Essay Abstract

This paper shows a backwards-in-time solution to Bell's Theorem. This solution assumes that antiparticles actually do travel backwards in time and therefore the experiment begins not at the usual source of particle pairs but at (say) Alice's measurement of a positron and ends at Bob's measurement of the electron. A second assumption is that the distribution of hidden variables in a polarised beam can be inferred using Malus Law. Once that is assumed, the simple calculations used in Malus Law complete the proof. If Alice measures the positrons then the electrons travelling to Bob are polarised either along Alice's vector a or along -a. So Bob's apparatus is acting like a Malus filter taking a polarised beam as input. However, although this arrangement satisfies the result of a Bell experiment having a correlation between Alice's and Bob's measurements of -cos θ, and uses the local hidden variables of particles, it is impossible to simulate the experiment using individualised local hidden variables. This is because of a disconnect in knowledge about the hidden variable vector of an individual particle after a measurement by a Stern - Gerlach detector apparatus or a filter. The polarisation state, if any, of the incoming beam of positrons is unknown. After measurement by Alice they are polarised along vector a, and after measurement by Bob the electrons are polarised along vector b. But the correlation is between the unknown hidden variables before Alice makes the measurement and the polarised beam measured by Bob. It is impossible to follow an individual hidden vector through these measurements even in a simulation.

Author Bio

Retired researcher into school examinations with a UK examining board. My B.Sc. degree is in mathematics and statistics.

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Dear

Your nice essay is telling that time travel into past is impossible even to simulate, well said that.

For support your words............ In conclusion, the results of a time-reversed Bell experiment is explainable without the complication of entanglement. The explanation cannot be simulated using individualised local hidden variables but can be explainable using a probabilistic treatment of local hidden variables......... and ........It is impossible to follow an individual hidden vector through these measurements even in a simulation.......

You analised correctly!!

In Dynamic Universe Model also , there is no traveling back in time!!

Hope you can spend a little time on my essay "A properly deciding, Computing and Predicting new theory's Philosophy" and give your valuable comments

Best Regards

=snp

    Dear Mr Gupta

    Thank you for your generous comments.

    I agree that my conclusion for the reverse-time Bell experiment is not good for showing the existence of local hidden variables, even with time reversed for antiparticles. But the use of local hidden variables to explain the normal Bell experiment result is also not apparent under the QM explanation. However, my essay suggests that Malus Law can be explained (under certain assumptions) using local hidden variables. And, incidentally, this would not need any time reversals. These assumptions are that the actual state of an electron/positron is not necessarily exactly identical to the state supposedly imposed upon it. I am suggesting/ assuming that the actual prepared state of a photon is not necessarily exactly in the direction of its preparation. And that the statistical distribution of the actual states can be reverse engineered using Malus Law. Using a classical analogy, prepare the state of a box by spinning it around its long axis. It can stay in that prepared state after preparation. But if you spin a box about its intermediate length axis, then it does not stay in its intended preparation spin state.

    How does one know that a particle actually has the intended prepared spin state? I have insufficient expertise to be absolutely sure about this, but I can only think of making a check measurement of its spin state say using an S-G apparatus. According to my calculations, the group of photons in the distribution of states in my calculations will behave exactly like a group of photons all individually prepared pointing exactly along the preparation vector.

    Reversed time for antiparticles is a matter on which I could comment later maybe. I am ambivalent about it, and also about the signs of mass and energy for antiparticles and others. I did have more in my earlier draft of the essay on these issues but pruned them down.

    I have already read your essay and also one of your online papers and will in due course comment on your very busy page. I was interested in your online take on cyclic universes but am not sure about some of your other points for example about BHs and complex i.

    Best wishes

    Austin

    7 days later

    Some additional notes.

    Malus's Law has results as two intensities, adding to 100%, and so having only one degree of freedom. Photons passing through a filter (at any set angle) and those which do not pass. So the results fit into a 2x1 table. If we repeat that experiment, at the same set angle, then the second set of results also forms an (ideally) identical 2x1 table. There are no further degrees of freedom available so the two tables can be joined into a composite single contingency table with a total of only one degree of freedom. This would look identical to the 2x2 contingency table for a restricted Bell test experiment where Alice and Bob chose only one angle each for their measurements.

    The results of the composite Malus tables can be converted from intensities into correlation coefficients in the normal way done in a Bell test. Take the proportion in the table with the degree of freedom. Say this is p. Then, as a short cut, the Bell correlation is 4*p - 1.

    If actual Malus results are treated this way then the artificial Bell correlation matches genuine Bell correlations for the same angles. (Beware that angles for electrons and photons need to be adjusted in order to be comparable.)

    However, the Malus test requires that the inputted beams are polarised. The Bell test assumes random beams from a source but with Alice and Bob receiving particles entangled after pair particle creation. Random entangled beams, with local hidden variables, in my previous simulations never produced the desired Bell results. But if Alice and Bob received polarised beams then using local hidden variables, the desired Bell result would be found. So we would have locality and hidden variables but would not need entanglement nor any fishy action-at-a-distance.

    But the price to pay for acquiring polarised beams inputted into a Bell test is that the antiparticles need to be travelling backwards in time.

    The connection to the essay competition theme is that it is impossible to track a hidden variable from before an interaction to after that interaction. So we still have locality, but in an untrackable form.

    Austin,

    I think your analysis is both interesting and solid. What I found most interesting about it is that you used starting points that are very different from the ones taught in physics classes on these issues, yet came to conclusions that are not much different from some much more complicated analyses of similar issues. I think your use of antiparticles going backward in time to explain Bell's inequality is actually quite viable, and reminiscent both of what Wheeler and Feynman did in their pre-QED advanced-retarded photon work. The point you are making (I think?) is this: If you can travel both ways in time, speed of light constraints become meaningless, and you can almost trivially get correlations. Not only is that analytically a valid argument, I'm pretty sure it's functionally equivalent to how Feynman QED calculations would end up modeling Bell's inequality, if you put them to that particular use. I've not done any search for paper on QED modeling of Bell's inequality, though.

    While I'm very familiar with it mathematically, I did not know that the rule for polarized light was called Malus' law, or that it went back more than two centuries. Intriguing! Since for photons the electromagnetic wave function and the quantum wave function are isomorphic (or something-morphic, I'm terrible with morphies), Malus was in effect one of the earliest researchers in quantum mechanics and the behavior of quantum wave functions! The behaviors of good ol' sunglasses-and-3D-movie-screens (linear and circular polarized light) are not classical at all: They are point-blank, in-your-face examples of quantum amplitudes and probabilities operating at human sensory levels, in literally observable ways. Thus your application of Malus' law for a quantum situation amounts to a rather ingenious invocation of standard quantum amplitude and probability rules, only starting with observations dating from over a century before quantum mechanics proper even acquired a name! I like that.

    I'm going to go out on a limb a bit and guess that even though your don't come right out and say it in your abstract, the connection between your novel approach to Bell's inequality and is in your last sentence in the abstract:

    "It is impossible to follow an individual hidden vector through these measurements even in a simulation.

    Thus I think that if I had to suggest an opening sentence for your essay that was more specific in defining how your essay is relevant to to this year's FQXi theme, and gussied it up with some terms that mean what you are saying but are taken from a broader literature set, my suggested first sentence for your abstract would look something like this:

    "In this essay I show that if you simply assume that Wheeler-Feynman style retrocausal interactions are an inherent component of Bell inequality dynamics, then unpredictability of the outcomes becomes an inherent and unavoidable consequence in all situations. This is true even if quasi-classical hidden variable models are assumed, and in fact this approach allows such models to meet Bell's inequality even while using hidden variables. Thus in this analysis, indeterminacy becomes a deep and unavoidable consequence of how quantum mechanics works in our universe."

    Terry

    Thank you for your kind comments on my essay.

    You mentioned: "reminiscent both of what Wheeler and Feynman did in their pre-QED advanced-retarded photon work". I have long had a copy, in book form, of Feynman's thesis so I am aware of advanced and retarded waves in time. You also mentioned on your essay website page that John Cramer's TIQM may be relevant in a similar way. I can now see that to be the case. However, I specifically have the electron travelling forward in time and the positron travelling backward in time whereas advanced and retarded waves may be more complicated than that. For example a photon travelling forward in time from A to B using minimum action has a transaction between A and B which implies B influences the photon even as it leaves A. My preon model was not used in my essay but it has an interesting property with respect to matter and antimatter that each individual standard model particle, for fermions and bosons, is composed of an equal number of matter and antimatter preons. And if positrons travel backwards in time then antimatter preons may do so too. This means that all particles are travelling in both time directions equally! This might make it more clear that even a single particle can, in my preon model, negotiate with both forwards and backwards-in-time influences in its own right. Which seems a positive point. However, preons are not the ones being acted upon direct by EM forces. And the observer standpoint always needs to be born in mind. The positron could be travelling backwards in time as a single entity while the preons inside it are travelling both ways in time. This could be similar to our universe having its own time direction, set by entropy increase, while still having antiparticles travelling backwards in time. Indeed, my idea of a time direction for an electron is actually a time direction within the electron, similar to the time direction of the universe in a particle-universe equivalence model. This would require electrons to have extended substance (ie preons)and to have internal processes ongoing such as entropy increase within the electron. This is similar for particles to the lifetimes of the universe in the Penrose CCC model. Measurement of an electron would involve catastrophic breakdown of its internal space metric (similar to that in CCC) and that process would not enable the electron position at point B to be calculable for an individual electron.

    You wrote: "If you can travel both ways in time, speed of light constraints become meaningless, and you can almost trivially get correlations. " Well, yes, the speed of light constraints do trivially disappear. But, the correlations only arise because the incoming beam of electrons to Bob has been polarised.

    I am glad that you liked the use of a 200 year old formula! I used Malus as I wanted to try to move away from all the Bell philosophical baggage. I have long had a hang up that complicated Bell experiments had issues with measurement loopholes. But I have no such hang up about Malus experiments. Yet I noticed that my simple simulations for Bell could not break the inequality (by getting correlation = 0.707 at 45 degrees for electrons). But neither could I get an intensity greater than 0.75 for Malus at 45 degrees for electrons, which is equivalent to the mundane classical correlation of 0.5. That led direct to the work comparing Bell with Malus. And then I realised that by time reversal for antiparticles I could get polarisation and hence QM results for Bell.

    Thank you for suggesting an opening wording for my essay: ""In this essay I show that if you simply assume that Wheeler-Feynman style retrocausal interactions are an inherent component of Bell inequality dynamics, then unpredictability of the outcomes becomes an inherent and unavoidable consequence in all situations. This is true even if quasi-classical hidden variable models are assumed, and in fact this approach allows such models to meet Bell's inequality even while using hidden variables. Thus in this analysis, indeterminacy becomes a deep and unavoidable consequence of how quantum mechanics works in our universe."

    I like the glossiness of this text but it does not sound like me, alas. I would only point to one ambiguity. The way I read this, it implies that unpredictability only arises from retrocausal interactions. IMO unpredictability can also be found without retrocausality. (However in my preon model I am not sure if an absence of retrocausality can exist anywhere.) I see unpredictability in the loss of wavefunction of a particle being exactly similar to the catastrophic loss of the space metric in the universe at the end of a CCC cycle. (Particle being equivalent to a universe.) By analogy if a soap bubble could retain unitary on catastrophic bursting, how could one calculate where that single final point would be? I do have a paper on this which can be found by a google search using my name and 'Rasch'. In the paper, I make metrics for various conditions of data. Some metrics embrace all the data, but some have catastrophic gaps where not all data are placed in the metric. The condition where the metric breaks down is where the data are widely separated from one another in space. This is exactly what occurs at the end of a cycle in CCC.

    10 days later

    Austin:

    A new era dawns.聽 Old questions become quaint and historical.聽 Is the whole community ready?聽 Or is physical reality too dangerous for our collective understanding at this time?聽

    I added this comment at https://fqxi.org/community/forum/topic/3550

    which is the page of Gyongyi Bokor

    Some of your ideas have resonance with my essay in which antimatter is suggested to travel backwards in time. In my essay I bypass Bell's Theorem by the use of antimatter travelling backwards in time. Bell's Theorem is absolutely correct of course in normal circumstances. By normal I mean for matter of every type travelling forwards in time. Bell's Theorem correctly rules out local hidden variables of particles but is IMO bypassed for antimatter travelling backwards in time as (if say for simplicity that Alice measures only antiparticles) Alice measures antiparticles travelling (from afar and inwards) towards the source of (supposed) creation of the particle pairs. So the correlation is not really between entangled pairs because Alice is measuring antiparticles well before they become entangled. They are only entangled between the Source and Alice. In relevance to the essay set theme, the hidden variables are not track-able through a measurement. So there is no way that Alice's measurement on a particular antiparticle can be followed through to a particular measurement by Bob on a particular particle. That introduces probability into the measurements which means that counterfactual determinism cannot be true in this context. Hence the Quantum Randi challenge cannot be beaten. The explanation for that is not that locality is forbidden but is that: antiparticles travel backwards in time; the particle pairs at the time of measurement are not entangled; the local hidden variables can exist and cause the results which exceed Bell Inequalities; but hidden variables travelling through a measurement are not computable. Further, the experimental results in this context are trivially correct and are in accordance with Malus Law, as the effect of the entanglement near the source is to provide Bob with a source of particles pre-polarised along Alice's detector's vector setting.

    I have not thought much about BHs and wormholes which are covered in your essay. I do have a paper, though, suggesting that dark energy (and dark matter) is caused by negative mass particles. See the professional paper by Farnes on this also. These DE particles are not necessarily antimatter but if they were to be then the accelerating expansion of the universe is being driven by antimatter. Antimatter as DE would also repel itself to the far distance. But if one adds in time reversal as well as negative mass, then from the point of view of an antiparticle ....? It is moving through time (which it can only view as forward) and instead of repelling matter it is attracting it. (Does it think it has derived from a point source anti-BB?) When it finds matter and examines it closely it will realise it is not matter but antimatter. Will it think that the universe is a bit short on content of what it considers to be antimatter? (Whereas in my scenario there is an equal balance but an unequal distribution in space and time). Need to think much more on this ... so thank you for your thought-provoking essay.

    Austin Fearnley