weirdness as an artifact of mathematical treatment is very interesting. I don't feel qualified to comment, but I do have a question: wouldn't "two entangled (anti-parallel) coins" be "spooky"?

Thanks for your wonderful essay.

Dan

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It seems we are on a parallel track. Your analysis of quantum weirdness as an artifact of mathematical treatment is very interesting. I don't feel qualified to comment, but I do have a question: wouldn't "two entangled (anti-parallel) coins" be "spooky"?

Thanks for your wonderful essay.

Dan

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Dan,

Unfortunately Robert doesn't seem to be participating in the conversation.

There are various entries in this contest which do a very credible job of addressing the topic of questionable assumptions built into theoretical physics, yours included. Given the rather conservative judging of previous contests, it seems reasonable to think the winner of this will be one which doesn't raise serious issues for the status quo. I'm thinking those of us who do think a serious review is necessary should select one entry to give a ten, then eights and nines for our other favorites. I feel Robert's entry would be the best candidate. Besides its many strengths for those us who have followed the topic for years, I think it would be most accessible and informative to the young technogeeks thinking of a career in theoretical physics. We don't need another generation chasing string theory and multiworlds.

What do you think?

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Unfortunately Robert doesn't seem to be participating in the conversation.

There are various entries in this contest which do a very credible job of addressing the topic of questionable assumptions built into theoretical physics, yours included. Given the rather conservative judging of previous contests, it seems reasonable to think the winner of this will be one which doesn't raise serious issues for the status quo. I'm thinking those of us who do think a serious review is necessary should select one entry to give a ten, then eights and nines for our other favorites. I feel Robert's entry would be the best candidate. Besides its many strengths for those us who have followed the topic for years, I think it would be most accessible and informative to the young technogeeks thinking of a career in theoretical physics. We don't need another generation chasing string theory and multiworlds.

What do you think?

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Why "spooky"? Suppose we had two real coins, like pennies, and I told you, so that you have a priori knowledge, that I have positioned them such that no matter how you look at one, the other will be in the opposite state (imagine them floating, motionless, in space). Then, at some latter time, I inform you that one is in the state "heads", when viewed from a particular aspect angle. Nothing spooky happens when you then view the other coin from the same aspect angle, and see that it is "tails". You knew, a priori, that that was bound to happen - I told you so previously. The real issue is that in the standard misinterpretation of quantum mechanics, the "state of the object's attribute", it's "heads" versus "tail-ness", is not supposed to be in any definite state until it is observed. But the "state" of an object like a coin is not an attribute of the coin at all. Rather, it is an attribute of the relationship between the coin and the observer. When you finally observe a two-sided coin, it does not suddenly "collapse" into a one-sided coin. Only the relationship between the coin and the observer has "collapsed" into a definite state, either "heads" or "tails".

Hi, Robert

OK, the state of a given coin is relative to the observer's position. But is the relationship between the two coins themselves also an artifact of the observer? By specifying that at the outset you have made it a matter of definition, but is it so in nature? A physical explanation of entangled correlations might be, for example, that they are two localities on a common wave front. How might that sort of explanation relate to the coin analogy, I wonder?

thanks,

Dan

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OK, the state of a given coin is relative to the observer's position. But is the relationship between the two coins themselves also an artifact of the observer? By specifying that at the outset you have made it a matter of definition, but is it so in nature? A physical explanation of entangled correlations might be, for example, that they are two localities on a common wave front. How might that sort of explanation relate to the coin analogy, I wonder?

thanks,

Dan

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Food for thought:

I was hoping someone would pick up on this, and generate some interesting discussion about

"What, exactly is the significance of the Uncertainty Principle?"

If you look at the relations given for the Uncertainty Principle and Shannon's Capacity, for the single particle case mentioned, in which S/N =1, then the uncertainty principle boils down to the statement that "1 = maximum number of bits of information that can be extracted from an observation, in the worst case."

Duh

So what is the big deal? What makes this so significant?

I was hoping someone would pick up on this, and generate some interesting discussion about

"What, exactly is the significance of the Uncertainty Principle?"

If you look at the relations given for the Uncertainty Principle and Shannon's Capacity, for the single particle case mentioned, in which S/N =1, then the uncertainty principle boils down to the statement that "1 = maximum number of bits of information that can be extracted from an observation, in the worst case."

Duh

So what is the big deal? What makes this so significant?

Robert, All,

isn't it the whole uncertainty idea that an observable isn't something definite until it is measured, and the measurement is what makes it something rather than a superposition of possibilities (as the where and when and what to sample has not yet been decided.) I'm starting to feel really comfortable with the idea now, whereas I used to find that strange. Having realised that it is also the case for macroscopic objects.

All of the ways in which an object might be observed must exist simultaneously as potential sensory data in the environment, as the observer can choose to regard the object from any distance away, from any orientation and at a time of choice. It is the selection of the data at a particular position and time that determines the manifestation that will be observed. That manifestation will be regarded by the observer as what the object is, not the other possibilities that were not selected. Though it is in truth all of them. The object being the "parent" of all of the possible manifestations of it, generated from interception and processing of EM data.

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isn't it the whole uncertainty idea that an observable isn't something definite until it is measured, and the measurement is what makes it something rather than a superposition of possibilities (as the where and when and what to sample has not yet been decided.) I'm starting to feel really comfortable with the idea now, whereas I used to find that strange. Having realised that it is also the case for macroscopic objects.

All of the ways in which an object might be observed must exist simultaneously as potential sensory data in the environment, as the observer can choose to regard the object from any distance away, from any orientation and at a time of choice. It is the selection of the data at a particular position and time that determines the manifestation that will be observed. That manifestation will be regarded by the observer as what the object is, not the other possibilities that were not selected. Though it is in truth all of them. The object being the "parent" of all of the possible manifestations of it, generated from interception and processing of EM data.

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Everyone might find this recent experimental result interesting, if you haven't seen it already:

http://arstechnica.com/science/2012/05/disentangling

-the-wave-particle-duality-in-the-double-slit-experiment/

Dan

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http://arstechnica.com/science/2012/05/disentangling

-the-wave-particle-duality-in-the-double-slit-experiment/

Dan

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Georgina,

The "idea" is something like that. And that is the problem. That idea is a misinterpretation of what is happening.

The point of my previous post, is that the uncertainty principle amounts to no more than the statement that the minimum amount of information that can be extracted from an observation, and still be an observation, is exactly one bit. In other words, it amounts to nothing more than a very curious way of stating the definition of a "bit of information". Consequently, the uncertainty principle says nothing at all about the real world; Nothing about particles, nothing about waves, nothing about physics. It is merely a truism; It is true, by definition.

Recall the distinction made above between the entangled gloves and the entangled coins. One involves an observation of an actual attribute of the object. The other does not. The two quantities, position and momentum, in the uncertainty relation, are not actual attributes of any object. Like the coin example, they are attributes of the relation between the observer and the object. Consequently, these types of observations are not about the object, and they can therefore not say anything about the object.

In the case of obtaining only a single bit of information about the actual object, this single bit signifies the answer to the question "Was an entity observed to exist, that is, detected, by the detector?" Yes or No - a single bit answer.

Thus, for example, when a particle is detected after passing through a double slit apparatus, as a spot on a screen behind the slits. Then you have observed exactly one bit of information about the particle -it exists -it has been detected. The location of the spot on the screen conveys no information about the particle. It only conveys information about the relationship between the particle and the observer.

Physicists have consistently confused these two very different things. That is the cause of all the "weirdness" in their misinterpretations of reality.

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The "idea" is something like that. And that is the problem. That idea is a misinterpretation of what is happening.

The point of my previous post, is that the uncertainty principle amounts to no more than the statement that the minimum amount of information that can be extracted from an observation, and still be an observation, is exactly one bit. In other words, it amounts to nothing more than a very curious way of stating the definition of a "bit of information". Consequently, the uncertainty principle says nothing at all about the real world; Nothing about particles, nothing about waves, nothing about physics. It is merely a truism; It is true, by definition.

Recall the distinction made above between the entangled gloves and the entangled coins. One involves an observation of an actual attribute of the object. The other does not. The two quantities, position and momentum, in the uncertainty relation, are not actual attributes of any object. Like the coin example, they are attributes of the relation between the observer and the object. Consequently, these types of observations are not about the object, and they can therefore not say anything about the object.

In the case of obtaining only a single bit of information about the actual object, this single bit signifies the answer to the question "Was an entity observed to exist, that is, detected, by the detector?" Yes or No - a single bit answer.

Thus, for example, when a particle is detected after passing through a double slit apparatus, as a spot on a screen behind the slits. Then you have observed exactly one bit of information about the particle -it exists -it has been detected. The location of the spot on the screen conveys no information about the particle. It only conveys information about the relationship between the particle and the observer.

Physicists have consistently confused these two very different things. That is the cause of all the "weirdness" in their misinterpretations of reality.

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The "Anonymous" post a few minutes ago was from me. For some reason, the system logged me out just before the post.

James,

You asked:

You think that the information conveyed by observing existence of anything at anytime is one bit of information???

Yes. That is the definition of what is meant by a "bit of information", in Information Theory.

If you ever learn anything else, other than the mere existence of the object, then that represents additional bits of information.

James,

You asked:

You think that the information conveyed by observing existence of anything at anytime is one bit of information???

Yes. That is the definition of what is meant by a "bit of information", in Information Theory.

If you ever learn anything else, other than the mere existence of the object, then that represents additional bits of information.

Dr. McEachern,

Hi. I think your essay was very good. While I can't say I understood it all, the main points I got out of it are that physicists seem to confuse the mathematical description of a thing with the thing itself and that the relationship between the observer and an observed thing can affect one's view of the observed thing (from above discussion). About these two things, I totally agree. In a previous FQXi essay and at my website, I make similar points about:

1. An observer's view of an infinite set as discrete or continuous depends on the reference frame of the observer relative to the set.

2. In regards to the question of "Why is there something rather than nothing?", I've tried to point out that the thinker's conception of a thing (non-existence in this case) is different than the thing itself. I think this leads to real problems not only in math and physics but in philosophy.

One more observation is that several essays in this contest seem to point out that physicists seem to confuse mathematical descriptions of the world with the world itself. Perhaps, this point should be considered by academic physicists? I doubt that it will be, though, since the use of unfounded and unexplained assumptions (ie, poor reasoning) by physicists seems to be rampant.

My entry in this year's contest is about what I believe to be a misapplication of a mathematical situation (comparing the size of an infinite set to the size of an infinite subset derived from it) to the corresponding real world situation.

Anyways, great essay!

Roger

(sites.google.com/site/ralphthewebsite)

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attachments: Gaussian_Filters.jpg

Hi. I think your essay was very good. While I can't say I understood it all, the main points I got out of it are that physicists seem to confuse the mathematical description of a thing with the thing itself and that the relationship between the observer and an observed thing can affect one's view of the observed thing (from above discussion). About these two things, I totally agree. In a previous FQXi essay and at my website, I make similar points about:

1. An observer's view of an infinite set as discrete or continuous depends on the reference frame of the observer relative to the set.

2. In regards to the question of "Why is there something rather than nothing?", I've tried to point out that the thinker's conception of a thing (non-existence in this case) is different than the thing itself. I think this leads to real problems not only in math and physics but in philosophy.

One more observation is that several essays in this contest seem to point out that physicists seem to confuse mathematical descriptions of the world with the world itself. Perhaps, this point should be considered by academic physicists? I doubt that it will be, though, since the use of unfounded and unexplained assumptions (ie, poor reasoning) by physicists seems to be rampant.

My entry in this year's contest is about what I believe to be a misapplication of a mathematical situation (comparing the size of an infinite set to the size of an infinite subset derived from it) to the corresponding real world situation.

Anyways, great essay!

Roger

(sites.google.com/site/ralphthewebsite)

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With regards to your comment that "physicists seem to confuse the mathematical description of a thing with the thing itself", I'd have to say that is not correct. Rather, they are confusing the attributes (properties) of the mathematical description of a thing with the attributes (properties) of the thing itself.

The distinction is important. Since you mention having an interest in...

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The distinction is important. Since you mention having an interest in...

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attachments: Gaussian_Filters.jpg

Roger,

"Nature decided to add noise and distortion (uncertainty) to the received TV symbols.

Then the TV receiver decided that the received symbols were noisy and distorted.

Then the TV receiver decided to replace the noisy and distorted symbols with clean ones."

"Rather, they are confusing the attributes (properties) of the mathematical description of a thing with the attributes (properties) of the thing itself."

So you are saying they confuse an inductive process, with a deductive process?

In my entry, I make the argument that by treating time as a measure from one event to the next in a sequence, it re-enforces the perception of time as a narrative series of events and not a physical dynamic, which is creating and replacing configurations. That it is not the present moving from past to future, but change turning future into past. Not the earth traveling the fourth dimension from yesterday to tomorrow, but tomorrow becoming yesterday because the earth rotates. This makes time an effect of action, like temperature, not the foundational basis for action. So when we create narrative out of the thermodynamic activity, we are selecting routes through this environment. Because our previous series has been determined by the confluence of input, it seems logical to assume future narrative is also determined, but in fact the lightcone of any event doesn't exist prior to its occurrence. So while we assume the decisions and directions are deduced from circumstance, they are actually induced from input. In other words, the decisions seem fated because our choices are often yes/no, left/right, up/down, but that is simply our need to distill lots of information into simple binary options?

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"Nature decided to add noise and distortion (uncertainty) to the received TV symbols.

Then the TV receiver decided that the received symbols were noisy and distorted.

Then the TV receiver decided to replace the noisy and distorted symbols with clean ones."

"Rather, they are confusing the attributes (properties) of the mathematical description of a thing with the attributes (properties) of the thing itself."

So you are saying they confuse an inductive process, with a deductive process?

In my entry, I make the argument that by treating time as a measure from one event to the next in a sequence, it re-enforces the perception of time as a narrative series of events and not a physical dynamic, which is creating and replacing configurations. That it is not the present moving from past to future, but change turning future into past. Not the earth traveling the fourth dimension from yesterday to tomorrow, but tomorrow becoming yesterday because the earth rotates. This makes time an effect of action, like temperature, not the foundational basis for action. So when we create narrative out of the thermodynamic activity, we are selecting routes through this environment. Because our previous series has been determined by the confluence of input, it seems logical to assume future narrative is also determined, but in fact the lightcone of any event doesn't exist prior to its occurrence. So while we assume the decisions and directions are deduced from circumstance, they are actually induced from input. In other words, the decisions seem fated because our choices are often yes/no, left/right, up/down, but that is simply our need to distill lots of information into simple binary options?

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John,

You asked:

"So you are saying they confuse an inductive process, with a deductive process?"

No. They are making a type of category mistake. As an analogy, it is as though they are confusing some property of a mathematical description, like the length of an equation describing an object, for the length of the object itself.

They also frequently "misattribute" a property (attribute) to the wrong entity. As an analogy, attributing the sound of your voice, as coming from the shirt you are wearing, rather than from your mouth. For example, in the double-slit experiment, where does most of the information content within the "interference pattern" come from? The particles or waves striking the slits? Or the slits? They assumed it came from the particles or waves. But it comes from the slits. The situation is analogous to a radio signal. There is a "carrier", that contains little information, and a "modulator", that modulates information onto the carrier. The particles and/or waves striking the slits, merely act as a carrier. The slits are spatial modulators. Think of sunlight as a carrier, and the objects in your visual field, that reflect the sunlight to your eyes, as the modulators. Your visual system largely ignores the attributes of the sunlight, while extracting large amounts of information about the objects modulating the sunlight. The properties of the sunlight matter so little, that you can replace the sunlight with light from a light-bulb, which has a very different spectrum than sunlight, yet it makes like difference to your ability to perceive the objects reflecting the light.

You asked:

"So you are saying they confuse an inductive process, with a deductive process?"

No. They are making a type of category mistake. As an analogy, it is as though they are confusing some property of a mathematical description, like the length of an equation describing an object, for the length of the object itself.

They also frequently "misattribute" a property (attribute) to the wrong entity. As an analogy, attributing the sound of your voice, as coming from the shirt you are wearing, rather than from your mouth. For example, in the double-slit experiment, where does most of the information content within the "interference pattern" come from? The particles or waves striking the slits? Or the slits? They assumed it came from the particles or waves. But it comes from the slits. The situation is analogous to a radio signal. There is a "carrier", that contains little information, and a "modulator", that modulates information onto the carrier. The particles and/or waves striking the slits, merely act as a carrier. The slits are spatial modulators. Think of sunlight as a carrier, and the objects in your visual field, that reflect the sunlight to your eyes, as the modulators. Your visual system largely ignores the attributes of the sunlight, while extracting large amounts of information about the objects modulating the sunlight. The properties of the sunlight matter so little, that you can replace the sunlight with light from a light-bulb, which has a very different spectrum than sunlight, yet it makes like difference to your ability to perceive the objects reflecting the light.

Typo Alert.

In the last sentence of my previous post, in this thread, "yet it makes like difference" should read

"yet it makes little difference"

In the last sentence of my previous post, in this thread, "yet it makes like difference" should read

"yet it makes little difference"

Robert,

I agree the wave effect is a consequence of the slits, as the quanta are a function of the energy absorption properties of the atomic structure of the "particle" detector. These are effects of the interaction of light with the material structures we use to judge it, much as the color of a shirt is an effect of how the material interacts with the light. I suspect light might best be...

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I agree the wave effect is a consequence of the slits, as the quanta are a function of the energy absorption properties of the atomic structure of the "particle" detector. These are effects of the interaction of light with the material structures we use to judge it, much as the color of a shirt is an effect of how the material interacts with the light. I suspect light might best be...

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In regard to Robert's statement, in the last paragraph, that elementary particles are "characterized by the attribute of being nearly devoid of information", my question is whether that is an attribute of the particles themselves or only of the QM description?

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It is an attribute of the particles themselves. For example, the "handedness" of a glove, can only be one of two possible "states", "right-handed" or left-handed", which can be represented by a single bit of information, in the "states" "1" or "0".

This lack of information is the reason why observations become "quantized" in the first place.

This lack of information is the reason why observations become "quantized" in the first place.

Yet gloves have other characteristics than handedness: number of fingers, material composition, stitching, etc. Can we ever be sure we have accounted for all properties? How can we distinguish between the reduced information of the quantum realm, compared to the classical realm, and the sort of limited information that belongs to conceptual systems that are simply defined in that way. In other words, how to distinguish the real attributes of gloves from those, like handedness, we have defined or specified?

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Dan,

You asked: "In other words, how to distinguish the real attributes of gloves from those, like handedness, we have defined or specified? "

First, Handedness is a real attribute of a glove. But more importantly, real attributes will always be determined to have the same "value" no matter how you look at it. If you look at a glove from any angle, it will always appear to have the same handedness, either left or right. An object like a coin is different. If you view a coin from different angles, it may change "state" from Heads to Tails.

The "state" of a coin is not an attribute of the coin. It is an attribute of the relationship between the coin and the observer.

You also asked: "Can we ever be sure we have accounted for all properties?" No. We cannot. We don't know what we don't know. On the other hand, we do know what we do know. That fact can be exploited in many very interesting and sophisticated ways. At the very least, it should be exploited, as in the case of "spin", to recognize that the observed phenomenon, "spin states", behave more like the "state" of a coin, than the state of an actual attribute of the particle.

You asked: "In other words, how to distinguish the real attributes of gloves from those, like handedness, we have defined or specified? "

First, Handedness is a real attribute of a glove. But more importantly, real attributes will always be determined to have the same "value" no matter how you look at it. If you look at a glove from any angle, it will always appear to have the same handedness, either left or right. An object like a coin is different. If you view a coin from different angles, it may change "state" from Heads to Tails.

The "state" of a coin is not an attribute of the coin. It is an attribute of the relationship between the coin and the observer.

You also asked: "Can we ever be sure we have accounted for all properties?" No. We cannot. We don't know what we don't know. On the other hand, we do know what we do know. That fact can be exploited in many very interesting and sophisticated ways. At the very least, it should be exploited, as in the case of "spin", to recognize that the observed phenomenon, "spin states", behave more like the "state" of a coin, than the state of an actual attribute of the particle.

Hi Robert:

I thoroughly enjoyed your interesting and deeply philosophical essay. The main conclusion of your essay states that mathematical descriptions provided by QM do not represent physical reality but rather “Made-up” or “Slapped-on” fiction. These include many well-known quantum paradoxes – uncertainty principle, measurement paradox, multi-verses, multi-dimensions,...

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I thoroughly enjoyed your interesting and deeply philosophical essay. The main conclusion of your essay states that mathematical descriptions provided by QM do not represent physical reality but rather “Made-up” or “Slapped-on” fiction. These include many well-known quantum paradoxes – uncertainty principle, measurement paradox, multi-verses, multi-dimensions,...

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Avter,

You stated:

"The main conclusion of your essay states that mathematical descriptions provided by QM do not represent physical reality but rather “Made-up” or “Slapped-on” fiction"

Not quite. The mathematical descriptions do a good job of describing the observations. My point is that they do little else. Thus, they provide few hints as to whether or not the "meaning" that has been slapped onto these descriptions, is even remotely correct.

For example, I noted in an earlier post, that the uncertainty principle amounts to little more than a peculiar way of stating that "The number of bits of information that can be extracted from an observation, must be greater than or equal to one."

Stated in that fashion, it seems rather odd to suppose that this self-evident statement would ever allow one to deduce things such as "The uncertainty principle enables quantum fluctuations of the vacuum, etc."

You stated:

"The main conclusion of your essay states that mathematical descriptions provided by QM do not represent physical reality but rather “Made-up” or “Slapped-on” fiction"

Not quite. The mathematical descriptions do a good job of describing the observations. My point is that they do little else. Thus, they provide few hints as to whether or not the "meaning" that has been slapped onto these descriptions, is even remotely correct.

For example, I noted in an earlier post, that the uncertainty principle amounts to little more than a peculiar way of stating that "The number of bits of information that can be extracted from an observation, must be greater than or equal to one."

Stated in that fashion, it seems rather odd to suppose that this self-evident statement would ever allow one to deduce things such as "The uncertainty principle enables quantum fluctuations of the vacuum, etc."

Hi Robert:

Thanks for your reply.

Please also respond to my second comment as to how I address the problem of "memory-less" particles in my posted paper -- -“ From Absurd to Elegant Universe”.

I would greatly appreciate your comments and rating on my paper.

Thanks

Avtar

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Thanks for your reply.

Please also respond to my second comment as to how I address the problem of "memory-less" particles in my posted paper -- -“ From Absurd to Elegant Universe”.

I would greatly appreciate your comments and rating on my paper.

Thanks

Avtar

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Robert,

You stated: "In a very real sense, Newton's law of gravity is perfectly analogous to the JPEG image compression algorithm. It is a "lossy" description of the original data, no more no less; the reconstructed, predicted "image" is slightly different from the original. In contrast, Einstein's theory of gravity appears to be a "lossless" compression algorithm."

I think that this sentence might be counter to everything else you are stating in your essay. By definition, the process of anti-differentiation (which Newton used to map gravitational force into his law of gravity) is a reduction of possible information into one interpretation of the data and which likely has passed into GR (i.e. still lossy). My essay has some questions but a sketch I just posted may be a simpler visual explanation.

Regards,

Jeff

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You stated: "In a very real sense, Newton's law of gravity is perfectly analogous to the JPEG image compression algorithm. It is a "lossy" description of the original data, no more no less; the reconstructed, predicted "image" is slightly different from the original. In contrast, Einstein's theory of gravity appears to be a "lossless" compression algorithm."

I think that this sentence might be counter to everything else you are stating in your essay. By definition, the process of anti-differentiation (which Newton used to map gravitational force into his law of gravity) is a reduction of possible information into one interpretation of the data and which likely has passed into GR (i.e. still lossy). My essay has some questions but a sketch I just posted may be a simpler visual explanation.

Regards,

Jeff

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Hi Robert,

Being an old copywriter, I cannot help to try to catch yor wonderful essay in a one-liner: "Confusing Mathematics for Physics is to Complicate the Simple and Simplify the Complex."

We are several authors in this contest who - from different points of wievs - question the role of mathematics in physics. Mathematics has for long been its lingua franca and the "shut up and calcilate" promotors are not just a few. The funny thing is that during the same period of time, since the mid seventies, when calculation capacity has been exponentially increasing, physical theory-building has been comparatively meagre. More is less, it seems.

Best regards,

Inger

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Being an old copywriter, I cannot help to try to catch yor wonderful essay in a one-liner: "Confusing Mathematics for Physics is to Complicate the Simple and Simplify the Complex."

We are several authors in this contest who - from different points of wievs - question the role of mathematics in physics. Mathematics has for long been its lingua franca and the "shut up and calcilate" promotors are not just a few. The funny thing is that during the same period of time, since the mid seventies, when calculation capacity has been exponentially increasing, physical theory-building has been comparatively meagre. More is less, it seems.

Best regards,

Inger

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Robert

"The speed of light is not directly observable; it is not an observable phenomenon at all. There is always a "privileged" observer."

"...When a light wave is first created, it is created in the reference frame of this privileged observer. It is created at the frequency observed by that observer, not the Doppler shifted frequency of an observer in a different frame of...

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"The speed of light is not directly observable; it is not an observable phenomenon at all. There is always a "privileged" observer."

"...When a light wave is first created, it is created in the reference frame of this privileged observer. It is created at the frequency observed by that observer, not the Doppler shifted frequency of an observer in a different frame of...

view entire post

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Peter,

Most of the basic ideas in my essay can also be found in a book I wrote, twenty years ago:

"Human and Machine Intelligence: An Evolutionary View"

After reading Roger Penrose's book, "The Emperor's New Mind", I was inspired to write my own book as a rebuttal to his. His was a best seller, mine fell into a black-hole shortly after being published. Used copies can still be found on amazon and other on-line book sellers.

The book is mostly about the nature of intelligence, viewed as an outgrowth of sensory signal processing. The quantum aspects came about, in order to refute Penrose's claim that intelligence is probably the result of some as yet undiscovered quantum oddity.

Most of the basic ideas in my essay can also be found in a book I wrote, twenty years ago:

"Human and Machine Intelligence: An Evolutionary View"

After reading Roger Penrose's book, "The Emperor's New Mind", I was inspired to write my own book as a rebuttal to his. His was a best seller, mine fell into a black-hole shortly after being published. Used copies can still be found on amazon and other on-line book sellers.

The book is mostly about the nature of intelligence, viewed as an outgrowth of sensory signal processing. The quantum aspects came about, in order to refute Penrose's claim that intelligence is probably the result of some as yet undiscovered quantum oddity.

Robert

I also disagree we have any intelligence, as a result of Penrose's quantum oddity or otherwise! I can however see both sides of that one. Having arrived at a recycling cosmology with largely (but not solely) re-ionized matter there is some certainty that with infinitely many recyclings some particles in of our brains may have originally been part of the brain of some intelligent being! Pretty crazy stuff I know, but I use rigorous logic, from where it emerges as implicit! So there may be hope for us yet. Of course mechanistically I agree entirely with you, which I'd expect is 99.99999% of the game. (I wonder if homeopathy really works, we may find out in the UK as our new Health Secretary is a fan!)

I'll track down a copy of your book. I'm sure it's more readable than Penrose. I'd also like to cite it, or perhaps your essay, in a current paper. I wasn't implying anything by my comment except the 'great minds think alike' commonality of our conclusions, and coming from such very different directions must imply some fundamental veracity. I've found some massive importance in your truths, touched on in my essay.

I do hope you'll get to read it, can find and extract the real gold nuggets, and give me your views. I also need a bit of maths thrown at the concepts as I'm averse to going too near the stuff myself.

Well done for yours. Certainly a top score coming from me I think. Have you read Tom Ray's yet, also nicely debagging Bell a la Joy Christian.

Peter

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I also disagree we have any intelligence, as a result of Penrose's quantum oddity or otherwise! I can however see both sides of that one. Having arrived at a recycling cosmology with largely (but not solely) re-ionized matter there is some certainty that with infinitely many recyclings some particles in of our brains may have originally been part of the brain of some intelligent being! Pretty crazy stuff I know, but I use rigorous logic, from where it emerges as implicit! So there may be hope for us yet. Of course mechanistically I agree entirely with you, which I'd expect is 99.99999% of the game. (I wonder if homeopathy really works, we may find out in the UK as our new Health Secretary is a fan!)

I'll track down a copy of your book. I'm sure it's more readable than Penrose. I'd also like to cite it, or perhaps your essay, in a current paper. I wasn't implying anything by my comment except the 'great minds think alike' commonality of our conclusions, and coming from such very different directions must imply some fundamental veracity. I've found some massive importance in your truths, touched on in my essay.

I do hope you'll get to read it, can find and extract the real gold nuggets, and give me your views. I also need a bit of maths thrown at the concepts as I'm averse to going too near the stuff myself.

Well done for yours. Certainly a top score coming from me I think. Have you read Tom Ray's yet, also nicely debagging Bell a la Joy Christian.

Peter

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P S

Dear Robert, please don't mistake my oneliner as a disrespectful and slipshod simplification of the complexity of your essay! Should it be so, i apoligize. D S

As four your old book, I´will try to find an purchase it. Not only to be able to better understand your essay, but also because there might be a possible connection with my PhD thesis, which deals with the contrast/controversy between the simoplifications of artificial intelligence and the complexity of human knowledge.

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Dear Robert, please don't mistake my oneliner as a disrespectful and slipshod simplification of the complexity of your essay! Should it be so, i apoligize. D S

As four your old book, I´will try to find an purchase it. Not only to be able to better understand your essay, but also because there might be a possible connection with my PhD thesis, which deals with the contrast/controversy between the simoplifications of artificial intelligence and the complexity of human knowledge.

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Hi Robert,

You were saying:

"If you look at the relations given for the Uncertainty Principle and Shannon's Capacity, for the single particle case mentioned, in which S/N =1, then the uncertainty principle boils down to the statement that "1 = maximum number of bits of information that can be extracted from an observation, in the worst case."

Duh

So what is the big deal? What makes this so significant?"

If I'm understanding this correctly, and my calculation is right, you're saying that the boundary between the quantum and classical world is fuzzy, and that the commutator vanishes when the signal (particle count) increases and particle count error stays constant.

So, if I had a ball of 1e200 fundamental particles (and I know this count precisely because I know their individual masses and I weighed the ball real good, etc, etc), this would give me a commutator with the value of 0.001, not 1. So, I would be 999/1000th into the classical regime.

To me, that is an absolutely fantastic calculation, because:

1) It makes sense to me even from a purely classical point of view: http://www.phys.unsw.edu.au/jw/uncertainty.html

2) As far as I can tell it's novel, because I read about theoretical physicists humming and hawing about what may or may not constitute the boundary between the quantum and classical regime all of the time, in not so specific language as yours.

Holy cow dude!

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You were saying:

"If you look at the relations given for the Uncertainty Principle and Shannon's Capacity, for the single particle case mentioned, in which S/N =1, then the uncertainty principle boils down to the statement that "1 = maximum number of bits of information that can be extracted from an observation, in the worst case."

Duh

So what is the big deal? What makes this so significant?"

If I'm understanding this correctly, and my calculation is right, you're saying that the boundary between the quantum and classical world is fuzzy, and that the commutator vanishes when the signal (particle count) increases and particle count error stays constant.

So, if I had a ball of 1e200 fundamental particles (and I know this count precisely because I know their individual masses and I weighed the ball real good, etc, etc), this would give me a commutator with the value of 0.001, not 1. So, I would be 999/1000th into the classical regime.

To me, that is an absolutely fantastic calculation, because:

1) It makes sense to me even from a purely classical point of view: http://www.phys.unsw.edu.au/jw/uncertainty.html

2) As far as I can tell it's novel, because I read about theoretical physicists humming and hawing about what may or may not constitute the boundary between the quantum and classical regime all of the time, in not so specific language as yours.

Holy cow dude!

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(yes, I realize that particle count is not a constant, but I'm sure there is a slick way to calculate a mean based on the various different field configurations... the point is that you totally just blew my mind)

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No, I believe I had it wrong just then.

I believe that in your formula for the commutator relationship

S seems to be the actual particle count, and N seems to be idealized particle count. For instance, if you had all kinds of particles bunched together and considered them to be a single baseball, then N = 1. On the other hand, if you consider every particle individually, then N = S (the actual particle count). As S/N goes to 1, a transition from the classical to the quantum regime occurs. I believe this to mean that when S is held constant, then a token amount of random quantum noise is added into the system whenever N is incremented by 1.

Maybe you could talk to S Hossenfelder about this. She has some very interesting things to say about gravity and singularities and a vanishing Planck action (h; the main commutator coefficient). Perhaps this is the mechanism in question. I believe that string theory kind of says that black holes are "one" particle, insomuch that they are a continuation of the particle spectrum, and so your calculation would probably apply to both electrons and black holes -- in a unified kind of way.

Altogether, I think that it's extremely impressive. I do believe it when you say that it's a mathematical truth, and also the physical interpretation is pretty convincing.

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I believe that in your formula for the commutator relationship

S seems to be the actual particle count, and N seems to be idealized particle count. For instance, if you had all kinds of particles bunched together and considered them to be a single baseball, then N = 1. On the other hand, if you consider every particle individually, then N = S (the actual particle count). As S/N goes to 1, a transition from the classical to the quantum regime occurs. I believe this to mean that when S is held constant, then a token amount of random quantum noise is added into the system whenever N is incremented by 1.

Maybe you could talk to S Hossenfelder about this. She has some very interesting things to say about gravity and singularities and a vanishing Planck action (h; the main commutator coefficient). Perhaps this is the mechanism in question. I believe that string theory kind of says that black holes are "one" particle, insomuch that they are a continuation of the particle spectrum, and so your calculation would probably apply to both electrons and black holes -- in a unified kind of way.

Altogether, I think that it's extremely impressive. I do believe it when you say that it's a mathematical truth, and also the physical interpretation is pretty convincing.

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There is a much simpler way of looking at the Shannon Capacity relation:

dt specifies the duration of the observation

df specifies that number of samples per second that must be taken to preserve the entire information content of the continuous, band-limited signal being observed.

The log term specifies the number of bits needed, within each sample (it is counting bits, that is why it is always given as base-2) to preserve all the information. Obtaining more bits per sample would not significantly increase the total number of recoverable bits of information.

So the Shannon Capacity boils down to the statement that the MAXIMUM number of recoverable bits of information, cannot exceed the number of bits required to "digitize" the signal in the first place.

The uncertainty principle, at the other end, boils down to the statement that the MINIMUM number of recoverable bits of information, corresponds to a signal that can be "digitized" with exactly one sample, with exactly one bit per sample = one bit.

If you obtain fewer bits than that, then you have failed to make any observation at all.

So, of course the uncertainty principle represents a fundamental limit. The point is that the limit is true by definition of what is meant by a bit of information. It says nothing at all "interesting" about the nature of reality. Heisenberg mistakenly thought he had discovered some deep, underlying mystery of nature. In fact, he merely discovered a very peculiar way of restating the definition of a bit of information.

Rob McEachern

dt specifies the duration of the observation

df specifies that number of samples per second that must be taken to preserve the entire information content of the continuous, band-limited signal being observed.

The log term specifies the number of bits needed, within each sample (it is counting bits, that is why it is always given as base-2) to preserve all the information. Obtaining more bits per sample would not significantly increase the total number of recoverable bits of information.

So the Shannon Capacity boils down to the statement that the MAXIMUM number of recoverable bits of information, cannot exceed the number of bits required to "digitize" the signal in the first place.

The uncertainty principle, at the other end, boils down to the statement that the MINIMUM number of recoverable bits of information, corresponds to a signal that can be "digitized" with exactly one sample, with exactly one bit per sample = one bit.

If you obtain fewer bits than that, then you have failed to make any observation at all.

So, of course the uncertainty principle represents a fundamental limit. The point is that the limit is true by definition of what is meant by a bit of information. It says nothing at all "interesting" about the nature of reality. Heisenberg mistakenly thought he had discovered some deep, underlying mystery of nature. In fact, he merely discovered a very peculiar way of restating the definition of a bit of information.

Rob McEachern

Dear Robert and All,

I follow this discussion with great interest – understand some of it, misunderstand some of it, and probably non-understand a great deal.

My question is: Which is the reasonablr role of mathematics in physics? That is, a role in which mathematics is not confused for physics, but an effective tool of it?

I take the double split experiment as an...

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I follow this discussion with great interest – understand some of it, misunderstand some of it, and probably non-understand a great deal.

My question is: Which is the reasonablr role of mathematics in physics? That is, a role in which mathematics is not confused for physics, but an effective tool of it?

I take the double split experiment as an...

view entire post

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Inger,

Let me tell you a little story.

Once upon a time, there was a man named Rene Descartes. Rene had written a wonderful, new essay, which he called "Meditations of First Philosophy." Being an ambitious, but cautious man, Rene sought help from the Powers-that-Be, to promote his essay. He wrote to them thus:

"To those Most Wise and Distinguished Men, the Dean and Doctors of...

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Let me tell you a little story.

Once upon a time, there was a man named Rene Descartes. Rene had written a wonderful, new essay, which he called "Meditations of First Philosophy." Being an ambitious, but cautious man, Rene sought help from the Powers-that-Be, to promote his essay. He wrote to them thus:

"To those Most Wise and Distinguished Men, the Dean and Doctors of...

view entire post

Dear Robert,

Thanks. That is very much the way I see the two-slit experiment.

I have not yet found very much data on various slit-widths, distances, separations, wave-lengths, momenta, etc. to test this perspective, and it is absolutely certain that no one has analyzed the wave function that I present in my current essay, The Nature of the Wave Function, in these terms. Therefore I too am an unbeliever in the various weirdnesses that various physicists insist must be believed in, and am ready to question their logic rather than give up local realism.

By the way, I enjoy your comments and would be very interested in any overall observation you might have deriving from the almost 300 essays submitted questioning the fundamental assumptions of physics. When one considers the fact that a large number of these come from quite competent individuals, this seems rather momentous to me.

Edwin Eugene Klingman

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Thanks. That is very much the way I see the two-slit experiment.

I have not yet found very much data on various slit-widths, distances, separations, wave-lengths, momenta, etc. to test this perspective, and it is absolutely certain that no one has analyzed the wave function that I present in my current essay, The Nature of the Wave Function, in these terms. Therefore I too am an unbeliever in the various weirdnesses that various physicists insist must be believed in, and am ready to question their logic rather than give up local realism.

By the way, I enjoy your comments and would be very interested in any overall observation you might have deriving from the almost 300 essays submitted questioning the fundamental assumptions of physics. When one considers the fact that a large number of these come from quite competent individuals, this seems rather momentous to me.

Edwin Eugene Klingman

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Dear Robert,

first of all, congratulations for your very impressive essay. I think you very proper explicated the logical flaws many scientists trap in and furthermore explicated what for example in this forum is more and more realized as being inevitable: namely due to the inaccessability of the physical details "as they really are out there" we attach our physical meanings (for example...

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first of all, congratulations for your very impressive essay. I think you very proper explicated the logical flaws many scientists trap in and furthermore explicated what for example in this forum is more and more realized as being inevitable: namely due to the inaccessability of the physical details "as they really are out there" we attach our physical meanings (for example...

view entire post

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Robert

I agree waves are still poorly understood. I've written the odd paper from optics and more original viewpoints. I eventually resolved to the term 'signal velocity' for the purposes of c, more equivalent to group velocity. I have no clue how this may relate to information theory. Does it?

An aspect poorly considered in representations is that, considering a soliton as a 'wave...

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I agree waves are still poorly understood. I've written the odd paper from optics and more original viewpoints. I eventually resolved to the term 'signal velocity' for the purposes of c, more equivalent to group velocity. I have no clue how this may relate to information theory. Does it?

An aspect poorly considered in representations is that, considering a soliton as a 'wave...

view entire post

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Thank you Robert for your long and detailed answer - and an essay that has lead to a most interesting discussion. I have more than a lot to learn from following it.

My very best wishes for your essay in the contest!

Inger

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My very best wishes for your essay in the contest!

Inger

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Dear Robert,

I have read your essay and I appreciate your viewpoint. Your essay is very well-written, most interesting and very impressive. I wish you good luck in the contest.

Recently, I have noticed some wild variations in community rated list of contest essays. There is a possibility of existence of a biased group or cartel (e.g. Academia or Relativists group) which promotes the essays of that group by rating them all 'High' and jointly demotes some other essays by rating them all 'Low'. As you know, we are not selecting the 'winners' of the contest through our ratings. Our community ratings will be used for selecting top 35 essays as 'Finalists' for further evaluation by a select panel of experts. Therefore, any biased group should not be permitted to corner all top 'Finalists' positions for their select group.

In order to ensure fair play in this selection, we should select (as per laid down criteria), as our individual choice, about 50 essays for entry in the finalists list and RATE them 'High'. Next we should select bottom 50 essays and rate them 'Low'. Remaining essays may be rated as usual. If most of the participants rate most of the essays this way then the negative influence of any bias group can certainly be mitigated.

I have read many but rated very few essays so far and intend to do a fast job now onwards by covering at least 10 essays every day.

You are requested to read and rate my essay titled,"Wrong Assumptions of Relativity Hindering Fundamental Research in Physical Space". Kindly do let me know if you don't get convinced about the invalidity of the founding assumptions of Relativity or regarding the efficacy of the proposed simple experiments for detection of absolute motion.

Finally I wish to see your excellent essay reach the list of finalists.

Best Regards

G S Sandhu

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I have read your essay and I appreciate your viewpoint. Your essay is very well-written, most interesting and very impressive. I wish you good luck in the contest.

Recently, I have noticed some wild variations in community rated list of contest essays. There is a possibility of existence of a biased group or cartel (e.g. Academia or Relativists group) which promotes the essays of that group by rating them all 'High' and jointly demotes some other essays by rating them all 'Low'. As you know, we are not selecting the 'winners' of the contest through our ratings. Our community ratings will be used for selecting top 35 essays as 'Finalists' for further evaluation by a select panel of experts. Therefore, any biased group should not be permitted to corner all top 'Finalists' positions for their select group.

In order to ensure fair play in this selection, we should select (as per laid down criteria), as our individual choice, about 50 essays for entry in the finalists list and RATE them 'High'. Next we should select bottom 50 essays and rate them 'Low'. Remaining essays may be rated as usual. If most of the participants rate most of the essays this way then the negative influence of any bias group can certainly be mitigated.

I have read many but rated very few essays so far and intend to do a fast job now onwards by covering at least 10 essays every day.

You are requested to read and rate my essay titled,"Wrong Assumptions of Relativity Hindering Fundamental Research in Physical Space". Kindly do let me know if you don't get convinced about the invalidity of the founding assumptions of Relativity or regarding the efficacy of the proposed simple experiments for detection of absolute motion.

Finally I wish to see your excellent essay reach the list of finalists.

Best Regards

G S Sandhu

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Hi Robert

Would you like read my essay?

http://fqxi.org/community/forum/topic/1413

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Would you like read my essay?

http://fqxi.org/community/forum/topic/1413

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Sketches Among the Ruins of My Mind (with apologies to Philip Jose Farmer)

Let us conduct a global scale, double slit experiment. I, Rob McEachern, will be the entity traveling through the slits. Here are the observable facts of the matter:

1) I will repeat the following journey many times, to enable observers to determine my probability of arriving at any particular destination:

2) I arrive at Los Angeles airport, and ask to be put on the first available flight to anywhere the airline travels.

3) The airline only has flights, from Los Angeles, to two destinations (the slits), Washington and New York, and the flights are equally probable to either destination.

4) I arrive at either New York or Washington, and ask to be put on the first available flight to anywhere the airline travels.

5) The airline only has flights, from these two airports, to airports in Europe. The probability distributions of the flights (the routing system as constructed by the airline) is such that, when the arrival destinations are graphed as a histogram of probability of arrival versus latitude, it looks just like an "interference pattern."

6) Observers record my arrival destinations, and generate the histogram noted above.

7) The observers then deduce, the I, Rob McEachern, must be some weird, supernatural entity, that must necessarily have traveled through both New York and Washington, simultaneously, because that is, without doubt, the only possible mechanism for producing the observed "interference pattern."

SPOILER ALERT: do not read any further until you have thought about the above.

If observers misattribute an attribute of the slits (the routing system) to be an attribute of the traveler, then observers can come to some pretty weird conclusions.

Let us conduct a global scale, double slit experiment. I, Rob McEachern, will be the entity traveling through the slits. Here are the observable facts of the matter:

1) I will repeat the following journey many times, to enable observers to determine my probability of arriving at any particular destination:

2) I arrive at Los Angeles airport, and ask to be put on the first available flight to anywhere the airline travels.

3) The airline only has flights, from Los Angeles, to two destinations (the slits), Washington and New York, and the flights are equally probable to either destination.

4) I arrive at either New York or Washington, and ask to be put on the first available flight to anywhere the airline travels.

5) The airline only has flights, from these two airports, to airports in Europe. The probability distributions of the flights (the routing system as constructed by the airline) is such that, when the arrival destinations are graphed as a histogram of probability of arrival versus latitude, it looks just like an "interference pattern."

6) Observers record my arrival destinations, and generate the histogram noted above.

7) The observers then deduce, the I, Rob McEachern, must be some weird, supernatural entity, that must necessarily have traveled through both New York and Washington, simultaneously, because that is, without doubt, the only possible mechanism for producing the observed "interference pattern."

SPOILER ALERT: do not read any further until you have thought about the above.

If observers misattribute an attribute of the slits (the routing system) to be an attribute of the traveler, then observers can come to some pretty weird conclusions.

Dear Robert,

You only can arrive at the belief that observers have misattributed an attribute of the slits to be an attribute of the particle(s), because of suppressing (forgetting?) some additional information. By suppressing this information, you indeed can come to the conclusion you made in the referring post. Here’s the missing information:

I presume that the routing system you...

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You only can arrive at the belief that observers have misattributed an attribute of the slits to be an attribute of the particle(s), because of suppressing (forgetting?) some additional information. By suppressing this information, you indeed can come to the conclusion you made in the referring post. Here’s the missing information:

I presume that the routing system you...

view entire post

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Stefan,

I'm having a bit of a hard time following your argument. You seem to be making some additional assumptions that I did not make. What does your independent observer in LA know, other than the time I departed? No one knows the flight's destination, for example, other than that it is equally likely to be headed to either NY or Wash. (it may not actually arrive, it may...

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I'm having a bit of a hard time following your argument. You seem to be making some additional assumptions that I did not make. What does your independent observer in LA know, other than the time I departed? No one knows the flight's destination, for example, other than that it is equally likely to be headed to either NY or Wash. (it may not actually arrive, it may...

view entire post

I was not being very precise in the previous post, when I stated "the Fourier Transform of the Southern slit, another sinc function, but offset in latitude." The Fourier Transform is a complex function. By "offset in latitude", I mean the latitude is encoded into the phase of the Fourier Transform. Hence, the Fourier Transform of the North and South slits differ in phase, but not magnitude.

Dear Robert,

if the slit geometry is/was the routing system that is/was responsible for the routing distributions (frequencies of the particles' impact), the inconsistency remains.

Because you write "Consequently, the slit geometry 'is' the routing system, whenever you change it, you change the routing". Obviously, following from your statements, in delayed-choice experiments the slit geometry must have changed *after* a particle succesfully went through the aperture with both slits open. Because the arrival distributions have suddenly changed for those cases - despite the fact that both slits were open.

But you assumed "The routing distributions are given by the Fourier Transform of the slit geometry". Even if i consider the system to be an analog computer in the classical fashion, this computer would be limited to only propagate its information with maximally the speed of light from the measurement plane ("europe") back to the slit geometry at the "east coast of the U.S.A." (double-slit geometry). If this would be the case, it would contradict the experimental observations obtained by delayed-choice experiments which exclude a backwards propagation of information with maximally the speed of light. The contradiction is, logically your routing system cannot at the same time be 'X' and be 'NOT X', if you think of it in classical terms like analog computers and such.

Consequently, you neither can think about the system as equipped with wave-like nor equipped with particle-like entities which "travel" between the U.S.A. and europe.

Best wishes,

Stefan

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if the slit geometry is/was the routing system that is/was responsible for the routing distributions (frequencies of the particles' impact), the inconsistency remains.

Because you write "Consequently, the slit geometry 'is' the routing system, whenever you change it, you change the routing". Obviously, following from your statements, in delayed-choice experiments the slit geometry must have changed *after* a particle succesfully went through the aperture with both slits open. Because the arrival distributions have suddenly changed for those cases - despite the fact that both slits were open.

But you assumed "The routing distributions are given by the Fourier Transform of the slit geometry". Even if i consider the system to be an analog computer in the classical fashion, this computer would be limited to only propagate its information with maximally the speed of light from the measurement plane ("europe") back to the slit geometry at the "east coast of the U.S.A." (double-slit geometry). If this would be the case, it would contradict the experimental observations obtained by delayed-choice experiments which exclude a backwards propagation of information with maximally the speed of light. The contradiction is, logically your routing system cannot at the same time be 'X' and be 'NOT X', if you think of it in classical terms like analog computers and such.

Consequently, you neither can think about the system as equipped with wave-like nor equipped with particle-like entities which "travel" between the U.S.A. and europe.

Best wishes,

Stefan

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Stefan,

An inconsistency does indeed remain. But that too is caused by additional misinterpretations of what is happening. Physicists have been using the wrong analogies, to think about this, for a very long time.

I want you to look at a diagram, while I describe this. But to avoid violating someone's copyright, I don't want to copy and paste it here. Please open another browser...

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An inconsistency does indeed remain. But that too is caused by additional misinterpretations of what is happening. Physicists have been using the wrong analogies, to think about this, for a very long time.

I want you to look at a diagram, while I describe this. But to avoid violating someone's copyright, I don't want to copy and paste it here. Please open another browser...

view entire post

Like the 26 letters of the English alphabet, the representations created by De Broglie and Fourier are sufficient, but not necessary, in order to describe probabilities of detection. De Broglie associated a frequency with an energy. But that is not necessary. Fourier enabled superpositions to be described in terms of frequencies and phases. But that is not necessary. They are merely sufficient.

It is often asked what exactly is the QM probability distribution, the probability of? Why does only the magnitude of the wave function matter? Because descriptions in terms of frequency and phase are merely sufficient. They are not necessary.

It should be clear from my previous post, that the magnitude of a Fourier Transform may me viewed as a filter-bank of tuned energy detectors. The point is, they can be DIRECTLY viewed as being tuned in ENERGY, rather than frequency. For example, in the Gaussian detection curves used to construct an FM detector, one can substitute (make a change of variables) energy, for frequency, and everything will still work. Instead of being viewed as a Frequency Modulation detector, it can be DIRECTLY viewed as an Energy Modulation detector. De Broglie's association of a given Energy with a given Frequency, becomes superfluous. It is sufficient, but not necessary.

Consequently, instead of viewing the description as a Fourier superposition of sinusoids, each associated with a given energy, one can directly view it as a superposition of tuned Energy Detectors. If a detector, a receptor, has a probability of detection versus energy that is a Gaussian function, then the paired detectors may be used to infer estimates of that energy, from the ratio of a pair of detectors' "total energy received" outputs. The process by-passes the wave versus particle distinction as unnecessary; what matters is energy detection. Whether you view the energy as arriving in single particles, or waves of particles, becomes superfluous.

It is often asked what exactly is the QM probability distribution, the probability of? Why does only the magnitude of the wave function matter? Because descriptions in terms of frequency and phase are merely sufficient. They are not necessary.

It should be clear from my previous post, that the magnitude of a Fourier Transform may me viewed as a filter-bank of tuned energy detectors. The point is, they can be DIRECTLY viewed as being tuned in ENERGY, rather than frequency. For example, in the Gaussian detection curves used to construct an FM detector, one can substitute (make a change of variables) energy, for frequency, and everything will still work. Instead of being viewed as a Frequency Modulation detector, it can be DIRECTLY viewed as an Energy Modulation detector. De Broglie's association of a given Energy with a given Frequency, becomes superfluous. It is sufficient, but not necessary.

Consequently, instead of viewing the description as a Fourier superposition of sinusoids, each associated with a given energy, one can directly view it as a superposition of tuned Energy Detectors. If a detector, a receptor, has a probability of detection versus energy that is a Gaussian function, then the paired detectors may be used to infer estimates of that energy, from the ratio of a pair of detectors' "total energy received" outputs. The process by-passes the wave versus particle distinction as unnecessary; what matters is energy detection. Whether you view the energy as arriving in single particles, or waves of particles, becomes superfluous.

In case it is not obvious, let me point out, that when the Discrete Fourier Transform is used, the Energy Detection Filter Bank, noted in the previous posts, produces detectors that are tuned to Discrete Energies. So, if Energy is quantized, you end up with detectors, with specified probabilities of detection versus energy, tuned to each of the quantized energy values.

The origination of experience is centrally tied to us, thereby limiting mathematical effectiveness fundamentally/ultimately.

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Robert, mathematics cannot comparatively bridge/accurately describe fundamentally equivalent/linked and yet also different realities/manifestations (of what is essentially the same, ultimately).

Combining, balancing, and including opposites is essential at the very depths of physics. Math comes up short. If we could soley communicate in the language of mathematics, what could we say regarding what we need to say (comparatively)?

Thank you for your interesting essay.

Can you read, comment on, and rate my essay please?

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Combining, balancing, and including opposites is essential at the very depths of physics. Math comes up short. If we could soley communicate in the language of mathematics, what could we say regarding what we need to say (comparatively)?

Thank you for your interesting essay.

Can you read, comment on, and rate my essay please?

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Dear Robert McEachern,

I strongly support your uttered elsewhere argument that the objective reality must not be confused with its mathematical description. See my Fig. 1.

What about your effort to explain the physics to physicists in a simplifying manner by means a crash course of the theory of signal processing, I see this attempt with mixed feelings.

Among the roughly 300 contestants you seem to be the one who outed himself as THE expert in the usual theory of signal processing. I see this theory affected by the same serious flaw that affects physics.

I ask you to look at my Fig. 2 and read the belonging text if necessary twice. Maybe some Figs. in my previous essays may also help you to understand my point. You will certainly know that MP3 works well on the basis of cosine transformation.

When you repeatedly wrote "sufficient but not necessary" then you might have understood the redundancies at least in part. Most experts I met at DAGA and ASA meetings were not completely aware of it.

I am curiously waiting for your comment on my Fig. 2.

Regards,

Eckard

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I strongly support your uttered elsewhere argument that the objective reality must not be confused with its mathematical description. See my Fig. 1.

What about your effort to explain the physics to physicists in a simplifying manner by means a crash course of the theory of signal processing, I see this attempt with mixed feelings.

Among the roughly 300 contestants you seem to be the one who outed himself as THE expert in the usual theory of signal processing. I see this theory affected by the same serious flaw that affects physics.

I ask you to look at my Fig. 2 and read the belonging text if necessary twice. Maybe some Figs. in my previous essays may also help you to understand my point. You will certainly know that MP3 works well on the basis of cosine transformation.

When you repeatedly wrote "sufficient but not necessary" then you might have understood the redundancies at least in part. Most experts I met at DAGA and ASA meetings were not completely aware of it.

I am curiously waiting for your comment on my Fig. 2.

Regards,

Eckard

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Eckard,

Your concern regarding the question "What is a negative frequency?", begs another question; "What is frequency?" Until frequency is defined, one cannot tell if a negative frequency is meaningful.

In communications theory, frequency is DEFINED to be the first derivative, with respect to time, of a time-varying phase. Thus, a positive frequency corresponds to an increasing phase angle. So, for example, on the face of a clock, if a second hand rotates clockwise, it is said to have a frequency of +1 cycle/minute. But if it rotates counter-clockwise, it is said to have a frequency of -1 cycle/minute. That seems perfectly meaningful to me. Counting downwards is every bit as "real" as counting upwards.

Your concern regarding the question "What is a negative frequency?", begs another question; "What is frequency?" Until frequency is defined, one cannot tell if a negative frequency is meaningful.

In communications theory, frequency is DEFINED to be the first derivative, with respect to time, of a time-varying phase. Thus, a positive frequency corresponds to an increasing phase angle. So, for example, on the face of a clock, if a second hand rotates clockwise, it is said to have a frequency of +1 cycle/minute. But if it rotates counter-clockwise, it is said to have a frequency of -1 cycle/minute. That seems perfectly meaningful to me. Counting downwards is every bit as "real" as counting upwards.

How about positive and negative curvature 2D copies of 3D space ?

See my essays:

http://www.fqxi.org/community/forum/topic/946

http://f

qxi.org/community/forum/topic/1413

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See my essays:

http://www.fqxi.org/community/forum/topic/946

http://f

qxi.org/community/forum/topic/1413

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Robert,

Don't confuse mathematics with physics. Mathematics has unfortunately become the bad habit to define anything at will. Physics is or at least should be bound to nature.

I think Dirac was not horribly wrong when he meant that there is no negative frequency in reality. Of course mathematicians do not have problems with anything negative. If there were 3 persons in a room before 5 left it then 2 have to come in as to make the room empty.

You might feel more familiar with some theories than me because I do not uncritically accept them. Didn't your attempt to explain negative frequency by means of the definition you mentioned just shift the question? Is there negative elapsed time alias absolute phase? My ears are unable to hear future signals because I am never drunk.

May I invite you to try and refute at least what one out of my five Figs. tries to tell?

Eckard

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Don't confuse mathematics with physics. Mathematics has unfortunately become the bad habit to define anything at will. Physics is or at least should be bound to nature.

I think Dirac was not horribly wrong when he meant that there is no negative frequency in reality. Of course mathematicians do not have problems with anything negative. If there were 3 persons in a room before 5 left it then 2 have to come in as to make the room empty.

You might feel more familiar with some theories than me because I do not uncritically accept them. Didn't your attempt to explain negative frequency by means of the definition you mentioned just shift the question? Is there negative elapsed time alias absolute phase? My ears are unable to hear future signals because I am never drunk.

May I invite you to try and refute at least what one out of my five Figs. tries to tell?

Eckard

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Dear Robert,

i suppose that physicists all over the world which every day are concerned with QM experiments of the kind we discuss here, surely have investigated the simple picture of emitter and reveiver you have drawn.

The reason, - at least for me - that they haven't adapted this picture is also simple: It does not fit into the observed facts, despite the fact that it may or may not explain the classical double-slit experiment.

You wrote:

"An inconsistency does indeed remain. But that too is caused by additional misinterpretations of what is happening. Physicists have been using the wrong analogies, to think about this, for a very long time."

The question then is, what is the "right" analogy?

Please think about the use of your model when it comes for example to the double-double-slit experiment. Your desription then, consistently should be, that if at one double-slit you want to measure the interference pattern, but you don't do this in coincidence with what happens behind the other double-slit, you *don't* gain the interference pattern.

But if you do measure with the same devices at both sides (the same devices that are also used for the classical double-slit experiment), you gain the interference pattern by measuring it like described by me in a post above.

I wrote this post as a new thread, because there are contestants who are also interested in this discussion but sometimes it's hard to check all hidden replies.

Best wishes,

Stefan

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i suppose that physicists all over the world which every day are concerned with QM experiments of the kind we discuss here, surely have investigated the simple picture of emitter and reveiver you have drawn.

The reason, - at least for me - that they haven't adapted this picture is also simple: It does not fit into the observed facts, despite the fact that it may or may not explain the classical double-slit experiment.

You wrote:

"An inconsistency does indeed remain. But that too is caused by additional misinterpretations of what is happening. Physicists have been using the wrong analogies, to think about this, for a very long time."

The question then is, what is the "right" analogy?

Please think about the use of your model when it comes for example to the double-double-slit experiment. Your desription then, consistently should be, that if at one double-slit you want to measure the interference pattern, but you don't do this in coincidence with what happens behind the other double-slit, you *don't* gain the interference pattern.

But if you do measure with the same devices at both sides (the same devices that are also used for the classical double-slit experiment), you gain the interference pattern by measuring it like described by me in a post above.

I wrote this post as a new thread, because there are contestants who are also interested in this discussion but sometimes it's hard to check all hidden replies.

Best wishes,

Stefan

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Stefan,

I pointed out that the delayed choice experiment, as described in the references I gave, was not merely badly designed, but badly conceived. The telescopes block the path from a slit just as surely as if the slit had been closed. It thereby precludes any possibility for this apparatus to produce an "interference pattern".

You then wrote "i suppose that physicists all over the world,... surely have investigated the simple picture of emitter and reveiver you have drawn."

You say they surely have. I say they surely have not. Show us a better design for the experiment. Show us one that removes the "interference pattern", by merely delaying some choice, any choice, other than the choice in which you choose to block one of the paths, just as surely as if you closed a slit. We await your better design.

I pointed out that the delayed choice experiment, as described in the references I gave, was not merely badly designed, but badly conceived. The telescopes block the path from a slit just as surely as if the slit had been closed. It thereby precludes any possibility for this apparatus to produce an "interference pattern".

You then wrote "i suppose that physicists all over the world,... surely have investigated the simple picture of emitter and reveiver you have drawn."

You say they surely have. I say they surely have not. Show us a better design for the experiment. Show us one that removes the "interference pattern", by merely delaying some choice, any choice, other than the choice in which you choose to block one of the paths, just as surely as if you closed a slit. We await your better design.

Dear Robert,

you wrote

"I pointed out that the delayed choice experiment, as described in the references I gave, was not merely badly designed, but badly conceived. The telescopes block the path from a slit just as surely as if the slit had been closed."

Robert, you say the telescopes block the path from a slit just as surely as if the slit had been closed. I say, if one slit would indeed be "closed", why are there two similar patterns behind each slits? Your "closed slit" approach would result in a different pattern, namely the pattern that is left over after one slit has been really *closed*.

I am sure you have a "mechanism" that explains how the two distinct telescopes do mutual exclusively indicate a hit, but never both at the same time.(I anyway don't have such a mechanism besides my interpretation i gave in my essay).

But that't not the point i want you to consider. The point is that for example the double-double-slit experiment (posted above) needs an explanation which fits into your explanatory scheme. Maybe you succeed, maybe not. Anyway it would, for the sake of better evaluating your model, be interesting what you can say about this experiment. That's all i wanted to remark.

Best wishes,

Stefan

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you wrote

"I pointed out that the delayed choice experiment, as described in the references I gave, was not merely badly designed, but badly conceived. The telescopes block the path from a slit just as surely as if the slit had been closed."

Robert, you say the telescopes block the path from a slit just as surely as if the slit had been closed. I say, if one slit would indeed be "closed", why are there two similar patterns behind each slits? Your "closed slit" approach would result in a different pattern, namely the pattern that is left over after one slit has been really *closed*.

I am sure you have a "mechanism" that explains how the two distinct telescopes do mutual exclusively indicate a hit, but never both at the same time.(I anyway don't have such a mechanism besides my interpretation i gave in my essay).

But that't not the point i want you to consider. The point is that for example the double-double-slit experiment (posted above) needs an explanation which fits into your explanatory scheme. Maybe you succeed, maybe not. Anyway it would, for the sake of better evaluating your model, be interesting what you can say about this experiment. That's all i wanted to remark.

Best wishes,

Stefan

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Hi Robert,

As promised, I read your (very thoughtful and nicely constructed) essay.

You write, "physicists seek to predict how physical substances behave. But they could never have predicted that cars would stop at red traffic lights, anymore than they could predict that they would drive on one side of the road in England and on the other in the United States."

I would argue, however, that -- on the assumption of symmetry -- physicists could predict negative acceleration that compels stopping as well as going; and they could predict that a two-way channel compels cars to drive on one side of the boundary or the other.

On the other hand, we agree a great deal on information theory and its role in physics. Particularly, " ... physicists have lost sight of the fact that the math is devoid of information and thus has very little to say about anything *interesting*." Most mathematicians would agree, I think -- mathematics isn't "about" anything any more than the alphabet is more than arbitrary symbols plus their rules for combination.

As regards relativity, though, we'll have to remain in absolute disagreement. If there is an observer in a privileged reference frame, the whole edifice of Minkowski space collapses. The lack of such an inertial frame doesn't mean that "all systems are equivalent," as you claim -- it means that one system can be smoothly and continuously transformed into another. Big difference, and the support for this is the assumption of symmetry as referenced above.

Good read, though -- best wishes in the contest!

Tom

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As promised, I read your (very thoughtful and nicely constructed) essay.

You write, "physicists seek to predict how physical substances behave. But they could never have predicted that cars would stop at red traffic lights, anymore than they could predict that they would drive on one side of the road in England and on the other in the United States."

I would argue, however, that -- on the assumption of symmetry -- physicists could predict negative acceleration that compels stopping as well as going; and they could predict that a two-way channel compels cars to drive on one side of the boundary or the other.

On the other hand, we agree a great deal on information theory and its role in physics. Particularly, " ... physicists have lost sight of the fact that the math is devoid of information and thus has very little to say about anything *interesting*." Most mathematicians would agree, I think -- mathematics isn't "about" anything any more than the alphabet is more than arbitrary symbols plus their rules for combination.

As regards relativity, though, we'll have to remain in absolute disagreement. If there is an observer in a privileged reference frame, the whole edifice of Minkowski space collapses. The lack of such an inertial frame doesn't mean that "all systems are equivalent," as you claim -- it means that one system can be smoothly and continuously transformed into another. Big difference, and the support for this is the assumption of symmetry as referenced above.

Good read, though -- best wishes in the contest!

Tom

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Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Robert

Superb essay. I was really lifted reading it. Perhaps there may be hope for us yet! I hope you'll read mine as I take the 'low road' of interpreting the findings themselves not abstracting them into numbers, and find a simple way of explaining CSL logically, consistent with Peter Jacksons brilliant anaysis and mechanism (which I don't think all have grasped). I see you saw some of the potential.

I hope you do well, my score should help, and also hope you'll also read and commnet on mine.

Regards

Rich

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Superb essay. I was really lifted reading it. Perhaps there may be hope for us yet! I hope you'll read mine as I take the 'low road' of interpreting the findings themselves not abstracting them into numbers, and find a simple way of explaining CSL logically, consistent with Peter Jacksons brilliant anaysis and mechanism (which I don't think all have grasped). I see you saw some of the potential.

I hope you do well, my score should help, and also hope you'll also read and commnet on mine.

Regards

Rich

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Dear Robert H McEachern

The main purpose for the "Mathematics of Physical" was born to "expand" for the testament of Alfred Nobel.

Perhaps because mathematics was not appreciated,so there should be this "marriage".

Have you suggestions the cancellation for this "marriage" ?

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The main purpose for the "Mathematics of Physical" was born to "expand" for the testament of Alfred Nobel.

Perhaps because mathematics was not appreciated,so there should be this "marriage".

Have you suggestions the cancellation for this "marriage" ?

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Dear Robert,

Very nice essay indeed. I think that the transition to a more "informational" physics is in its way. One can see it all over, specially in theories of quantum gravity but also in more traditional subfields. Even in orthogonal disciplines such as biology. I find very interesting the way you present the idea that initial conditions have more information content than the equations...

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Very nice essay indeed. I think that the transition to a more "informational" physics is in its way. One can see it all over, specially in theories of quantum gravity but also in more traditional subfields. Even in orthogonal disciplines such as biology. I find very interesting the way you present the idea that initial conditions have more information content than the equations...

view entire post

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Hector,

Regarding the "Unreasonable Effectiveness of Mathematics", in an earlier post, under Matt Visser's essay, and repeated somewhere under my own, I wrote:

"In your summary, you ask "Exactly which particular aspect of mathematics is it that is so unreasonably effective?" in describing empirical reality.

I would argue, that is not an aspect of mathematics at all, but...

view entire post

Regarding the "Unreasonable Effectiveness of Mathematics", in an earlier post, under Matt Visser's essay, and repeated somewhere under my own, I wrote:

"In your summary, you ask "Exactly which particular aspect of mathematics is it that is so unreasonably effective?" in describing empirical reality.

I would argue, that is not an aspect of mathematics at all, but...

view entire post

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Hi Robert,

Here's another attempt at answering your question... "So what is the big deal? What makes this so significant?"

After reading:

- Your essay

- 'The Heisenberg Uncertainty Principle and the Nyquist-Shannon Sampling Theorem' by Pierre Millette

- 'An Introduction to Information Theory: Symbols, Signals and Noise' by John Pierce

- 'Communication in the Presence of Noise' by Claude Shannon

I am left with the impression that Shannon and Piece predicted that the holographic principle would become a naturally accepted concept in physics. They detail how the volume of the signal space "creeps" away from the origin of the space as the dimension of the space increases; how there is dimensional reduction in the message space when compensating for phase "differences" (same message, different phase) that can arise when sampling of the signal. Seems at first glance to be hint at how to get rid of singularities at the centres of black holes.

Perhaps it's not quite the same thing. On the other hand, if it's the same thing, then that's quite significant. In any case, I note that Shannon was not directly referenced in 't Hooft's first paper called 'Dimensional Reduction in Quantum Gravity'.

- Shawn

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Here's another attempt at answering your question... "So what is the big deal? What makes this so significant?"

After reading:

- Your essay

- 'The Heisenberg Uncertainty Principle and the Nyquist-Shannon Sampling Theorem' by Pierre Millette

- 'An Introduction to Information Theory: Symbols, Signals and Noise' by John Pierce

- 'Communication in the Presence of Noise' by Claude Shannon

I am left with the impression that Shannon and Piece predicted that the holographic principle would become a naturally accepted concept in physics. They detail how the volume of the signal space "creeps" away from the origin of the space as the dimension of the space increases; how there is dimensional reduction in the message space when compensating for phase "differences" (same message, different phase) that can arise when sampling of the signal. Seems at first glance to be hint at how to get rid of singularities at the centres of black holes.

Perhaps it's not quite the same thing. On the other hand, if it's the same thing, then that's quite significant. In any case, I note that Shannon was not directly referenced in 't Hooft's first paper called 'Dimensional Reduction in Quantum Gravity'.

- Shawn

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Shawn,

Personally, I do not see that much significance in the holographic principle. It is another manifestation of the problem I noted in my essay; A description of the world/reality, and the world/reality itself, have different properties. Is the holographic principle, a property of the description, a property of the world, or both?

I previously noted that the Shannon Capacity...

view entire post

Personally, I do not see that much significance in the holographic principle. It is another manifestation of the problem I noted in my essay; A description of the world/reality, and the world/reality itself, have different properties. Is the holographic principle, a property of the description, a property of the world, or both?

I previously noted that the Shannon Capacity...

view entire post

Hi Robert,

From what I've been told about the original papers on the holographic principle, it is a statement that there is a kind of gauge redundancy that ultimately separates the root states from the alias states brought on by noise and phase distortion. As far as I'm concerned, this is too similar to the dimensional reduction of signal space in Shannon's theory for Shannon's theory to be cast aside in a cavalier fashion.

The major critical difference between this Shannon-esque point of view and the traditional pre-holographic view is that the Shannon POV goes to show that the states "leak" out of the black hole right from the start; there is no information loss paradox when you go this non-traditional route; the traditional view sees the energy leak out due to the noise and phase distortion in a similar fashion, but there is ambiguity as to what occurs to the states (do they stay behind with the black hole proper, do they leak out, do they vanish). If you prefer to say that the holographic principle is bunk because it does not account for Shannon's work, then fine, but you're basically discrediting Shannon too and I'm left unimpressed by the raw butchery.

I'm not really sure if your other comment is for or against black hole complementarity.

- Shawn

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From what I've been told about the original papers on the holographic principle, it is a statement that there is a kind of gauge redundancy that ultimately separates the root states from the alias states brought on by noise and phase distortion. As far as I'm concerned, this is too similar to the dimensional reduction of signal space in Shannon's theory for Shannon's theory to be cast aside in a cavalier fashion.

The major critical difference between this Shannon-esque point of view and the traditional pre-holographic view is that the Shannon POV goes to show that the states "leak" out of the black hole right from the start; there is no information loss paradox when you go this non-traditional route; the traditional view sees the energy leak out due to the noise and phase distortion in a similar fashion, but there is ambiguity as to what occurs to the states (do they stay behind with the black hole proper, do they leak out, do they vanish). If you prefer to say that the holographic principle is bunk because it does not account for Shannon's work, then fine, but you're basically discrediting Shannon too and I'm left unimpressed by the raw butchery.

I'm not really sure if your other comment is for or against black hole complementarity.

- Shawn

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P.S. Perhaps it's a more appetizing concept if I don't mention the word "state" and instead talk about signals, alias signals, and the Hawking radiation being a manifestation of the alias signals. Or, perhaps not.

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Dear Robert,

You present a very interesting, and, I believe, useful point of view here. I particularly appreciate your remarks about Bell's theorem. I must confess that I am not yet quite sure what I think about all your conclusions, but I certainly agree that equations (at least, the usual differential equations that make up much of the language of modern physics) carry negligible intrinsic information, and that a legitimately information-theoretic view of fundamental physics is needed. Of course, fundamental physics (particularly quantum gravity) is already trending in this direction, but I believe that paradigms predating the information age still exert significant inhibitory influence. Personally, I think that covariance (Lorentz invariance, etc.) has more to do with order theory than with Lie group symmetry, and this viewpoint is more congenial to an information-theoretic perspective. In any case, I enjoyed reading your work! Take care,

Ben Dribus

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You present a very interesting, and, I believe, useful point of view here. I particularly appreciate your remarks about Bell's theorem. I must confess that I am not yet quite sure what I think about all your conclusions, but I certainly agree that equations (at least, the usual differential equations that make up much of the language of modern physics) carry negligible intrinsic information, and that a legitimately information-theoretic view of fundamental physics is needed. Of course, fundamental physics (particularly quantum gravity) is already trending in this direction, but I believe that paradigms predating the information age still exert significant inhibitory influence. Personally, I think that covariance (Lorentz invariance, etc.) has more to do with order theory than with Lie group symmetry, and this viewpoint is more congenial to an information-theoretic perspective. In any case, I enjoyed reading your work! Take care,

Ben Dribus

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Benjamin,

With regard to "what I think about all your conclusions", bear in mind that my main conclusion is this:

1) QM claims to be a good description of how "elementary particles" behave; they have a "wave-function"

2) QM claims to be a good description of how "human observers of elementary particles" behave; they too have a "wave-function"

I believe the first proposition is true. But the second is false.

The problem is not that the particles behave weirdly, but that the physicists are behaving weirdly, when they have attempted to interpret their own observations and theories. They have completely misinterpreted what their own equations actually "mean". While applying the concepts of information theory to the behaviors of "the observed" would be helpful, applying them to the behaviors of "the observers" is imperative.

On a more technical level, my conclusion is that, while treating reality as a "Fourier Superposition" may be "sufficient" for many purposes, it is neither "Necessary" nor even "Desirable", for many others. Physicists have yet to appreciate that fact.

Rob McEachern

With regard to "what I think about all your conclusions", bear in mind that my main conclusion is this:

1) QM claims to be a good description of how "elementary particles" behave; they have a "wave-function"

2) QM claims to be a good description of how "human observers of elementary particles" behave; they too have a "wave-function"

I believe the first proposition is true. But the second is false.

The problem is not that the particles behave weirdly, but that the physicists are behaving weirdly, when they have attempted to interpret their own observations and theories. They have completely misinterpreted what their own equations actually "mean". While applying the concepts of information theory to the behaviors of "the observed" would be helpful, applying them to the behaviors of "the observers" is imperative.

On a more technical level, my conclusion is that, while treating reality as a "Fourier Superposition" may be "sufficient" for many purposes, it is neither "Necessary" nor even "Desirable", for many others. Physicists have yet to appreciate that fact.

Rob McEachern

Rob,

Once again you put your finger on the problem. I agree that the first proposition is true, the second false. As I note in my essay, The Nature of the Wave Function, the assumption that wave functions are Fourier superpositions of sine waves has 'built into it' the assumption of single frequency sinusoidals of infinite extent. This has (mis)lead some physicists to speak of "the wave function of the universe", and confused John Bell, who claimed: "nobody knows just where the boundary between the classical and quantum domain is situated" [p.29, 'Speakable...']. He claimed the "shifty split" between microscopic and macroscopic defies precise definition.

And yet the physical wave described in my essay has finite extent [p.5]. It has real dimensions and the 'trailing vortex' is finite -- typically the length of an atomic orbit [see essay]. Fourier decompositions of infinite extent are believed by many to be limitless. With a real field, there is a real boundary.

Keep fighting the good fight.

Edwin Eugene Klingman

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Once again you put your finger on the problem. I agree that the first proposition is true, the second false. As I note in my essay, The Nature of the Wave Function, the assumption that wave functions are Fourier superpositions of sine waves has 'built into it' the assumption of single frequency sinusoidals of infinite extent. This has (mis)lead some physicists to speak of "the wave function of the universe", and confused John Bell, who claimed: "nobody knows just where the boundary between the classical and quantum domain is situated" [p.29, 'Speakable...']. He claimed the "shifty split" between microscopic and macroscopic defies precise definition.

And yet the physical wave described in my essay has finite extent [p.5]. It has real dimensions and the 'trailing vortex' is finite -- typically the length of an atomic orbit [see essay]. Fourier decompositions of infinite extent are believed by many to be limitless. With a real field, there is a real boundary.

Keep fighting the good fight.

Edwin Eugene Klingman

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Robert

I think article of Frank Wilczek interesting for you.

Total Relativity: Mach 2004

http://ctpweb.lns.mit.edu/physics_today/phystoday/%28356

%29Total%20Relativity.pdf

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I think article of Frank Wilczek interesting for you.

Total Relativity: Mach 2004

http://ctpweb.lns.mit.edu/physics_today/phystoday/%28356

%29Total%20Relativity.pdf

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Yuri,

Thanks. I did find it to be interesting.

Rob McEachern

Thanks. I did find it to be interesting.

Rob McEachern

Robert,

Yuri Manin smartest modern person, expert of relation between physics and mathematics

http://www.emis.de/journals/SC/1998/3/pdf/smf_sem

-cong_3_157-168.pdf

http://www.ams.org/notices/200910/rtx0910

01268p.pdf

I hope interesting for you.

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Yuri Manin smartest modern person, expert of relation between physics and mathematics

http://www.emis.de/journals/SC/1998/3/pdf/smf_sem

-cong_3_157-168.pdf

http://www.ams.org/notices/200910/rtx0910

01268p.pdf

I hope interesting for you.

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If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is and was the quantity of people which gave you ratings. Then you have of points. After it anyone give you of points so you have of points and is the common quantity of the people which gave you ratings. At the same time you will have of points. From here, if you want to be R2 > R1 there must be: or or In other words if you want to increase rating of anyone you must give him more points then the participant`s rating was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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Sergey Fedosin

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Robert,

I'm just a pedestrian bystander here, but I'd like to attempt a couple of observations about particle-wave duality, the double slot experiment and entanglement.

- As I understand, 'particles' can only traverse spacetime as propagating waves.

- Conversely, particles are manifested when its propagation energy is localized (I think physically reconfigured as rest mass-energy) or absorbed.

- Even a single particle emission propagating as a wave can simultaneously pass through two (proximal) slots, to be manifested as a single localized particle upon detection.

Regarding entanglement, I agree with your assessment. As I understand, entangled particles are most often physically produced from a single particle. I think that the particles' properties, or their manifestation frequencies, are entangled during that initial process...

Jim

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I'm just a pedestrian bystander here, but I'd like to attempt a couple of observations about particle-wave duality, the double slot experiment and entanglement.

- As I understand, 'particles' can only traverse spacetime as propagating waves.

- Conversely, particles are manifested when its propagation energy is localized (I think physically reconfigured as rest mass-energy) or absorbed.

- Even a single particle emission propagating as a wave can simultaneously pass through two (proximal) slots, to be manifested as a single localized particle upon detection.

Regarding entanglement, I agree with your assessment. As I understand, entangled particles are most often physically produced from a single particle. I think that the particles' properties, or their manifestation frequencies, are entangled during that initial process...

Jim

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Dear Robert,

Reading your essay, I tend to agree with many of your conclusions, but there was one particular passage that does not seem to be correct to me. In the description of the double slit experiment, you describe the particle detectors as only counting particles. I think it is critical to consider that they also record the location of the particle detection which, as it happens,...

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Reading your essay, I tend to agree with many of your conclusions, but there was one particular passage that does not seem to be correct to me. In the description of the double slit experiment, you describe the particle detectors as only counting particles. I think it is critical to consider that they also record the location of the particle detection which, as it happens,...

view entire post

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James,

Interpreting the double-slit pattern as being produced by interfering waves has been the standard interpretation for decades. But I perceive two major problems with it:

First, why does it look like the Fourier Transform of the double-slit geometry? This "pattern" is independent of the existence of particles, waves, physics or physicists. In other words, the information seems to come from the slits, not the entities passing through the slits, whether particles or waves. The latter seem to merely act like the carrier of a radio transmission, but the information being modulated unto the carrier comes entirely from the geometry of the slits.

Second, as described in the second half of my post on Sept. 7, in response to Inger Stjernqvist, the pattern can just as easily be described as a "particle scattering pattern" as a "wave interference pattern". Consequently, it is not NECESSARY to view the latter as the only possibility.

Lastly, regarding my choice of title, formulae that are mathematically identical, can be interpreted as corresponding to very, very different physical realities. As I pointed-out in other posts, one cannot actually observe a "wave-function", one can only observe a probability distribution, that seems to correspond to the magnitude of the "wave-function". But that magnitude is mathematically identical to the output of a filter-bank, that simply histograms particles (hence the correspondence with probability distributions); but that filter-bank does not depend on the existence of "wave-functions", de Broglie frequencies, Fourier superpositions, entanglement, or any of the other supposed wavelike properties. In other words none of those properties are NECESSARY to explain what is going on. They are merely SUFFICIENT.

Rob McEachern

Interpreting the double-slit pattern as being produced by interfering waves has been the standard interpretation for decades. But I perceive two major problems with it:

First, why does it look like the Fourier Transform of the double-slit geometry? This "pattern" is independent of the existence of particles, waves, physics or physicists. In other words, the information seems to come from the slits, not the entities passing through the slits, whether particles or waves. The latter seem to merely act like the carrier of a radio transmission, but the information being modulated unto the carrier comes entirely from the geometry of the slits.

Second, as described in the second half of my post on Sept. 7, in response to Inger Stjernqvist, the pattern can just as easily be described as a "particle scattering pattern" as a "wave interference pattern". Consequently, it is not NECESSARY to view the latter as the only possibility.

Lastly, regarding my choice of title, formulae that are mathematically identical, can be interpreted as corresponding to very, very different physical realities. As I pointed-out in other posts, one cannot actually observe a "wave-function", one can only observe a probability distribution, that seems to correspond to the magnitude of the "wave-function". But that magnitude is mathematically identical to the output of a filter-bank, that simply histograms particles (hence the correspondence with probability distributions); but that filter-bank does not depend on the existence of "wave-functions", de Broglie frequencies, Fourier superpositions, entanglement, or any of the other supposed wavelike properties. In other words none of those properties are NECESSARY to explain what is going on. They are merely SUFFICIENT.

Rob McEachern

Rob,

I read through your Sep. 7 story - I empathize with your perspective (see my brief essay). As basically a retired information systems analyst myself, it seems to me that the slots encode additional 'particle' location selection information within the separated signals.

Not being indoctrinated by any physics education, IMO the fundamental difference between detected particles and particles propagating as waves is that detected particle are physically localized while propagating waves are physically distributed in space and time. As such, a localized particle cannot physically traverse spacetime, and the location of a propagating wave cannot be definitively determined without producing a detected, non-propagating particle.

Why would the interference pattern disappear if the detection screen were moved too near the slots? Let me put it simply: if you shine your flashlight on the house across the street a much larger area will be (dimly) illuminated by the reflection of dispersed photons than if you put your hand in front of the lens.

Waves passing through two slots must disperse through spacetime before their signals can physically interact. Likewise, if two slots are separated by a distance that exceeds the amplitude of the input emitted wave, particles will be detected behind no more than one slot.

Regardless of what the consensus of physicists is, I think these observation support the interpretation that waves propagate; particles do not.

Thanks for your consideration, Jim

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I read through your Sep. 7 story - I empathize with your perspective (see my brief essay). As basically a retired information systems analyst myself, it seems to me that the slots encode additional 'particle' location selection information within the separated signals.

Not being indoctrinated by any physics education, IMO the fundamental difference between detected particles and particles propagating as waves is that detected particle are physically localized while propagating waves are physically distributed in space and time. As such, a localized particle cannot physically traverse spacetime, and the location of a propagating wave cannot be definitively determined without producing a detected, non-propagating particle.

Why would the interference pattern disappear if the detection screen were moved too near the slots? Let me put it simply: if you shine your flashlight on the house across the street a much larger area will be (dimly) illuminated by the reflection of dispersed photons than if you put your hand in front of the lens.

Waves passing through two slots must disperse through spacetime before their signals can physically interact. Likewise, if two slots are separated by a distance that exceeds the amplitude of the input emitted wave, particles will be detected behind no more than one slot.

Regardless of what the consensus of physicists is, I think these observation support the interpretation that waves propagate; particles do not.

Thanks for your consideration, Jim

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Dear Robert!

Great essay and profound ideas! Obviously the new physics of the information age is not "physics formulas" and "physics forms"?.. The highest score. Good luck in the contest. Sincerely, Vladimir

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Great essay and profound ideas! Obviously the new physics of the information age is not "physics formulas" and "physics forms"?.. The highest score. Good luck in the contest. Sincerely, Vladimir

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Dear Robert,

You are right in emphasizing that the amount if information written in states is much more than that corresponding to evolutions I.e the physical law. But you overlooked the huge algorithmic compression of the physical law. Moreover, the goal of physics is to connect preparations with observations, I.e. to make predictions with initial conditions known. Inducing a mechanism forom just observation is speculative, as it is often in cosmology.

My best

Mauro

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You are right in emphasizing that the amount if information written in states is much more than that corresponding to evolutions I.e the physical law. But you overlooked the huge algorithmic compression of the physical law. Moreover, the goal of physics is to connect preparations with observations, I.e. to make predictions with initial conditions known. Inducing a mechanism forom just observation is speculative, as it is often in cosmology.

My best

Mauro

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Mauro,

Far from overlooking "the huge algorithmic compression", I noted that it is the very sparse information content, of the phenomenon that physicists have chosen to observe, that has made such large compressions possible.

I then noted that the "problem of interpretation", is that the behavior of the "observer", as opposed to the "observed", has never been based on "predictions with initial conditions known", precisely because, unlike the "observed", the "observer" is not a sparse information content phenomenon; by assuming they can treat the "observer" in the same manner that they treat the "observed", physicists have made a very bad assumption.

Rob McEachern

Far from overlooking "the huge algorithmic compression", I noted that it is the very sparse information content, of the phenomenon that physicists have chosen to observe, that has made such large compressions possible.

I then noted that the "problem of interpretation", is that the behavior of the "observer", as opposed to the "observed", has never been based on "predictions with initial conditions known", precisely because, unlike the "observed", the "observer" is not a sparse information content phenomenon; by assuming they can treat the "observer" in the same manner that they treat the "observed", physicists have made a very bad assumption.

Rob McEachern

Dear Rob,

As I said in my first comment, your essay was one of the best. I'm glad everyone else agreed with me.

Edwin Eugene Klingman

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As I said in my first comment, your essay was one of the best. I'm glad everyone else agreed with me.

Edwin Eugene Klingman

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Many thanks for your fine essay!

I suspect that many of the FQXi authors have experienced criticisms from referees and editors who have not considered your argument. I too have a small collection of journal referee comments stating that my nuclear model is "inconsistent with the uncertainty principle" and therefore "not quantum mechanical" and therefore simply wrong - no matter what kind of agreement with experimental data is found.

The antidote for what has become a worldwide scandal would be to append your essay to every discussion of the uncertainty principle in the textbooks!

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I suspect that many of the FQXi authors have experienced criticisms from referees and editors who have not considered your argument. I too have a small collection of journal referee comments stating that my nuclear model is "inconsistent with the uncertainty principle" and therefore "not quantum mechanical" and therefore simply wrong - no matter what kind of agreement with experimental data is found.

The antidote for what has become a worldwide scandal would be to append your essay to every discussion of the uncertainty principle in the textbooks!

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Dear Rob McEachern,

Your focus on the uncertainty principle receives some support in Physical Review Letters 109, 100404 (7 Sept 2012) in which the authors experimentally observe a violation of Heisenberg's "measurement-disturbance relationship" and demonstrate Heisenberg's original formulation to be wrong.

Edwin Eugene Klingman

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Your focus on the uncertainty principle receives some support in Physical Review Letters 109, 100404 (7 Sept 2012) in which the authors experimentally observe a violation of Heisenberg's "measurement-disturbance relationship" and demonstrate Heisenberg's original formulation to be wrong.

Edwin Eugene Klingman

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Dear Robert McEachern,

I think this part of your abstract is deeply mistaken:

"Equations contain very little information. This fact is what makes it possible to symbolically represent them, in a computer memory, by a very small number of bits. As a direct result of this fact, we can conclude, contrary to the fervent belief of most physicists, that equations cannot describe anything other than the most trivial physical phenomenon; those nearly devoid of all information."

This would be exactly true if the terms of an equation did not vary in their numerical values. You have treated a bit of algebra as if it was a single set of numbers. But because the equation is a kind of shorthand, it actually contains a lot of information. When you add this information up, you need to take into account every possible combination of numbers that equation can represent. This shows the limitations of looking at things that way - trying to assess the information content of something is sometimes a futile game, because information is a human idea that is more mental than fundamental.

I hope this information is useful...

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I think this part of your abstract is deeply mistaken:

"Equations contain very little information. This fact is what makes it possible to symbolically represent them, in a computer memory, by a very small number of bits. As a direct result of this fact, we can conclude, contrary to the fervent belief of most physicists, that equations cannot describe anything other than the most trivial physical phenomenon; those nearly devoid of all information."

This would be exactly true if the terms of an equation did not vary in their numerical values. You have treated a bit of algebra as if it was a single set of numbers. But because the equation is a kind of shorthand, it actually contains a lot of information. When you add this information up, you need to take into account every possible combination of numbers that equation can represent. This shows the limitations of looking at things that way - trying to assess the information content of something is sometimes a futile game, because information is a human idea that is more mental than fundamental.

I hope this information is useful...

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The "terms of an equation" CANNOT "vary in their numerical values", unless the auxiliary conditions vary. Hence all this additional information you make note of, is contained, not in the equations, but in the auxiliary conditions, as I have stated in the essay.

Rob McEachern

Rob McEachern

Anonymous,

"information is a human idea that is more mental than fundamental." ?? I would like to support Robert.

Moreover there is definitely an objective difference between past and future data. The distinction between them is not a futile game but overdue. See also here and the subsequent correction.

Eckard

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"information is a human idea that is more mental than fundamental." ?? I would like to support Robert.

Moreover there is definitely an objective difference between past and future data. The distinction between them is not a futile game but overdue. See also here and the subsequent correction.

Eckard

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An equation often contains information about a very wide range of auxillary conditions. In one way of looking at it, that's a lot of information. One of the things we find beautiful in physics is that this high information content can be expressed in such an elegant and economical way.

The amount of information depends on how you look at it, because information is a mental idea, not fundamental to the universe. When we get over the novelty of computing, it will go down in importance. Your statement that "equations cannot describe anything other than the most trivial physical phenomenon" attempts to diminish equations, and physics itself. But you may have stumbled onto a way of showing that information is a thin concept, because of the nonsense that comes out of your approach to it.

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The amount of information depends on how you look at it, because information is a mental idea, not fundamental to the universe. When we get over the novelty of computing, it will go down in importance. Your statement that "equations cannot describe anything other than the most trivial physical phenomenon" attempts to diminish equations, and physics itself. But you may have stumbled onto a way of showing that information is a thin concept, because of the nonsense that comes out of your approach to it.

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"An equation often contains information about a very wide range of auxillary conditions" Please give an example of such an equation, if you know one, together with the "wide range of auxillary conditions" that you think it contains.

"showing that information is a thin concept, because of the nonsense that comes out of your approach to it" The approach is not mine, it was invented before I was born. As for it being nonsense, you would not be reading this on your computer, or be able to watch HDTV, or use a cell-phone or any other modern communication device, if it were in fact nonsense.

Rob McEachern

"showing that information is a thin concept, because of the nonsense that comes out of your approach to it" The approach is not mine, it was invented before I was born. As for it being nonsense, you would not be reading this on your computer, or be able to watch HDTV, or use a cell-phone or any other modern communication device, if it were in fact nonsense.

Rob McEachern

The "nonsense" was only where you say that the physical phenomena we have described with equations are the most trivial ones. Gravity equations, for instance, describe what the relationship between the terms will be in a very wide range of situations, so telling us a lot about what gravity does, and therefore (indirectly) telling us something about many "auxillary conditions". If this is short on "information", then it contains a lot of something else that is important, which you haven't defined, but which makes the phenomenon better than trivial.

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You do not seem to understand what is meant by "auxiliary conditions" in mathematical physics. The term refers to the additional information required in order to actually solve the equations, in any given circumstance. It has nothing to do with "telling us something about" what gravity does, or anything else.

I was careful to define what I meant by "trivial"; "trivial physical phenomenon; those nearly devoid of all information." The "laws" of gravity can be completely specified by a very small number of bits of information. On the other hand, in order to fully describe a specific gravitational interaction (solve the equations), like the exact motions of all the stars in a galaxy, one needs to know more than just the "law". One also needs to specify auxiliary conditions, such as all the masses, positions and velocities of all the stars in the galaxy, at some given point in time. That requires trillions of times more bits of information than merely specifying the "law". Of course, if one does not desire an exact description, if one only desires a statistical description, far fewer bits of auxiliary information will be required.

In contrast, other physical phenomenon, like that occurring right now in your brain, cannot be described by "trivial" laws, specifiable by a small number of bits.

You stated that "it contains a lot of something else that is important, which you haven't defined." My point is that "it", the "law", does not "contain" that "something else that is important". That "something else" is not contained within the "law", it is in addition to the "law" and I did define it; "auxillary information."

Rob McEachern

I was careful to define what I meant by "trivial"; "trivial physical phenomenon; those nearly devoid of all information." The "laws" of gravity can be completely specified by a very small number of bits of information. On the other hand, in order to fully describe a specific gravitational interaction (solve the equations), like the exact motions of all the stars in a galaxy, one needs to know more than just the "law". One also needs to specify auxiliary conditions, such as all the masses, positions and velocities of all the stars in the galaxy, at some given point in time. That requires trillions of times more bits of information than merely specifying the "law". Of course, if one does not desire an exact description, if one only desires a statistical description, far fewer bits of auxiliary information will be required.

In contrast, other physical phenomenon, like that occurring right now in your brain, cannot be described by "trivial" laws, specifiable by a small number of bits.

You stated that "it contains a lot of something else that is important, which you haven't defined." My point is that "it", the "law", does not "contain" that "something else that is important". That "something else" is not contained within the "law", it is in addition to the "law" and I did define it; "auxillary information."

Rob McEachern

The fact that the law tells us so much with so little of what is defined as "information" shows how thin the concept of information is.

You say this point makes what the law describes trivial, I say it makes the idea of information trivial (certainly compared with anything fundamental). Let's leave it there, each to his own.

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You say this point makes what the law describes trivial, I say it makes the idea of information trivial (certainly compared with anything fundamental). Let's leave it there, each to his own.

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Bob,

In spite of the quality of a few of the top esssays, yours should have been at or near the very top. It's been a pleasure reading your essay and your comments, and I hope that you participate again.

Edwin Eugene Klingman

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In spite of the quality of a few of the top esssays, yours should have been at or near the very top. It's been a pleasure reading your essay and your comments, and I hope that you participate again.

Edwin Eugene Klingman

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