Initially you wrongly referred to this experiment:
http://www.nist.gov/public_affairs/releases/aluminum-atomic-
clock_092310.cfm
as an example of lifting one of the clocks and then bringing the two clocks together in order to compare them. Then you took refuge in the GPS system, and now you want to discuss the Hafele-Keating experiment which was not meant for measuring gravitational time dilation. Let us stop here.
Pentcho Valev
Dear Tim,
Thank you for your answer as it's a very interesting insight regarding how new theories come to be. I don't find it particularly odd that no one thought of your idea before, because most people don't feel the need to innovate as long as there exists a functional theory, all the more since the effort of creating a logically sound new approach is considerable. Also I'm sure your unique intuition has to do with this, because I think I understand that your approach allows for discreetness, not necessarily requiring infinitesimals.
Cheers,
Alma
Dear Tim Maudlin,
I will comment mainly on the first part of your essay. (The second part of the essay, in which you outline your new foundations for geometry, is interesting in it's own right, but it does not seem to address the original question as directly.)
One aspect that I liked is that you distinguish the surprise due to discovering a connection between seemingly distinct parts of mathematics from the wide applicability of mathematics to empirical sciences.
In the first part, you also think about how the world needs to be in order for the counting numbers to be relevant. You give mountains and cells as examples of concepts that are not (always) sharp enough (conceptually) for counting, and atoms as an example of a concept that is. In my view, however, the sharpness of our concepts is a matter of degree. The concept of an 'atom' is still a vague one, to some degree; hence the question of whether something is an atom or not -and whether to count something as an atom or not- may still be ambiguous in certain situations. For instance, one can imagine an electron and a proton: they will always 'feel' each other's electrical field. When, exactly, do they form a hydrogen atom? This question is also relevant in foundations of chemistry (with competing partition schemes in computational chemistry to identify 'atoms in molecules').
Viewed in this way, there are many degrees of freedom in applying mathematics to empirical findings - something which is rarely discussed in relation to the perceived effectiveness of mathematics.
Best wishes,
Sylvia Wenmackers - Essay Children of the Cosmos
Dear Sylvia Wenmackers,
Thanks for the comment. I do completely agree with what you say, which is why also the term "atom" is not used in the formation of fundamental physical law. First it was replaced by reference to electrons, protons and neutrons and then by reference to electrons and quarks. Since atoms are bound states of these things, the concept is only as sharp as "bound state", which is somewhat vague. At this point, "electron" and "quark" appear to be fundamental, and admit of not further analysis. But we may be wrong about that.
Cheers,
Tim
Dear Tim, I very much enjoyed your essay and hope you can clarify one point for me. It seems that your argument suggests that there may be equivalent frameworks for describing physical systems (such as topology or linear structures) but that only one corresponds to physical reality. This suggests that we could be using the wrong mathematics to describe reality purely because distant branches of mathematics that seem unrelated are actually deeply related. How would we ever know then that we had the "right theory"?
Dear Tim :
Your essay is very interesting,
In my opinion, mathematics that reflects reality, remains a priority for the current science.The Bi-iterative calculation could be the right one, because it has all the characteristics of a pure mathematics.
"NUMBERS"
first are integers
second are geometric shapes
third are physical entities, with infinite degrees of freedom
fourth maintain always the aspect ratio
fifth are elastic ... ..
Sixth are compact, and unseverable by two egual part.
We take an example:
1 + 5 + 7 + 12 =
= 1 + 5 + 7 + (6 + 8 + 10)
= 1 + 5 + 7 + (3 + 4 + 5) + 8 +10)
= 1 + 5 + 7 + (3 +4 +5) + (1 + 6 - 9) + 10
= 1 + 5 + 7 + (3 +4 +5) + (1 + 6 - 9) + 10
= 1 + 5 + 7 + (3 +4 +5) + (1 + (3 + 4 + 5) - 9) + 10
= 13
=2197
Of course, we speek about a cubic equazion.
Recursive calculation, the Fibonacci series and Fractal are wrongly linear, because they consider the space as a bi-dimensional sheet.
The system's Bi-iterative calculation is different, it consider the space, multi-directional and multi-dimensional. In fact, exist only set and sub-set. with (1) we mean (1 * 1 * 1).
Because we live in a complex and varied reality, only a struture able to transform can describe it.
The human brain is divided into two halves, the left hemisphere is masculine, active, called "rational". The right hemisphere is feminine, passive called "irrational".
The most important thing is that these two opposing positions should coexist. (x + 1) and (x - 1) are two limits , i meam the linear structure and the non-linear structure are inseparable.
A system that can not stop,follow the arrow of time. Or rather, it coping itself, reflecting itself. So, we have (x + 1), + 1, + 1, + 1 ....
"The universe was born like that, one bit after another, and continues to do so even now".
(See ANNEX)"The teorem"
sincerly yours
BannouriAttachment #1: 1_1_Theorem_1.jpgAttachment #2: 1_1_Theorem_345.jpg
Dear Sara,
I don't think we will ever we absolutely sure we have the right theory. All we can do is formulate different theories, using different mathematical resources, see what sorts of testable, observable behavior they predict, and try to gather data to test them. But there will always be different theories that agree with all the data we have. Choice among these different theories that are consistent with observations will either be made on grounds of simplicity, elegance, etc. or else not be made at all: we will just have to admit that we don't know for sure which, if any, if these theories is correct. But whatever we do, we have to acknowledge that we cannot be certain that any particular theory is right. That's just the situation we are in.
Cheers,
Tim
Tim,
A very interesting essay. I was skeptical at first but your explanation gradually resolved most of my reservations. Then I found just as it was getting to the climax with 'discrete Relativistic space-times' the last chapter was missing!
If you've read any of my recent essays (all finalists) you'll see various aspects of such discrete 'space-time' systems or 'fields' explored. I hope you may direct me where I may find your own last paragraph!
A few points;
1. I noticed your reply to Pentcho ref Hafele Keating above. If you'd read Hafele's NY lecture you wouldn't be so sure. He expressed his concerns that the data did NOT confirm theory as expected. It was only when the paper first didn't pass review that any such reference and data disappeared. The NY lecture text is also difficult to find (I can provide quotes if you wish). Nonetheless most still cite the work as the key excluder of many otherwise possibly valid theoretical approaches. Perhaps some gold plated 'confirmation bias'?
2. A question. Does your linear sequence model allow, say, expanding helical paths, and such paths which may form cascades on 'interaction requantizations' (via say atomic absorption and re-emission/'scattering', or perhaps 'decay' in particle terms) By 'cascades', consider a massive particle forming a shower through an atmosphere. The linear' structure would then have branches. Does your theory particularly exclude or support such models?
3. You say Wigners "..claim is indisputable', as commonly assumed. I'd like to challenge that. Lets say he had a friend 'd'Espagnolet' and they derived an 'inequality', later used by a chap called Bell, who cited a friend's odd red and green socks to prove its mathematical limits. All fine. But now let's give Dr Bertelmann a pair of reversible green socks with red linings. After their squash game they had to dress in the dark, so either foot could then have either colour! - giving a kind of 'stacked twin pair' probabilities, independent to each foot. Now we can have a perfectly physically feasible set of findings NOT constrained by Wigners 'amazingly effective' maths, or requiring 'quantum wierdness', or feet that can see in the dark and talk to each other! Some maths may then give the right bottom line but won't model the actual physical mechanism faithfully.
I propose the Wigner comment may then not prove indisputable, but that the situation he correctly identifies in the paragraph below applies - that there may be other truths. (A full description including complementarity referenced in my essay).
If we know that there are inconsistencies in current assumptions and theories is it right that we so consistently reject alternatives to doctrine? I just feel your own model may be on a track I recognize as being more widely consistent. Is "track" also consistent with your "linear", I've never considered 'lines' to exist any more than points!?
I do hope you'll also be able to read, consider and discuss my own essay, even after the score deadline.
Many thanks.
Peter
Tim Maudlin wrote on Apr. 17, 2015 @ 18:08 GMT: "I stopped the discussion because you do not know the situation with respect to either the predictions or tests of General Relativity. The basic scheme of actually comparing clocks has been going on for over three decades. These are not gravitational redshifts. Everyone knows the gravitational redshift is a weak test, but the tests moving and comparing clock readings are just different. Your insistence that they are not just demonstrates your mack of understanding of the situation."
I do understand the situation - you don't:
"A new paper co-authored by U.S. Energy Secretary Steven Chu measures the gravitational redshift, illustrated by the gravity-induced slowing of a clock and sometimes referred to as gravitational time dilation (though users of that term often conflate two separate phenomena), a measurement that jibes with Einstein and that is 10,000 times more precise than its predecessor."
"Einstein's relativity theory states a clock must tick faster at the top of a mountain than at its foot, due to the effects of gravity. "Our performance means that we can measure the gravitational shift when you raise the clock just two centimetres (0.78 inches) on the Earth's surface," said study co-author Jun Ye."
Pentcho Valev
Dear Peter,
As I'm sure you know, a complete discussion of the presently available evidence in favor of GR would be quite extensive, and go far beyond the three "classic tests", including the rotational rate of binaries, all sorts of precise clock and timing experiments, as everyone always mentions corrections needed for GPS etc. GR should at least be recovered as a limit of a more fundamental theory that may imply corrections, but the discussion with Valev was not productive, and irrelevant to my paper in any case. The fact that he continues it despite being asked to stop (see below) is already indicative of a certain state of mind.
There is no problem at all about converging or diverging sets of trajectories in my account of space-time geometry. Such "branching paths" will be ubiquitous in the geometry.
Your "reversible socks" scenario is obviously a completely local physics, and no sets of observations of socks put on in the way you describe will violate any Bell inequality. So I can't really see what you are trying to get at with the example. If it is more direct, try to come up with a theory that predicts the GHZ statistics using whatever kinds of reversible socks you like, but where the socks are examined at space-like separation. No such theory will make the predictions of standard quantum theory. (It is easier with GHZ because we don't have to worry about long-term statistics.)
By the way, although the 3-polarizer experiment is, indeed, often presented as a "paradox", there is nothing quantum-mechancial about it, and the phenomenon can be received by purely classical models. So, unlike the 2-slit interference effects or, more strikingly, violations of Bell's inequality, it is not an experiment that displays any particularly quantum-mechanical behavior. Curiously, I even remember a TV show long ago showing how to get 3-polarizer behavior using a rope and some blocks of wood with rectangular channels in them that stand in for the polarizers. If you line up two of the blocks with the channels are right angles to one another and put the rope through, vibrations of the rope at one end all get damped out by the blocks. But if you add a third block in between, with the channel running at 45°, some vibration of the rope gets through all three blocks. Clearly, this is a purely classical system which shows the same sort of phenomenon.
Cheers,
Tim
"the discussion with Valev was not productive, and irrelevant to my paper in any case. The fact that he continues it despite being asked to stop (see below) is already indicative of a certain state of mind."
Thanks. Kind of you. I did stop the discussion but just found references (see below) disproving the following text of yours:
Tim Maudlin replied on Apr. 4, 2015 @ 23:49 GMT: "Put two high-precision atomic clocks on the floor together Synchronize. Lift one up on a table. Wait a while. Return to the floor and compare synchronization. This has been done. The clocks go out of syntonization, and the amount out is a function of how long the one is up on the table. No redshift or light involved. Experiments at this precision have only been possible recently."
Pentcho Valev
Dear Tim
I never learn topology, so I do not understand everyting. First I need to learn some background. But, it is known, that special relativity (according to Newtonian physics) defines causality. The now thing is also unsimultaneity. How can you connect your explanation with unsimultaneity?
I think that every new explanation from new aspect can tell a lot, so it seems to me that you have a good essay.
In my essay I speculated, that Pythagora theorem is consequence of kinetic energy conservation in ortogonal direction. Do you have opinion about this?
I thing also that Planck's dimensionless nature of space and time tells a lot ... Maybe still your approach fails to complete explanation.
Best regards
Janko Kokosar
Dear Dr. Maudlin,
Thank you. Your response is helpful. I tend to favor either the second or third possible position, probably inclining more towards the second of the three. I realize that the availability of a particular mathematical structure is not of itself an argument that an aspect of physical reality is one way rather than another. Still, it is important, I think, that we are not compelled to use a mathematical language which, if time is inherently asymmetrical, leaves that asymmetry out of the mathematical representation. It is good to know that there is an alternative language which would capture this important feature of the physical reality.
Best wishes,
Laurence Hitterdale
Tim,
I understand your views, all conventional. You seem to take agreement with convention as always a priori falsification, so are happy to ignore anomalous findings and assume they'll disappear. I do understand as an educator that's the easiest position to maintain.
I must say my approach differs, seeking out and trying to remove or rationalise anomalies and paradoxes. It proved a bigger task than I anticipated. i.e one of the toughies is the increased weight of spinning objects, trillions of times more than GR predicts! I long studied GPS and Galileo and wrote a paper on GPS showing most of the 'relativity proof' to be nonsense. GPS can just as easily be said to DISprove SR! Don't get me wrong; I've found absolutely NO evidence against Einstein's postulates, so disagree with Pentcho, however there's a stack suggesting a flawed original interpretation, indicating an adjusted interpretation far more in line with his 1952 paper. It's only theoretical inertia that's stopping it being countenanced not the evidence, which is ALL more consistent with the adjusted one.
The very same simple 'QG' mechanism hypothesized as underlying space-time is what reproduces the predictions of QM 'quasi' classically (as it unifies the descriptions it would do!) You're quite wrong about the 'sock switch con' not producing the correlations from 'entanglement' which we call 'quantum non-locality'. Again you seem to just dismiss the possibility a priori without looking! (Bell's 'sleepwalking') - but the derivation is exactly what Bell predicted! Sure there are 7 concepts to track when human brains alone have a limit of ~3, but I'm sure a man of your intellect can follow it. I'd be delighted if anyone falsified it but nobody who'se looked has done, yet. Most don't look. Ken Wharton identifies the same narrownness of vision!
Do have a go. The draft paper is web-archived here.
P Jackson, J Minkowski; https://www.academia.edu/9216615/Quasi-classical_Entanglement_Superposition_and_Bell_Inequalities._v2. My previous (top 10) essays from 2011 also cover much of the ground of this 'discrete field' model.
The classical 3 polarizer effect for instance can equally be taken as a hint that QM MIGHT possibly have a classical 'type' solution as Bell predicted. It's just one of the 7 'jigsaw puzzle' pieces that you'll find fit to produce to coherent picture. Unlikely? Of course. So is the chance of the ground swallowing you up, but it happens!
Do report back on my blog, or direct to; pj.ukc.edu@physics.org
Peter,
The link you post is dead. In any case, I was making a couple of points, which you seem happy to dismiss with talk of convention, which I cannot even follow. One is that the so-called "3-polarizer paradox" is not a phenomenon at all difficult to replicate and completely understand even in a classical setting. In that sense, there is nothing paradoxical about it at all, and certainly nothing that could shed any light on quantum theory. The second is that no amount of putting on and taking off reversible socks, using any local physics, can replicate the predictions of GHZ and, in the long term, the statistics of spin experiments on entangled pairs in different experimental conditions. These are mathematical theorems, and they contain no mathematical errors. There is really no point in producing your theory...however many concepts it has... without first identifying an error in the theorem. My confidence in Bell's result arises from understanding the theorem. Other people in the contest who claim to "refute" Bell also demonstrate lack of comprehension of what he proved.
The GHZ case is simpler than the standard spin/polarizer cases because one does not have to worry about statistics. There are four possible experimental conditions and predictions about what will be observed under all four. And it is demonstrably impossible to reproduce those predictions using local physics. Since your socks--whether I put them on in the dark or not--are governed by local physics, they cannot reproduce the predictions.
There is actually nothing in your FQXi paper that explains how these socks are supposed to work, so nothing to analyze: just an assertion that everything is OK. If there really were a flaw in Bell's proof, the obvious thing to do is actually explain what is it, and if there is a local physical model violating the inequalities the thing to do is explain it. That is how a theory gain credibility.
Tim
