Can Special Relativity Explain the Alice and Bob Spin Measurement Paradox?

[AndrzejB]

TL;DR

measurement in frame of reference

Alice measures the spin, also Bob measures.
If we assume that the signals (from Alice to Bob) were sent, they had to be with the speed e.g. 10 c
But in another frame of reference Bob first measures, next Alice.
Measurement of Alice was cause and was sent back in time, or measurement of Bob was cause.
Since Alice and Bob case is symmetrical, it cannot be said that the first measurement reduced the wave function and the second was just a formality.
We have paradox.

 

[PeroK]

Alice measures the spin, also Bob measures.
If we assume that the signals (from Alice to Bob) wwere sent

There are no signals between entangled particles in QM.

 

[StevieTNZ]

There are no signals between entangled particles in QM.

Solves the apparent paradox. "Assume x, therefore y. It is, further, a fact there is a paradox." Work that out.

 

[AndrzejB]

I knew there were no signals, I put myself wrong, I meant that the time distance between the events was small and the spatial distance was large, so that if there were signals they would have to be> c which is impossible.
Problem is that it is impossible to say which measurement was the cause of the reduction of the wave function

 

[PeroK]

Problem is that it is impossible to say which measurement was the cause of the reduction of the wave function

The collapse of the wavefunction is not a physical process. It's an interpretation of the mathematics of QM.

The important point here is that the measurement results are correlated. QM does not specify a mechanism by which that correlation is achieved.

 

[Demystifier]

Problem is that it is impossible to say which measurement was the cause of the reduction of the wave function

You tacitly assume that cause must be before the consequence, i.e. that there is a time arrow that distinguishes the past from the future. But an arrow of time is an emergent phenomenon making sense only at the macroscopic level. At the fundamental microscopic level there is no arrow of time, i.e. one cannot distinguish the past from the future. From that point of view, there is no paradox.

Note also that the notion of signal assumes a time arrow. So the solution of the paradox can also be expressed by saying that there are no superluminal signals between the two systems. However, it does not mean that there are no superluminal influences. The influence, unlike signal, is a fundamental microscopic notion that does not need a time arrow; a microscopic event can influence both the future and the past. So it's possible that the two systems are correlated because they influence each other faster than light, without sending signals faster than light. An explicit model for such influences is provided by Bohmian interpretation, where special relativity is violated at the fundamental microscopic level, but in such a way that those violations cannot directly be observed in outcomes of macroscopic measuring apparatuses.

 

[vanhees71]

The collapse of the wavefunction is not a physical process. It's an interpretation of the mathematics of QM.

The important point here is that the measurement results are correlated. QM does not specify a mechanism by which that correlation is achieved.

Of course QM does specify "a mechanism" by which that correlation is achieved. It's due to the preparation of the system in an entangled state. E.g., you get entangled photon pairs using parametric down conversion, i.e., shouting with a laser on certain birefringent crystals and select the entangled pairs:

https://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion

When thinking about the question of locality or non-locality one has to use relativistic QT since in non-relativistic physics there's no constraint for the signal speed to begin with. Now the only successful relativistic QT is local (sic!) relativistic QFT, which is constructed such that the causality structure of special relativistic spacetime is fulfilled. This is done by defining only such self-adjoint operators as representing observables which lead to local observables (like energy, momentum, charge densities), i.e., for which the operators commute if their arguments are space-like separated. This implies that there cannot be any causal influences between any two space-like separated events. Particularly signaling cannot be achieved at speeds faster than light (in vacuo).

 

[vanhees71]

You tacitly assume that cause must be before the consequence, i.e. that there is a time arrow that distinguishes the past from the future. But an arrow of time is an emergent phenomenon making sense only at the macroscopic level. At the fundamental microscopic level there is no arrow of time, i.e. one cannot distinguish the past from the future. From that point of view, there is no paradox.

The causality of the natural phenomena is a prerequisite for any natural science to make sense to begin with. If there were no laws of nature to discover, you'd not need any natural sciences, and the causal arrow of time is thus just one of the basic postulates underlying all of physics. Maybe that changes in the future when a quantum theory of gravitation and thus most probably also a quantum theory of spacetime has been found, but as long as this is not the case, all such statements are just speculative.

Given this "causal arrow of time", all the other "arrows of time" (like the "thermodynamic arrow of time" and the "radiation arrow of time") then follow. The thermodynamic arrow of time follows, e.g., from coarse graining of microscopic descriptions to effective descriptions of collective, macroscopic observables (Boltzmann's H theorem). The radiation arrow of time is of pretty similar origin: It's simply impossible FAPP to prepare the time-reversed solution of the Maxwell equations to the retarded solution for radiating out from a localized charge-current distribution.

Note also that the notion of signal assumes a time arrow. So the solution of the paradox can also be expressed by saying that there are no superluminal signals between the two systems. However, it does not mean that there are no superluminal influences. The influence, unlike signal, is a fundamental microscopic notion that does not need a time arrow; a microscopic event can influence both the future and the past. So it's possible that the two systems are correlated because they influence each other faster than light, without sending signals faster than light. An explicit model for such influences is provided by Bohmian interpretation, where special relativity is violated at the fundamental microscopic level, but in such a way that those violations cannot directly be observed in outcomes of macroscopic measuring apparatuses.

There are no "superluminal influences" by construction in local relativstic QFTs. There are strong correlations between far-distant observations on entangled quantum systems, but correlations are no causations!

 

[Demystifier]

and the causal arrow of time is thus just one of the basic postulates underlying all of physics.

Given this "causal arrow of time", all the other "arrows of time" (like the "thermodynamic arrow of time" and the "radiation arrow of time") then follow.

No. Causal arrow of time is not a postulate, but an observed phenomenon. The standard view is that the causal and other arrows of time emerge from the thermodynamic one. The thermodynamic arrow of time can be traced back to a low entropy initial condition. Why the initial entropy was low? That question does not have a standard or widely accepted answer, it's one of the deepest unsolved problems in physics. The microscopic postulates as we know them are equations of motion which do not have any a priori causal arrow of time. Solving those equations requires fixing initial conditions, but in general we don't have a law telling us how to fix them. The observed phenomenon of thermodynamic time arrow tells us the initial condition must have a low entropy, but that of course does not fix the initial condition uniquely.

 

[vanhees71]

The fact that indeed the microscopic equations are time-reversal invariant (neglecting the weak interaction here) implies that we have to take the assumption of a causal arrow of time as a postulate. For me that's the most fundamental arrow of time since it's really to be assumed, and all the other arrows of time follow from it. Of course the arrow of time we experience in everyday life indeed is the thermodynamic arrow of time and is due to the macroscopic nature of our surroundings.

I cannot judge your cosmological argument. Do you have any references for this?

 

[Demystifier]

I cannot judge your cosmological argument. Do you have any references for this?

- A general introduction is wikipedia https://en.wikipedia.org/wiki/Past_hypothesis
- Particularly lucid and clear discussion is given in the book R. Penrose, The Emperor's New Mind, Chapter 7.
- See also my https://arxiv.org/abs/gr-qc/0403121 Sec. 2, where I give more references and briefly explain how causal time arrow emerges from the thermodynamic one (and not the other way around).

 

[vanhees71]

Hm, I still think, it's the other way around since you want to understand the macroscopic phenomena from the fundamental elementary building blocks, and to establish relativistic QFT as a theory about these elementary building blocks (i.e., the particles of the standard model) a basic ingredient is the causal arrow of time, and then by statistical arguments you derive the H-theorem and thus show that the so defined thermodynamic arrow of time is the same as the causal arrow of time, but also here you introduce the asymmetry between future and past by hand, i.e., you through away information in the future, i.e., going forward in time in the sense of the causal arrow of time (e.g., when deriving the Boltzmann equation from QFT, the Schwinger-Keldysh timepath uses the causal direction of time and leads to an increase of entropy in this direction of time).

The same holds for the radiative or electrodynamic arrow of time, i.e., the fact that we choose the retarded solution of Maxwell's equations to describe wave fields radiating out from compact distributions of charges and currents. The time-reversed situation is not impossible as far as we know, but it's FAPP impossible to realize since one is unable to construct over a far distance a wave field in an accurate way that is so finetuned that it's completely absorbed by some localized charge distribution.

 

[Demystifier]

The time-reversed situation is not impossible as far as we know, but it's FAPP impossible

You would probably agree with me that the time-reversed situation violates the causal time arrow. But if the causal time arrow was fundamental, then it would be absolutely impossible, not merely FAPP impossible. On the other hand, FAPP impossibility, rather than absolute impossibility, implies that it's a consequence of a FAPP law, not of an absolute law. This is a clear indication that the reason for impossibility of time-reversed situation lies in the thermodynamic time arrow, which is a FAPP statistical law, not an absolute law.

since one is unable to construct over a far distance a wave field in an accurate way that is so finetuned that it's completely absorbed by some localized charge distribution.

I agree, but there is always a small probability that the fine tuned configuration will be realized by chance. This is again a clear indication that the FAPP impossibility has a statistical origin, namely in the thermodynamic time arrow.

But here is a crucial detail that may confuse you. By "thermodynamic" time arrow in this context one does not assume that the system has a well defined temperature. It is really a generalized "thermodynamic" time arrow, which states that a coarse grained entropy increases, but in general this entropy does not need to be thermodynamic entropy. The usual thermodynamic time arrow, in which entropy is thermodynamic entropy, is just a special case.

Or to make the long story short, the causal time arrow is a FAPP statistical law. It emerges from a more general FAPP statistical law saying that coarse grained entropy increases. This general statistical law is misleadingly called thermodynamic time arrow, even though it refers to general systems that do not need to be thermodynamic systems with a well defined temperature.

 

[vanhees71]

You would probably agree with me that the time-reversed situation violates the causal time arrow. But if the causal time arrow was fundamental, then it would be absolutely impossible, not merely FAPP impossible. On the other hand, FAPP impossibility, rather than absolute impossibility, implies that it's a consequence of a FAPP law, not of an absolute law. This is a clear indication that the reason for impossibility of time-reversed situation lies in the thermodynamic time arrow, which is a FAPP statistical law, not an absolute law.

Why should the time-reversed situation violate the causal arrow of time? If I'd be an almighty experimentalist, able to prepare a spherical ingoing wave in such a precise manner that it's the time reversed wave of the outgoing wave from a charge-current distribution this same charge-current distribution would completely absorb the wave precisely. It's only because of the complexity of this initial state of the ingoing wave that we are practically unable to prepare it.

It's as with the time-reversed process of a shattering glass: If we'd be able to prepare precisely the time reversed final state, the glass would reassamble completely, but that's of course impossible because of the complexity of this initial state.

In general it's very difficult to prepare initial states which lead to a time evolution of decreasing entropy when described in the coarse-grained manner of statistical physics. This is the reason, why almost always we observe states with increasing entropy and that's why the causal arrow of time usually coincides with the thermodynamic arrow of time, i.e., the state in the future has larger entropy than the initial state.

I agree, but there is always a small probability that the fine tuned configuration will be realized by chance. This is again a clear indication that the FAPP impossibility has a statistical origin, namely in the thermodynamic time arrow.

Sure, but the probability is really very small.

But here is a crucial detail that may confuse you. By "thermodynamic" time arrow in this context one does not assume that the system has a well defined temperature. It is really a generalized "thermodynamic" time arrow, which states that a coarse grained entropy increases, but in general this entropy does not need to be thermodynamic entropy. The usual thermodynamic time arrow, in which entropy is thermodynamic entropy, is just a special case.

Of course not. If the initial macroscopic state is equilibrium, it's static, but entropy is not only defined in equilibrium.

Or to make the long story short, the causal time arrow is a FAPP statistical law. It emerges from a more general FAPP statistical law saying that coarse grained entropy increases. This general statistical law is misleadingly called thermodynamic time arrow, even though it refers to general systems that do not need to be thermodynamic systems with a well defined temperature.

We agree to disagree. For me the causal arrow of time is a fundamental postulate of our physical theories, and the thermodynamical arrow of time can be shown to coincide with this causal arrow.

 

[Demystifier]

We agree to disagree. For me the causal arrow of time is a fundamental postulate of our physical theories

Fair enough. But I don't see this postulate explicitly stated in any of our fundamental theories. When I read a list of postulates for the Standard Model, or for quantum mechanics, or for general relativity, or for classical electrodynamics, or for classical mechanics, I don't see the causal time arrow postulate. Do you know any textbook, or lecture notes, or even a research paper, that states this postulate explicitly?

This, perhaps, is a meta-postulate, that is, a postulate that lies behind "ordinary" postulates. If so, then it belongs to meta-physics, rather than "ordinary" physics. But I know that you don't have a high opinion on meta-physics, so it's a bit ironical that you put such a strong emphasis on a postulate that seems to be a meta-postulate.

Can you imagine a though experiment that, in principle, could decide whether the causal time arrow postulate is true or false? In other words, can you describe at least one example of how the world look like if this postulate were wrong? If not, then it's another indication that it is a non-scientific postulate belonging to meta-physics.

 

[vanhees71]

Of course, it's not stated explicitly, because it's taken for granted, because it's the prerequisite for natural science, i.e., if there were no causal laws, there'd be no natural science. It's of course used all the time. The first expclicit need to use it usually occurs in classical electrodynamics, where you solve the time-reversal invariant wave equation, and where you have to choose the retarded Green's function from all the other possible Green's functions of the d'Alembert operator. Of course, you could as well introduce this idea of the retarded Green's function already much earlier, i.e., when you discuss the harmonic oscillator with an external force (or even the free particle with a given external force as a function of time).

 

[gentzen]

Of course, it's not stated explicitly, because it's taken for granted, because it's the prerequisite for natural science, i.e., if there were no causal laws, there'd be no natural science.

I guess you are talking about "the causal time arrow postulate". (I am glad that nearly nobody is following your example of not quoting what you are responding to.)

There are two things I don't get about your argument:

1. Why should a FAPP causal time arrow not be sufficient for natural science?
2. Why should we be able to conclude anything from "it's the prerequisite for natural science"? You probably know my example of the placebo effect in medicine (together with the fact that experiments are not repeatable), which of course makes everything much harder, but not impossible. But let me try a more physical example instead: The closed timelike curves in general relativity seem incompatible with a causal time arrow.

While I am at general relativity, let me just test the general ability to accept incompatibilities of general relativity with other "principles": For example Daniel Greenberger thinks that the equivalence principle of general relativity is incompatible with quantum mechanics:

If you put a particle into a really strong external gravitational field, it should behave like any other particle in that field and its mass should drop out, according to the weak equivalence principle. But quantum mechanically, that doesn’t happen. We give the particle a mass at the beginning, and the mass enters the calculation, and this violates weak equivalence.

And since this thread was about compatibilty between special relativity and quantum mechanics, let me just mention that the predicted phenomenology of quantum mechanics is compatible with special relativity, independent of whether "local relativistic QFT" can be extended (or used) beyond scattering of asymptotic states or not. At least no incompatibilities are currently known.

 

[vanhees71]

I guess you are talking about "the causal time arrow postulate". (I am glad that nearly nobody is following your example of not quoting what you are responding to.)

If I don't quote what I'm responding to I respond to the posting directly before the new posting. We are discussing the causal arrow of time indeed.

There are two things I don't get about your argument:

1. Why should a FAPP causal time arrow not be sufficient for natural science?

I think one needs causality to have natural sciences to begin with. If there were no causal laws, we couldn't discover them. Whether it's FAPP or not, I don't care.

1. Why should we be able to conclude anything from "it's the prerequisite for natural science"? You probably know my example of the placebo effect in medicine (together with the fact that experiments are not repeatable), which of course makes everything much harder, but not impossible. But let me try a more physical example instead: The closed timelike curves in general relativity seem incompatible with a causal time arrow.

While I am at general relativity, let me just test the general ability to accept incompatibilities of general relativity with other "principles": For example Daniel Greenberger thinks that the equivalence principle of general relativity is incompatible with quantum mechanics:

I don't understand, what Greenberger means, because there's QFT in curved spacetimes, describing particles in a given general relativistic "background spacetime". Why should this be incompatible with the (weak) equivalence principle. A quantum gravity of the gravitational interaction doesn't exist yet, and it may well be that the equivalence principle is not valid any more in such a theory.

And since this thread was about compatibilty between special relativity and quantum mechanics, let me just mention that the predicted phenomenology of quantum mechanics is compatible with special relativity, independent of whether "local relativistic QFT" can be extended (or used) beyond scattering of asymptotic states or not. At least no incompatibilities are currently known.

Of course. What has this to do with the causality principle, which is an important ingredient to establish local relativistic QFTs to begin with?

 

[gentzen]

Of course. What has this to do with the causality principle, which is an important ingredient to establish local relativistic QFTs to begin with?

It is unrelated to the causality principle. It is just my opinion regarding the original question of this thread.
(And I wanted to make it clear that while I am open to the possibility that general relativity might be incompatible with other "sacred physical principles" including quantum mechanics, I am strictly opposed to suggesting a similar possible incompatibility for special relativity.)

 

[PeterDonis]

Problem is that it is impossible to say which measurement was the cause of the reduction of the wave function

That's because it doesn't matter. Since the measurements are spacelike separated, they commute: their results do not depend on the order in which they are made. Which is good because the order in which they are made is frame dependent.

That is usually taken to mean that there cannot be any cause and effect relationship between them, since any such relationship would require the order of the measurements to be invariant, and it's not.

 

[Demystifier]

Of course, it's not stated explicitly, because it's taken for granted, because it's the prerequisite for natural science, i.e., if there were no causal laws, there'd be no natural science.

Then it belongs to philosophy of science, not to physics proper. But physics, as the most fundamental science, often has aspirations to explain some general scientific principles from more fundamental physics principles. The causal time arrow is certainly one of them. Another example is the "free will" postulate, namely the phenomenological fact that experimentalists have some freedom to choose initial conditions at will. This principle seems to be contradicted by both deterministic and probabilistic fundamental laws of physics, so many physicists believe that "free will" postulate, similarly to the causal time arrow postulate, cannot be fundamental bust must emerge somehow at the macroscopic level only.

 

[malawi_glenn]

Almost all threads in this subforum ends up in a battle between demyst and vanhees :)

 

[vanhees71]

Then it belongs to philosophy of science, not to physics proper. But physics, as the most fundamental science, often has aspirations to explain some general scientific principles from more fundamental physics principles. The causal time arrow is certainly one of them. Another example is the "free will" postulate, namely the phenomenological fact that experimentalists have some freedom to choose initial conditions at will. This principle seems to be contradicted by both deterministic and probabilistic fundamental laws of physics, so many physicists believe that "free will" postulate, similarly to the causal time arrow postulate, cannot be fundamental bust must emerge somehow at the macroscopic level only.

The causality principle clearly belongs to physics proper, because it is used to select the physical from all possible solutions of the equations of motion. That's why we discuss it to begin with.

That you can choose initial conditions "at will" is also an empirical fact, and that's part of why the physical laws look as they look, i.e., why you have, e.g., second-order differential equations for the coordinates of a mechanical system.

 

[martinbn]

I don't think the arrow of time is relevant here. Two events can be cause effect related if there is a causal curve connecting them. The time orientation only determines which can be the cause and which the effect. But if the two events are space-like separated, then all this is irrelevant. Part of the confusion comes from treating coordinate time as some sort of classical absolute time. You chose a frame in which one event is first and the other second, in the sense that one has smaller value of the chosen time coordinate, then you fool yourself that there might be an influence from the first to the second event because the first event was in the past. But it isn't in the past, they are space-like. Coordinates are just lables. This is either due to missunderstanding of relativity, or simply being careless and slipping into thinking norelativistically (could also be deliberate). Same for the retrocausality. If the events are space-like choosing a frame doesn't make one in the future of the other.

 

[vanhees71]

Nevertheless, relativistic spacetimes admit a causality structure (at least locally), and you can always choose your time-like coordinate such that the causal ordering is as usual, i.e., if two events have a cause and effect relation you can always make the time-like coordinate such that the event at the smaller time coordinate must be the cause.

 

[Demystifier]

Almost all threads in this subforum ends up in a battle between demyst and vanhees :)

But this a friendly battle, we respect each other, often like each other, and agree on most physics issues (except those on which we have a battle).

 

[Demystifier]

Whether it's FAPP or not, I don't care.

That's it! That's the single most important reason why we have "battles" in this subforum at all. Almost all the "battles" we had in this subforum originate from the the deep difference between you and me that you don't care much about the difference between FAPP and "truly" fundamental laws, while I do.

 

[malawi_glenn]

But this a friendly battle, we respect each other, often like each other, and agree on most physics issues (except those on which we have a battle).

But maybe the OP become "discouraged" to continue?

 

[vanhees71]

That's it! That's the single most important reason why we have "battles" in this subforum at all. Almost all the "battles" we had in this subforum originate from the the deep difference between you and me that you don't care much about the difference between FAPP and "truly" fundamental laws, while I do.

But the point is that whatever "truly fundamental laws" might be, they cannot be checked by experiments and thus are fictions which are not subject of a natural science. At best they provide some interesting pure math (like "string theory" et al).

 

[Demystifier]

But the point is that whatever "truly fundamental laws" might be, they cannot be checked by experiments and thus are fictions which are not subject of a natural science. At best they provide some interesting pure math (like "string theory" et al).

True, but one can always think about what is fundamental according to a given theory, even if this is not a theory of everything. For example, if one imagines that classical electrodynamics is fundamental, then, since it is a deterministic theory in which all variables are determined by initial conditions in the far past, then human experimentalists cannot have a fundamental ability to choose initial conditions at will. It's a clear logical consequence of this theory, so within this theory one must accept it even if this contradicts our common sense. In particular, if our common sense tells us that our free will is fundamental, one must reject the common sense and accept that free will is somehow emergent, not fundamental. Or alternatively, if one insists that free will is fundamental, then classical electrodynamics cannot be. Similar conclusions can be made about quantum electrodynamics, Standard Model, string theory, etc. We cannot check these conclusions by experiments, but we can think logically and trust our logical conclusions. If logic is not science, that's a deficiency of science, not of logic.