@Miroslav

I will try to answer Miroslav. The problem dates back longtime ago (in the 1930s) when Einstein was not at all pleased with the Copenhagen interpretation of quantum mechanics (wave mechanics at that time) laid out by Niels Bohr, and especially with its probabilistic nature.  Einstein was convinced that quantum mechanics (QM) is an incomplete picture of the microscopic world, and he strongly believed that the probabilistic nature of  QM is the outcome of our limited (specific) knowledge. The Einstein-Podolsky-Rosen (EPR) paradox (1935) is a challenge of Einstein addressed to Bohr (other challenges were lauched at the Solvay Conferences in 1927 and 1930) and the adepts of the Copenhagen interpretation, in an attempt to prove the existence of "hidden variables" in QM, that would enable the experimenter to predict the outcome of an experiment with certainty. In other words, Einstein was trying to prove that QM might also have a deterministic nature, such as classical mechanics. In this gedanken experiment, Einstein emphasizes that 'orthodox' Copenhagen interpretation of QM would imply "spooky, action-at-distance effects". Focusing on the entangled states coined in by E. Schrodinger (the "dead" and "alive" cat),  Einstein shows that such a 'picture' calls for "faster than light" influence between separated parts of a quantum system, which he utterly disagreed. This is why such a concept  contradicts relativity. David Bohm is the one to have tested the "EPR experiment" using an atom at rest that is stimulated to emit two photons simultaneously and two polaroid detectors located at large distance (with respect to the other).  If you have a space distribution of electric charges, Maxwell's theory says that any "perturbation" or force exerted upon one of these charges will be transmitted by the electric field with the speed of light.  The idea that such action exerted on a specific charge would instantaneously affect charges located at very large distance can not be taken into consideration. The response of Bohr was very unpleasing to Einstein, because it said that both the polarizers and photons have to be considered as "a single quantum system" and that it would make no sense to talk about the effect of a measurement performed, with respect to the other part of the system. Bohr's 'explanation' intrinsically implied that QM must exhibit 'exotic' action at distance properties. After that we can talk about the Bell inequality and how it enabled to put QM at test. The experiments performed 40 years ago by Alain Aspect and his team, aimed at measuring EPR correlations, have proved that Bell's inequality was violated while showing that QM predictions agree with experimental data. Fortunately, violations of Bell's inequality clearly prove that no hidden variable theory is validated by experiment. And the action-at-distance property is definitely out of the question, which is in agreement with the theory of (general) relativity.     

The first problem Francis is that non-locality does not only apply to photons,it applies to other massive particles e.g Leptons,Hadrons e.t.c..

To prove that the non-locality of photons has to do with the relativistic considerations you have put forth,it would be important to come up with some form of transformation law,possibly based on the lorentz transformations, that would show how non locality of photons in their own "frame of reference" transforms into the non-locality observed.

Carringtone, i was only thinking of photons. Of course, it doesn't work for massive particles -- unless you think of the de Broglie wave associated with them. The phase speed of these waves is c^2/v according to special relativity (see Wolfgang Rindler's on relativity and cosmology), where v is the speed of the particle (possibly the group speed of the wave?). I've wondered for some time if the de Broglie phase speed is the connection between entangled particles and the mechanism by which the so-called collapse of the wave function occurs. Note that for photons the de Broglie phase speed is the same as the particle speed, that is, c. Because of the Lorentz transformation of spacetime, there is no need for a faster than light collapse of the wave function of correlated photons. This is all speculation, of course.

Hi colleagues,

"Quantum action at a distance" cannot exist BECAUSE it contradicts relativity. "Quantum nonlocality" is a very bad and confusing term for correlations that violate Bell's inequalities. This kind of correlation IN CLASSICAL MECHANICS would imply action at a distance. Bell stipulates that BECAUSE of this fact violation of his inequalities allows one to experimentally distinguish - and reject - hidden variable theories from QM.

@Plimak,

>"Quantum action at a distance" cannot exist BECAUSE it contradicts relativity.

@Miroslav

I will try to answer Miroslav. The problem dates back longtime ago (in the 1930s) when Einstein was not at all pleased with the Copenhagen interpretation of quantum mechanics (wave mechanics at that time) laid out by Niels Bohr, and especially with its probabilistic nature.  Einstein was convinced that quantum mechanics (QM) is an incomplete picture of the microscopic world, and he strongly believed that the probabilistic nature of  QM is the outcome of our limited (specific) knowledge. The Einstein-Podolsky-Rosen (EPR) paradox (1935) is a challenge of Einstein addressed to Bohr (other challenges were lauched at the Solvay Conferences in 1927 and 1930) and the adepts of the Copenhagen interpretation, in an attempt to prove the existence of "hidden variables" in QM, that would enable the experimenter to predict the outcome of an experiment with certainty. In other words, Einstein was trying to prove that QM might also have a deterministic nature, such as classical mechanics. In this gedanken experiment, Einstein emphasizes that 'orthodox' Copenhagen interpretation of QM would imply "spooky, action-at-distance effects". Focusing on the entangled states coined in by E. Schrodinger (the "dead" and "alive" cat),  Einstein shows that such a 'picture' calls for "faster than light" influence between separated parts of a quantum system, which he utterly disagreed. This is why such a concept  contradicts relativity. David Bohm is the one to have tested the "EPR experiment" using an atom at rest that is stimulated to emit two photons simultaneously and two polaroid detectors located at large distance (with respect to the other).  If you have a space distribution of electric charges, Maxwell's theory says that any "perturbation" or force exerted upon one of these charges will be transmitted by the electric field with the speed of light.  The idea that such action exerted on a specific charge would instantaneously affect charges located at very large distance can not be taken into consideration. The response of Bohr was very unpleasing to Einstein, because it said that both the polarizers and photons have to be considered as "a single quantum system" and that it would make no sense to talk about the effect of a measurement performed, with respect to the other part of the system. Bohr's 'explanation' intrinsically implied that QM must exhibit 'exotic' action at distance properties. After that we can talk about the Bell inequality and how it enabled to put QM at test. The experiments performed 40 years ago by Alain Aspect and his team, aimed at measuring EPR correlations, have proved that Bell's inequality was violated while showing that QM predictions agree with experimental data. Fortunately, violations of Bell's inequality clearly prove that no hidden variable theory is validated by experiment. And the action-at-distance property is definitely out of the question, which is in agreement with the theory of (general) relativity.     

Dear @Bogdan,

thank you, but you see, I am a physicist, I know all that stuff already. My point is something different. I am talking about ill defined concepts, unproved statements, etc. Here is one, you write:

"Bohr's 'explanation' intrinsically implied that QM must exhibit 'exotic' action at distance properties."

Must? No, it must not! In my world "must" means "there is no any other possibility", so, please, prove your statement. 

Or, define "action at distance". It means that A measures spin at point A, B measures spin of ent. particle at point B, but before that, from A travels some signal that interacts with particle at B and produces the opposite spin with certainty? Interesting. I'd like to know about such an interaction. So, my question stays: what contradicts the principle of relativity? Define such an "action", give me mathematical properties and I'll listen. For a while, I choose to be really careful about conclusions.

Best wishes,

Miroslav

Dear @Miroslav,

I will try to summarize your point of view. It seems that you are looking for a deterministic Quantum Mechanics (QM), contrary to the experimentally proven probabilistic nature of QM. As long as the only approach to describe a quantum mechanical system is made using the associated wavefunction, you have to accept such fact. Electronics, nanoelectronics and quantum engineering are all very solid proofs that the foundation of QM is solid, as it was experimentally tested many times. Quantum systems exhibit the unique feature of being able to exist in a superposition of several quantum states simultaneously. The process of measurement causes the quantum superposition to collapse into a classical state. This is the so-called quantum jump, where instead of a spread-out wavefunction in space, the probability amplitude collapses all particle positions down to one (as it happens in the double slit experiment with electrons).  The Schrodinger wave equation accurately describes the spread of the quantum probability wave for an electron, but it can not predict the quantum jump of the electron to a particular location or quantum state. This is the paradox of quantum measurement. When you perform a measurement on  a quantum superposition, only one of the possible outcomes is achieved. Different interpretations have been also suggested, such as  the many worlds interpretation that suggests that all possible results are realized, but each in a different copy of the universe. There is also the decoherence hypothesis, verified by the experiments with photons performed by Serge Haroche (Nobel Prize winner in 2012 together with Dave Wineland) and J-M Raimond.

What I am trying to make you understand is the fact that Quantum Mechanics is still an open theory. As I am implied in quantum engineering with ion traps, I can tell you that a lot of current and future ESA experiments and missions are focused on testing quantum mechanics and the theory of relativity. And this is where optical clocks and new quantum detectors are expected to shed new light on the Universe and the laws that govern it. One of the hottest direction lies in unifying gravity and the Standard Model, and you have probably heard about quantum gravity or quantum geometry (loop quantum gravity). You will find a lot of literature on such aspects. If I can help you, don't hesitate to ask.

Best regards,

Bogdan 

Dear @Bogdan ,

I have no idea why you are writing this. I was writing only about strange terms and unproven sentences. Thats all! 

"It seems that you are looking for a deterministic Quantum Mechanics"

Where did you found this? 

Best,

Miroslav

The main problem in your question relies on the assumption that Lorentz group can be extended to transformations with abs(v)=c which is not true. It does not make senso to consider how Lorentz transformations change the world at velocities equal to the speed of light. So, thinking about the entanglement between two photons seen from the photon's reference frame is unphysical.

The other point of the question looks at the problem of compatibility between quantum entanglement and relativity. This is actually one that puzzled the community for many years, and still does. The "simplest" answer, independent from the interpretation of quantum mechanics that you choose to consider, is that through entanglement there is no actual transfer of information. That is you cannot use an entangled pair to transfer information faster than light. The change of the wave function, and of the eventual hidden variables, is instantaneous, but, since the experimenter cannot know the state of the system if not performing a system changing experiment, he cannot detect such a change.

Well, the Lorentz transformation can at least be extended arbitrarily close to c, which is all you really need, i'm thinking. This is just speculation, but it seems to me the only thing we have going for us that we know of as far as this spooky entangled stuff and wave-function collapse is concerned, is the phase velocity of the de Broglie wave, which is equal to the speed of light for massless particles and greater than that of light for massive particles. In classical (non-quantum) physics it is the speed of light squared divided by the particle speed. I suspect the particle speed should be the group speed of the wave function in quantum mechanics, since that is the speed associated with a particle. One thing about phase velocity, which can be greater than the speed of light in classical physics (electromagnetics), is that it is not causal and thus doesn't  contradict special relativity. The entanglement situation is also not causal; that is, the measurement of one entangled particle does not cause the measurement of the other to be what it turns out to be. I don't know of any mechanism by which the phase velocity of de Broglie waves can cause the so-called collapse of the wave function, but right now, looks to me like it is a plausible candidate.

I see there are more responses than just that of Lorenzo Fant. I hadn't seen those when i wrote the above. Thinking of de Broglie waves as players in the questions of measurement and so-called collapse of the wave function is not new, of course. All i'm referring to is to look at the situation with respect to the local reference frames of the particles themselves. I chose photons, but you can look at very light particles such as neutrinos as well. The universe is very nearly flat in the reference frame of a neutrino traveling close to the speed of light. It's wave function will be likewise pretty flat. What i'm asking more generally is, is it possible that a measurement made on a pair of correlated neutrinos might be nearly simultaneous in the frame of either one of the pair? And close together in space as it exists in that frame? In our frame the particles could be light years apart and the measurements at very different times. This is just speculation on my part. De Broglie waves may be involved in this.

P.S. For massive particles not moving close to the speed of light, the de Broglie waves would be very fast (>>c). What role they may or may not have in the collapse of the wave function, i don't know.

Hey, guys (gals?) here's another weird thought related to this subject. If you consider a particle to be described by a plane wave (wave train, actually) the argument kx-wt is actually the scalar product of two 4-vectors: (k,w/c) and (x,ct). When you transform the former vector to a frame moving with speed v in the opposite direction of the propagation of the wave, the wavelength approaches zero and the frequency approaches infinity. So, can you think of it his way? Does a photon traveling in the opposite direction of a second photon see the second photon as having infinite energy, E = hf? Can this be OK because the time existence of the photon is delta t = 0 and by the uncertainty relation, delta t delta E >= h, delta E can be infinite (or, infinitely uncertain) when delta t is zero?

I should have said with speed v approaching c.

IMHO, the critical question in QM is that of DISTINGUISHABILITY. We have to look at a system as microscopic no matter how large it becomes over time (cf EPR). This inconsistency between the physical content of the term "microscopic" and its etymology is the major source of nonlocality paradoxes. Surely this is all IMHO.

Hey L.I., what is IMHO?

IMHO = In My Humble Opinion

Dear Prof. Redfern,

                                   Sorry to come so late in this string. I would like to point out to our research on String Theoretic Quantum Econophysics of Coal Mining using Nobel Coal Mining Reservoir Information System Stock Market potential using Genetic Stock and Flow jump quantum continuum quantum mechanics in hidden particles String Field Matching Genetic Algorithmic motion over spacextime. (Mallick (1989, 1993, 2012, 2013, 2014), Mallick, Hamburger, Mallick (2016, 2016)). The quantum field is integrated systemically by special relativistic fractal geometry method as measured by String Matching Meanfield random simulation using Copenhagen Quantum Information Functor category Systems Classification and Systems Group Homologous Integration Statistics - year end mean P/E ratio=0 in Bombay Stock Exchange Strong Law of Large Numbers data experiment over 2016 (Mallick (2015)). I hope these research findings over the Field and Methods are of help to you. 

Soumitra K. Mallick

for Soumitra K. Mallick, Nick Hamburger, Sandipan Mallick

 Dear Prof. Redfern,

                                       We would like to add that, The CERN "jump quantum" conductance linear accelerator Field-Method experimental verification of our Nobel Potential Geometric String Field Matching Field and Method Group Homologous (hidden particles Higgs-Englert-Bosonic) unit root experimental test is clear (courtesy CERN and Prof. Sir P.W.Higgs CH FRS FRSE Nobel Physics Laureate , over the Nobel Prize website communication channel).

SKM

for SKM, NH, SM

As far as I can see, the difficulty in Aspect-like experiments arises not so much at the level of the microscopic system as at the level of the measuring apparatus. There is nothing non-local in itself about a pair of entangled photons. Issues arise when both are *measured* and these two measurements are spatially separated events. Then the measurements' outcomes cannot be explained in simple local terms.

If this is not quite wrong, then the fact that photons move at the speed of light, and the ensuing difficulties in defining a proper time for them do not seem to resolve the problem.

Another thought. Wouldn't there be violation of conservation laws if, for example, one correlated photon had a spin of +1 and its partner also had a spin of +1 when the original spin of the pair was zero? Is this the way nature enforces conservation?

Question: "Does special relativity explain quantum action at a distance?"

Given the way it is formulated, this question admits no straightforward answer – indeed, no answer as it stands.

Firstly, ‘special’ relativity (SR) cannot explain any kind of action at a distance. In ‘special’-relativistic physics, all physical influences must be propagated or locally transferred. Thus, not only does not SR contribute to any explanation of action at a distance, quantum or not, but it does not permit it.

Secondly, the question takes it for granted that there is some specifically ‘quantum’ sort of action at a distance. Lots of half-baked speculation and popular science, but also imprudent statements by (too) many physicists, might give the erroneous impression that such ‘quantum action at a distance’ is a well-established fact. It is not.

 At their most basic level, quantum formalisms raise conceptual issues that are notoriously unsettled. One typically arises in relation to discussing so-called entanglement. The latter comes down to the non-factorability of certain formal expressions. In and of itself, this characteristic of quantum theories need not be – and had rather not be – interpreted in a simple-minded manner as a spooky physical (an oxymoron?) link between arbitrarily distant objects. There is as yet no fully satisfactory and uncontroversial interpretation of such non-factorability. Unfortunately, the word ‘entanglement’ is not ‘neutral’ enough to prevent ontological misconceptions or hasty interpretations, such as the existence of ‘entangled particles’, whatever that could mean (just pause and think about it).

 It might be worth noting that when Schrödinger introduced, in 1936, the expression ‘entangled systems’, the systems that he had in mind were abstractions rather than concrete entities. He thought of their ‘being entangled’ as meaning – and he clearly wrote it – that our knowledge of the two systems as a whole cannot be split into separate knowledge regarding each of them separately. This means that, as long as the whole pair is ‘described’ by, or more cautiously assigned, for predictive purposes, a single mathematical object in quantum theory (wave function, ‘state’ vector, statistical operator a.k.a. density matrix…), it no longer seems possible to think of the pair as separate entities with their own sets of properties, the properties of the pair being a simple set-theoretical union of those of its members, and shared properties the intersection of two such sets.

 Decades after John Bell’s mid-1960s contribution, this conflict of quantum mechanics with (often implicit) logico-set-theoretical assumptions has been rehearsed at nauseam, and it is here to stay. If it remains possible to see in it a shortcoming or evidence of ‘incompleteness’ of the theory, Bell’s theorem and a host of other results like GHZ show that it is not possible to ‘complete’ the theory in terms of ‘commonsense’, locally set parameters. This should not come as a surprise given that such setting implies understanding properties of parts of a system as ‘belonging’ to it and them in set-theoretical fashion, whereas probabilities and correlation coefficients are evaluated in quantum theory in/from a linear space framework, and linear (sub)spaces are not ‘trivially’ like (sub)sets.

 Thus, some of the statistics implied by the linear (Hilbert) space structure of quantum theories do not match our ordinary statistical ‘intuitions’, which are associated with set-theoretical preconceptions (according to which things ‘have’ properties that ‘belong’ to them, that they may ‘share’ etc.). This being said, what has to be re-emphasized, time and again, is that correlation of any kind is not causation. Quantum-mechanical or ‘EPR’ correlations are no exception to the rule. Thinking about entanglement as pointing to some sort of ‘non-separability’ is little more than playing with words; worse still, expressing it this way breeds unwarranted conceptions, such as some kind of woolly ‘holism’. Such rewording does not bring us closer to a reliable, non-deceptive ‘picture’ of non-factorable systems, or to understanding what they physically mean ‘beyond’ statistical data. What it is essential to realize in any case is that no actual conflict with SR arises. Entanglement may enable ‘strange’ feats like quantum ‘teleportation’ or dense coding, but there is nothing spooky or preternaturally weird about those. Most importantly, a number of proofs have been given that quantum correlations cannot enable instant or superluminal signalling. This has prompted Abner Shimony to coin the expression ‘passion at a distance’ to characterize the (abstract) ‘link’ that is established between parts of a composite quantum-mechanical system whose ‘description’ involves entanglement. Passion, not action. Correlated parts of a composite quantum system do not influence each other remotely. Such correlation does not in any way violate SR, which can neither oppose nor of course explain it.

I sort of threw this question out on a whim. In retrospect, i'm sorry. The answer is "no" because of the following. Say two particles are separating at nearly the speed of light, starting from the same point in space and time. Call this speed u as seen in the "lab" frame. By the relativistic addition of velocities, the parting speed of one particle with respect to the other is v = 2u/(1 + u2/c2). If one particle sends a light signal to the other at a time to after parting (its local time), the second particle has moved a distance of 2uto/(1 + u2/c2) by that time as measured in the first particle's frame. This means the light signal arrives at the second particle after a time of 2ucto/(c - u)2 in the first particle's reference frame. As you can see, this is a very long time when u is close to c. When i first thought of this question i was thinking in a naive manner (actually, not thinking much at all). I moved on, but then i felt i needed to clarify the question and put it to rest. I still think the only thing we have going for us when it comes to the "collapse" of the wave function is the phase velocity of the de Broglie wave. How that happens....????

I got to thinking about this question again. The above is not the last word. That is because to, being proper time in the particle's frame, goes to zero as the particles approach the speed of light (this means that their rest mass m times gamma approaches h/(c lambda), the "mass" of a photon as v approaches c.) So, the time the light signal reaches the second particle depends on the limit of the quantity to/(c - u)2 as to approaches zero and u approaches c.That is, it appears as if the time it takes for the light signal issued from the first particle to reach the second particle is indeterminate, which would be the case for one member of a photon pair trying to signal the other member. So I was mistaken above thinking the time to was finite.

For particles with rest mass, de Broglie waves travel faster than light. For particles with reasonably well-defined momenta, not just the phase velocity of the de Broglie waves travels this fast, but also the group velocity. For photons and other massless particles, de Broglie waves travel at the speed of light. It isn't clear to me what the relationship is if any, between electromagnetic waves and de Broglie waves.

I still wonder if de Broglie waves are somehow involved in the spooky actions at a distance. Consider this. Say observers A and B measure the spins of two entangled particles with mass, where A and B are too far apart for any light signal to connect the measurements. You can define moving observers X and Y such that, due to the relativity of simultaneity, observer X sees A make the first measurement whereas observer Y sees B make the first measurement. X will claim that A's measurement led to the outcome of B's measurement, but Y will claim that A's measurement was determined by B's. Who is right? Or is anyone right? (or wrong?)

If a "signal" (not one that could transport information) went back in time from A's measurement to B's measurement in Y's reference frame (and a similar situation for A and X), the measurements could be correlated. De Broglie waves can go backward in time in a given reference frame. It seems to me that de Broglie waves might be the means (however that works) of correlations between entangled particles.

Sigh. One "little" misstatement in the previous post. You apparently cannot presume the group velocity of de Broglie waves is faster than light. That would mean the particles themselves would travel faster than light! Duh. I forgot that the velocity of a Dirac particle is the expectation value of the four-by-four matrix constructed from the Pauli spin matrices often designated "alpha" in the literature times the speed of light. This gives a group velocity of the Dirac wave function that consists of a classical-like quantity (less than the speed of light) and the Zitterbewegung motion due to interference between the positive and negative electron energy solutions. If the phase velocity of de Broglie waves somehow in involved with entangled correlations and how that works is a mystery to me.

OK, i doubt anyone is interested in this question anymore. Like i wrote, i threw this question out there, probably because i didn't have anything better to do at the time. I then got involved in other things. Now, however, i've finally dusted off my old quantum books and here is my final (i'm pretty sure) contribution.

If you take the general solution of the Klein-Gordon equation, good for spinless particles, you find that the magnitude of the phase speed of the wave of a particle with mass is w/k = c(1 + c2/(h-bar2k2))1/2. Here w is the angular speed and k is the wave number. If you assume (h-bar)(k) = m(gamma)v2, the relativistic particle momentum, you find that w/k = c2/v, the same as the classical result. If you further take v as the group velocity of the wave function, then, since w/k is always greater than c according to the first equation above, the group velocity is always less than c. If you do an expansion of w in terms of k in the general K-G solution, you find that dw/dk is the group velocity when w/k is close to c, that is for photons and very light particles. This agrees with assuming the classical velocity v is the group velocity of the de Broglie wave, so i think this conclusion is valid.