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Trick or Truth Essay Contest (2015)
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Mathematics: Science of the Possible, or the Probable? by Thomas Howard Ray
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Author Thomas Howard Ray wrote on Mar. 5, 2015 @ 21:00 GMT
Essay AbstractMathematics is not physics. Rationally speaking, though, a physical result that corresponds one-for-one to a mathematical model forms a closed logical judgment on the truth of a falsifiable physical theory. Because it is not possible to make a closed logical judgment on physical probability for more than two possible outcomes of one event—no mathematical model can be one-for-one correspondent to the physics of probability, in a rationally complete scientific theory. We show that parity between all mathematical models and all physical results is possible if, and only if, probability exists independent of random events. Therefore, Max Tegmark’s Mathematical Universe Hypothesis is probably true.
Author BioA student of complex systems, Tom Ray is a retired technical writer-editor whose newest contribution to the field of complex systems science, on net-centric logistics, was published by Springer in January 2015, in the book collection Conflict and Complexity. http://www.springer.com/physics/complexity/book/978-1-4939-1
704-4
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Edwin Eugene Klingman wrote on Mar. 6, 2015 @ 01:31 GMT
Hi Tom,
Your essay contains fascinating information. Although many statements exist to the effect that
experiments prove non-locality, the fact is that the experiments prove [or come very close to proving] that
the experimentally found correlations agree with the correlations predicted by quantum mechanics. It is not physical experiment, but
mathematics, that proves...
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Hi Tom,
Your essay contains fascinating information. Although many statements exist to the effect that
experiments prove non-locality, the fact is that the experiments prove [or come very close to proving] that
the experimentally found correlations agree with the correlations predicted by quantum mechanics. It is not physical experiment, but
mathematics, that proves that Bell's models, as formulated, are incompatible with local realism. If Bell's model is correct, this seems to have physical implications for local causality, a.k.a. local realism.
Bell assumes as the basis of his model that the precession occurs in a constant field, which leads to a null result for Stern-Gerlach apparatus, and therefore an
implicit contradiction, since 0 is not equal to +/-1; [zero being the result of the assumed constant field and +/-1 the result of the actual SG non-constant field employed in the experiment.]
In an attempt to avoid this inherent contradiction of Bell's constant-field model, I have analyzed the physics of the inhomogeneous field and constructed a local model that
does produce the quantum correlation,
-a.b,
unless it is subjected to Bell's constraints.
This leads to the question,
why does Bell impose these constraints, and I have attempted to answer this; Bell not being available to answer for himself. You are welcome to read
my essay to see what I'm talking about.
It is for these reasons that I find your following statements fascinating [and find I must buy Solow's book, which I believe you have recommended before.]
You say:
"…
Bell's Inequality – the formal mathematical statement of Bell's theorem – is only locally real. The issue of non-locality arises in the proof of the theorem and that proof is only by way of double negation."
"
What double negation means is that the proposition A is proved by assuming it's negation (~A), and then proving A by contradiction without ever explicitly constructing A…"
As you remark "
It's a perfectly legitimate proof technique; mathematicians use it all the time. However, in order to apply such a mathematical proof to physics, it would have to be explicitly shown that the physics is independent of the mathematics, which is impossible in the case of Bell's inequality … the result being derived by inductive inference."
Although you state quantum theorists know this, if so, they keep it well hidden. I have never seen it so clearly stated. Thank you for stating it so clearly. As soon as I finish this comment I will go buy Solow's book,
How to Read and Do Proofs. Thanks for that, too.
Finally, congratulations on your contribution to the Springer book.
Good luck in the contest, and best wishes,
Edwin Eugene Klingman
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Author Thomas Howard Ray wrote on Mar. 6, 2015 @ 13:59 GMT
Hi Edwin,
Thanks for the kind comments. In fact, I had read your essay previously, and was impressed -- it's your clearest and most direct, in my opinion, of all your entries over these years. I am finally convinced that we're talking about the same thing.
Key to our agreement in principle is the value of a continuous function. Just as Einstein originally formulated mass-energy...
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Hi Edwin,
Thanks for the kind comments. In fact, I had read your essay previously, and was impressed -- it's your clearest and most direct, in my opinion, of all your entries over these years. I am finally convinced that we're talking about the same thing.
Key to our agreement in principle is the value of a continuous function. Just as Einstein originally formulated mass-energy equivalence in terms of the Lagrangian, I think your energy exchange theorem in terms of the Hamiltonian underscores the scale independence of analytical continuity in a physical system.
Quantum theorists are not bothered by the double negation foundation of conventional quantum theory, because they consider it irrelevant. The Bell model is what topologists call multiply connected -- i.e., local pathwise connections are independent of global structure; the assumption of nonlocality is an unavoidable assumption of a multiply connected space.
That's how we get the inductive inference, “If nonlocality exists in the present, it does not not-exist in the future.” One simply cannot discard nonlocality as an experimental assumption of Bell's theorem, because were the mathematical assumption correspondent to the experiment, the conclusion would have to be that nonlocality is an empty set. In Solow's chapter 11 ("Nots of Nots Lead to Knots") one finds that " ... to use the contrapositive method ... you must be able to write down the statement NOT B so that you can work forward from it. Similarly, you must know exactly what the statement NOT A is so that you can work backward from it." The statement A in Bell's theorem is never constructed; it is only found to be not not-A. Again, this assumption does not bother quantum theorists because counterfactual definiteness is exactly equivalent to, “If nonlocality exists in the present, it does not not-exist in the future.” There's a problem with causality here:
Think of it in terms of the Schrodinger's cat gedanken experiment. So long as the cat is in a state of superposition, neither dead nor alive, there's no problem with the counterfactual. Dead and alive are equally likely. Doing a measurement on the box "collapses" the state into a classical bit.
That creates the illusion of observer determinacy -- the free will to look or not, and find the locally real state. Schrodinger's wave equation, though, is fully deterministic, backward and forward in time. The experimenter's assumption in preparing the experiment is that the cat is in a state called "alive" as opposed to the other binary state called "dead." The contrapositives not-alive and not-dead, however, are never constructed -- the experimenter assumes when placing the cat in the box that it is not not-alive. Try and make the assumption that the cat is not not-dead, and I think there is little doubt about the state one will find the cat in, when the box is opened. The initial condition makes the difference between the states -- yet the experiment assumes that not not-alive = not not-dead. It begs its own conclusions.
I'll get around eventually to commenting in your forum. Good luck and all best,
Tom
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Edwin Eugene Klingman replied on Apr. 20, 2015 @ 22:56 GMT
Tom,
I had meant to get back and discuss more about your fine essay. But time is running out, so at least I can give you an appropriate score.
Best,
Edwin Eugene Klingman
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John R. Cox wrote on Mar. 8, 2015 @ 02:26 GMT
Tom,
Your essay is as usual, a Tour de Force of highly condensed mathematical acumen. I've given it two readings and find much I have to learn more about. In general, however, the theme is clear and is concisely stated where you say,
"- if nothing exists in reality save random events, there is no natural correspondence of mathematics to physics."
I was impressed by your carefully avoiding a philosophic character of argument, and keeping matters very much on message of the nuts and bolts of math needing an independent yet true correspondence to physics being about that which is physical, without any ad hoc contrivance of the math to match the physical empiricism. The point you make about QM conventionally constraining measurement space to the Bloch sphere provides a conceptual 'visual aid' when contemplating that a continuous function must exist in metamorphizing a spherical (curved) space and a cubic (flat) space. The 1500 year old edifice Hagia Sophia comes to mind, and with it the geometric sense of strength in physical spacetime.
I think you have made a good argument that what distinguishes where math is exemplary of physical reality is where there is continuity, and your approach to the Contest Topic by way of probabilities is challenging. I still have my sticky note of your conjecture and think it has a good fit in your presentation. Good Luck, don't let the back-biters bug. jrc
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Author Thomas Howard Ray replied on Mar. 8, 2015 @ 20:35 GMT
Hi John,
It's been a constant source of pleasure and delight to me, that you truly get what I'm saying. And I don't just mean the words -- I mean the essential message of a committed rationalist.
Thank you and all best,
Tom
John R. Cox replied on Mar. 9, 2015 @ 02:01 GMT
Tom,
The pleasure has been mine, I can only understand rationalists and have learned much from you. I was especially pleased to learn from your essay the logic of Euler's equation. It never bothered me that he once said that any first rate mathematician would immediately see it, because I've never imagined myself a mathematician. But it has pestered me that I couldn't see it. Forest for the trees sort of thing, I was hung up on the numerical values. The manner you introduced it in your argument displays the simple logic both geometrically of a 1pi rotation, and algebraically of 'e'; it is the real function of each, not the arithmetic values that are at work! My horizons have been greatly enlarged. Thank-you very much. jrc
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Author Thomas Howard Ray wrote on Mar. 9, 2015 @ 12:01 GMT
Hi John,
I think it was Gauss who said that. You're right, though -- analysis is far more compelling as a physical language than arithmetic. We actually experience geometry, as 3-dimension beings with 4-dimension brain-minds. Einstein in fact made what seems a mystical statement on first blush -- that he experienced relativity kinesthetically. Rotation, though, is a physical sense in more basic terms than a simple discrete point or line.
Best,
Tom
Author Thomas Howard Ray replied on Mar. 11, 2015 @ 19:11 GMT
John,
Haters gonna hate. :-) I know from past experience that a couple of knuckleheads will knock a new entry down without reading it, just to try and suppress competition. Along with some others, I have been critical of the 'peer' voting system; it does no service to science that the peer group is limited only by one's capacity to use a keyboard.
You write, "Could you briefly...
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John,
Haters gonna hate. :-) I know from past experience that a couple of knuckleheads will knock a new entry down without reading it, just to try and suppress competition. Along with some others, I have been critical of the 'peer' voting system; it does no service to science that the peer group is limited only by one's capacity to use a keyboard.
You write, "Could you briefly explain the sqrt2 lower bound on information?"
It's as old as the first proof of Pythagoras's theorem, which actually may be even older than the Pythagoreans. Independent of the respective values for the lengths of legs in a given right triangle, the hypotenuse gives up no rational information about its own length with the exception of square integrable values -- even though sqrt2 is an algebraic number, i.e. the solution to an algebraic equation, it is defined only in terms of the nonzero endpoints of its pair of legs. Take the smallest real integral result of a^2 + b^2 = c^2: 3^2 + 4^2 = 5^2:
It's pretty obvious that 9 + 16 = 25. The values are square integrable. If measurements consisted only of square integrable results, the theorem would be uninteresting. Not only are real 2-dimension measures generalized to every pair of straight lines forming a right triangle, however, all information of the hypotenuse is reduced to an irrational number. If one asks the question: what is the exact length of the hypotenuse? -- there will be no exact answer. It can only be given in terms of the squares of each side of the triangle; the area is bounded, even though the endpoints of sqrt2 are not.
This mathematics only becomes interesting, when raised to a four-dimension Pythagorean theorem (Riemannian geometry). That's beyond the scope of my essay.
"Also I'm a little fuzzy on your construction of M=4P, though I see how it is necessary that four physical states must evolve from the possible outcomes of pairs of coin tosses."
Remember, we are talking about relativity. The coefficient 4 is a constant that includes the observer as a physical state, just as the constant c^2 in Einstein's equation defines rest energy directly proportional to mass. The whole set of coin tosses for all time is encoded in the relation -- as Tegmark says, his MUH will be refuted if there is fundamental randomness in the universe. M = 4P tells us that there is no fundamental randomness. As I show in the essay, only pairwise initial conditions have a definite Truth Value -- so there is only classical, i.e., binary, probability and no fundamental randomness.
Best,
Tom
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Author Thomas Howard Ray replied on Mar. 11, 2015 @ 19:12 GMT
Dang it. My posts keep appearing outside the thread that I thought I placed them in. Sorry.
Tom
Michael James Goodband wrote on Mar. 12, 2015 @ 10:59 GMT
Dear Tom
I liked your quote of John Barrow’s interpretation of Gödel: “if mathematics is a religion, it is the only religion that can prove it is a religion”. As I discussed in my
2012 essay I have found such a proof. The problem is that we have a religion that doesn’t want to admit the truth that it is a religion. The expedient way of dealing with such a proof is to deny it exists. As you discuss in your essay, Bell-like analysis on the border between maths and physics is not straightforward. It is possible to make implicit assumptions that undermine the generality of the result – as you are saying about Bell. In
my essay I adopt a physics realism approach to the same questions on the basis that the true physical dynamics is hidden by simply being too fast for any experiment to measure. This option isn’t covered by Bell, and I find that quantum theory results can be reproduced. Where my essay was cut short by the word count, is on the issues of probability, locality and non-locality you discuss in your essay. I would be interested in your view of my new approach to Bell-like analysis, and what it implies for probability and non-locality.
Regards
Michael Goodband
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Author Thomas Howard Ray replied on Mar. 13, 2015 @ 21:10 GMT
Hi Michael,
I'm ashamed of myself that I've had your book for a couple of years now, and haven't penetrated it -- though I know we have so many ideas in common.
Please let me beg off commenting until I read your essay -- and thanks for dropping by!
Till later, all best,
Tom
Joe Fisher wrote on Mar. 12, 2015 @ 16:29 GMT
Dear Tom,
I am so sorry that you apparently cannot understand written English.
Remedial courses are available at very low cost.
Congenially,
Joe Fisher
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Author Thomas Howard Ray replied on Mar. 12, 2015 @ 20:18 GMT
Thanks, Joe. It's just all those abstractions that confound me. Words, you know.
Joe Fisher replied on Mar. 13, 2015 @ 14:26 GMT
Dear Tom,
I am having an awful time with my credentialed fellow essayist. Several of them have reported my post as being inappropriate and had it removed.Thank you for your gracious humorous response to my comment.
Thankfully,
Joe Fisher
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Author Thomas Howard Ray replied on Mar. 13, 2015 @ 20:48 GMT
Joe, you're not wrong. There's just no possible framework in which you could be proved right, that isn't self-referential.
As Popper said, "All life is problem solving." The problem here is that life can't apparently communicate with sentient life other than by using abstract symbols and signals. How do you know, in fact, that you aren't communicating with an abstract being (me) through the abstract symbols on your keyboard that you are using? How do you know that I am 'real'?
I don't know your level of knowledge or interest in philosophy or philosophical problems; however, if you agree with Wittgenstein's view, there are no philosophical problems at all -- just "language games and forms of life." At the end of the day, that may be a great truth, and it's still a philosophy I reject outright -- for the same reason that I reject your claim that the world includes no abstractions:
Your conclusions, and Wittgenstein's, are based on inductive inference -- "Seeing is believing."
I am a rationalist, though. In order to solve a problem, one must identify it -- even a guess is good -- and find the logical correspondence between the problem and its solution in order to consider it solved. I quote J. Bronowski often: "All science is the search for unity in hidden likenesses."
Rationalism unites the world. Inductive inference divides it.
All best,
Tom
Joe Fisher replied on Mar. 14, 2015 @ 20:01 GMT
Dear Tom,
"All science is the search for unity in hidden likenesses." If the abstract likenesses are hidden, how are you going to prove what they are likenesses of? There are no hidden abstract likenesses in reality.” Therefore, all of science as you know it is erroneous. My contentions that real light is the only stationary substance in the real Universe and there is no physical space show that it is reality that is unified.
Warm Regards,
Joe Fisher
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Author Thomas Howard Ray replied on Mar. 14, 2015 @ 23:46 GMT
Joe, you're all territory and no map. You can never be lost; neither, though, is there anywhere to go. Nor is there any science.
Joe Fisher replied on Mar. 15, 2015 @ 14:27 GMT
Tom,
Reality does not need a map. Because all surfaces travel at the same constant speed, land maps and blueprints can be accurately drawn.
Joe
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Author Thomas Howard Ray replied on Mar. 15, 2015 @ 15:09 GMT
That's where you're wrong, Joe. It doesn't mean anything to say that "surfaces travel at the same constant speed" -- because all motion is relative, as we've known since Mach wrote The Science of Mechanics in the 19th century.
When you walk on a surface -- the ground -- is the surface traveling at the same constant speed as the surface of your feet that meet the ground? You wouldn't be going anywhere, would you? -- imagine that you are on a treadmill turning at the same speed as your stride, in the opposite direction; you would be walking "in place" relative to the surface of the treadmill. Have you been on a moving sidewalk at the airport? -- if the sidewalk is moving at say, 5 mph relative to the floor, and you are walking in the same direction as the mover at 5 mph -- are you not moving at 10 mph relative to the floor? If you dismount the sidewalk and stand still on the floor, are you not at rest relative to the floor?
You want to say the floor is carrying the surface of your feet along at a speed constant with all other surfaces in nature -- in which case, nothing moves, ever. Not you, your feet, or the floor. Which contradicts your claim, "all surfaces travel at the same constant speed."
"Reality," the way you are using it, only amounts to the old saying, "Wherever I go, there I am." Yes, that doesn't need a map, though it also contributes nothing to our knowledge of the territory. It isn't science's idea of reality.
Joe Fisher replied on Mar. 17, 2015 @ 14:53 GMT
Dear Tom,
Each real surface is attached to a real sub-surface. All real surfaces travel at the same constant speed. Each real sub-surface travels at a unique speed that is less than the constant speed of surface. When you stand on a treadmill, your surface and the surface of the treadmill travel at the same constant speed. The area of your feet that touches the treadmill belt form a sub-surface and that covered area travels at a unique speed that always remains less than the constant speed of surface. This is why although all surfaces always travel at the same constant speed, and each sub-surface always travels at a unique speed, each and every thing stays in a unique position.
Incidentally, FQXi.org has labeled my idea “OBNOXIOUS SPAM” and has removed it from several sites where I have posted it.
Thank you for not reporting my post as being inappropriate.
Joe Fisher
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Author Thomas Howard Ray replied on Mar. 18, 2015 @ 03:13 GMT
Joe, the only world I can think of, in which every surface is moving at a constant speed relative to the surface beneath it, is a 2-dimension expanding Euclidean plane of uniformly separated points. Imagine a sheet of paper uniformly growing in size in every direction.
If you were a dot on this sheet, and could see in every direction around you -- on each axis of observation you choose, in...
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Joe, the only world I can think of, in which every surface is moving at a constant speed relative to the surface beneath it, is a 2-dimension expanding Euclidean plane of uniformly separated points. Imagine a sheet of paper uniformly growing in size in every direction.
If you were a dot on this sheet, and could see in every direction around you -- on each axis of observation you choose, in every direction all the other dots would be moving away from you.
Now the kicker:
There is no mass in this world. What you call 'real' doesn't include you, the 3-dimensional observer. So suppose you want to say that the 3 dimension world is an illusion -- that we are all really 2-dimension creatures. Then you would have to explain the apparent existence of the directions up-down and left-right as well as forward-backward.
You should be able to deduce that the existence of six degrees of freedom on three axes instead of four degrees of freedom on two axes implies rotation in a spherical space. As a consequence, the curved motion you could not detect locally, on your 2-dimension plane, is evident in 3 dimensions as two components of relative motion: one component rigidly straight to your origin of measurement, and one around the curved space in your vicinity.
Here is what Galileo found:
In the field of your observation, the local gravity field in which you are at rest (not moving in relation to points of the field) other objects of 3-dimension mass that move toward your position accelerate at the same constant rate regardless of whether they move in a path straight to your plane (i.e.,in straight line free fall), or in a curved trajectory.
So whereas your 2-dimension world can only expand from the center of every point in one direction at uniform speed, the motion in our 3-dimension world is both uniform and accelerated. These two kinds of motion are described in Einstein's theory of special relativity (straight line uniform motion) and general relativity (accelerated motion).
So you're clearly wrong with your idea that all motion is only in 2 dimension (a surface and its sub surface). How about 4 dimensions, though?
When Einstein took the step of adopting 4-dimension Minkowski space for general relativity, the addition of a time component ("4th dimension") explained accelerated motion relative to uniform motion -- i.e., the rate of change in a system of coordinates is referred to your (the observer's) position in time as well as space, and physical reality is that of spacetime, not of either space or time independently.
So let's return to your world of uniformly expanding points on a 2 dimension surface:
That surface IS part of our real world! The most popular (and physically validated) solution to general relativity cosmology (the big bang) informs us that the universe is expanding at every point of spacetime. The origin of creation is literally both in you, and around you.
Abstractions regarding relative motion are actually more real than our naive perceptions of motion. Our physical space is 3 dimensional -- our brain-minds, however, are 4 dimensional.
Best,
Tom
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Joe Fisher replied on Mar. 18, 2015 @ 15:31 GMT
Please open your eyes. Everywhere you look you will see a plethora of real surfaces. Those surfaces must all be travelling at the same speed, otherwise, you could not see them instantaneously and simultaneously. The real sub-surface cannot relate to an abstract conjecture. Each sub-surface must travel at a unique speed in order to keep each thing in its own unique place. A real surface can travel in any direction. A real sub-surface can only expand or contract. Picture a cannonball and an air-filled blue party balloon on your front lawn. If you run towards them they will both grow bigger, yet their surfaces must travel at the same speed. The only way they could grow bigger would be if each one of their sub-surfaces was expanding at a unique rate. We do know from careful experiment that air-filled balloons are constructed differently from cannonballs.
Calmly,
Joe Fisher
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Author Thomas Howard Ray replied on Mar. 18, 2015 @ 17:05 GMT
Joe, open you own eyes, and you will see that your naive view does not differ from that of a religious creationist. Everything is "just so." Enough of this.
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James Lee Hoover wrote on Mar. 12, 2015 @ 21:32 GMT
Tom,
I must confess that I have not yet mastered the erudite arguments you pose, but knowing a small bit about Tegmark's MUH, I wondered about the "independence of humans" aspect of the ERH. Current physics theories are the math equations and structures describing the theory and their concepts, thus explaining the connections to our observations. The equations are built by humans and are their baggage. I don't see the separation.
My "Connection of Math, Physics and Mind," I know, seem mundane, but I don't see the physical world as completely independent of humans.
What am I missing? Many scientists say that humans adhere to the ERH concept.
Jim
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Author Thomas Howard Ray replied on Mar. 13, 2015 @ 21:03 GMT
Well, Jim, all I can say is that if you agree with Max's ERH table (slide 14 in this PowerPoint: www.fqxi.org/iceland/images/Iceland%20Talks/tegmark.ppt) you'll find my view at the extreme of "less baggage."
I am a rationalist. An external reality and metaphysical realism are fundamental assumptions.
Thanks for the note. I'll get to your essay when I can.
Best,
Tom
James Lee Hoover replied on Mar. 26, 2015 @ 00:55 GMT
Tom,
Thank for taking the time to read my essay. I am not a mathematician but more another reading brought me closer to your well-thought-out vision and argument.
Jim
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Author Thomas Howard Ray replied on Mar. 26, 2015 @ 01:50 GMT
That's very kind of you, Jim. Thanks!
Best,
Tom
John R. Cox wrote on Mar. 15, 2015 @ 20:52 GMT
Tom,
I'll start a new thread to get back on topic. I detect a hidden variable in your essay approach, namely the original EPR wave equation which seems to be ignored in speculative arguments about the double slit experiment. EPR's argument was that it could be possible to discover a state of position or momentum of a particle following the correlating event of impact with another without...
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Tom,
I'll start a new thread to get back on topic. I detect a hidden variable in your essay approach, namely the original EPR wave equation which seems to be ignored in speculative arguments about the double slit experiment. EPR's argument was that it could be possible to discover a state of position or momentum of a particle following the correlating event of impact with another without disturbing the first mentioned particle ( let's use working class terms of solids and stripes referring to pool balls when betting prefers the faster game of 8-Ball, to Rotation ). Let's call the particle we'll subject to measurement 'solid' and the unmeasured object particle 'stripe'.
The EPR argument was that to deduce the position or momentum of the 'stripe' after impact with the 'solid', did not require measuring 'stripes' properties, but could be found from knowing one parameter such as position of 'solid' by it's passage through one of the double slits and by measuring the momentia change of the screen itself imparted by both particles. Consequently a measurement was not necessary of 'stripe' which would change its state. That was the argument, position and momentum can be determined from other properties without effecting or losing the intrinsic pair (q,p). And in your essay the prime criteria is that a closed logical argument can only be had if the probability has a binary outcome, q or p in the EPR scheme of things.
We can go on with other examples where your essay generalizes to math. Let's look at Schrodinger's Cat (anybody that would suggest doing that to a cat has some issues, anyway). Firstly, its only true of spherical cats and felines are predatiously linear, so is light. Illumination can be treated spherically, but to subject the detection of a 'photon' to a random probability on a spherical surface projection which relativistically increases eightfold with doubling of the time parameter, only means that the initial direction of emission is not known, or sought within the source.
In answer to the question posed by EPR, if QM is a complete theoretical description of reality, we really needn't resort to arguments on QM's terms. Max Planck, himself, fully expected that his self-avowed 'lucky guess' would eventually be rationalized. In the immediacy of events of that era, following two centuries of progressive Newtonian predeterminism intellectuals were starving for a ration of free will, and the new maths were simply more inviting than constructing a classical model of light that would reveal cause of the Quantum. The catch-22 of fundamental randominity is that it too results in not having means to determine choice. We have come full circle sociologically. Humanity does have free will to choose between two probable causal results, and none if the outcome is random anyway.
It is really time to let Schrodinger's cat out of the bag, and answer Planck's question. :-> jrc
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John R. Cox replied on Mar. 16, 2015 @ 12:37 GMT
Tom,
I crammed the EPR argument a bit. Their wave equation finds foundation in the momentum imparted to the screen by both particles and the known measured separation of the two slits. Their point being that direct observation would naturally disturb the q,p state of a particle, but simply knowing other parameters does not constitute an action. jrc
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Author Thomas Howard Ray replied on Mar. 17, 2015 @ 12:48 GMT
Very nice, John! I delayed replying until I could read a few times without distraction.
We are fortunate to have you in the forum.
I'll just add one comment -- you say, mirroring the EPR view, that " ... if QM is a complete theoretical description of reality, we really needn't resort to arguments on QM's terms."
In fact, though, the argument from binary probability does meet QM terms -- it just limits the probability distribution and eliminates prior probability. I am gratified that you agree that the prior probability of randomness obviates free will.
Best,
Tom
John R. Cox replied on Mar. 17, 2015 @ 16:30 GMT
Tom,
I also agree that arguments must also address QM probabilities. As the saying goes, 'to beat a mathematician you have to hit'em in the math'. I don't want to be a distraction, and hope you get some competent feedback. Probabilities become anavoidable in complex systems, and systems don't need to be very extended to become complex. Not my bag of tricks though, and I tend to look at probability as a pry-bar to open inquiry as to what it evolves from. Good Luck, jrc
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James A Putnam wrote on Mar. 20, 2015 @ 17:10 GMT
Tom,
Looking in from outside of your universe, you continue to present your case brilliantly.
James
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Author Thomas Howard Ray replied on Mar. 20, 2015 @ 18:02 GMT
James, that is very kind of you.
In this context, I interpret Bar-Yam's theory of multi-scale variety thus: Though we may all see the world through our own unique eyes, it doesn't make the world any different for any of us. It only means that the marvelous variety of viewpoints available is many times bigger than any one of us. Isn't it the greatest pleasure to participate in, and increase, that variety?
Thanks, and all best to you in the essay competition!
Tom
Mohammed M. Khalil wrote on Mar. 20, 2015 @ 19:30 GMT
Hi Thomas,
Great essay! You provide compelling arguments for the mathematical universe hypothesis. However,
my essay takes an opposing view; I would be glad to take your opinion.
Best regards,
Mohammed
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Author Thomas Howard Ray replied on Mar. 21, 2015 @ 14:04 GMT
Sure, Mohammed. As soon as I can make time. Thanks for commenting.
Best,
Tom
Steven P Sax wrote on Mar. 20, 2015 @ 22:41 GMT
Tom, it's a very fascinating essay and a great contribution. Your philosophical approach on non-locality and Bell's theorem which you backed up by a thorough technical analysis, is quite inspiring. Also very enlightening is the last section on the Correspondence Principle and Popper Falsifiability. Thanks again, Steve
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Steven P Sax replied on Mar. 20, 2015 @ 22:50 GMT
Also (as I mentioned in my reply to your post)- congratulations on being published by Springer :)
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Author Thomas Howard Ray replied on Mar. 21, 2015 @ 13:43 GMT
Thanks, Steve -- as I posted in your forum, we are in accord on many things, and the foundations of computability is, I think, the most important issue in frontier science.
Beyond the scope of the essay question, the growing fields of brain science and artificial intelligence depend strongly on resolving the issues of network robustness and integrity -- i.e., the amount of information...
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Thanks, Steve -- as I posted in your forum, we are in accord on many things, and the foundations of computability is, I think, the most important issue in frontier science.
Beyond the scope of the essay question, the growing fields of brain science and artificial intelligence depend strongly on resolving the issues of network robustness and integrity -- i.e., the amount of information that can be effectively used at each decision point such that positive feedback doesn't overpower the computing function.
It's a key point -- the number (1) in your concluding remarks, that twice applying the self-referential operation generates a true statement. It's the identical point I was making with the Popper example of pairwise correlations followed by a single result that may or may not be correlated with the pairwise value. Length restrictions kept me from exploring the basis of Popper's program -- which is Richard von Mises's theory of the independence of collectives -- Popper notes (p. 196) in *Realism and the Aim of Science*:
"von Mises's 'axiom' (which postulates the existence of a limit of the relative frequency of the occurrence of a property P in any probabilistic sequence of events or 'collective') may be written as a universal-existential-universal-existential-universal statement, of the following form: '*For every* probabilistic sequence, *there exists* a real number x between 0 and 1, called the limit of the relative frequency, such that *for every* given fraction y, however small, for which y > 0 holds, *there exists* a natural number n, such that *for every* natural number n (for which n > m holds) the relative frequency of m/n, of m occurrences of the property P up to the nth event of the sequence does not deviate from x by more than y, that is to say, - y =/< x - (m/n) =/< + y."
In network terms, adding a time parameter, this implies that information lost to one decision node is not lost to the network hub at which it originated, such that continuously shifting hubs of decision activity are self-organized in the same context that you take to be self-referential.
As I think it is pertinent to the content of both of our essays, if you don't mind, I am going to repost this in toto in your forum.
Thanks again and all best,
Tom
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Christian Corda wrote on Mar. 23, 2015 @ 13:59 GMT
Hi Tom,
As I told you in my FQXi page, I have read your intriguing Essay. Here are my comments:
1) Although I am a collector of aphorisms (particularly of Einstein's ones) I did not know the aphorism of Bronowski that "All science is the search for unity in hidden likenesses". It is very nice.
2) I think that black hole physics and its importance in the route to quantize gravity is an example of your beautiful statement that "Mathematics research will uncover further physical regularities in nature". I also find intriguing your extending to symmetry between mathematics and physics the Tegmark's MUH.
3) I find profound your question "What determines the objective result of a measurement - hidden variables or hidden assumptions?".
4) Can you give details on your statement that "Hawking radiation is a theoretical example of a locally real quantum phenomenon with simultaneous past and future equality"? This could indeed have implications for the black hole information puzzle.
5) I find very nice your Einstenian equation M=Pb^2=4P
6) I think your pretty final sentence that "In this game of unlimited possibilities called mathematics, our bet is on human imagination" should have been appreciated by Einstein.
In any case, the reading of your very nice Essay enjoyed me a lot. It deserves the highest score that I am going to give you.
I wish you best luck in the Contest.
Cheers, Ch.
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Author Thomas Howard Ray replied on Mar. 23, 2015 @ 16:21 GMT
Thanks, Christian!
The Bronowski quote is from his collection of post-war essays in the 1950s, called, *Science and Human Values.* It is a very inspiring little volume that I return to often to renew my optimism for the future of the human race and the role of science in it.
My view on Hawking radiation is based on the
Hawking-Hartle no-boundary/imaginary time proposal: "This absence of boundaries means that the laws of physics would determine the state of the universe uniquely, in imaginary time. But if one knows the state of the universe in imaginary time, one can calculate the state of the universe in real time. One would still expect some sort of Big Bang singularity in real time. So real time would still have a beginning. But one wouldn't have to appeal to something outside the universe, to determine how the universe began. Instead, the way the universe started out at the Big Bang would be determined by the state of the universe in imaginary time."
The state of the universe in imaginary time is local -- every point of the Minkowski space-time in an expanding universe, is the origin of creation. (I'll send you something privately that explains it in more technical terms.)
Thanks again, and all best -- looking forward to more dialogue,
Tom
Christian Corda replied on Mar. 24, 2015 @ 11:13 GMT
Thanks for clarifying Tom.
Cheers, Ch.
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Member Rick Searle wrote on Mar. 26, 2015 @ 02:40 GMT
Tom,
You've got to be one of the most eloquent mathematical writers I have ever read. Phenomenal clarity and rigor.
I've given you my highest mark in this contest so far.
Best of luck!
Rick
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Author Thomas Howard Ray replied on Mar. 26, 2015 @ 11:36 GMT
That's very kind of you, Rick. Thanks!
Best,
Tom
John R. Cox replied on Mar. 27, 2015 @ 17:10 GMT
Tom,
Its great to see your essay getting attention of serious and informed people, and free of those whom like to dance on the bar and start fights. That's probably because your approach of possible vs. probable is presented with math results that many people don't know enough about what they come from. I sure can't contribute much! I do have more a curio than a question that might be pertenent...
Steven Sax provided an e-address for a thesis on laser experiments with Rubidium that I've waded into and think you would find interesting, and from which he launches his discourse on decidability. Here 'tis; http://www.bgu.ac.il/atomchip/Theses/Amir_Waxman_MSc_2007.pd
f
Its QM, of course, and uses the Bloch Sphere as the spin co-ordinate system. I realized that in their protocols what they specify as 'free precession' is in fact 'freely gimballed', in that the axis of precession intersects the origin at intersection of the orthogonals. To be 'free precession', the antipodal points of the axis of precession must be free to wander like the magnetic poles of the earth, the p-axis does not necessarily intersect the orthogonal. Intuitively this must fundamentally alter the landscape of co-ordinate pairs. And what seems to be already decided in QM is symmetric precession. Would that not impose an undecidable condition?
I don't get into coin tossing, I pinch pennies like to bring a tear to Lincoln's eye. So maybe this niave observation is a standard issue. Your comment would be instructive, at your leisure, I'm just now off on errands.
All the best, as always. jrc
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Author Thomas Howard Ray replied on Mar. 27, 2015 @ 18:12 GMT
Hey, John -- I have always thought of *you* as a serious and informed person! :-)
Give me your email address, and I'll send you something privately that addresses your question.
Thanks for the link to Steve's research -- it's on my list.
All best,
Tom
John R. Cox replied on Mar. 27, 2015 @ 22:12 GMT
Thanks much Tom,
I just posted my e-address to your 1209, sent this date 5:59pm.
I'm getting myself a little swamped, but appreciate any help in learning 'the language'. And things just matured that are time sensitive that I have to concentrate on to finalize and make sure my ducks are in a row. I'm in for a long weekend but will acknowledge receipt of your post. If your check for receipt of my post to: 'contact' on your blog and don't find me, let me know here.
Thanks again, I rely on the acumen of you and others whom come to converse rather than convert. Like the song goes, 'I can make my own mistakes just fine.' :-> jrc
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John R. Cox replied on Mar. 27, 2015 @ 23:49 GMT
Tom,
Got it! Six short pages! I gave it a quick read and its really well written. There will be questions, and once I have a list I'll try posting through my e-mail. Thanks very much and good luck with it! Later, Friend - jrc
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Author Thomas Howard Ray wrote on Mar. 27, 2015 @ 20:00 GMT
One of the advantages of being as old as I am, is that distant memories come into sharp focus with the right trigger.
The trigger to my recollection of
Jim Cowan's wonderful short story was David Hestenes's discussion of modeling in his essay forum.
The Cowan story ("The Spade of Reason") and Jose Luis Borges's "Library of Babel" are two pieces of fiction that have had a deep impact on my intellectual life. Remarkably enough, Borges's story is referenced in Cowan's story.
All best,
Tom
Member Marc Séguin replied on Mar. 28, 2015 @ 21:14 GMT
Dear Thomas,
I just read Jim Cowan's short story "The Spade of Reason" at your suggestion. Indeed, it is great: philosophical science-fiction just the way I like it! I especially like it when the main character says that "one kind of madness is not knowing that the model is all we will ever know."
Marc
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Author Thomas Howard Ray replied on Mar. 29, 2015 @ 00:58 GMT
Marc, that's my favorite line, too. :-) Thanks.
Tom
Michel Planat wrote on Mar. 28, 2015 @ 17:17 GMT
Dear Thomas,
Thank for the comments on my blog and the high rate. I had your essay in my list and you write about CHSH!
You can expect my feedback soon.
All the best,
Michel
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Author Thomas Howard Ray replied on Mar. 29, 2015 @ 02:31 GMT
Thanks, Michel! I look forward to productive dialogue and wish all the best to you and your essay in the competition.
Tom
Michel Planat replied on Mar. 29, 2015 @ 17:27 GMT
Dear Tom,
Your essay is multivalued in the sense that
* you clarify the relationship between physics P and mathematics M, postulating a linear (Tegmarkian) equation E = k*P,
* you put this in perspective with Bell's (or CHSH) inequality and a establish a link to number theory (the unsoved Goldbach conjecture as revisited by Popper),
* you question the role of probabilty in the MP correspondance (as commented by John Cox in his post),
* you relate to Euler's identity (James Hoover has an essay on this topic as you know)...
All this aspects are justified in technical terms sometimes in an unexpected way. You received many valuable comments, a proof of respect. I add my congratulations and my good community mark.
Best wishes.
Michel
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Author Thomas Howard Ray replied on Mar. 29, 2015 @ 19:48 GMT
Michel, I am deeply honored. Thank you so much for your careful reading, feedback, and vote of confidence.
All best wishes for success in the essay contest,
Tom
Member Marc Séguin wrote on Mar. 28, 2015 @ 21:30 GMT
Dear Thomas,
Thank you for your comments about my essay. I have left a reply on my page.
Yours is an intriguing and very ambitious essay!!! You tackle deep fundamental issues such as probability and free will, and I have to confess that I'm having some difficulty in following all the details, since I am not familiar enough with many theoretical results that you build upon.
I have questions about the "quadratic" relationship that you postulate between math M and physics P: M = P q^2, which becomes M = 4P because q = 2.
1. Why does the constant have to be the square of something? I see the parallel with E = m c^2, but I don't see why it has to hold.
2. Is your equation M = 4P dimensionless? In E = m c^2, E is in joules, m is in kilograms and c^2 is in joules per kilogram (or in meters squared by seconds squared). What are the "units" (if any) of physics P and math M?
So far, your essay is looking good in the ratings... Good luck!
Marc
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Author Thomas Howard Ray replied on Mar. 29, 2015 @ 02:30 GMT
Thanks, Marc. Indeed, I fretted all the time I was writing it, over whether this work might be *too* ambitious. Details can run away from one, if the scope gets too big. In the end, I could not escape the conclusion that if free will exists, it cannot be a property of random observer choice. This being so:
Only a binary decision that is square integrable can share a reciprocal relation *continuously* with a continuous range of variables in a finite interval of time (Buridan's principle is limiting). The linear relation M = 4P is not physically meaningful in the first degree, because it is not dynamic; M - 4P = 0. The second degree equivalent, M = Pq^2, q = 2, accounts for the full range of possible binary decisions in any finite interval where M = P. Tracing the relation back to the cosmological initial condition, the rest state of the universe is a "fourity" of possibilities in any locally bounded interval.
The units of M and P are dimensionless to the extent that M = P is unitary. In the reciprocal relationship M = Pq^2, the fundamental dimensionality M = 4P (P = M/4) gives us the division algebras we know to exist (R, C, O, H) as a complete algebraically closed range of computational fields relating binary choice to a continuous range of variables limited by a finite time interval.
Physical units are derived from empirical observations in a bounded measure space. Since four pure physical states imply the Hawking-Penrose singularity theorem, and insofar as four are the minimum necessary and sufficient for dynamic interaction between physics and mathematics (i.e., between measure and model), maybe we can move a little closer to Hawking's question of what "puts the fire in the equations" with number-theoretic arguments alone. Just thinking out loud here.
All best to you and your essay, too!
Tom
Robert MacDuff wrote on Mar. 28, 2015 @ 22:18 GMT
Tom,
An excellent essay. Although I am not certain I fully understand your solution, but the issue of whether or not reality is objective or observer dependent is critical to understanding how math integrates with science. Might it be the case that the reality is objective but measurement is observer dependent and is that consistent with your thinking?
thanks
Rob
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Author Thomas Howard Ray replied on Mar. 29, 2015 @ 01:28 GMT
Rob, that's exactly right. The question -- "What determines the objective result of a measurement, hidden variables or hidden assumptions"? -- refers to metaphysical realism (measurement outcome) vs anti-realist assumptions.
The assumption of non-locality is obviated by the time parameter (Hess-Philipp) in that every point of a 4 dimension Minkowski space is an operator.
Because the time parameter is not real, independent of spacetime (special relativity), pairwise measurement outcomes are simultaneous with past-future local spacetime states that obviously include the observer as an element. The assumption of nonlocality is therefore superfluous, with the implication that the assumption of a nonlocal measurement value is superfluous. The observer -- whether human or point particle -- is one more degree of freedom than allowed by 3 dimension measure.
In a continuous function classical measure, the macroscopic description of position in time as well as space is bounded only by the cosmological state. A microscopic state is therefore dependent on the cosmological state, and not discontinuous with the operator that exists at every point of local 4 dimension spacetime.
All best,
Tom
John R. Cox replied on Mar. 29, 2015 @ 03:33 GMT
Tom,
I was just looking in and your responses to both Robert and Marc are helpful to understanding your maths and your thinking. You do speak to mathematicians, and that assumes an 'ideal reader'. I've been hoping good questions would draw you into something of tutorial discussion.
Robert puts it succinctly that reality is objective and measurement is observer dependent. Math, like the color purple, is a figment of human imagination. The reality is that randominity is limited by necessity. 'There is no such thing as cold, cold is the absence of heat' - (Louie Ritchey). When we reach absolute Zero Kelvin, they can have pure randominity. I won't care. ;-> jrc
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John R. Cox replied on Mar. 29, 2015 @ 16:28 GMT
Tom,
Let me elaborate on my last comment before returning to some personal matters.
I think your identification of escape velocity with any point in space is a profound insight. It is both physical and at the same time mathematically versatile. It is where the path of least resistance is provided to the random walk. The escape velocity at any given point in space will naturally vary...
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Tom,
Let me elaborate on my last comment before returning to some personal matters.
I think your identification of escape velocity with any point in space is a profound insight. It is both physical and at the same time mathematically versatile. It is where the path of least resistance is provided to the random walk. The escape velocity at any given point in space will naturally vary with the dynamics of change in position of masses that come within relativistic proximity to that point. Conversely, the escape velocity initially observed will migrate to another (and potentially others) as the dynamic evolves.
If I am meandering in a crowd of people, my easiest path will be toward an adjacent space that momentarily opens up, which will effectively reduce that openness. Continually. I will eventually find my way to the periphery.
This generality was touched on in dialogue I've been having with Constatinos Ragazas and in communication with Ed Klingman in regard to Planck's solution to the violet catastrophe. The exponential increase in the possible numbers of waves per second as frequency increases across the continuous spectrum, would result in an equal chance of thermal energy in Wien's furnace, to choose an ever higher frequency over a lower one. That doesn't happen, obviously. The curve of intensity of spectroscopic frequency analysis was only matched
when Planck introduced a finite constant energy value into his equation of probability distribution. Effectively showing that a specific quantity of energy in any given wave event results in the energy in the furnace seeking equilibrium with the ambient environment, must avail itself of lower frequencies as well as randomly chosen higher ones. The Quantum is causal of that distribution by the physical necessity that the furnace must shed thermal energy in every path available to maintain a stable temperature. Wien's furnace was a furnace, it was continuously heated. It would melt if the energy didn't take the path of least resistance in its random walk.
Well, I've indulged in putting things off this morning long enough. Do continue to expound the elements in your math arguments. The pedagogical role is part of scientific writing, and it should not offend anyone if you present things as if rudimentary operations need explained. The explosion of mathematics in the last couple centuries actually require it. Maybe we should call it Accumulated Math Disorder. Best, jrc
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Author Thomas Howard Ray replied on Mar. 29, 2015 @ 16:48 GMT
Thanks, John. So as not to confuse the reader, though -- your comments refer to something I sent you privately, and not the contents of the essay per se. I'm not quite ready for wide distribution of that Email piece.
All best,
Tom
John R. Cox replied on Mar. 29, 2015 @ 18:57 GMT
Author Thomas Howard Ray replied on Mar. 29, 2015 @ 19:04 GMT
No problem, John. I've given it some limited exposure, just not prepared to take questions yet. :-)
Best,
Tom
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Author Thomas Howard Ray wrote on Mar. 31, 2015 @ 20:02 GMT
I find myself in the position of defending the views of both Alan Kadin and Michel Planat, who crossed swords in Alan's blog.
No surprise -- there is probably no sharper demarcation of philosophies in physics, than between Einstein-Bohm represented by Kadin, and Bohr-Peres represented by Planat.
I'm not neutral -- I agree with Karl Hess (*Einstein was Right* 2015) and the late...
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I find myself in the position of defending the views of both Alan Kadin and Michel Planat, who crossed swords in Alan's blog.
No surprise -- there is probably no sharper demarcation of philosophies in physics, than between Einstein-Bohm represented by Kadin, and Bohr-Peres represented by Planat.
I'm not neutral -- I agree with Karl Hess (*Einstein was Right* 2015) and the late Walter Philipp that introduction of a time parameter generates the Bell "impossible" result E (a,b) = - a . b
That's only half the story, though. The other half is that the assumption of fundamental particle reality obviates that dot-product result a priori, while the assumption of a fundamental field theory requires no a priori assumption of fundamental particle existence (Kadin's claim).
Though I don't mean to be self-promoting -- my own view, that the Hilbert space (and the linear superposition of particles to which Alan refers) is deficient, is based on my
prior research that metric continuity in the Hilbert space depends on deriving a real valued well ordered sequence without invoking the axiom of choice.
This would be true, regardless of whether one assumes particle discreteness or wave continuity. It comes down to the perennial question of what is being measured. Alan is very clear that his program obviates a domain boundary between classical and quantum. Bell-Aspect and CHSH programs, on the other hand, actually create a domain boundary, by observer dependence, and therefore cannot survive without an assumption of particle nonlocality.
So how would one show what is being measured, unless 'what' is discrete? And Is it a sharp point particle, or a wave packet? A quantum of something only implies measurability; it does not imply a definition of something. A field of something presents the same problem.
I think we are left with the same question that Einstein identified so many years ago -- that if we don't improve the mathematical methods, we can't expect resolution of the gap between quantum and classical mechanics.
I think that Planat and Kadin are equally sincere, honest and competent in their mutual quest to improve the mathematical methods. That's how science progresses.
Tom
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John R. Cox replied on Apr. 1, 2015 @ 06:11 GMT
Tom,
'So how should one show what is being measured..." You do say a lot in short posts.
Many times we all have imperfect knowledge of the fullness of measures that have become used in particular ways that tend to relegate one parameter or another to obscurity. So what the quantum is as a measure, is generally treated as if it is only a specific quantity of energy because it doesn't tell us whether it is a particle or a wave. Added to that, the time normalization in QM denudes the quantum of its 'per second' realism.
But the original Quantum finds more measure than given credit for. Boltzman's Constant obtains from the Gas Constant/Avagadros Number, and so Boltzman is a physical proportion that gives the energy/temperature associated with a single source particle. By relation with Planck's Constant as a physical proportion of energy/time, there is a complex measure of a single physical wave at any specified frequency which carries the celebrated energy quantity per every 1/f from a single source. That's a lot of information to start with.
To an experimentalist, CHSH isn't half the story. What is the wave doing and how, such that some ranges of frequencies penetrate deep into the dirt and others bounce off airplanes? Each single wavelength carries the same energy. How's it do that?! - Duhhoohhhh - :) jrc
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Author Thomas Howard Ray replied on Apr. 2, 2015 @ 13:51 GMT
Hi John,
Perceptive and interesting, as always. :-)
I expect you will relish reading this
Andrei Khrennikov paper on sampling contextually with different statistical properties.
My own answer to the question of time-dependent quantum measurement in a number theoretic context is in the attached.
All best,
Tom
attachments:
Something_I_discovered_from_my_research_into_the_properties_of_Sophie_Germain_primes.pdf
John R. Cox replied on Apr. 2, 2015 @ 15:32 GMT
Tom,
Thanks for the links, anybody looking in can access them also, and that is one of the real values of this forum. When participants assume the role of sounding board in the bouncing of ideas off one and another 'The Beat Goes On'. If it starts sounding like a Ping-Pong match, its time to quit the game.
The Khrennikov link is a free sign in to what looks to be an extensive archive, I'll content myself with the download of your att'mt but others might find it fruitful. You are obviously enjoying your retirement giving you the time to pursue what you have long wanted, and that's refreshing, and perhaps more satisfying than those whom have had careers requiring intense research and find themselves now in real proximity to 'publish or perish'. Enjoy! jrc
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Author Thomas Howard Ray replied on Apr. 2, 2015 @ 16:56 GMT
Thanks for pointing that out, John. I learned that the site accepts my publications, so I signed on as a member myself.
I've been a professional writer since teenage, so it's always been "publish or perish" for me in terms of making a living. The career I'm retired from (government service) is my third career, that I undertook after going bankrupt in 1999, and finding myself in need of some security for my family and me.
It's still publish or perish -- the level of security we need isn't there -- and that's fine with me also, and I do enjoy it, because it's all I've ever known. The academic form of publish or perish isn't something I would have been happy with, I think, seeing all of the publications from academics who have so very little of significance to say. It's a bit of a crime for a talented researcher to have to survive on a publication list of questionable content -- when given the freedom of serious research, she or he might have produced just one work of importance.
All best,
Tom
Anonymous replied on Apr. 4, 2015 @ 21:39 GMT
My attachment of 2 April -- which demonstrates reversibility of the counting function by the natural properties of recursion and parity -- got me thinking about the Monty Hall problem and why reversibility of the time metric is equivalent to experimenter free will in a Bell-Aspect type experiment. Switching choices implies physical time reversibility, and here's why:
Mathematicians will...
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My attachment of 2 April -- which demonstrates reversibility of the counting function by the natural properties of recursion and parity -- got me thinking about
the Monty Hall problem and why reversibility of the time metric is equivalent to experimenter free will in a Bell-Aspect type experiment. Switching choices implies physical time reversibility, and here's why:
Mathematicians will always agree -- that given n contestants choosing 1 of 3 doors, two of which hide a goat, and the third a new car -- one can predict that over many iterations, or even if many contestants simultaneously choose from sets of doors, that by the law of large numbers 1/3 of the contestants will win cars. This how Richard Gill describes the independent "counts" of four 2 X 2 tables of results in a Bell-Aspect type experiment, with 4 instead of 3 "doors.".
The singular case in which the host (Monty) opens one door of the two that a contestant has not chosen -- and reveals a goat, then asks the contestant if she would like to switch choices -- raises the question of whether the contestant has a winning advantage by switching the choice, or staying with the first.
Naively, one thinks that -- because Monty has shown one of two doors that the car is *not* behind, that the odds of choosing the winning door have been increased some 16% (from 1/3 to 1/2) by choosing to switch. In fact, though, the odds are still 1 in 3 whether the contestant switches the choice or not. The question is whether one has a better choice of winning the car by switching choice, or not.
Even though the contestant knows in advance that Monty will never open the door with a car behind it, this information adds nothing to her knowledge of what door the car is behind. In other words, a potential choice (the door identified but not yet opened), does not change the energy state of the system. It does, however, add to the information of the energy state -- one now has a 66.6% chance of winning the car if one switches choices of door -- and this is equivalent to the Hess-Philipp result (+ 3) for their Bell-Aspect type inequality that I cited in the attachment; i.e., there is a 3 to 1 advantage (my paper explains) for the result not observed, over the P(1/2) probability for the result that is observed. That difference of initial condition vs. measurement outcome is a hidden variable.
To see why, compare this scenario to the Schrodinger Cat experiment. The decay rate of the substance that emits a particle and triggers the hammer that breaks the vial that releases the poison that kills the cat -- is precisely known. The energy potential of the hammer is identical to the pre-choice of door in the MH problem -- If Monty lifts the lid on the box and declares "the cat is alive," or "the cat is dead," it has no effect on the decay rate of the material or the energy potential of the hammer.
Monty, however, *cannot choose* to say "the cat is dead," because we *know* that the conditions under which the cat dies are fully determined, even though hidden in a black box. There is absolutely no point in Monty communicating to us that the cat is dead, because:
If the cat were dead, the experiment is ended -- just as if Monty opened the door with the car behind it while the contestant still has a choice pending. It doesn't happen, because Monty knows which door the car is behind. He isn't an observer making a binary choice; he's the guiding principle *behind* the measurement choice. This is the same principle by which Joy Christian successfully argues for the choice that Nature makes independently of conscious observers, and which guarantees real binary measurement in a locally real and objective way.
Ultimately, the free will hypothesis prevails, because -- and I made this point repeatedly in the great "debate" over Christian's result -- *unless* Nature has a choice, human observers have no free will. The energy cost to remove the middle value is equal to the observer's choice to change the state of the system.
So in support of Tegmark's hypothesis and Christian's measurement framework (which was published by the International Journal of Theoretical Physics recently as "Macroscopic Observability of Sign Changes under 2(pi) Rotations"-- nature is not fundamentally random, even though conscious observers switch their choices.
As my attachment shows, observer choices that change the measurement outcome deterministically, also change the initial condition randomly -- consonant with my claim that free will exists IFF nature is not fundamentally random. The question of whether the initial condition is positive or negative obviates the independence of tables that Richard Gill describes. The measurement is observer entangled -- and that entanglement is equivalent to classical orientation entanglement (spinor property).
More to come.
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Author Thomas Howard Ray replied on Apr. 4, 2015 @ 21:40 GMT
Sorry, lost my log in. Last was mine.
Tom
Author Thomas Howard Ray replied on Apr. 5, 2015 @ 17:55 GMT
Here's the rest of the story, that I added to my attachment of 2 April.
attachments:
My_attachment_of_2_April_contd.pdf
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Vladimir F. Tamari wrote on Apr. 8, 2015 @ 13:59 GMT
Hello Tom
I read your essay twice and am still not very clear about what you are saying. The fault is entirely mine - for example a lack of background in the type of mathematical/logical arguments you used. Another reason is that at my age (73) I was reading not to explore new ideas, but to confirm my own half-cooked ones in a view to develop them further! For example, based on my
Beautiful Universe Theory concepts I think there is no inherent probability in Nature, nor is there particle-wave duality, no wave function collapse (which you agree with) and that Bell's Theorem only confuses the issue. At least about the latter I can point to Edwin Klingman's essay here for a more substantive analysis than my one-liners. In my essay here I argue that in a causal local absolute discrete Universe mathematics and physics reduce to the same thing - not themselves, but the micro structure of Nature itself. As always I value your feedback.
With best wishes
Vladimir
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Author Thomas Howard Ray replied on Apr. 8, 2015 @ 16:14 GMT
Hi Vladimir,
I always enjoy your essays. They are delightfully illustrated, meaningful and fun to read.
Our views of science are diametrically opposed, though. I do not subscribe to the idea that if we just look at the evidence of nature in new ways, all will be clear and obvious. This trendy new philosophy (some call it "embodied cognition") is actually as old as Aristotle and...
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Hi Vladimir,
I always enjoy your essays. They are delightfully illustrated, meaningful and fun to read.
Our views of science are diametrically opposed, though. I do not subscribe to the idea that if we just look at the evidence of nature in new ways, all will be clear and obvious. This trendy new philosophy (some call it "embodied cognition") is actually as old as Aristotle and completed by Kant and Wittgenstein. In extreme contrast:
I am a rationalist.
To me, the universe only becomes beautiful (or even comprehensible) by demonstrating correspondence -- between the language by which the universe is described, and the mode in which it is experienced. If one wishes to join language to experience as if they were identical, I don't think one is doing science at all. At least, it isn't the science we practiced for over 300 years between Newton and Einstein, as a rationalist enterprise. So when you say:
" ... although the concept of flexible spacetime ‘works’ in (SR) and (GR), and that of probability waves ‘works’ in (QM), they are just mathematical ideas that must be discarded if better models closer to nature can be found ..."
... it does not relate an iota to what I think of science, and that is probably why you don't understand the essay.
Just as you prize your graphic art (and I prize you for it -- your work is extraordinarily graceful and rich with beauty), I prize the art of mathematics as highly as I prize natural language or any other art. It's a knife to my heart when you write:
"This is more than just a way to seek more elegant theories: understanding nature at its own level is a necessary step to pave the way for further theoretical, experimental and technological discoveries."
Mathematical theories are independent of experiment and technology. We and our mathematics *do* live at nature's own level, which is why mathematical physicists seek to understand the language of nature, rather than being satisfied with the nature of language. The former speaks to existence on its own terms; the latter fetishizes existence and language. Here's why I think as I do -- you write:
"The human brain evolved over millions of years in organisms that interacted directly, causally and locally with inanimate nature on a molecular scale15. Is it too much to ask now that our understanding of Mother Nature should also be as simple, direct and realistic as possible?"
Well of course, I would answer "no." Naive realism driven by direct experience has no independent correspondence to language. The metaphor Mother Nature itself is an anthropomorphic conceit -- when we fetishize the brain as a creation of the mother, we limit our capacity to participate in our own continuing creation. We become alienated from ourselves, and tend to invest the meaning of our existence in such things as technology, artifacts rather than art.
I admire the honesty in your art, Vladimir, as I admire the honesty in your person. I hope to return the favor. I am younger than you by only 5 years; maybe it's a characteristic of our generation. :-)
I don't rate essays that I don't understand, nor do I downrate essays that I disagree with. I trust that ethic in you, as well.
All best in life, and in the competition,
Tom
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Vladimir F. Tamari replied on Apr. 25, 2015 @ 04:20 GMT
Thank you Tom for your kind words about my graphics.
I do understand and respect how science works and am puzzled why you think I do not ! You quote from my Beautiful Universe theory which, as I stated at the outset, is an incomplete and speculative model of how the universe might work. I know I have not treated my ideas mathematically but I have certainly thought out their physical implications. For example in an absolute discrete universe in which signals travel at a maximum of c but at slower rates in regions of higher potential, moving meter sticks get shorter and moving clocks tick at a slower rate, not space and time as dimensions distort. Hence a physics bypassing SR and GR is possible. I did not yet prove it mathematically, but it certainly played out from physical arguments expressed in words and figures.
The math can be added later but the physical ideas have to come first. That is how Einstein worked - he thought of the weightlessness of a falling man, and it took him (and Grossman) 10 years to clothe the idea mathematically into his General Relativity theory of gravity. I do not see what the problem is with my how I do physics - ideas first and the math to be detailed later.
In no way do I downplay the importance of mathematics in describing physical ideas. In my fqxi essay I try to show why it can describe physics at its own level so well. What I do object to (the tricky part) is that mathematics is so prodigious it can also describe scenarios that have no parallel in Nature. Kepler's ellipses yes, Ptolemy's epicycles no. Both described the same phenomena - is it wrong for me to say we must choose the scenario that is closer to how nature actually works?
And even if I take your advice and work only with mathematics I would say I work with geometrical ideas - a friend swears only algebra can describe nature. It is all fun, and in the end what advances physics will remain.
With appreciation and all best wishes,
Vladimir.
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Fred Diether wrote on Apr. 12, 2015 @ 20:57 GMT
Hi Tom,
I have printed out your essay and I am going to study it on my next lie down rest my back break. :-)
Looks like you have been busy here but thought I would inform you if you don't already know that the core part of Joy Christian's model has been proven by Albert Jan Wonnink via the computer program GAViewer. For those interested look
here.
Looks like FQXi's panel of experts were very wrong. But you already knew that.
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Author Thomas Howard Ray replied on Apr. 12, 2015 @ 22:33 GMT
Fred,
I didn't know the latest -- though I knew it was in the works -- and that is really great news! Like you, I have not doubted Joy's framework for a long time now.
Thanks for the update.
(I have arthritis, so I relate to back pain. Calm down, take it easy and feel better!)
All best,
Tom
Author Thomas Howard Ray wrote on Apr. 14, 2015 @ 15:01 GMT
Richard Gill continues to attack Joy Christian's measurement framework. My response attached.
attachments:
Continuing_misguided_attacks_by.docx
Author Thomas Howard Ray replied on Apr. 14, 2015 @ 15:10 GMT
Oops. Forgot to save as pdf. Re-attached.
attachments:
Continuing_misguided_attacks_by.pdf
Fred Diether replied on Apr. 14, 2015 @ 20:25 GMT
Yeah, it is rather sad that Gill seems to not realize that he has lost the debate since Albert Jan's computer proof of Joy's model. He quite frankly is carrying on like it didn't happen. Maybe some day he will understand geometric algebra and what Joy's true big discovery is. I'm not holding my breath though.
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Jonathan J. Dickau replied on Apr. 14, 2015 @ 21:46 GMT
I would not hold my breath Fred..
Let each out breath inexorably lead to an in breath, then vice versa, and so on. That each inward path leads to an outward one, and outward to inward, is a suitable imitation of the connectedness of S3. I too enjoyed your summary, Tom, and I have to wonder what it would take - because it appears Gill's criteria are a moving target, just as he claims for Joy.
It is ironic that RG wants to use Joy's first paper as the bellwether, given that it is only a sketch of the full proof, and that he has ignored that Bell's first paper contained an error that was later glossed over or corrected - as clearly pointed out by M. Goodband. I think perhaps Joy's use of the Kronecker delta is partially at fault; it is a convenient but lossy abbreviation that leaves too much room for interpretation.
More later,
Jonathan
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Fred Diether replied on Apr. 15, 2015 @ 19:43 GMT
Hi Jonathan,
Good to hear your take on this. I do believe that the proof Albert Jan did was all done analytically here on FQXi in the debates of the past. But now there is proof via a geometric algebra computer program that Joy's classical realistic model does in fact produce the prediction of QM, -a.b.
FQXi is going to have some real embarrassment to deal with in the not too far future concerning their so called panel of experts that claimed the model was wrong. The model works as advertised.
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Jonathan J. Dickau wrote on Apr. 15, 2015 @ 03:52 GMT
An enjoyable essay Tom..
It took me a while to work through this paper, but it appears your logical reasoning is solid, even though I found some portions confusing. There is a lot I agree with, though it runs counter to prevailing opinion. I especially like that you wove Euler's equation into the story in such a meaningful way. I'll likely have more to say, but a ratings boost is all for now.
Regards,
Jonathan
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Author Thomas Howard Ray replied on Apr. 15, 2015 @ 14:43 GMT
Thanks, Jonathan! We agree more than we disagree, actually.
I think Euler's equation is the real center of the mathematical universe -- the origin of arithmetic and geometry.
All best,
Tom
Richard Gill wrote on Apr. 16, 2015 @ 12:50 GMT
Hi everyone
I see there is some discussion here of Albert Jan Wonnink's GAViewer program with which he attempted to verify one line in the first "Bell refutation" paper of J J Christian ... from way back in 2007: quant-ph/0703179
He immediately ran into Christian's trademark algebraic error. This is the (-1)^2 = -1 error which Christian needs in order to make embarassing...
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Hi everyone
I see there is some discussion here of Albert Jan Wonnink's GAViewer program with which he attempted to verify one line in the first "Bell refutation" paper of J J Christian ... from way back in 2007: quant-ph/0703179
He immediately ran into Christian's trademark algebraic error. This is the (-1)^2 = -1 error which Christian needs in order to make embarassing bivectorial terms cancel out of his "correlation" (the answer has to be scalar, right?).
Of course it is easy to "fix" that mistake locally, by an ad hoc subtraction of what you don't want to have. He shows what you have to subtract to Christian's (17) in order to make the left hand side equal to the right hand side.
What Albert Jan *didn't* do is simulate the whole model. His computer program verifies a patched version of formulas (17) and (19) of quant-ph/0703179. So on the one hand, he shows that Christian's original math was wrong. On the other hand, he still has not checked whether the patch which he introduces to fix the gap between LHS of (17) and RHS of (19) is consistent with the rest of the story. After all, if you change the very definition of geometric product locally in one formula in a complex story, that might have repercussions elsewehere, right?
In fact, Albert Jan hasn't addressed the challenge yet of actually generating the measurement outcomes A_n(mu) of Christian's equation (16). Most readers, on a superficial reading, would suppose that (16) was a definition of the two measurement functions A(a, mu) and B(b, mu). However if you read carefully it is not a definition at all: in order to make it a definition one still has to specify the mapping from bivectorial measurement outcomes to {-1, +1}. Many are possible. None, of course, can deliver the goods ... because of Bell's theorem.
It's at this point that one sees the other major error in Christian's attempts to refute Bell: he computes some kind of bivectorial correlation between the outcomes represented as points in S^2, instead of the correlation between the corresponding values +/- 1. Bell is about experiments with binary outcomes. His "correlation" is just the probability that Alice's outcome equals Bob's, minus the probability that it doesn't. Quantum mechanics predicts probabilities; experimentalists observe relative frequencies. The problem is how to explain the relative frequencies?
In Christian's one page paper, four years later, it is clear that he has seen that there was something missing. He does give a definition of the measurement outcomes and now comes up with his daring bivectorial Pearson correlation instead of the "straight" correlation between the binary outcomes. After all, the labelling of the outcomes +/-1 is just convention.
His definition of the measurement functions is A(a) = -B(b) = +/- 1 (with equal probabilities for the two possibilities). Thus his model predicts that the correlation is -1. Bob's outcome is always opposite to Alice's.
"Out of the frying pan into the fire".
I have written up a postmortem which includes a tutorial section on geometric algebra, so that no one has any excuse any more not to be able to work through the math of these classics, line by line, and check everything for themselves.
http://www.math.leidenuniv.nl/~gill/GA.pdf
Amusing
ly, I was not allowed to post this on arXiv.org: it was seen as a personal attack. I must say that my earlier drafts had a title which was a little bit over the top. Now the paper is simply entitled "Does Geometric Algebra provide a loophole to Bell’s Theorem?". The answer is of course, "no".
Showing that geometric algebra provides an alternative and beautiful way to describe the maths of spin half, including several spin half particles, entanglement and all that, was one of David Hestenes' greatest achievements. Two whole chapters are devoted to this topic in the textbook of Doran and Lasenby. They are worth careful study.
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Author Thomas Howard Ray replied on Apr. 16, 2015 @ 13:44 GMT
Hi Richard,
Thanks for dropping by. I'll be happy to entertain an exchange here, if it remains collegial.
Your arguments vis a vis Christian always come back to, " ... because of Bell's theorem." Yes, of course, we know that the literature assumes quantum entanglement, such that spin zero decays to spin - 1/2, + 1/2. Because you don't acknowledge that quantum entanglement is no more than an assumption, your argument does not even address the issue of an alternative measurement framework.
Christian, on the other hand, HAS constructed a measurement framework -- published last year in the International Journal of Theoretical Physics -- that purports to demonstrate quantum correlations are NOT " ... because of Bell's theorem." Since one can't demonstrate constructively that the mathematical proof of Bell's theorem is independent of the experimental protocol -- any scientist should welcome an *objective* test that eliminates ad hoc assumptions.
That is what my essay is about -- the possibility of rational correspondence between mathematical model and physical result. Such correspondence cannot be shown valid, without demonstratiing independence of mathematics and physics. Otherwise, one appeals to mystical, non-realistic explanations for correlated phenomena. Should one prefer realism over mysticism? -- a rationalist is so compelled. If science is a rationalist enterprise, science is also so compelled.
Your interpretation of Joy's application of geometric algebra is wrong, and the answer to your title question is "yes." You have neglected Hestenes' interchangeability of geometric algebra with Minkowski space, as well as the topological property of simple connectedness in the 3-sphere. Both of which lead to spinor characteristics in our ordinary measure space, which is 4 dimensional.
Best,
Tom
Fred Diether replied on Apr. 16, 2015 @ 18:01 GMT
I will give some further explanation about what Albert Jan
did with GAViewer so that others are not hoodwinked by Gill's misrepresentations.
The geometric algebra program GAViewer is fixed in a right handed bivector basis. So in order to see the left handed bivector basis part of Joy's model, all one has to do is reverse the order of the geometric product AB to BA. IOW, from a right handed perspective, one sees the order reversed for the left handed part. Lambda simply toggles between the two orders to correctly represent the model from the right handed only perspective. Pretty easy to understand and the model works as advertised. And what Albert Jan did is simple and elegant.
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John R. Cox replied on Apr. 16, 2015 @ 18:50 GMT
Fred,
Thanks for pointing that out, GAViewer sounds like 'graphic arts drawing' tool to me, and would not be built to select between a right or left mathematical handedness. It also points out the importance of thinking through any proposed experimental protocol, and especially with the growing reliance on computerized simulation. In Theory, a process is an interactive dynamic. In physical practice, a process is a something - like the bump at the end of a bone that the muscles connect to. In Theory all you need for a mathematical process to be complete is to specify an initial state, it will stick together just fine. In Experiment, to get two things to physically stick together initially, you need to add a mechanical process and that can introduce an asymmetry into an otherwise mathematically symmetrical dynamic. Measure twice, cut once. jrc
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Author Thomas Howard Ray replied on Apr. 16, 2015 @ 19:40 GMT
Thanks for that explanation, Fred. To my memory, Joy explained it years ago in terms of a video game screen where a character or object disappears at one edge and reappears at the opposite edge. It makes a perfect analogy with the flatness of parallelized spheres.
Such reversibility is also supported in my explanation of 4 dimensional metric signature reversal using prime pairs.
Author Thomas Howard Ray replied on Apr. 16, 2015 @ 19:43 GMT
That's a truly interesting way to put it, John. The lazy way is just to assume an indescribable phenomenon called "quantum entanglement." :-)
John R. Cox replied on Apr. 16, 2015 @ 20:25 GMT
Tom,
Thanks, I admit looking first at the entrance to the rabbit hole. A deceased friend of mine had been a machinist, and we were talking once about the decline of the U.S. pre-eminence in hard production capability. He told of a domestic precision spring manufacturer that had sent a Japanese competitor a sample of their tiniest, finest caliber coil spring, and the competitor sent it back with a hole drilled through the wire and one of theirs threaded through it. :-( jrc
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Author Thomas Howard Ray replied on Apr. 17, 2015 @ 00:56 GMT
Great story, John. I think it's kind of ironic that W. Edwards Deming -- the father of statistical process control -- found his first customers among the Japanese. After all, a statistical method that puts power in the hands of the individual production worker seems to go against the grain of Japanese business culture, of which one Japanese manager I knew said, "the nail that sticks up gets hammered down."
And then they proceeded to kick our butts, by exporting American ingenuity. :-)
Fred Diether replied on Apr. 17, 2015 @ 01:03 GMT
Hi Tom,
Actually it is more simple that what you describe. It is just due to the non-communitivity in the algebra. Which is familiar by just rotating a book two different ways. Anyways, the classical local realistic model does in fact produce the prediction of QM, -a.b.
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Richard Gill replied on Apr. 17, 2015 @ 04:45 GMT
I just respond to the remark "GAViewer sounds like 'graphic arts drawing' tool to me, and would not be built to select between a right or left mathematical handedness".
GAViewer is a research tool built by the authors of Geometric Algebra for Computer Science: Leo Dorst, Daniel Fontijne, Stephen Mann; see http://www.geometricalgebra.net/
I wouldn't call it a "graphic arts drawing tool".
It is built to select between right or left handedness: if "a b" is a right-handed geometric product then "b a" is left-handed.
The challenge to program Joy Christian's model in GAViewer is still open. Going back to Christian's 2007 paper there would not appear to be much work to do: the model is contained in formulas (16) to (19). Albert Jan Wonnink has therefore got about half way - he has done the second half. Only the first half still to do.
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Author Thomas Howard Ray replied on Apr. 17, 2015 @ 12:39 GMT
Hi Fred,
Yes. Except that one cannot realize the full rotation in less than 4 dimensions. Early on, what made Joy's framework attractive to me is that it is compatible with Minkowski space. I tried every way I knew to create discontinuity in the result and thus falsify it. This is the same approach Gill uses in "finding" a nonexistent algebraic error.
And even though David Hestenes has been silent on the issue -- I cannot justify an alleged error based on quaternion algebra, when Christian clearly extends the measure space to octonions. "Spacetime algebra," therefore, fulfills time evolution without having to refer to time, given the extended measure space.
Best,
Tom
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Richard Gill wrote on Apr. 17, 2015 @ 09:26 GMT
This essay appears indeed highly erudite but I wonder how much the author has understood of the authors he is citing. Let me illustrate this with the citations he gives to papers in an area I know well: Bell inequalities.
Instead of plugging the Joy Christian model, Thomas Ray is now plugging Hess and Philipp, who more than ten years ago published a bunch of papers with the main theme that...
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This essay appears indeed highly erudite but I wonder how much the author has understood of the authors he is citing. Let me illustrate this with the citations he gives to papers in an area I know well: Bell inequalities.
Instead of plugging the Joy Christian model, Thomas Ray is now plugging Hess and Philipp, who more than ten years ago published a bunch of papers with the main theme that Bell had forgotten about time. Actually, if you take the care the read Bell's famous Bertlmann's socks paper, you will see that Bell was very aware of the role of time, and gave specific experimental instructions so that one would *not* be able to blame a violation of his inequality on time.
Apart from an erudite verbal discussion of the issue of time in these experiments, Hess and Philipp also professed to have constructed a local hidden variables model which reproduced the singlet correlations but unfortunately -- inevitably, of course, by Bell's theorem -- their elaborate construction concealed a little math error. They forgot one of three subscripts somewhere deep in the computations and failed to normalise a measure to be a probability measure. This was pointed out by myself and others, and the model died a natural death. The time issues they raised *are* interesting. The possibility of a memory loophole was already being studied by several researchers including myself. All this activity led to Jan-Ake Larsson and myself discovering a "new" loophole in Aspect type experiments due to the fact that experimenters do not use a framework of predetermined time intervals for measurements. Instead, the detection times of two photons being close to one another is used to post-select the pair i.e. to discard all detection events which seem not to be paired. Disaster! A very non-local selection of which outcomes to keep, which to throw away. Biased sampling ... It turns out to be a far *worse* loophole than the famous detection loophole.
Later Hess used the Larsson-Gill approach to build simulation models for past experiments with these defect, together with Hans de Raedt. In his recent book, Hess claims that Larsson and I had *stolen* the idea from him. Well we were certainly inspired by his work, and as he pointed out, other people had noticed that there was an issue, before him.
The hidden title of Hess' book (published as "Einstein was Right!") is "Karl Hess was always right, at least, in retrospect".
Then a second authority whom Ray quotes is my friend Han Geurdes from the Netherlands who recently got a paper published in the journal RIP (results in physics) which is Elseviers' answer to predatory journals where, I am sorry to say, the author gets to pay an exhorbitant fee to have just about anything published. Geurdes' amazing insight is that an experimentally observed correlation might differ by some amount, in either direction, from the "true" theoretical correlation, hence that a local realist simulation model of a loophole free Bell-CHSH type experiment can easily produce a result larger than 2. The paper is discussed on PubPeer: https://pubpeer.com/publications/DBFF182E87F04FB92102CAC7E33
046
Yes! The measured value of some physical quantity might be larger than the true value! Disaster? The end of experimental physics?
Smart people have already known that about half the time, the "observed" value of CHSH would be bigger than 2, half the time it would be smaller. That's why physicists who actually do experiments make sure that the sample size is rather larger and they compute a standard error and do a statistical significance test in order to show that the deviation they have observed above 2 could not be ascribed to merely chance variation around a "true" value equal to 2.
Regarding Bell, EPR and all that I note that Ray does *not* refer to Christian's work so I wonder if this means that he has now abandoned support of that direction?
Before spending just a few words on that, it should be mentioned that Doran and Lasenby's book on geometric algebra contains two whole chapters "doing" spin half, the singlet state, and all that, with geometric algebra. It is very elegant, and very interesting, and just the tip of the iceberg in this area. The only thing they don't do is provide a local realist model for the singlet correlations. (For obvious reasons ... Bell's theorem).
However it seems that geometric algebra is not so popular in this area any more. I suppose it did a good job at describing all the facts - all the facts which are also described in the conventional Hilbert space approach. It links them nicely to geometry. But it didn't take us any further. And just like the conventional Hilbert space approach, it does not tell us what is going on "under the hood" event by event. It is "just" another (mathematically isomorphic) way to derive the probabilities of what happens.
My recent analysis of Christian's early works including a tutorial on geometric algebra is on viXra: http://vixra.org/abs/1504.0102 "Does Geometric Algebra Provide a Loophole to Bell's Theorem?"
and Ray has given a link to a pdf discussing my paper here: http://fqxi.org/data/forum-attachments/Continuing_misguided_
attacks_by.pdf
The point I want to make is that time and time again in this essay, I am sorry to say, the essayist does show that he does not know what he is talking about. IMHO. Sorry.
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Author Thomas Howard Ray replied on Apr. 17, 2015 @ 12:15 GMT
Gill's wordy reply support's Karl Hess's claim that Gill "makes himself a pretzel" to defend his views while disparaging constructive alternatives with irrelevant misdirection.
" ... Bell was very aware of the role of time, and gave specific experimental instructions so that one would *not* be able to blame a violation of his inequality on time".
Uh ... yeah. That's the core of what Hess-Philipp (and I) have been saying. The Bell-Aspect program does no more than prove its own assumptions.
Gill's "friend" Han Geurdes is cited (not quoted) as an example of a trivial proof that "The free will to choose both a proposition and the negation of that proposition is contradictory of free will in any physical sense." And I have discussed this with Han -- it is in fact, Gill himself who characterized the proof as 'trivial,' in the PubPeer discussion to which he refers, and I happen to agree with the characterization. The fact that it is trivial only underscores its importance to measure theory.
I have never "plugged" Joy Christian or anyone else. It is Gill who is so enamored of personality cults that he confuses science with scientist. At any rate, Joy Christian's program does not contradict the contents of the essay -- I just didn't need it to make my point.
Time and events to follow will reveal whether "the essayist knows what he is talking about." And whether the voice of authority is stronger than rational science.
Tom
Author Thomas Howard Ray replied on Apr. 17, 2015 @ 14:55 GMT
I have never doubted Richard Gill's sincerity and expertise in defending Bell's theorem orthodoxy. He is certainly misguided, though, in his assumption that Bell's
Bertlmann's Socks analogy eliminates the issue of a missing time parameter.
Consider Bell's illustrations 4 & 5. Bell (and Gill) would have us believe that the Stern-Gerlach magnet rotation produces separated groups (quantum mechanical pattern) of particle detections as a result of fundamental quantum non-locality.
Einstein, however -- using the mathematical convention of Minkowski space -- never considered this spatial parameter independent of the time parameter. The problem arises in the microscopic scale. Every point of spacetime in relativity carries its own clock independent of scale, a point that
Karl Hess and Walter Philipp made quite elegantly to apply on the quantum microscopic scale, and which Gill's (with Weihs, Zeilinger and Zukowski) criticism -- despite his claim -- fails to refute.
A modified version of the 2-slit experiment (Young), where particles are sent one at a time through the slits -- and nevertheless arrange themselves in the classical wave interference pattern as if each particle "knows" where the other went -- is local and time dependent. It is unmotivated, other than by mere assumptions of quantum entanglement and non-locality, that measurement scale affects hidden-variable continuity in the spacetime subspace of local measure. (I have an existence proof of this claim that I am not yet ready to discuss publicly.)
In the words of Hess-Philipp " ... a properly chosen sum of what we call setting dependent subspace product measures (SDSPM) does not violate Einstein-separability and does lead to the quantum result ..."
Tom
Author Thomas Howard Ray replied on Apr. 18, 2015 @ 11:20 GMT
Bertlmann's Socks link: https://hal.archives-ouvertes.fr/jpa-00220688/en/
John R. Cox replied on Apr. 19, 2015 @ 01:29 GMT
Tom,
I thought your approach to the essay topic via the mathematics of probabilities was rather challenging in the first place, and it is provocative of further questioning of what we *do* with math. On the surface its quite a simple thing to correlate probabilities to a space frame, like throwing darts. But having come to understand some of your theoretical thinking, you are reaching well beyond that concept.
I have known a number of people for years whom, once I dealt with it enough working with them, I came to recognize that they don't see things in a geometric sense though they are quite adept at shooting pool, operating cranes, or racing automobiles. They might rough out a sketch on a scrap of paper of how they want a site laid out for a small footer and spacing pilasters, but there will be no proportion at all in the sketch and it will as likely show the short dimension of a rectangle as the longer length. It is the numerical relationship that they see and the actual spatial relationship only in a moment to moment instinctive reaction. The final result, here to there.
There have been recent advances in brain mapping and studies of mathematic abilities that make me wonder. Even though algebra comes from geometry, do we as a species have an inherent disjunct between our spatial perception with its temporal dimension, and the perception of mathematical relationships in an abstract dimension? Brain scans of 'math whizzes' at work show areas larger than common, consuming high levels of oxygen. But is that only in the abstract, does it correspond to a sense of spatial environment?
That correspondence at a foundational level is what you seem to be driving at in your essay. And a perceptual lack of such a correspondence almost guarantees a perception of non-locality as the reality. Good luck getting that across, jrc
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Author Thomas Howard Ray replied on Apr. 19, 2015 @ 11:35 GMT
John, you are leaving your footprints on my mind, and I do appreciate it.
I am at work on a paper -- partial draft attached -- that shows rigorously and conclusively how Gill et al, fail to refute Hess-Philipp. They got it wrong, because their assumptions based on Bell's theorem are wrong.
Gill claims, "They forgot one of three subscripts somewhere deep in the computations and failed to normalise a measure to be a probability measure."
Gill fails to realize that normalization of a complete function in spacetime -- which is deterministic -- is not equivalent to normalization of an algebraic function in probability space. The attachment explains.
All best,
Tom
attachments:
Special_relativity_and_the.pdf
Richard Gill replied on Apr. 19, 2015 @ 11:40 GMT
Dear Tom
Thanks for adding the link to Bertlmann's socks! Required reading for anyone interested in Bell and all that.
You mentioned: Hess-Philipp " ... a properly chosen sum of what we call setting dependent subspace product measures (SDSPM) does not violate Einstein-separability and does lead to the quantum result ..."
Unfortunately, their mathematical proof contained a fatal error. As of course it had to: if their model had been correct, it would have contradicted Bell's theorem. Of course, not many people actually worked through the pages and pages of computations using all kinds of advanced math stuff.
Before promoting the Hess-Philipp construction you should take a look at http://arxiv.org/abs/quant-ph/0204169 (Europhys. Lett. (2003) 61, 282-283) and http://arxiv.org/abs/quant-ph/0208187 (PNAS 2002, 99: 14632-14635). Hess and Philipp did acknowledge their mistake in one of their many later publications and came up with an incredible story about some elements of reality not being elements of reality and how hard it was to decide what was real and what was not real! Because they did need a *nonlocal* hidden variable to get their maths to work. Hence it was obviously not an element of reality. (I guess that Walter Philipp, the mathematician, realised that there was a mathematical error; I suspect that Karl Hess, the physicist, left the hard math stuff to his friend and colleague).
Well that sounds to me like BS. But of course, people like those guys must always be right.
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Author Thomas Howard Ray replied on Apr. 19, 2015 @ 12:30 GMT
Richard, I do not share your disparaging opinion of Hess and Philipp.
Computability is an issue separate from elements of reality. I understand the difference between nonlocal hidden variables (string theory is a theory of nonlocal hidden variables) and local realism. If we take Einstein on his own terms ("all physics is local") then metaphysically real elements are also local.
Our latest posts crossed. My attachment explains why I think you are wrong about the Hess-Philipp program. I don't see that you even addressed separability -- it is not at all a matter of experimenter choice.
Best,
Tom
Author Thomas Howard Ray replied on Apr. 19, 2015 @ 13:52 GMT
A good example of how Bell (and Gill et al) confuse local realism with non-local probability is the abuse of terminology, Gill's "non-local distribution."
There is no such thing as a non-local probability distribution in a physical model. In fact, a demonstration of this fact is integral to Hess-Philipp's introduction of the time parameter.
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Author Thomas Howard Ray wrote on Apr. 20, 2015 @ 15:33 GMT
John Cox has an elegant way of bringing the issues in line with everyday experience.
Having devoted part of my misspent youth to the pool table, John's reference to the relation between shooting pool and moment-to-moment instinct got me thinking about Hess-Philipp's timelike correlated parameters (TLCPs) .
Because initial condition changes with time, moment-to-moment action (event...
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John Cox has an elegant way of bringing the issues in line with everyday experience.
Having devoted part of my misspent youth to the pool table, John's reference to the relation between shooting pool and moment-to-moment instinct got me thinking about
Hess-Philipp's timelike correlated parameters (TLCPs) .
Because initial condition changes with time, moment-to-moment action (event by event in QM simulation terms) avoids action at a distance " ... by letting the probability measure be a superposition of setting-dependent subspace product measures with two important properties: (i) the factors of the product measure depend only on parameters of the station that they describe, and (ii) the joint density of the pairs of setting-dependent parameters in the two stations is uniform."
The multiple time scales of a pool game range from the interval of contact of hand with cue, cue with cue ball, cue ball with object ball, ball with rail, etc. These are well understood causal events whose outcomes are all dependent on initial condition and energy content in the specified interval.
Gill, et al, criticism of Hess-Philipp completely avoids the causal framework -- they claim, " ... "(Hess-Philipp) forgot one of three subscripts somewhere deep in the computations and failed to normalise a measure to be a probability measure" -- which is completely irrelevant to the point made by H-P above (and well supported by the mathematics of the paper). Normalization of probability density in a time dependent causal relation is independent of energy density and initial condition. Hess-Philipp show that initial energy condition determines joint probability -- while Gill et al avow that (" ... because of Bell's theorem" as Gill claims) probability is prior to measurement. The measurement protocol of Bell-Aspect merely demonstrates its own prior conclusion.
While Gill et al are completely off the mark in convincing themselves that they have refuted Hess-Philipp -- the science of complex systems, in line with Bar-Yam's theory of multi-scale variety, supports timelike correlated parameters at multiple scales: http://home.comcast.net/~thomasray1209/ICCS2007PP.ppt
Tom
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Author Thomas Howard Ray wrote on Apr. 22, 2015 @ 13:09 GMT
More should be said about why the Karl Hess and Walter Philipp PNAS paper of 2001 is a breakthrough in our understanding of time dependent systems, because it accents the physical identities among time, information and energy that characterizes complex systems -- and as the authors make explicit, the problem of decidability between Einstein and Bohr.
Criticisms of Hess-Philipp have failed...
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More should be said about why
the Karl Hess and Walter Philipp PNAS paper of 2001 is a breakthrough in our understanding of time dependent systems, because it accents the physical identities among time, information and energy that characterizes complex systems -- and as the authors make explicit, the problem of decidability between Einstein and Bohr.
Criticisms of Hess-Philipp have failed to even address the key issues of Einstein separability and special relativity that drive the paper's conclusions. The critics know that these issues cannot be confronted head-on, because they are well-understood physical principles that cannot be refuted.
Let's return to a point I made in my essay (p.6), that Einstein's original quest for E = mc^2 substituted the Lagrangian (a system's energy content) for the E term, where E was then generalized to rest energy, so we get that famous equation. The continuous values of the Lagrangian, however -- vary with mass -- local measured. In reply to critics, Philipp-Hess simplified their explanation of the model (attached), such that " ... Imagine the time axis wrapped around a circle of circumference that corresponds to a time interval related to a simple measurement and normalized to 1. We suppose that for a fixed N each interval [(m − 1)/N, m/N ], m = 1, 2, . . . , N of arc length 1/N on the circle gets about its proper share of time measurement points over the measurement period." The authors go on to show time correlations that the critics ignore, and reproduce quantum correlations in a complete framework of distributed time-dependent energy/information. These results satisfy Einstein separability and special relativity in a way that the critics do not and cannot:
Because a continuous range of time-dependent energy values attends every classical measure, normalization of the time interval locally does not imply a global normalization (as Gill claims) -- because of the special relativity limit. Each measure carries its own time stamp, and it is always local.
Tom
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attachments:
Walter2002.pdf
Peter Jackson wrote on Apr. 22, 2015 @ 16:44 GMT
Tom,
I'm glad I managed to get to your essay. Again I found little to disagree with, but then I'm now down to speed-reading so resolution is reduced! There's also now little time for discussion, which I suspect may be a blessing, though our fundamental views may have more in common than is often apparent. Certainly I found the essay beautifully 'bookended' with Bronowki's quote (always a guiding star for my own work) and your concluding paragraph.
"In this game of unlimited possibilities called mathematics, our bet is on human imagination."
As you're a mathematician I'm particularly impressed with that. I see you're struggling to make the break point so I hope my score helps.
best wishes.
Peter
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Author Thomas Howard Ray replied on Apr. 22, 2015 @ 18:28 GMT
Peter,
Thank you, that's very kind. There's no mystery to why my score languishes below the cut -- never in my memory, from the first time I entered these competitions (which dates from the very beginning), has a fully relativistic viewpoint in foundational physics gotten due respect, while some of the fringiest views in quantum theory have won big prizes. So I have long abandoned any...
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Peter,
Thank you, that's very kind. There's no mystery to why my score languishes below the cut -- never in my memory, from the first time I entered these competitions (which dates from the very beginning), has a fully relativistic viewpoint in foundational physics gotten due respect, while some of the fringiest views in quantum theory have won big prizes. So I have long abandoned any illusions I might have had. It is enough that the FQXi forum gives voice to a minority viewpoint that it de facto opposes, and I am grateful to the Institute for that, even when I think it could do more.
There is an even lower score than mine, given for a far better essay by Vesselin Petkov, and -- I expect -- is low for the same reasons. I am going to do a lazy thing, and quote Vesselin's reply to a recent forum participant, because it matches my opinion: " ... if Minkowski had lived to see the advent of general relativity, he would have realized, as a mathematician, that the mathematical formalism of general relativity implies that gravitational phenomena are merely manifestation of the non-Euclidean geometry of spacetime (not an interaction). Einstein made a gigantic step by linking gravity with spacetime geometry, but even he was unable to overcome the seemingly self-evident 'fact' that gravitational phenomena are caused by gravitational interaction (which, unfortunately, is still the accepted view in physics)."
Things are changing. I got an Email from The Minkowski Institute Press just a few days ago that they are publishing
Cristi Stoica's PhD thesis (congratulations, Cristi!) , which is relativity-based, with a perturbative path to quantum gravity (my own solution is non-perturbative, but we are pretty close).
In regard to your own defense of conventional quantum theory in the Bertlmann's Socks analogy, I applaud your expansion of the pedagogy, and give high marks for that. It is deservedly among the best of Bell's output.
If you don't mind, I am going to do another lazy thing, and reproduce this reply in your forum.
All best,
Tom
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Akinbo Ojo wrote on Apr. 22, 2015 @ 19:08 GMT
We don't agree most times but we get to exchange ideas. It is good to rate those who are here come rain come shine and who have also contributed a nice essay. We continue our arguments (or 'quarrels') after the contest. You should now be able to make the list.
Akinbo
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Author Thomas Howard Ray replied on Apr. 23, 2015 @ 01:49 GMT
Thanks, Akinbo. Looking forward to it. :-) You got my upvote, too.
Best wishes,
Tom
Alma Ionescu wrote on Apr. 22, 2015 @ 20:20 GMT
Dear Tom,
I'm sorry but it's late and I don't have time to comment properly, except to say that I really enjoyed your essay a lot; I hope to be able to comment properly tomorrow if the system still allows. I believe too that Vesselin should have received more attention. For what it's worth, you have my vote.
Alma
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Author Thomas Howard Ray replied on Apr. 23, 2015 @ 01:52 GMT
Alma,
Your essay is an absolute treasure, as I commented in your forum. Thanks for reading mine.
By the way, though the spelling is different, you wouldn't be related to one of my favorite playwrights, Eugen Ionesco, would you? :-)
All best,
Tom
Alma Ionescu replied on Apr. 23, 2015 @ 17:22 GMT
Dear Tom,
Since the reply button is still active so I’m back to tell you how much I enjoyed your essay and why. Firstly, I think you write really well, and here I mean your style and not the technical side. Actually it’s impressive that the essay itself is
very technical and attacks
difficult problems that I am sure took time to develop and yet it’s expressed in a very...
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Dear Tom,
Since the reply button is still active so I’m back to tell you how much I enjoyed your essay and why. Firstly, I think you write really well, and here I mean your style and not the technical side. Actually it’s impressive that the essay itself is
very technical and attacks
difficult problems that I am sure took time to develop and yet it’s expressed in a very fluent language that has a natural feeling to it. The presentation is as dense as a textbook but dressed in the silk of a novel. I like it how you keep your eyes on the landmarks such as Perelman, Erdos or Bell and at the same time prove a very close attention to the community as it stands today – such as Woit and Leifer. To end the part about the form I’ll add that I enjoyed the few hilarious style jewels such as the
effectiveness of religion in theology and the
formalized Buridan Principle - regardless of the formalization level, the donkey still dies.
I found impressive the ingenuity with which you found a way to falsify the MUH, which is generally criticized as infalsifiable. I found even more impressive the subtle and complex construction you used to elaborate on determinism and realism in the context of physical and non-physical outcomes. Here I am mentioning determinism although you do not do so explicitly, because I am referring the path analyticity that you require as a condition in page 4 (column 2) - and please correct me if I misunderstood the point. I found the proof you made and the probabilistic arguments you used not only unique and ingenious but truly remarkable. I also enjoyed the striking formalism of the equivalence you drew between math and physics, putting them on equal footing and indeed here we need to consider Witten’s work and the progress that his physical intuition brought into mathematics. Even if he is perhaps the only appropriate example, his work is a proof of existence – in the mathematical sense - of your equivalence.
I need to add something which I hope you will not take as a critique, because I think of it as a reason for which you should not be disheartened that you work was not as widely appreciated as it should have been. Your essay was one of the most difficult to properly understand in this contest. The argumentation is completely non-trivial, you are relating a lot of concepts and I had to come back more than once to some steps. It is possible, even likely, that many readers did not allocate enough time to go through it with enough attention. I think it was simply not well enough understood (and not because it lacks clarity!).
To answer your question, Ionescu is a pretty common Romanian name – something like Smith - that Eugen had to modify when he moved to Paris so as to avoid a certain misfortunate, brazen pun. He was afraid that the Frenchmen will make his name rhyme with a lady’s backside. Oh, the embarrassment, the tragedy! :)
Before I go, I should let you know that I’ve also answered your comment on my
page.
Warmest regards,
Alma
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Author Thomas Howard Ray replied on Apr. 24, 2015 @ 08:03 GMT
Dear Alma,
A writer's greatest reward is to be understood. Thank you! I sometimes feel I should apologize for being subtle, and yet I find that one can't apply natural language with the desired precision, without putting a fine point on it. Someday, I expect, we will communicate in a universal language -- if not mathematics as we know it, then something like mathematics -- that smooths...
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Dear Alma,
A writer's greatest reward is to be understood. Thank you! I sometimes feel I should apologize for being subtle, and yet I find that one can't apply natural language with the desired precision, without putting a fine point on it. Someday, I expect, we will communicate in a universal language -- if not mathematics as we know it, then something like mathematics -- that smooths the edges of ambiguity and allows a polished thought to reflect its intended glow. (Computer science maverick Lev Goldfarb is making strides in this direction.)
It's remarkable that you caught the irony of Lamport's "Buridan's Principle." There's a story behind that -- several years ago, I was perusing Leslie's
publication page and ran across what I considered an important unpublished paper (though it was written over 30 years ago) and I suggested he try Foundations of Physics, where it was reviewed and published in 2012. To Lamport, the paper is not ambitious -- it is simply an acknowledgment of a hard problem (decidability) in computer programming, along with strategies to deal with it. To me, the principle implies deeper fundamental issues. I made the mistake, in referencing Lamport, of calling him a mathematician (he is most certainly educated and highly competent in the art) -- in which he corrected me, "I am not a mathematician; I am a computer scientist." I subsequently corrected the mistake, though it stuck with me, the difference between mitigating a problem in computer science and trying to solve it mathematically. Perhaps all programming is mitigation -- there are hardly any computer scientists who think P = NP. Do you?
That "the donkey still dies" led me to ponder
the perfect first question. For if we could actually do the Schrodinger cat experiment with a dead cat as the initial condition, there would be no decidability problem. Dead cat in, dead cat out, with probability 1 in a bounded interval of time. The same principle that keeps a computer-simulated "cat" alive, assures us that dead cats don't spontaneously come to life.
Yet, conventional quantum theory would have us believe the contrary -- all life is a superposition of alive and dead. So you are right on point that I take the view that " ... the path analyticity that you require as a condition ..." is the sum of all Feynman path integrals in every bounded interval, i.e., -- to use the words of Karl Hess and Walter Philipp, every "timelike correlated parameter" (TLCP). This view supports Einstein's finding from special relativity that all physics is local.
Tegmark actually provided his own criterion for falsifiability. If all measured events are random choices between "alive and dead" the MUH is refuted. Probability without randomness, however, falls to cosmology -- the initial condition of the universe. That's why the multiverse hypothesis (an extension of Everett's many worlds interpretation of quantum theory) is inevitable in Max's program. Every free will choice, of what to measure, being a product of local events, implies global continuity; i.e., analytical continuation that I equate to the sum of Feynman path integrals. The multiverse is totally ordered, to satisfy our partially ordered measures of the universe.
Thanks again and all best,
Tom
P.S. -- thanks for the skinny on Ionesco. I didn't know that! LOL!
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Cristinel Stoica wrote on Apr. 22, 2015 @ 21:00 GMT
Dear Tom,
I kept some of the most beautiful essays for the end. Yours is really nice. I agree with many of your viewpoints, and you presented them so good. Many make confusion between Tegmark's MUH and mathematical Platonism, and it is great you clarify this. And the rest of the essay contains so many intriguing remarks. I hope your essay will do fine!
Best regards,
Cristi
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Author Thomas Howard Ray replied on Apr. 23, 2015 @ 01:47 GMT
Cristi,
I'm honored. Thanks.
Tom
Author Thomas Howard Ray wrote on May. 6, 2015 @ 14:33 GMT
Some of my further work in
the origin of probability Tom
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