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RECENT POSTS IN THIS TOPIC

**Darius M**: *on* 6/22/14 at 9:48am UTC, wrote I think reality how it is in itself is analog, while appearances are...

**VimanaPro**: *on* 12/22/12 at 1:19am UTC, wrote Good Time, Jarmo My English is poor, so formulas only 3-dimensional front...

**xexz**: *on* 6/13/11 at 15:55pm UTC, wrote Does God allow we apply 'natural number' to 'electron' ?Especially , We...

**Tommy Gilbertson**: *on* 6/12/11 at 16:38pm UTC, wrote Congratulations, Dr. Mäkelä: Well-earned recognition! After reading...

**Sridattadev**: *on* 6/9/11 at 19:03pm UTC, wrote Dear Jarmo, Congratulations. I would like to say this about your...

**Author Frank Martin DiMeglio**: *on* 6/8/11 at 19:57pm UTC, wrote Jarmo, you mention area and distance in space. The following is essential...

**Peter Jackson**: *on* 6/6/11 at 19:57pm UTC, wrote Jarmo Congratulations, Very well deserved. I hope you got those documents...

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FQXi FORUM

September 4, 2015

CATEGORY:
FQXi Essay Contest - Is Reality Digital or Analog?
[back]

TOPIC: Is Reality Digital or Analog? by Jarmo Matti Mäkelä [refresh]

TOPIC: Is Reality Digital or Analog? by Jarmo Matti Mäkelä [refresh]

A report of a discussion with Isaac Newton.

I received my PhD in theoretial physics from the University of Jyväskylä, Finland, in 1994, and did a post-doc in the Department of Applied Mathematics and Theoretical Physics of the University of Cambridge during the years 1995-1996. Since the year 2000 I have worked as a Senior Lecturer of mathematics and physics in the Vaasa University of Applied Sciences located in Vaasa, Finland.

Very enjoyable -- a most clever and creative way to approach this topic. I have a question: Toward the very end, Newton proposes "a still unknown law of nature," related to the 2nd law of thermodynamics, which recovers time and causality at macroscopic scales. This sounds a lot like decoherence. Is it?

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Hi,

I am not quite sure what Newton really had in mind. I think that he simply meant that at appropriate length scales the metric tensor, which depends on the quantum states of the constituents of spacetime, has a signature (-,+,+,+). The process, which brings this result may or may not have something to do with decoherence, but I am not sure about that.

Best,

Jarmo

I am not quite sure what Newton really had in mind. I think that he simply meant that at appropriate length scales the metric tensor, which depends on the quantum states of the constituents of spacetime, has a signature (-,+,+,+). The process, which brings this result may or may not have something to do with decoherence, but I am not sure about that.

Best,

Jarmo

Dear Jarmo,

Nice! I said first, but then I remembered about "Conversation with a mummy" by E.A. Poe.

Otherwise, there is clearly something about quantization of area, but to me the link with the distance and the 4 simplex is just numerology.

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Nice! I said first, but then I remembered about "Conversation with a mummy" by E.A. Poe.

Otherwise, there is clearly something about quantization of area, but to me the link with the distance and the 4 simplex is just numerology.

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Hi,

I have not read Poe's story before reading your post. The four-simplex really has as 10 edges and 10 triangles. You may try this by yourself: Write the numbers 1,2,3,4 and 5 on the paper and make a list of all different pairs and triples of numbers. You will find 10 pairs and 10 triples. The areas of the 10 triangles of the four-simplex are functions of the 10 edge lengths of the four-simplex. When you write the triangle areas in terms of the edge lengths, you will get a system of 10 equations for 10 unknowns (edge lengths), and you may solve edge lengths from your equations in terms of areas.

Best,

Jarmo

I have not read Poe's story before reading your post. The four-simplex really has as 10 edges and 10 triangles. You may try this by yourself: Write the numbers 1,2,3,4 and 5 on the paper and make a list of all different pairs and triples of numbers. You will find 10 pairs and 10 triples. The areas of the 10 triangles of the four-simplex are functions of the 10 edge lengths of the four-simplex. When you write the triangle areas in terms of the edge lengths, you will get a system of 10 equations for 10 unknowns (edge lengths), and you may solve edge lengths from your equations in terms of areas.

Best,

Jarmo

Really this is not a big deal. You mean euclidean area and length, so you are going to use this in the hypothesis, along with the "amazing" (5 choose 2) = (5 choose 3), for what? For proving that in fact in this very particular euclidean space there is a formula which expresses some lenghts in term of some areas.

The problem is that the formula you are going to use is true only in euclidean space of dimension 4 (maybe there is some extension of it to some configurations of points in Hilbert spaces). Therefore you already put R^4 (with a scalar product) in the hypotheses and you try to justify that (euclidean) area is somehow quantized.

Newton was a great mathematician, there are no reasons to put in his mouth such sloppy reasonings.

Best, Marius

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The problem is that the formula you are going to use is true only in euclidean space of dimension 4 (maybe there is some extension of it to some configurations of points in Hilbert spaces). Therefore you already put R^4 (with a scalar product) in the hypotheses and you try to justify that (euclidean) area is somehow quantized.

Newton was a great mathematician, there are no reasons to put in his mouth such sloppy reasonings.

Best, Marius

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Hi,

Sloppy reasoning is certainly not on Newton's side. In the discussion Newton said: "At macroscopic scales one may reduce the concept of distance to the concept of area." When talking about macroscopic scales he was talking about ordinary, classical spacetime at everyday (say 1 meter) scales. At such scales you may consider spacetime inside the four-simplex as a flat Minkowski spacetime, and to calculate the edge lengths and the triangle areas (in an appropriate system of coordinates) by means of the flat Minkowski metric. Thus you obtain a one-to-one relationship between the edge lengths and the triangle areas.

For a more technical account on how to reduce the concept of distance to the concept of area in four-dimensional Riemannian manifolds you may have a look at my recent pre-print in arXiv:1011.2052. More generally, one finds that equations equivalent to Eintein's field equations (the so-called Regge-Einstein equations) may be expressed in terms of the concept of area (see J. Mäkelä, Class. Quant. Grav. 17 4991 (2000) and J. Mäkelä, together with J. Mäkelä and R. Williams, Class. Quant. Grav. 18 L43 (2001)).

Best,

Jarmo

Sloppy reasoning is certainly not on Newton's side. In the discussion Newton said: "At macroscopic scales one may reduce the concept of distance to the concept of area." When talking about macroscopic scales he was talking about ordinary, classical spacetime at everyday (say 1 meter) scales. At such scales you may consider spacetime inside the four-simplex as a flat Minkowski spacetime, and to calculate the edge lengths and the triangle areas (in an appropriate system of coordinates) by means of the flat Minkowski metric. Thus you obtain a one-to-one relationship between the edge lengths and the triangle areas.

For a more technical account on how to reduce the concept of distance to the concept of area in four-dimensional Riemannian manifolds you may have a look at my recent pre-print in arXiv:1011.2052. More generally, one finds that equations equivalent to Eintein's field equations (the so-called Regge-Einstein equations) may be expressed in terms of the concept of area (see J. Mäkelä, Class. Quant. Grav. 17 4991 (2000) and J. Mäkelä, together with J. Mäkelä and R. Williams, Class. Quant. Grav. 18 L43 (2001)).

Best,

Jarmo

Dear Jarmo,

I enjoyed reading this beautiful essay. The story flows nicely and the explanations are clear - I particularly liked that of the black hole entropy. I agree that the BH entropy may be the major key to the unification between general relativity and quantum theory.

I do have one question. The Newton character said: "When reading Wald [11] I learned that an observer in a uniformly accelerating motion will detect thermal radiation of particles even when all inertial observers detect a vacuum". We know about the Unruh effect because is predicted by the standard (based on continuous spacetime) QFT, applied to an accelerated observer. Then the Newton character said "to me it seems likely that to explain effects like this one must assume a sort of atomic structure of spacetime". Why would Newton use an unobserved effect, which is predicted by a theory, as a supporting argument for a rival theory?

Best regards,

Cristi

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I enjoyed reading this beautiful essay. The story flows nicely and the explanations are clear - I particularly liked that of the black hole entropy. I agree that the BH entropy may be the major key to the unification between general relativity and quantum theory.

I do have one question. The Newton character said: "When reading Wald [11] I learned that an observer in a uniformly accelerating motion will detect thermal radiation of particles even when all inertial observers detect a vacuum". We know about the Unruh effect because is predicted by the standard (based on continuous spacetime) QFT, applied to an accelerated observer. Then the Newton character said "to me it seems likely that to explain effects like this one must assume a sort of atomic structure of spacetime". Why would Newton use an unobserved effect, which is predicted by a theory, as a supporting argument for a rival theory?

Best regards,

Cristi

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Hi,

I am happy that you liked my essay.

An observer in an accelerating motion will experience the so-called Rindler horizon, which has properties very similar to those of the black hole horizon. There is some evidence that whenever you take a finite part of a Rindler horizon, that part possesses entropy which, in natural units, is one-quarter of the area of that part. Such an assumption was used, in effect, by Ted Jacobson in a remarkable paper (Phys. Rev. Lett. 75 1260 (1995)), where he obtained Eintein's field equations by means of thermodynamical arguments. I think that to explain the entropic properties of the Rindler horizon, and thus the Unruh effect, one should construct the Rindler horizon, in the same way as the black hole horizon, out of discrete constituents.

Best,

Jarmo

I am happy that you liked my essay.

An observer in an accelerating motion will experience the so-called Rindler horizon, which has properties very similar to those of the black hole horizon. There is some evidence that whenever you take a finite part of a Rindler horizon, that part possesses entropy which, in natural units, is one-quarter of the area of that part. Such an assumption was used, in effect, by Ted Jacobson in a remarkable paper (Phys. Rev. Lett. 75 1260 (1995)), where he obtained Eintein's field equations by means of thermodynamical arguments. I think that to explain the entropic properties of the Rindler horizon, and thus the Unruh effect, one should construct the Rindler horizon, in the same way as the black hole horizon, out of discrete constituents.

Best,

Jarmo

Hi,

thank you for your answer. From the Newton character I understand that:

(1) Unruh effect => "a sort of atomic structure of spacetime"

But how do we know about the Unruh effect? It is not an experimental fact in search of an explanation. We know about it because it follows from the principles of QFT. So we have:

(2) QFT => Unruh effect

From (1) and (2) we have

(3) QFT => "a sort of atomic structure of spacetime"

But QFT is based on continuous spacetime. So, we have something like

continuous spacetime (combined with other principles) => "a sort of atomic structure of spacetime"

This is what I don't understand.

Best regards,

Cristi

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thank you for your answer. From the Newton character I understand that:

(1) Unruh effect => "a sort of atomic structure of spacetime"

But how do we know about the Unruh effect? It is not an experimental fact in search of an explanation. We know about it because it follows from the principles of QFT. So we have:

(2) QFT => Unruh effect

From (1) and (2) we have

(3) QFT => "a sort of atomic structure of spacetime"

But QFT is based on continuous spacetime. So, we have something like

continuous spacetime (combined with other principles) => "a sort of atomic structure of spacetime"

This is what I don't understand.

Best regards,

Cristi

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Actually, the Hawking effect (black hole radiation) also follows from ordinary QFT, although applied in curved spacetime. Also, the derivations of the Hawking and the Unruh effects are petty similar. The point is that in both effects one may (at least in principle) measure some temperature for matter coming out of the vacuum. Since spacetime interacts with matter, one may consider the temperature of the matter as the temperature of spacetime from the point of view of an appropriate observer. If spacetime has temperature, it presumably has some internal structure, which produces that temperature. For more dwetails you may have a look at Refs. [13] and [14] in my essay.

Best,

Jarmo

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Best,

Jarmo

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Newton was convinced: God is more important than physics or mathematics. God winds up the big clock again and again. Time and space time are absolute.

Leibniz argued that this does restrict God too much. God is not obliged to wind up the big clock, i.e. the universe, which was created by himself. Samuel Clarke who spoke on behalf of Newton in their correspondence commented: This makes God redundant and puts Leibniz at the brink of atheism.

I reminded strong Newtons religiosity in order to stress that Newton would hardly have said "... it would be a strong violation of causality ...". To him causality was given by God.

Who knows any case where causality is violated except for phantasm of mediocre physicists? How to manage violation of causality? Plagiarism is not a violation of causality.

Eckard Blumschein

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Leibniz argued that this does restrict God too much. God is not obliged to wind up the big clock, i.e. the universe, which was created by himself. Samuel Clarke who spoke on behalf of Newton in their correspondence commented: This makes God redundant and puts Leibniz at the brink of atheism.

I reminded strong Newtons religiosity in order to stress that Newton would hardly have said "... it would be a strong violation of causality ...". To him causality was given by God.

Who knows any case where causality is violated except for phantasm of mediocre physicists? How to manage violation of causality? Plagiarism is not a violation of causality.

Eckard Blumschein

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Eckard, An excellent comment. I found Valdes-Marin's essay on 'Structure and Force' to define causality rather well.

Jarmo, An interesting and enjoyable format.

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Jarmo, An interesting and enjoyable format.

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Jarmo, Thanks for a very enjoyable read. The technical discussions were too specialized for me, but the idea of Newton surveying modern physics is delicious. You could have made him say "I told you so" about General Relativity's conclusion that starlight bends slightly around the sun. You might have - in your dream - taken as a present a graphing calculator which I am sure he would have found extremely amazing and useful! You did not mention how Newton knew the meaning of the phrase "analog or digital" - An interesting discussion of how the words got their current meaning only in 1940 is here Cheers. Vladimir

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Jarmo,

Your paper is interesting and it suggests a more complete form of this theory is to consider the set of partitions of the integers. G.H. Hardy and Ramanujan did some work along these lines.

Your depiction of Newton has him a bit more congenial than I would have imagined. He was a pretty disagreeable and barbed, and taken to unamicable relationships with people. In particular Robert Hooke became his main nemesis. He also ran the mint in a pretty draconian way, and was a supporter of the repression of Ireland after the Jacobites were defeated at the Boyne. That little episode killed off about 100,000 Irish. He was an odd man, for he was clearly one of the greatest geniuses our somewhat tawdry species has produced, yet morally he was also a bit on the order of one of the more craven characters from a Dicken’s novel.

Cheers LC

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Your paper is interesting and it suggests a more complete form of this theory is to consider the set of partitions of the integers. G.H. Hardy and Ramanujan did some work along these lines.

Your depiction of Newton has him a bit more congenial than I would have imagined. He was a pretty disagreeable and barbed, and taken to unamicable relationships with people. In particular Robert Hooke became his main nemesis. He also ran the mint in a pretty draconian way, and was a supporter of the repression of Ireland after the Jacobites were defeated at the Boyne. That little episode killed off about 100,000 Irish. He was an odd man, for he was clearly one of the greatest geniuses our somewhat tawdry species has produced, yet morally he was also a bit on the order of one of the more craven characters from a Dicken’s novel.

Cheers LC

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Hi,

I guess that Newton thought at first of identifying the microscopic states with the unordered, instead of ordered strings, of the quantum numbers associated with the constituents of the event horizon of the black hole. That would have taken him to the partitions of integers. Indeed, such choice would have been justified on grounds of possible symmetries between the quantum states of the constituents of the horizon: If constituent 1 is in a quantum state identified by a quantum number n1, and constituent 2 in a state identified by a quantum number n2, the state should, according to this view, be the same as the one where the constituent 1 is in a state n2 and constituent 2 in a state n1. In other words, the constituents are, like bosons in quantum mechanics, indistinguishable.

However, it seems that there are no reasons for such symmetries. The symmetry properties of many-particle states in quantum mechanics follow from the spin-statistics theorem which, in turn, follows from the symmetries of flat spacetime. In the Planck scale of distances there are no such symmetries.

I think that there are some grounds to believe that Newton was, at least in his private relations, more congenial than it is usually thought. For instance, the well-known story that Newton laughed only once in his life, was known already during his life time. However, one of his contemporaries, when he was told this story, said that he had seen Newton laughing several times, and it was easy to make him smile. (See Gleick's book)

One of the best reasons for thinking that Newton was far from an inhuman monster is that his niece Catherine Barton, who was one of the most admired women of the London of her time, and known both for her beauty and wit, worked as Newton's house-keeper for a pretty long time. Several years later, after getting married, Ms. Barton, her husband and her little daughter lived together with Newton. I do not think such arrangements would have been possible, if Newton had been an entirely unbearable person.

Best,

Jarmo

I guess that Newton thought at first of identifying the microscopic states with the unordered, instead of ordered strings, of the quantum numbers associated with the constituents of the event horizon of the black hole. That would have taken him to the partitions of integers. Indeed, such choice would have been justified on grounds of possible symmetries between the quantum states of the constituents of the horizon: If constituent 1 is in a quantum state identified by a quantum number n1, and constituent 2 in a state identified by a quantum number n2, the state should, according to this view, be the same as the one where the constituent 1 is in a state n2 and constituent 2 in a state n1. In other words, the constituents are, like bosons in quantum mechanics, indistinguishable.

However, it seems that there are no reasons for such symmetries. The symmetry properties of many-particle states in quantum mechanics follow from the spin-statistics theorem which, in turn, follows from the symmetries of flat spacetime. In the Planck scale of distances there are no such symmetries.

I think that there are some grounds to believe that Newton was, at least in his private relations, more congenial than it is usually thought. For instance, the well-known story that Newton laughed only once in his life, was known already during his life time. However, one of his contemporaries, when he was told this story, said that he had seen Newton laughing several times, and it was easy to make him smile. (See Gleick's book)

One of the best reasons for thinking that Newton was far from an inhuman monster is that his niece Catherine Barton, who was one of the most admired women of the London of her time, and known both for her beauty and wit, worked as Newton's house-keeper for a pretty long time. Several years later, after getting married, Ms. Barton, her husband and her little daughter lived together with Newton. I do not think such arrangements would have been possible, if Newton had been an entirely unbearable person.

Best,

Jarmo

The partition of integers is important in counting the number of states on a black hole horizon. The area of a black hole is composed of little quanta of areas given by a sum of integers n_i >= 0,

A = 4 π a(n_1 + n_2 + ... n_m)

where this total number N = n_1 + n_2 + ... n_m can be written according to the integer partition. Another way of thinking about this is that the string modes can exist in a distribution which is an integer parition. This is the holographic principle in action, where the event horizon or stretched horizon is composed of a "gas" of strings.

The density of states for a string is tr(w^N) , which for N = \sum_nα_{-n}α_n the string number operator. Given there are 24 string operator the computation of this generating function is tr(w^N) = f(w)^{-24} for

F(w) = prod_{n=1}^∞(1 – w^n)

This is a form of the Dedekind η-function and the remaining calculation leads to a form of the Hardy-Ramanujan approximation for the integer partitions.

The black hole in the holographic setting has a stretched horizon which is a gas of strings. If we consider the string to be the bosonic string in d = 26 then 24 correspond to the SO(24) group for the graviton plus dilaton and a gauge field. So the Newtonian insight here seems to be pointing in this direction.

Cheers LC

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A = 4 π a(n_1 + n_2 + ... n_m)

where this total number N = n_1 + n_2 + ... n_m can be written according to the integer partition. Another way of thinking about this is that the string modes can exist in a distribution which is an integer parition. This is the holographic principle in action, where the event horizon or stretched horizon is composed of a "gas" of strings.

The density of states for a string is tr(w^N) , which for N = \sum_nα_{-n}α_n the string number operator. Given there are 24 string operator the computation of this generating function is tr(w^N) = f(w)^{-24} for

F(w) = prod_{n=1}^∞(1 – w^n)

This is a form of the Dedekind η-function and the remaining calculation leads to a form of the Hardy-Ramanujan approximation for the integer partitions.

The black hole in the holographic setting has a stretched horizon which is a gas of strings. If we consider the string to be the bosonic string in d = 26 then 24 correspond to the SO(24) group for the graviton plus dilaton and a gauge field. So the Newtonian insight here seems to be pointing in this direction.

Cheers LC

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The Question wether Reality is digital or analogue struck me as extremely unrealistic: those are just different ways humans can handle what they believe to be reality. Of course reality is neither and is beyond any human approach except by intuition. Therefore I think this question can only be put by extremely short-sighted people. It is not really aserious problem at all.

I know this is not the subject here, but I saw a possibility to make my point.

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I know this is not the subject here, but I saw a possibility to make my point.

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Jarmo Matti Mäkelä,

I just printed off your essay. I will be looking for why you asked Newton about the 2nd law of thermodynamics instead of asking Clausius:

"I am not quite sure what Newton really had in mind. I think that he simply meant that at appropriate length scales the metric tensor, which depends on the quantum states of the constituents of spacetime, has a signature (-,+,+,+). The process, which brings this result may or may not have something to do with decoherence, but I am not sure about that."

I don't believe that either of them, even today, would state the quote above. I think that both of them would have first determined what thermodynamic entropy is before skipping past it to what I consider to be sidestepping the question. In other words, giving it later assigned meaning that I do not see applying to Clausius' definition.

James

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I just printed off your essay. I will be looking for why you asked Newton about the 2nd law of thermodynamics instead of asking Clausius:

"I am not quite sure what Newton really had in mind. I think that he simply meant that at appropriate length scales the metric tensor, which depends on the quantum states of the constituents of spacetime, has a signature (-,+,+,+). The process, which brings this result may or may not have something to do with decoherence, but I am not sure about that."

I don't believe that either of them, even today, would state the quote above. I think that both of them would have first determined what thermodynamic entropy is before skipping past it to what I consider to be sidestepping the question. In other words, giving it later assigned meaning that I do not see applying to Clausius' definition.

James

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Jarmo Matti Mäkelä,

If you think that my point was silly and not worth your time to respond I understand. I don't agree, but I understand that my viewpoint is not the same as a professionally trained physicist. I thought it was important to point out that I think that no one knows what thermodynamic entropy is. I will move on to other essays. We have a very good quantity along with sufficient quality this year.

James

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If you think that my point was silly and not worth your time to respond I understand. I don't agree, but I understand that my viewpoint is not the same as a professionally trained physicist. I thought it was important to point out that I think that no one knows what thermodynamic entropy is. I will move on to other essays. We have a very good quantity along with sufficient quality this year.

James

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I said that no one knows what thermodynamic entropy is. The point I am making is that Clausius' definition of entropy is the real definition of entropy. The transferrence of Boltzmann's constant onto Boltzmann's entropy was the beginning of losing sight, if we ever had it in sight, of the meaning of Boltzmann's constant. Boltmann's interpretation of entropy was the first step in ignoring Clausius' definition and finding some more simplistic substitute. I think that Newton would have first said: What is thermodynamic entropy? Perhaps there are others here who will clarify the meaning of thermodynamic entropy for me?

James

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James

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An excellent and entertaining entrance to your essay Jarmo, congratulations on your imagination and ingeniuty. I have a burning question which I've always wanted to ask Newton though, which is this:

Q: Since he equated the ancient greek philosophy of the smallest irreducible particle, called an atom, with the motions of the planets as observed by Galileo Galilei, does he want to know what his very large unspoken logical assumption was, which has now meant that humanity has been led down the wrong scientific path?

Ans: He assumed that the cores of the planets and sun are composed of the same everyday matter which is found on the external crust. (It's not necessarily the case and so invalidates the whole of Einstein's space-time concept imo and also invalidates the results of the Cavendish experiment to 'weigh' the Earth).

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Q: Since he equated the ancient greek philosophy of the smallest irreducible particle, called an atom, with the motions of the planets as observed by Galileo Galilei, does he want to know what his very large unspoken logical assumption was, which has now meant that humanity has been led down the wrong scientific path?

Ans: He assumed that the cores of the planets and sun are composed of the same everyday matter which is found on the external crust. (It's not necessarily the case and so invalidates the whole of Einstein's space-time concept imo and also invalidates the results of the Cavendish experiment to 'weigh' the Earth).

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Enormously clever! And I don't just mean the conceit of talking to Isaac Newton (with a nice paradox-saving ending). I mean the journey through algebra, combinatorics, geometry, to the 4-simplex whose edges correspond to the 10 non-redundant points of the Riemann metric tensor. That is literally where "the rubber meets the road," as they say -- where the discrete comes smack up against the continuous, where " ... the causal properties of spacetime ..." imply the existence of " ... a still unknown law of nature ..." that we hope quantizes spacetime.

I'm betting that you're a very popular lecturer. Bravo.

Tom

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I'm betting that you're a very popular lecturer. Bravo.

Tom

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Hi Mäkelä,

Your article is ingenious because you put in Newton autority mouth, your ideas.

Guessing, I supose that Newton will agree more with an universal gravitation law modified than with Einstein TGR.

If you replace Beta in the partition formula by one divided Boltzmann constant times Temperature, and as Hawking temperature in a Black Hole is proportional to the inverse of Energy the formula doesn´t diverge.

Bests,

JC

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Your article is ingenious because you put in Newton autority mouth, your ideas.

Guessing, I supose that Newton will agree more with an universal gravitation law modified than with Einstein TGR.

If you replace Beta in the partition formula by one divided Boltzmann constant times Temperature, and as Hawking temperature in a Black Hole is proportional to the inverse of Energy the formula doesn´t diverge.

Bests,

JC

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Hi,

When you calculate the partition function, you must assume that the inverse temperature Beta is a constant, and therefore independent of the energy. Once after you have calculated the partition function, you will find the relationship between energy and temperature using the formula of Note 6.

Best,

jarmo

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When you calculate the partition function, you must assume that the inverse temperature Beta is a constant, and therefore independent of the energy. Once after you have calculated the partition function, you will find the relationship between energy and temperature using the formula of Note 6.

Best,

jarmo

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Your metric tensor, and your Newton analogy are very clever. I would like to understand how that contributes to the quantum limit as you propose.

Could you elucidate this point more clearly ?

Andy

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Could you elucidate this point more clearly ?

Andy

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Hi,

Thanks for your message. I you want a really technical account on how metric tensor arises from the quantum states of the constituents of spacetime, (I suppose that was your question?) I advice you to have a look on my paper in arXiv:0805.3952 (Ch. 5). When expressed in very broad, non-technical terms the basic idea is that when a sufficiently large aggregate of the constituents of spacetime is considered, it becomes possible to talk meaningfully about four-simplices. The areas of the triangles of those four-simplices depend on the quantum states of their constituents, and we may express the components of the metric tensor in terms of those triangle areas.

Best,

Jarmo

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Thanks for your message. I you want a really technical account on how metric tensor arises from the quantum states of the constituents of spacetime, (I suppose that was your question?) I advice you to have a look on my paper in arXiv:0805.3952 (Ch. 5). When expressed in very broad, non-technical terms the basic idea is that when a sufficiently large aggregate of the constituents of spacetime is considered, it becomes possible to talk meaningfully about four-simplices. The areas of the triangles of those four-simplices depend on the quantum states of their constituents, and we may express the components of the metric tensor in terms of those triangle areas.

Best,

Jarmo

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I really like this discrete geometric treatment of a continuous area. Unless I've missed something in the literature that I shouldn't have, it's nonstandard -- however, I don't think it's a stretch to compare it to Euler's geometric interpretation of the complex plane (e^ipi = - 1) in principle, because it provides a straightforward way to convert a continuous metric into an algebraicaly manageable object.

Tom

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Tom

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Dear Tom,

Looking in vain for something possibly valuable here or at least a reply to my comment concerning Newton, I got aware of your comment on Euler (1707-1783) who interpreted the complex plane introduced by Gauss (1777-1855).

I agree, that non-linear functions like sin, cos, exp, lg, etc. provide links between continuous and discrete quantities. Can you please explain to me the notion continuous metric?

Regards,

Eckard

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Looking in vain for something possibly valuable here or at least a reply to my comment concerning Newton, I got aware of your comment on Euler (1707-1783) who interpreted the complex plane introduced by Gauss (1777-1855).

I agree, that non-linear functions like sin, cos, exp, lg, etc. provide links between continuous and discrete quantities. Can you please explain to me the notion continuous metric?

Regards,

Eckard

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Dear Jarmo

I am embarrassed to admit I seem to have a confession to make. Some time ago I heard someone fall down some stairs and went to help, he was in a bad way, mumbling is some alien language and delirious. I picked him up with his papers and bits and carried him off to hospital.

I found afterwards I still had his papers and a strange little machine with HG Wells stamped on it.. but the poor fellow had mysteriously disappeared. I read the papers but they had no name or address. They were entitled "The Complete Quantum Theory of Gravitation". I really didn't know what to do with them. If I'd known they were yours I'd have put them in a time capsule...

As it was I thought I must try to put them and the machine to good use. They both rather scared me! I was worried about causality. What I decided to do was pop forward the 300 years the machine was set to and check if all was ok and we'd managed to find the theory.

Imagine my horror when I discovered it was my fault that we hadn't, ..and that science seemed to have gone backwards in time! I didn't have a clue if you were around or where to find you. The world was strange to me but I managed to survive by popping back and making the odd bet and investment, and have had fun directing some great blockbuster films about a land I visited using your... well never mind about that. I spent a few years checking the theory and it seemed spot on so I eventually decided it best to write it up in my own way and give it to the world. - the complete atomic structure of space time, unifying SR, GR and QM.

But apparently the world doesn't understand it! As only you will I hope you'll read my essay, gently slipping in that the sub space-time medium condenses into an atomic structure to produce space-time itself. The quantum states are ions, re-polarised by black holes, and distributed as plasma in such a way that the every day notion of time and causality are recovered. Actually I think that wording is yours, I mean Sir Isaac's, not mine!

It's been a difficult time, but a massive relief to have found it's owner. I did tentatively refer to it in last years contest, and touch on it quite lightly in my current essay languishing some way below yours (2020 Vision..) But it's better covered in a number of preprints I can pass to you. Here are some recent ones; http://vixra.org/abs/1001.0010 and http://vixra.org/abs/1102.0016

I hope you're able to finally confirm I'm not totally insane. The only way I've managed to hide from the men in white coats so far is to be secretly the 3rd richest man in the world.

I pass it all to you, in Isaac's name. - Do you think I should withdraw or just give you both credits and citations in the paper currently accepted for review!

With massive relief

Peter Jackson

PS. You have a well earned 10 from me. But please do reply asap.

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I am embarrassed to admit I seem to have a confession to make. Some time ago I heard someone fall down some stairs and went to help, he was in a bad way, mumbling is some alien language and delirious. I picked him up with his papers and bits and carried him off to hospital.

I found afterwards I still had his papers and a strange little machine with HG Wells stamped on it.. but the poor fellow had mysteriously disappeared. I read the papers but they had no name or address. They were entitled "The Complete Quantum Theory of Gravitation". I really didn't know what to do with them. If I'd known they were yours I'd have put them in a time capsule...

As it was I thought I must try to put them and the machine to good use. They both rather scared me! I was worried about causality. What I decided to do was pop forward the 300 years the machine was set to and check if all was ok and we'd managed to find the theory.

Imagine my horror when I discovered it was my fault that we hadn't, ..and that science seemed to have gone backwards in time! I didn't have a clue if you were around or where to find you. The world was strange to me but I managed to survive by popping back and making the odd bet and investment, and have had fun directing some great blockbuster films about a land I visited using your... well never mind about that. I spent a few years checking the theory and it seemed spot on so I eventually decided it best to write it up in my own way and give it to the world. - the complete atomic structure of space time, unifying SR, GR and QM.

But apparently the world doesn't understand it! As only you will I hope you'll read my essay, gently slipping in that the sub space-time medium condenses into an atomic structure to produce space-time itself. The quantum states are ions, re-polarised by black holes, and distributed as plasma in such a way that the every day notion of time and causality are recovered. Actually I think that wording is yours, I mean Sir Isaac's, not mine!

It's been a difficult time, but a massive relief to have found it's owner. I did tentatively refer to it in last years contest, and touch on it quite lightly in my current essay languishing some way below yours (2020 Vision..) But it's better covered in a number of preprints I can pass to you. Here are some recent ones; http://vixra.org/abs/1001.0010 and http://vixra.org/abs/1102.0016

I hope you're able to finally confirm I'm not totally insane. The only way I've managed to hide from the men in white coats so far is to be secretly the 3rd richest man in the world.

I pass it all to you, in Isaac's name. - Do you think I should withdraw or just give you both credits and citations in the paper currently accepted for review!

With massive relief

Peter Jackson

PS. You have a well earned 10 from me. But please do reply asap.

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Hi,

Thanks for your interesting post. It would really be wonderful, if the papers written by Sir Isaac still existed! I have been reading your pre-prints. They are interesting, but I am not quite sure, whether they are quite similar to the ones, which I was reading just before that unfortunate fall in Newton's stairs. Maybe you have misunderstood some points in Newton's draft? Do you still have the originals? If you do, please take photocopies of them, and send them to the address mentioned in my essay. Many thanks for taking me to the hospital after my fall in Newton's stairs, although I have no recollection of that.

Best,

Jarmo

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Thanks for your interesting post. It would really be wonderful, if the papers written by Sir Isaac still existed! I have been reading your pre-prints. They are interesting, but I am not quite sure, whether they are quite similar to the ones, which I was reading just before that unfortunate fall in Newton's stairs. Maybe you have misunderstood some points in Newton's draft? Do you still have the originals? If you do, please take photocopies of them, and send them to the address mentioned in my essay. Many thanks for taking me to the hospital after my fall in Newton's stairs, although I have no recollection of that.

Best,

Jarmo

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Dear Jarmo,

I must agree with many of your other readers, in that you have given a very creative presentation. The introduction and conclusion are very well and clearly written and are enjoyable. Unfortunately, not being a physics specialist, I found the middle of the essay too technical to follow. Also as I have limited mathematical skill I can not judge if what you have said is technically correct and rigorously argued. I will have to leave that judgment to others.I can see some lively debate and much interest in your comments thread. It is certainly topical and foundational.I suspect it is far more interesting and goes far deeper than I can appreciate and understand.I wish you good luck, Georgina.

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I must agree with many of your other readers, in that you have given a very creative presentation. The introduction and conclusion are very well and clearly written and are enjoyable. Unfortunately, not being a physics specialist, I found the middle of the essay too technical to follow. Also as I have limited mathematical skill I can not judge if what you have said is technically correct and rigorously argued. I will have to leave that judgment to others.I can see some lively debate and much interest in your comments thread. It is certainly topical and foundational.I suspect it is far more interesting and goes far deeper than I can appreciate and understand.I wish you good luck, Georgina.

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Dear FQXi community,

There are three kinds of essays in our contest: 1) the essays with original physics research where all physics' information was created by their authors. Often such papers contain some errors or unclear information because it is very difficult to create a NEW physical theory (information). 2) There are essays-stories about physics which contain physics' information copied from physics textbooks or other published papers (for example authors Jarmo Makela, Singh, Durham, Funakoshi and so on). The author's commentaries like 'this theory is good, or not are neither original physics research nor new physics information. These essays-stories cannot have any errors by definition because all physics' information was copied from the textbooks and other published papers. (However, if these authors have added original physics research information in their articles, I'm sure we'll find physical errors in their papers).3) There are essays of mixed type containing mixed information (original research plus physics' information copied from the textbooks and papers). It is clear that the authors of the essays-stories have advantages because their essays never contain errors since all Physics' information was copied from the textbooks. However, it does not mean these essays-stories are better than essays with original research.

What kind of the essays must FQXi community support? If we support the essays-stories then we'll transform FQXi community into the entertainment community. For example, instead of my ''interpretation of quantum mechanics'' I could send the anecdotes about Bohr, Einstein or stories like Gamov's Mr. Tompkins in paperback. It would be very interesting and fun. Another option is to create essays-discussions with Einstein, Bohr, or Aristotle following the example of Jarmo Makela. In this context, the next logical step is to organize a banquet for the authors of essays where we tell jokes and funny stories about physics. What is Our Purpose?

However, since the goals of the FQXi (the "Contest") are to: ''Encourage and support rigorous, innovative, and influential thinking about foundational questions in physics and cosmology; Identify and reward top thinkers in foundational questions'' therefore I ask readers to vote for essays with original physics research rather than for essays-stories about physics. In this way we'll encourage the fundamental physics research but not entertainment essays.

Sincerely,

Constantin

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There are three kinds of essays in our contest: 1) the essays with original physics research where all physics' information was created by their authors. Often such papers contain some errors or unclear information because it is very difficult to create a NEW physical theory (information). 2) There are essays-stories about physics which contain physics' information copied from physics textbooks or other published papers (for example authors Jarmo Makela, Singh, Durham, Funakoshi and so on). The author's commentaries like 'this theory is good, or not are neither original physics research nor new physics information. These essays-stories cannot have any errors by definition because all physics' information was copied from the textbooks and other published papers. (However, if these authors have added original physics research information in their articles, I'm sure we'll find physical errors in their papers).3) There are essays of mixed type containing mixed information (original research plus physics' information copied from the textbooks and papers). It is clear that the authors of the essays-stories have advantages because their essays never contain errors since all Physics' information was copied from the textbooks. However, it does not mean these essays-stories are better than essays with original research.

What kind of the essays must FQXi community support? If we support the essays-stories then we'll transform FQXi community into the entertainment community. For example, instead of my ''interpretation of quantum mechanics'' I could send the anecdotes about Bohr, Einstein or stories like Gamov's Mr. Tompkins in paperback. It would be very interesting and fun. Another option is to create essays-discussions with Einstein, Bohr, or Aristotle following the example of Jarmo Makela. In this context, the next logical step is to organize a banquet for the authors of essays where we tell jokes and funny stories about physics. What is Our Purpose?

However, since the goals of the FQXi (the "Contest") are to: ''Encourage and support rigorous, innovative, and influential thinking about foundational questions in physics and cosmology; Identify and reward top thinkers in foundational questions'' therefore I ask readers to vote for essays with original physics research rather than for essays-stories about physics. In this way we'll encourage the fundamental physics research but not entertainment essays.

Sincerely,

Constantin

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Dear Jarmo

You ask; "Maybe you have misunderstood some points in Newton's draft?" I can absolutely reassure you that after many years of study I have in no way fully understood almost all the points of Newtons draft. Indeed using your Wells machine I've searched back and forth for the solution. I've met many interesting people, Florin who made a copy of the machine, Dr Cosmic Ray who told me of the 32 different dimensions, and Albert, who told me of the "infinitely many spaces in relative motion", but we all still have our own perspective, and I learnt that that's a strength not a weakness of humankind.

I disagree with Constantin, content is different to presentation. If you are a top Oxford maths professor and disagree with unreal abstract maths it does no good complaining, you should write a satire about the ridiculous 'Wonderland' it creates so thousands buy the book... ..and .. well.. you can at least retire rich! ..Hmmm. Anyway, I think some have been distracted from the important scientific point!

I'll try to find those papers. But you'll have seen my own exploration of nature is based on nature itself not abstraction. I've interpreted the papers differently, but still seem to have unified SR, GR and QM, and derived quantum gravity, with rigorous logic alone. I'd be eternally grateful if you could either tell me where I've gone wrong, or confirm they're consistent, or where they're not. In return I'll see if I can pop back a bit earlier to see if I can find them on the mantlepiece.

I await your conclusions with the utmost excitement and trepidation.

Your obedient servant.

Peter

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You ask; "Maybe you have misunderstood some points in Newton's draft?" I can absolutely reassure you that after many years of study I have in no way fully understood almost all the points of Newtons draft. Indeed using your Wells machine I've searched back and forth for the solution. I've met many interesting people, Florin who made a copy of the machine, Dr Cosmic Ray who told me of the 32 different dimensions, and Albert, who told me of the "infinitely many spaces in relative motion", but we all still have our own perspective, and I learnt that that's a strength not a weakness of humankind.

I disagree with Constantin, content is different to presentation. If you are a top Oxford maths professor and disagree with unreal abstract maths it does no good complaining, you should write a satire about the ridiculous 'Wonderland' it creates so thousands buy the book... ..and .. well.. you can at least retire rich! ..Hmmm. Anyway, I think some have been distracted from the important scientific point!

I'll try to find those papers. But you'll have seen my own exploration of nature is based on nature itself not abstraction. I've interpreted the papers differently, but still seem to have unified SR, GR and QM, and derived quantum gravity, with rigorous logic alone. I'd be eternally grateful if you could either tell me where I've gone wrong, or confirm they're consistent, or where they're not. In return I'll see if I can pop back a bit earlier to see if I can find them on the mantlepiece.

I await your conclusions with the utmost excitement and trepidation.

Your obedient servant.

Peter

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Dear Peter,

I read again Jarmo Mäkelä's essay and I can say that this essay has artistic value only. All PHYSICS' information used by Jarmo is generally known information, copied from the textbooks and published papers. The dialogue with Newton is the only contribution of the author Jarmo Mäkelä. Therefore this essay has ARTISTIC VALUE ONLY, and is not scientifically important.

Sincerely,

Constantin

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I read again Jarmo Mäkelä's essay and I can say that this essay has artistic value only. All PHYSICS' information used by Jarmo is generally known information, copied from the textbooks and published papers. The dialogue with Newton is the only contribution of the author Jarmo Mäkelä. Therefore this essay has ARTISTIC VALUE ONLY, and is not scientifically important.

Sincerely,

Constantin

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The divergence of the partition function and the microscopic origin of black hole entropy are long-standing, fundamental problems of black hole physics. The "Newton Model" (to give a name to the model) may be regarded as a suggestion for a simple solution to both of these problems, using an assumption that the event horizon of a black hole consists of a finite number of discrete constituents as a starting point. The success of the model is then used as an argument for a discrete nature of spacetime, and the reduction of the metric and the causal properties of spacetime to the quantum states of its contsituents is outlined. Technically, the key point of the model is Eq. (9), which gives an expression for the partition function of the Schwarzschild black hole. According to my best knowledge Eq. (9) has never been published anywhere. The reduction of the metric and the causal properties of spacetime to the quantum states of its cosntituents in a manner described in the model has been considered in some of my earlier works, but nowhere else.

Jarmo

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Jarmo

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Jarmo,

OK, I'm glad you found some original information in your essay. I wish you success in the contest.

Dear Readers, about 70 percents of all theoretical papers in Physics published in the World are wrong, the Standard Model is a mathematical model only that can compute only but explain nothing. The SM theory will fall in nearest future if you support my theory. This theory is a revolution in physics; Nobody found errors in my theory ever. We need the true Science, without powerful science our civilization may die. Science is our only hope to survive.

Please vote for the FUTURE physics , for teleportation and for life.

Constantin

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OK, I'm glad you found some original information in your essay. I wish you success in the contest.

Dear Readers, about 70 percents of all theoretical papers in Physics published in the World are wrong, the Standard Model is a mathematical model only that can compute only but explain nothing. The SM theory will fall in nearest future if you support my theory. This theory is a revolution in physics; Nobody found errors in my theory ever. We need the true Science, without powerful science our civilization may die. Science is our only hope to survive.

Please vote for the FUTURE physics , for teleportation and for life.

Constantin

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Jarmo,

What a novel way of approaching the topic. When encountered with the brilliance of Newton, I now think of the revelation regarding his first passion of alchemy. I wonder if this has been sensationalized of late.

Jim Hoover

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What a novel way of approaching the topic. When encountered with the brilliance of Newton, I now think of the revelation regarding his first passion of alchemy. I wonder if this has been sensationalized of late.

Jim Hoover

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A close friend of mine has informed me of your insolence to associate me with your ideas about reality. As you know very well, I find your work lacking any physical validity and think that the mathematical rigor glows by its absence.

I urge you to immediately rectify the many erroneous statements attributed to me in your Essay and to publish what I actually said about your work, as well as about the books and papers that you sent me.

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I urge you to immediately rectify the many erroneous statements attributed to me in your Essay and to publish what I actually said about your work, as well as about the books and papers that you sent me.

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Hello,

Have you heard of "hypothesis non fingo"?

http://en.wikipedia.org/wiki/Hypotheses_non_fingo

"I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction."

I wonder why FQXi even accepted this paper. It is plain insult to the memory of one of the greatest empiricists of all times.

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Have you heard of "hypothesis non fingo"?

http://en.wikipedia.org/wiki/Hypotheses_non_fingo

"I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction."

I wonder why FQXi even accepted this paper. It is plain insult to the memory of one of the greatest empiricists of all times.

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Dear Jarmo, dear readers,

this is absolutely false, I am NOT "Peter".

On the other hand, the fake who signed as "Sir Issac Newton" is the same crank who signed a post in my Essay-page as "Albert Einstein". In fact, the sentences in the above post are almost the same of the ones in my Essay-page. I suspect that he is a poor man who is obsessed by me, but I will not mention his name for a sake of mercy.

Cheers,

Ch.

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this is absolutely false, I am NOT "Peter".

On the other hand, the fake who signed as "Sir Issac Newton" is the same crank who signed a post in my Essay-page as "Albert Einstein". In fact, the sentences in the above post are almost the same of the ones in my Essay-page. I suspect that he is a poor man who is obsessed by me, but I will not mention his name for a sake of mercy.

Cheers,

Ch.

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Hi,

Apparently, you failed to understand that the story was a description of a dream. In dreams people may experience strange things which, however, have nothing to do with reality. Nobody would take dreams seriously, even less feel offended by them.

Best,

Jarmo

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Apparently, you failed to understand that the story was a description of a dream. In dreams people may experience strange things which, however, have nothing to do with reality. Nobody would take dreams seriously, even less feel offended by them.

Best,

Jarmo

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I urge you to immediately rectify the many erroneous statements attributed to me in your Essay and to publish what I ACTUALLY SAID IN YOUR DREAM.

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Dear Jarmo,

Congratulations on your dedication to the competition and your much deserved top ten placing. I have a bugging question for you, which I've also posed to all the top front runners btw:

Q: Coulomb's Law of electrostatics was modelled by Maxwell by mechanical means after his mathematical deductions as an added verification (thanks for that bit of info Edwin), which I highly admire. To me, this gives his equation some substance. I have a problem with the laws of gravity though, especially the mathematical representation that "every object attracts every other object equally in all directions." The 'fabric' of spacetime model of gravity doesn't lend itself to explain the law of electrostatics. Coulomb's law denotes two types of matter, one 'charged' positive and the opposite type 'charged' negative. An Archimedes screw model for the graviton can explain -both- the gravity law and the electrostatic law, whilst the 'fabric' of spacetime can't. Doesn't this by definition make the helical screw model better than than anything else that has been suggested for the mechanism of the gravity force?? Otherwise the unification of all the forces is an impossiblity imo. Do you have an opinion on my analysis at all?

Best wishes,

Alan

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Congratulations on your dedication to the competition and your much deserved top ten placing. I have a bugging question for you, which I've also posed to all the top front runners btw:

Q: Coulomb's Law of electrostatics was modelled by Maxwell by mechanical means after his mathematical deductions as an added verification (thanks for that bit of info Edwin), which I highly admire. To me, this gives his equation some substance. I have a problem with the laws of gravity though, especially the mathematical representation that "every object attracts every other object equally in all directions." The 'fabric' of spacetime model of gravity doesn't lend itself to explain the law of electrostatics. Coulomb's law denotes two types of matter, one 'charged' positive and the opposite type 'charged' negative. An Archimedes screw model for the graviton can explain -both- the gravity law and the electrostatic law, whilst the 'fabric' of spacetime can't. Doesn't this by definition make the helical screw model better than than anything else that has been suggested for the mechanism of the gravity force?? Otherwise the unification of all the forces is an impossiblity imo. Do you have an opinion on my analysis at all?

Best wishes,

Alan

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I am not sure, whether I understood your question, but anyway, to understand the Coulomb force you do not need any mechanical models. Instead, you consider the symmmetry properties of ordinary, four-dimensional flat spacetime.

To undestand the Coulmb force in terms of the properties of spacetime you may begin with spin 1/2 particles (electrons, or example). If you construct a field equation for a spin 1/2 particle in flat spacetime, the resulting equation must be compatible with Einstein's special relativity. More precisely, it must be Lorentz invariant. The Lorentz invariance is one of the symmetries of flat spacetime. The Lorentz invariant equation in question is known as Dirac equation. It turns out that the Dirac equation, in turn, possesses internal, global symmetry, which is known as U(1)symmetry. To make the U(1) symmetry a local symmetry, you need the so-called gauge connection, and a coupling constant, which may be interpreted as the electric charge of the electron. So, in addition to the Dirac field, you now have also a gauge connection. To make a theory consistent, you need, in addition to the Dirac equation, for the gauge connection a field equation, which possesses both the U(1) and the Lorentz symmetries. The simplest possible equation with these properties may be shown to be equivalent with Maxwell equations for the electric and the magnetic fields. So to obtain the Coulomb interaction you only have to consider the implications of the symmetries of spacetime, and no mechanical analogues are needed.

Best,

Jarmo

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To undestand the Coulmb force in terms of the properties of spacetime you may begin with spin 1/2 particles (electrons, or example). If you construct a field equation for a spin 1/2 particle in flat spacetime, the resulting equation must be compatible with Einstein's special relativity. More precisely, it must be Lorentz invariant. The Lorentz invariance is one of the symmetries of flat spacetime. The Lorentz invariant equation in question is known as Dirac equation. It turns out that the Dirac equation, in turn, possesses internal, global symmetry, which is known as U(1)symmetry. To make the U(1) symmetry a local symmetry, you need the so-called gauge connection, and a coupling constant, which may be interpreted as the electric charge of the electron. So, in addition to the Dirac field, you now have also a gauge connection. To make a theory consistent, you need, in addition to the Dirac equation, for the gauge connection a field equation, which possesses both the U(1) and the Lorentz symmetries. The simplest possible equation with these properties may be shown to be equivalent with Maxwell equations for the electric and the magnetic fields. So to obtain the Coulomb interaction you only have to consider the implications of the symmetries of spacetime, and no mechanical analogues are needed.

Best,

Jarmo

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Jarmo,

Thanks for the reply. We have a difference of opinion on this one then. No problem.

Kind regards,

Alan

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Thanks for the reply. We have a difference of opinion on this one then. No problem.

Kind regards,

Alan

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Dear Sir,

Special Relativity is not only conceptually, but also mathematically wrong. This is what Einstein describes in his 30-06-1905 paper "On the Electrodynamics of Moving Bodies":

Einstein: We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:

5. If the...

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Special Relativity is not only conceptually, but also mathematically wrong. This is what Einstein describes in his 30-06-1905 paper "On the Electrodynamics of Moving Bodies":

Einstein: We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:

5. If the...

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Dear Sir,

You talk about space-time without properly defining the terms. Both space and time are related to the order of arrangement in the field, i.e., sequence of objects and events contained in them like the design on a fabric. Both space and time co-exist like the fabric and its back ground color. The perception of each sequence is interrupted by an interval however infinitesimal. The...

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You talk about space-time without properly defining the terms. Both space and time are related to the order of arrangement in the field, i.e., sequence of objects and events contained in them like the design on a fabric. Both space and time co-exist like the fabric and its back ground color. The perception of each sequence is interrupted by an interval however infinitesimal. The...

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This is somewhat off-topic, but then again, perhaps not.

Consider the basic Kerr metric equation: J = aGm^2/c,

where J = total momentum

a = dimensionless rotational parameter.

If J = (j{j+1})^1/2 h-bar

and we use G = G' = 2.18 x 10^31 cm^3/g sec^2

(call it the strong force coupling constant)

then: m = (j{j+1}/a^2)^1/4 (h-bar c/G')^1/2.

--------------------------------------------------

---------------------

PROTON

For j = 1/2 and a = 4/9 [i.e., ~1/2], m = 942.935 MeV

(proton mass = 938.3 MeV)

We notice that (h-bar c/G')^1/2 has the form of the Planck mass.

-------------------------------------------------------

-------------------

ELECTRON

If we choose (alpha^2 e^2/G')^1/2 as our fundamental mass,

in place of (h-bar c/G')^1/2, i.e., replace (h-bar c) with (alpha^2 e^2)

and call it the "Einstein mass", our mass equation becomes

m = (j{j+1}/a^2)^1/4 (alpha^2 e^2/G')^1/2.

For j = 1/2 and a = 7/12 [again ~1/2], m = 0.5131 MeV

(electron mass = 0.511 MeV)

--------------------------------------------------------

----------------

NEUTRON

Neutron mass = proton mass + 3(Einstein mass) = 939.5354 MeV

(neutron mass = 939.566 MeV).

-------------------------------------------------------

------------------

The electron mass, and the proton-neutron mass difference,

have never been explained.

For scientists who would like to see a more detailed summary

of these theoretical results, I have a brief 3-page summary that

explains the retrodictions in more detail.

If you send me an email I will attach a doc. file or pdf (your choice)

in my reply.

RLO

http://www3.amherst.edu/~rloldershaw

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Consider the basic Kerr metric equation: J = aGm^2/c,

where J = total momentum

a = dimensionless rotational parameter.

If J = (j{j+1})^1/2 h-bar

and we use G = G' = 2.18 x 10^31 cm^3/g sec^2

(call it the strong force coupling constant)

then: m = (j{j+1}/a^2)^1/4 (h-bar c/G')^1/2.

--------------------------------------------------

---------------------

PROTON

For j = 1/2 and a = 4/9 [i.e., ~1/2], m = 942.935 MeV

(proton mass = 938.3 MeV)

We notice that (h-bar c/G')^1/2 has the form of the Planck mass.

-------------------------------------------------------

-------------------

ELECTRON

If we choose (alpha^2 e^2/G')^1/2 as our fundamental mass,

in place of (h-bar c/G')^1/2, i.e., replace (h-bar c) with (alpha^2 e^2)

and call it the "Einstein mass", our mass equation becomes

m = (j{j+1}/a^2)^1/4 (alpha^2 e^2/G')^1/2.

For j = 1/2 and a = 7/12 [again ~1/2], m = 0.5131 MeV

(electron mass = 0.511 MeV)

--------------------------------------------------------

----------------

NEUTRON

Neutron mass = proton mass + 3(Einstein mass) = 939.5354 MeV

(neutron mass = 939.566 MeV).

-------------------------------------------------------

------------------

The electron mass, and the proton-neutron mass difference,

have never been explained.

For scientists who would like to see a more detailed summary

of these theoretical results, I have a brief 3-page summary that

explains the retrodictions in more detail.

If you send me an email I will attach a doc. file or pdf (your choice)

in my reply.

RLO

http://www3.amherst.edu/~rloldershaw

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Dear Jarmo,

Congratulations on winning the first prize! Brilliant and well-deserved.

Cheers,

Tejinder Singh

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Congratulations on winning the first prize! Brilliant and well-deserved.

Cheers,

Tejinder Singh

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Congratulations Jarmo. I stand by everything I said in my original post on this thread. Your essay seemed to be a popular choice with the community throughout the contest.I am glad that the judges found what they were looking for in your essay. I have discovered the meeting with sir Issac vehicle published elsewhere, so it is not as original an idea as I at first thought but that does not diminish the quality of the writing or the correctness of the scientific and mathematical content. Well done you.

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Dear Jarmo

I think Sir Isaac is a bit baffled by email addresses - his message to you ended up in my Inbox for some reason - first he he offers his congratulations to you, but then asks if you are in league with Leibnitz? He also asks if fqxi is some sort of an alchemical symbol? His new email address is newton_fluxions@royalmint.eng

Best wishes from Vladimir

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I think Sir Isaac is a bit baffled by email addresses - his message to you ended up in my Inbox for some reason - first he he offers his congratulations to you, but then asks if you are in league with Leibnitz? He also asks if fqxi is some sort of an alchemical symbol? His new email address is newton_fluxions@royalmint.eng

Best wishes from Vladimir

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Jarmo

Congratulations, Very well deserved.

I hope you got those documents back!

Best wishes

Peter

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Congratulations, Very well deserved.

I hope you got those documents back!

Best wishes

Peter

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Jarmo, you mention area and distance in space. The following is essential to your discussion.

The key is to show distance in/of space that is represented by equivalent inertial and gravitational force/energy. This balances attraction and repulsion and gives us middle distance in/of space in keeping with the middle force/energy of equivalent gravity and inertia. Here we have quantum gravity and space manifesting as electromagnetic/inertial/gravitational energy.

Equivalent and balanced inertia and gravity balance attraction and repulsion in conjunction with the experience of what is the middle distance in/of space. There will never be a unified understanding of physical reality apart from this.

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The key is to show distance in/of space that is represented by equivalent inertial and gravitational force/energy. This balances attraction and repulsion and gives us middle distance in/of space in keeping with the middle force/energy of equivalent gravity and inertia. Here we have quantum gravity and space manifesting as electromagnetic/inertial/gravitational energy.

Equivalent and balanced inertia and gravity balance attraction and repulsion in conjunction with the experience of what is the middle distance in/of space. There will never be a unified understanding of physical reality apart from this.

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Dear Jarmo,

Congratulations. I would like to say this about your intelligent time travelling essay and the question you posed on what is space time composed of.

The atomic structure of space time is composed of conscience. Conscience is the underlying reality of all, including intelligence. Scientific community is calling conscience singularity in cosmology.

who am I?

Love,

Sridattadev.

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Congratulations. I would like to say this about your intelligent time travelling essay and the question you posed on what is space time composed of.

The atomic structure of space time is composed of conscience. Conscience is the underlying reality of all, including intelligence. Scientific community is calling conscience singularity in cosmology.

who am I?

Love,

Sridattadev.

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Congratulations, Dr. Mäkelä:

Well-earned recognition! After reading Newton's Principia, I a) was glad I never had to face his Genius (I always imagined Newton could make you cry with his towering intellect) b) was glad I was never his enemy (he could hold a grudge for years and had the power and resolve to really ruin your day or career), and c) was glad I didn't have to admit I could only completely understand about 90% of it (see a and b).

After reading your essay & thread, I've warmed a little to Dr. Newton and see him in another historical perspective. Think I would have the courage to speak to him now, if given the chance. Again, pleasurable essay.

As I'm still working the day-job, it help s to have a list of contest winners to guide me in my readings (time certainly didnn't allow this Author to properly peruse all the essays). Next: second place essays. Can't wait and will comment on those \Authors threads in due course. Hope somebody still read s these!

P.S. The fact that fqxi chose not to select Non-Professional REcognition is encouraging (they said the winners represented the Goals of the Contest suitably). I have another take on this: there were at least ;4 or us that had a chance (to name a few G. Parry, R. Jergenson, U. Matfolk) and the Quality to get the prize. How do you choose only two, right?

That's the way it appears to me, and I can't wait for the next Contest! Thanks fqxi, for spurring my thinking into ordered and scientific research paths. It has changed my life. I approach everything with this new excellence of thought and Method. Please see my site: QuantumWidgets.com and Quantum FAcebook and Threads if you find the extra time. These were all created in the course of writing my Entry and Threads and are real-world solutions of the generalization derived in my Essay. And are a continuation of said essay in the form of Art, Philosophy, and emergent Properties... next contest: the other half of the Theory of EVerything to be equated to the first half already derived! Joy!

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Well-earned recognition! After reading Newton's Principia, I a) was glad I never had to face his Genius (I always imagined Newton could make you cry with his towering intellect) b) was glad I was never his enemy (he could hold a grudge for years and had the power and resolve to really ruin your day or career), and c) was glad I didn't have to admit I could only completely understand about 90% of it (see a and b).

After reading your essay & thread, I've warmed a little to Dr. Newton and see him in another historical perspective. Think I would have the courage to speak to him now, if given the chance. Again, pleasurable essay.

As I'm still working the day-job, it help s to have a list of contest winners to guide me in my readings (time certainly didnn't allow this Author to properly peruse all the essays). Next: second place essays. Can't wait and will comment on those \Authors threads in due course. Hope somebody still read s these!

P.S. The fact that fqxi chose not to select Non-Professional REcognition is encouraging (they said the winners represented the Goals of the Contest suitably). I have another take on this: there were at least ;4 or us that had a chance (to name a few G. Parry, R. Jergenson, U. Matfolk) and the Quality to get the prize. How do you choose only two, right?

That's the way it appears to me, and I can't wait for the next Contest! Thanks fqxi, for spurring my thinking into ordered and scientific research paths. It has changed my life. I approach everything with this new excellence of thought and Method. Please see my site: QuantumWidgets.com and Quantum FAcebook and Threads if you find the extra time. These were all created in the course of writing my Entry and Threads and are real-world solutions of the generalization derived in my Essay. And are a continuation of said essay in the form of Art, Philosophy, and emergent Properties... next contest: the other half of the Theory of EVerything to be equated to the first half already derived! Joy!

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Does God allow we apply 'natural number' to 'electron' ?Especially , We konw that electron isn't 'Apple' or Richard Feynman's 'clicks' . as he said that all the surprising wisdom of quantum mechanics is hiding in the double slit experiment. I think maybe the field of natural number's application is restricted by nature, e.g. quantum phenomenon. If we do not reconstruct quantum phenomenon on the old picture(natural number) , that could be think as another reality?

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Good Time, Jarmo

My English is poor, so formulas only

3-dimensional front propagation 4(3+2)-dimensional gravity vulgarly called space has the following minimum dimensions.

Accordingly, the minimum time of transition of the universe from the previous one in the subsequent state is

Good Luck

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My English is poor, so formulas only

3-dimensional front propagation 4(3+2)-dimensional gravity vulgarly called space has the following minimum dimensions.

Accordingly, the minimum time of transition of the universe from the previous one in the subsequent state is

Good Luck

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I think reality how it is in itself is analog, while appearances are digital.

https://www.academia.edu/7347240/Our_Cognitive_Frame

work_as_Quantum_Computer_Leibnizs_Theory_of_Monads_under_Kan

ts_Epistemology_and_Hegelian_Dialectic

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https://www.academia.edu/7347240/Our_Cognitive_Frame

work_as_Quantum_Computer_Leibnizs_Theory_of_Monads_under_Kan

ts_Epistemology_and_Hegelian_Dialectic

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