Bell's Theorem and Nonlocality

[quantum_wave]

quantum_wave:

By saying "space had to come first" I just meant that before anything happened, there had to have existed a pure non-material universal space. To me, that's intuitively rational. -If you don't agree that's your prerogative.

I've already discussed the hypothesis that prior to the first appearance of directional forces, space had a property of self-compatibility manifested by symmetric reciprocal oscillation of point localities.

OK, I'll exercise my perogative to disagree, unless you tell me where the space came from if it didn't always exist.

 

[brucep]

Alright, I decided to let this topic lapse because I felt that the facts I was stating here were being ignored by some of the people they were directed at, and that little interest in analyzing any of the arguments was being shown. Nonetheless, as I promised to do a few months ago, I shall demonstrate an example of the simple quantum calculations which correctly predict the results of Bell test experiments. Let's consider the simple experimental example involving measurements of entangled electron spins as already discussed in this topic. Experimentally, we know that the measurements are coincidental 75% of the time and opposite for the remaining 25%.

Suppose one of the electrons is measured along axis A (z-axis) with positive spin. We shall denote this spin state as $$|+z\rangle$$. Since the system is initialized in a spin-0 state, measurement on the first electron automatically sets the second electron to have negative spin along axis A, which we denote by the state $$|-z\rangle$$. If, just prior to measurement, the second apparatus randomly chooses axis B as the axis of measurement (at angle $$120^\circ$$ relative to A), we wish to calculate the probability of the second electron yielding a positive value for spin measurement along this axis.

Without loss of generality, suppose that axis B is produced by counter-clockwise rotating axis A $$120^\circ$$ in the x-z plane, and that a positive electron spin state along this axis is denoted by $$|+w\rangle$$. The desired probability we wish to calculate for coincidental spin measurements is given by $$\left|\langle-z|+w\rangle\right|^2$$.

First we must express $$+w\rangle$$ in the z-basis by performing an electron spin rotation:
$$|+w\rangle=e^{-\frac{i}{\hbar}\hat{S_y}\frac{2\pi}{3}}|+z\rangle$$, where $$\hat{S_y}$$ is the Pauli spin operator for the y-axis.

Converting spin z-basis to spin y-basis, we may write: $$|+z\rangle=\frac{1}{\sqrt{2}}\left(|+y\rangle+|-y\rangle\right)$$. Then we obtain:

$$|+w\rangle=\frac{1}{\sqrt{2}}\left(e^{-\frac{i}{\hbar}\frac{\hbar}{2}\frac{2\pi}{3}}|+y\rangle+e^{-\frac{i}{\hbar}\frac{-\hbar}{2}\frac{2\pi}{3}}|-y\rangle\right)=\frac{1}{\sqrt{2}}\left(e^{\frac{-i\pi}{3}}|+y\rangle+e^{\frac{i\pi}{3}}|-y\rangle\right)$$

Writing $$|+y\rangle=\frac{1}{\sqrt{2}}\left(|+z\rangle+i|-z\rangle\right)$$ and $$|-y\rangle=\frac{1}{\sqrt{2}}\left(|+z\rangle-i|-z\rangle\right)$$, we ultimately obtain the following:

$$|+w\rangle=\frac{1}{2}\left(e^{\frac{-i\pi}{3}}+e^{\frac{i\pi}{3}}\right)|+z\rangle+\frac{i}{2}\left(e^{\frac{-i\pi}{3}}-e^{\frac{i\pi}{3}}\right)|-z\rangle$$.

We may thus conclude: $$\langle-z|+w\rangle=\frac{i}{2}\left(e^{\frac{-i\pi}{3}}-e^{\frac{i\pi}{3}}\right)=\sin\left(\pi/3\right)=\frac{\sqrt{3}}{2}$$, and therefore $$\left|\langle-z|+w\rangle\right|^2=75\%$$

So the quantum mechanical prediction is for a 75% coincidence rate, 25% anti-coincidence rate, makes no assumptions about the specific details of the experiment, and precisely matches the experimental results. As proven earlier in this thread, any arbitrary local hidden variables theory requires at least a 33% anti-coincidence rate and is therefore experimentally falsified, but we can see that non-local quantum mechanics nails it without difficulty.

Your posts are, generally, very informative for me. Thanks for taking the time to write some stuff down.

 

[Schmelzer]

The Hidden Variables Interpretations (HVI) of Quantum Mechanics are held by people who think that there is a local explanation that will resolve the paradox between the predicted FTL and "local reality".

No. There are a lot of different hidden variable interpretations of QM, the most prominent are de Broglie-Bohm theory (Bohmian mechanics) and Nelsonian stochastics, recently entropic dynamics appeared. But they all share the property that they violate Einstein causality (thus, are "non-local" in the established sloppy language). Thus, they give exactly no hope for a compromise with "local" (Einstein-causal) realism.

 

[quantum_wave]

No. There are a lot of different hidden variable interpretations of QM, the most prominent are de Broglie-Bohm theory (Bohmian mechanics) and Nelsonian stochastics, recently entropic dynamics appeared. But they all share the property that they violate Einstein causality (thus, are "non-local" in the established sloppy language). Thus, they give exactly no hope for a compromise with "local" (Einstein-causal) realism.

A lot is said about hidden variables interpretations of quantum mechanics, but you can't say the end game is established, even if it seems to be so perfect in your mind. Much is not yet understood.


http://phys.org/news/2015-06-physicists-quantum-coherence-entanglement-sides.html


http://arxiv.org/pdf/1502.05876v4.pdf

 

[Schmelzer]

A lot is said about hidden variables interpretations of quantum mechanics, but you can't say the end game is established, even if it seems to be so perfect in your mind. Much is not yet understood.

The existing hidden variable theories are far away from being perfect, there is a lot of room for improvements, and I'm working on this. But Einstein-causal hidden variables are nothing worth to work on. They have no real chance.

 

[quantum_wave]

The existing hidden variable theories are far away from being perfect, there is a lot of room for improvements, and I'm working on this. But Einstein-causal hidden variables are nothing worth to work on. They have no real chance.

That is essentiall true. FYI, I distinguish between hidden variable theories (HVT) and hidden variables interpretations (HVI), as elaborated on earlier in this thread.

 

[Schmelzer]

A "local" hidden variable theory is one which not only suggests that hidden deterministic variables/properties are responsible for the apparently randomized behaviour of nature, but also restricts all forms of communication and interaction to propagating no faster than a certain speed, usually the speed of light.

A nice example illustrating the point that the notion "locality" is misleading and causes confusion. Because, I fully agree that how CptBork has interpreted it would be the natural way to interpret it. But in this case, we would have no chance to falsify local realistic theories, simply because there will always be upper limits for speed we are able to distinguish from infinite speed by observation, so, there will be always theories with sufficiently large limiting speed which are indistinguishable from theories with infinite speed by existing observation.

In fact, "local" in the misleading use of the actual mainstream means that speed of information transfer greater than c is forbidden. As if information transfer with c would be somehow local but information transfer with 1.1 c somehow nonlocal.

In general, local theories are the only hidden variable theories seriously considered by hidden variables proponents, because nonlocal deterministic theories, in which signals can exceed the speed of light, instantly run into problems with time paradoxes forming inside Relativity, a problem which does not occur in the probabilistic approach of quantum mechanics.

False. All the hidden variable theories considered today - de Broglie-Bohm theory, Nelsonian stochastics, entropic dynamics - are "nonlocal" in this misleading terminology. And they don't run into any paradoxes at all, not even if they consider relativistic fields, like Bohm has done already in his first paper, which contains a variant for the EM field.

All one needs for avoiding paradoxes is a hidden preferred frame. People may not like hidden things, but if they accept the idea of hidden variables, they have no reason to have a problem with hidden preferred frames. So, the following:

The value of Bell's Theorem is that it provides us with a way to conclusively demonstrate that nonlocal effects do indeed occur in nature, thus leaving us with only two choices for an explanation: 1) A nonlocal hidden variable theory which generates time paradoxes in Relativity, or 2) quantum mechanics which, in its modern quantum field theory formulation, incorporates Special Relativity as a vital component, or else some other theory based on a probabilistic interpretation of the universe.

is simply wrong.

Would you like me to give a brief overview and derivation of Bell's Theorem in its basic form, or would you like to start by introducing the postulates for your hidden variable theory?

I could accept this challenge myself too.

Given that I have already a publication in the Annalen der Physik which defends Bell's theorem against a "refutation" which has succeeded to be published, and actually also engaged in the defense of Bell against "refutations" in http://www.sciphysicsforums.com I don't need any intro to Bell's theorem and would start with introducing some basic ideas for a hidden variable theory.

The first and conceptually most important "hidden variable" would be absolute time. It would be approximately the same as the time after Big Bang of something in rest relative to CMBR, and, more accurate, it would be described by the harmonic equation. Thus, is not really hidden for practical purposes.

 

[Schmelzer]

Bell's theorem has nothing whatsoever to do with any of that. Bell's own view was that his theorem indicated a potentially disturbing incompatibility between quantum physics and relativistic causality, and not that it implied space was an "aether" or anything like that. Even there, that Bell expressed this view does not mean anyone reading it is obligated to agree with it.

One does not need much more to end up with an ether.

All one needs is a complete causal theory - causal in the sense of Reichenbachs principle of common cause, and of the non-existence of causal loops.

Then, Reichenbach's principle of common cause gives us that for the observable correlation A = -B there has to be a causal explanation, which is or a causal influence A->B, or B->A, or some common cause C->A, C->B. Then, Bell's theorem shows that the common cause explanation leads to Bell's inequalities, thus, can be excluded experimentally. It remains or A->B, or B->A. If QM is universally true, this holds for arbitrary pairs of events, except for may be some degenerated cases of measure 0.

Above A->B and B->A cannot be true at the same time, this would be a causal loop. Thus, a causal theory has to tell us what is true - A->B or B->A, for all pairs of events, else it would not be complete. Then, if there are no causal loops, the relation A->B defines an order. The future of A, F(A) is what can be influenced causally by A, the past P(A) what can causally influence A, and the present is the intersection of their closures, and given that for every event B there is arbitrary close some event B' so that Bell's inequality is violated for (A,B'), B' is or in the past or the future, thus, B or in the closure of the future or of the past, thus, itself of past, present or future.

Thus, a complete causal theory contains a preferred time-like foliation.

The next step, given a preferred foliation, is the ADM decomposition of the metric into a scalar field, a three-vector field, and a three-metric. One can, then, try to interpret them as density, velocity, and stress tensor of the ether.

 

[Michael Anteski]

In the ether model I have given on page 11, Time is the rate of vibration of the elemental ether units in a given cosmic macrocosmic region. Thus, the regional energic setting would be what determines the time rate. -In a relatively-etheric, less magnetically-energized, setting such as outer space, the rate time passes would be slower than in regions near a body like Earth, which has a magnetic field. (In my model, Earth's magnetic field is stronger, and more etheric, than currently believed by science.) -Also, in my model, another factor determining the rate of time as measured by a clock inside a moving vehicle such as a satellite, would be the velocity of the vehicle, which would affect the degree of etheric resonations between the etheric constituents of the clock and the ambient ether outside. -The faster the velocity, the greater the interaction with the ambient ether, and the slower the time rate of the clock.

A theoretic point of interest in this model for time would be that if a clock is located within a relatively-more etheric zone, perhaps due to proximity to an extraterrestrial ether technology below ground, a clock's etheric constituents could slow the clock's time rate, because the "etherized" clock would be in resonance with the less-magnetically energized, more-etheric, outer space ether, through resonances transmitted between highly-etheric regions. -This can explain why a clock runs slower at a lower elevation above the surface of earth, while it runs faster at higher elevations, where the magnetic field is exerting its influence.

 

[brucep]

In the ether model I have given on page 11, Time is the rate of vibration of the elemental ether units in a given cosmic macrocosmic region. Thus, the regional energic setting would be what determines the time rate. -In a relatively-etheric, less magnetically-energized, setting such as outer space, the rate time passes would be slower than in regions near a body like Earth, which has a magnetic field. (In my model, Earth's magnetic field is stronger, and more etheric, than currently believed by science.) -Also, in my model, another factor determining the rate of time as measured by a clock inside a moving vehicle such as a satellite, would be the velocity of the vehicle, which would affect the degree of etheric resonations between the etheric constituents of the clock and the ambient ether outside. -The faster the velocity, the greater the interaction with the ambient ether, and the slower the time rate of the clock.

A theoretic point of interest in this model for time would be that if a clock is located within a relatively-more etheric zone, perhaps due to proximity to an extraterrestrial ether technology below ground, a clock's etheric constituents could slow the clock's time rate, because the "etherized" clock would be in resonance with the less-magnetically energized, more-etheric, outer space ether, through resonances transmitted between highly-etheric regions. -This can explain why a clock runs slower at a lower elevation above the surface of earth, while it runs faster at higher elevations, where the magnetic field is exerting its influence.

LOL. GR explains [predicts] the proper tick rate of clocks without the need for "highly etheric regions" or magnetic fields. LOL. "Etherized " clock. LOL.

 

[CptBork]

Hidden variables are contained in such a universe, but our lack of knowledge and understaning of that universe and the hidden variables at work, makes it impossible to describe a local hidden variables theory that would properly convey them, and so the mathematical proof cannot correspond precisely to reality until all of the unknowns are resolved.

Isn't this the exact same hand-waving argument you've been giving us all along? It doesn't matter what unknowns remain to be resolved, because Bell's Theorem requires that at least some of those unknowns would have to be nonlocal (communicating faster than light) in order to match existing experiments, regardless of the specific details of the deterministic theory in question.

 

[CptBork]

A nice example illustrating the point that the notion "locality" is misleading and causes confusion. Because, I fully agree that how CptBork has interpreted it would be the natural way to interpret it. But in this case, we would have no chance to falsify local realistic theories, simply because there will always be upper limits for speed we are able to distinguish from infinite speed by observation, so, there will be always theories with sufficiently large limiting speed which are indistinguishable from theories with infinite speed by existing observation.

In fact, "local" in the misleading use of the actual mainstream means that speed of information transfer greater than c is forbidden. As if information transfer with c would be somehow local but information transfer with 1.1 c somehow nonlocal

I believe I've specified earlier in this thread that my arguments here don't themselves support the notion of instantaneous communication, but they do punch a gaping hole in the notion of a causal universe with communications limited to the speed of light. Last I checked, Quantum Wave continues to insist on the speed of light being a universal limit in accordance with the Theory of Relativity. On the other hand, if you're willing to disregard $$c$$ as a universal limit, then you run into serious problems with Relativistic causality. Furthermore, with any faster-than-light communication you can always find a physical reference frame in which that communication appears instantaneous, so Relativity truly does dichotomize everything into either local or nonlocal.

False. All the hidden variable theories considered today - de Broglie-Bohm theory, Nelsonian stochastics, entropic dynamics - are "nonlocal" in this misleading terminology. And they don't run into any paradoxes at all, not even if they consider relativistic fields, like Bohm has done already in his first paper, which contains a variant for the EM field.

As far as I'm aware, the only working alternatives to the Copenhagen interpretation of QM are those which attribute the quantum randomness to the hidden actions of mathematical leprechauns whose own deterministic mechanics have yet to be specified.

 

[Schmelzer]

As the best description of Bell's theorem I have seen yet (of course, except of my own popular game http://ilja-schmelzer.de/realism/game.php ;-) I would recommend
Norsen T., Bell Locality and the Nonlocal Character of Nature, Foundations of Physics Letters, 19(7), 633-655 (2006), arxiv:0601205[quant-ph].

Essentially, it makes quite clear that determinism, as far as one needs it in the proof of Bell's theorem, is derived by the EPR argument from what I would simply name Einstein causality, and Norsen names Bell locality.

 

[Schmelzer]

On the other hand, if you're willing to disregard $$c$$ as a universal limit, then you run into serious problems with Relativistic causality. Furthermore, with any faster-than-light communication you can always find a physical reference frame in which that communication appears instantaneous, so Relativity truly does dichotomize everything into either local or nonlocal.

This is problematic only if I consider Lorentz symmetry as some true, fundamental symmetry of Nature. I don't. For me, it is simply the natural symmetry group of a wave equation, and covers everything which distributes following this wave equation, nothing more. So, on a fundamental level, it does not hold, and there will be a preferred frame. In this preferred frame, there may be another maximal limiting speed, much greater than c, and nonetheless the theory would be "local" in any meaningful interpretation of the word.

As far as I'm aware, the only working alternatives to the Copenhagen interpretation of QM are those which attribute the quantum randomness to the hidden actions of mathematical leprechauns whose own deterministic mechanics have yet to be specified.

No. In de Broglie-Bohm theory, which is deterministic, all the laws are well specified.

It requires a preferred frame, but in any other sense it does not have any problems with relativity.

 

[Michael Anteski]

LOL. GR explains [predicts] the proper tick rate of clocks without the need for "highly etheric regions" or magnetic fields. LOL. "Etherized " clock. LOL.

I didn't refer to ticking clocks in orbiting satellites. Atomic clocks and light-energy clocks have been used. -I may have also tried to oversimplify how my ether model would treat the question of the effects of motion on the time rate of the clock. -Leaving the stationary, the clock's auric resonances, being put into motion, the clock's magnetic resonances with its surroundings would be broken, and its magnetic auric resonance would be mainly with the vehicle itself. -I would not attempt to sort out the various gravitational and magnetic etheric/auric resonances for the clock in motion, in any detail. We still are not able to detect the ether.

 

[Schmelzer]

Michael, why do you play around with your own unprofessional ether theory if there is a simple professional one which is published?

To avoid any discussions with various doubters, you can use its simplest variant, the limit X,Z->0 of my published theory, which simply includes the Einstein equations of GR themself. With these equations, you will have no problems with experiments which the GR supporters claim support GR at all. Then, you can simply add the hypothesis that there exist preferred coordinates - and remember how they are named, harmonic coordinates. The formula for them is $$\partial_m (g^{mn}\sqrt{-g}) = 0$$. If necessary, you can easily survive a discussion with those who think no preferred coordinates exist: The preferred coordinates are simply coordinates where the equations become much easier - nobody forbids to use other coordinates, say, in Newtonian theory too. But the harmonic coordinates really simplify the Einstein equations.

Then, to obtain the ether, you can simply use the equations $$\rho = g^{00}\sqrt{-g}, v^i = g^{0i}/g^{00}, \rho v^i v^j + \sigma^{ij} = g^{ij}\sqrt{-g}$$, which define density, velocity, and stress tensor of the ether. The condition that the ether density is positive is, then, simply that the time coordinate is time-like. And, this was the point of these strange identifications, you obtain classical continuity and Euler equations for the ether:
$$\partial_t \rho + \partial_i (\rho v^i) = 0 \quad \partial_t \rho v^i + \partial_i (\rho v^i v^j + \sigma^{ij}) = 0$$.

The formula for clock time is, then, simply the standard GR formula for this.

 

[Michael Anteski]

Michael, why do you play around with your own unprofessional ether theory if there is a simple professional one which is published?

To avoid any discussions with various doubters, you can use its simplest variant, the limit X,Z->0 of my published theory, which simply includes the Einstein equations of GR themself. With these equations, you will have no problems with experiments which the GR supporters claim support GR at all. Then, you can simply add the hypothesis that there exist preferred coordinates - and remember how they are named, harmonic coordinates. The formula for them is $$\partial_m (g^{mn}\sqrt{-g}) = 0$$. If necessary, you can easily survive a discussion with those who think no preferred coordinates exist: The preferred coordinates are simply coordinates where the equations become much easier - nobody forbids to use other coordinates, say, in Newtonian theory too. But the harmonic coordinates really simplify the Einstein equations.

Then, to obtain the ether, you can simply use the equations $$\rho = g^{00}\sqrt{-g}, v^i = g^{0i}/g^{00}, \rho v^i v^j + \sigma^{ij} = g^{ij}\sqrt{-g}$$, which define density, velocity, and stress tensor of the ether. The condition that the ether density is positive is, then, simply that the time coordinate is time-like. And, this was the point of these strange identifications, you obtain classical continuity and Euler equations for the ether:
$$\partial_t \rho + \partial_i (\rho v^i) = 0 \quad \partial_t \rho v^i + \partial_i (\rho v^i v^j + \sigma^{ij}) = 0$$.

The formula for clock time is, then, simply the standard GR formula for this.

My point is that this is a question of ether theory versus standard theory over a wide range of phenomena, not just Time. -The model I outline here, of etheric/auric magnetic energic forces, can, as another example, address the phenomenon of spontaneous human combustion (SHC), which standard theory cannot. -In a typical case, an elderly victim, who may have spotty arterial degenerative disease, suffers a case of SHC, which typically begins in a certain spot on the body. -Applying the model for etheric auras, the explanation would be that an abnormal portion of the victim's aura where the SHC began had undergone a change in which there was an abnormal resonance of auric energy between the victim's aura and a second aura belonging to an object (for example, a TV set near the victim), with a buildup of energy in that part of the body, leading to spontaneous combustion.

 

[CptBork]

This is problematic only if I consider Lorentz symmetry as some true, fundamental symmetry of Nature. I don't. For me, it is simply the natural symmetry group of a wave equation, and covers everything which distributes following this wave equation, nothing more. So, on a fundamental level, it does not hold, and there will be a preferred frame. In this preferred frame, there may be another maximal limiting speed, much greater than c, and nonetheless the theory would be "local" in any meaningful interpretation of the word

Well most of my arguments here have been addressing Quantum Wave's and similar ideas, which retain the core features of Relativity but attempt to do away with the concept of Quantum randomness, the Big Bang and other theoretical concepts they don't like. As for your own approach, the laws of Relativity aren't set in stone, but you're only offering "maybe's" as an alternative. When your theory can explain results such as the Bell experiments and other established quantum phenomena, and can answer all the questions as to what we're supposed to replace Relativity with, only then can you claim to have a working theory. Right now it sounds like you only have an outline of what you'll hope to achieve based on modifying previously unsuccessful approaches, but hopes don't amount to a math proof.

No. In de Broglie-Bohm theory, which is deterministic, all the laws are well specified.

It requires a preferred frame, but in any other sense it does not have any problems with relativity.

To my understanding, all it does is sweep the randomness seen in experiments under the rug by attributing it to hidden players we can't directly observe. According to this same understanding, deterministic mechanisms have never been specified in such a way as to produce the required statistical outcomes. In pilot wave theory, I haven't seen or heard of any specification whatsoever as to how the pilot wave decides in advance what it's ultimately going to collapse to or how it's going to guide the accompanying particle.

 

[brucep]

I didn't refer to ticking clocks in orbiting satellites. Atomic clocks and light-energy clocks have been used. -I may have also tried to oversimplify how my ether model would treat the question of the effects of motion on the time rate of the clock. -Leaving the stationary, the clock's auric resonances, being put into motion, the clock's magnetic resonances with its surroundings would be broken, and its magnetic auric resonance would be mainly with the vehicle itself. -I would not attempt to sort out the various gravitational and magnetic etheric/auric resonances for the clock in motion, in any detail. We still are not able to detect the ether.

You should have since that's a theoretical prediction that gets verified 24/7 . All you're doing is spewing a bunch of nonsense. Commonly referred to as word salad.

 

[arfa brane]

I think there's a little confusion too, about measurements of quantum states. CptBork presents an experimental setup in a lab where we can assume that both measurers can define the same direction for 'up'.

But the measurements and the particles can be separated by any distance, say a number of light years, in which case, how do they maintain the same direction for 'up' or any other axis they choose? The answer seems to be, they can't preserve their initial orientations, and measurement direction is therefore completely arbitrary for both measurers.

Suppose that two spin-1/2 particles are produced by a the decay of a spin-0 particle at some central point, and that the two move directly outwards in opposite directions. By conservation of angular momentum, the spins (of say an electron and positron) must sum to zero. The two particles could be light-years apart, yet a choice of measurement on one particle seems instantaneously to fix the spin axis of the other.

.

The key then seems to be a pair of identical devices, with say, the three axes of measurement separated by 120°. But that isn't a necessary condition, although it's a sufficient one.