A Assumptions of the Bell theorem

[facenian]

I never understood these arguments. We have a working local theory, relativistic QFT, violating Bell's inequality in all observed cases. The locality of relativistic QFT is built in its foundations. As Weinberg writes in his Quantum Theory of Fields Vol. I: QFT looks as it looks because the assumption of Poincare invariance + locality=microcausality inevitably leads to it.

As I wrote above, you don't need the assumption of acausal spooky actions at a distance when you just take the quantum state (in this case a Bell state) as it is: It's prepared in the very beginning and describes the strong correlations as well as the maximum randomness of the single-particle-observables' values. The correlations are prepared in the very beginning and stay intact until the local measurements made (with registration events space-like separated, so that there cannot be any causal influence of one measurement on the other). So what must be abandoned is the part of Bell's assumption called "realism". From the mathematics I deduce what's meant by "realism" in this case really just is that in fact the measured single-particle observables have determined values before the measurement, and the randomness is just because of our ignorance of the hidden variables, but this assumption is indeed refuted by observation, which all are in accordance with local relativistic QFT.

This philosophical paper is indeed completely incomprehensible to me.

I agree, unfortunately, Van Fraassen's rational paper is hard to read (unless perhaps for a trained philosopher). Ironically, he says the same thing as you, that we have a successful working theory and we have to listen to it (but he recognizes that to make QM local, we must give up causal explanations of QM's perfect correlations).
Lamentably, we cannot communicate with each other, or maybe you did not read what I wrote before carefully enough. If you want to argue for quantum locality you have to explain why ordinary quantum mechanics' objective nonlocal predictions are indeed local, not simply declare their local character. This, in principle, has nothing to do with the Bell inequality or realism.
I think that it would be wise to end the discussion right here and accept that QM interpretation is a hard problem.

 

[Fra]

So what must be abandoned is the part of Bell's assumption called "realism". From the mathematics I deduce what's meant by "realism" in this case really just is that in fact the measured single-particle observables have determined values before the measurement, and the randomness is just because of our ignorance of the hidden variables,

I agree with this. The emphasis here is also that it presumes that it's the "physicists" ignorance, and that that the form of the expectation follows the ansatz in bell theorem. But there are perhaps other forms of a sort of "solipsist" HV, that aren't cast into that form.

/Fredrik

 

[martinbn]

If you want to argue for quantum locality you have to explain why ordinary quantum mechanics' objective nonlocal predictions are indeed local, not simply declare their local character.

Because there are no infinite speed signals anywhere in sight.

 

[gentzen]

Because there are no infinite speed signals anywhere in sight.

But there is randomness, and it appears to be nonlocal. Why? Because the randomness only occurs when the entangled particles are measured, and you can compare the random outcomes of the spatially separated measurements later to confirm that they are not independent.

 

[facenian]

Because there are no infinite speed signals anywhere in sight.

That is one of my previously listed solutions: reject Bell's local causality and replace it with local signaling.
However, there are many people that think that is not enough. It does not matter if we are able to build a telephone or not out of those "spooky actions", they exist nonetheless.
It occurs to me that giving up uncontrollable spooky actions as nonlocal effects sounds a little counterintuitive. It is like giving up absolute simultaneity in SR, is how the world is.

 

[Demystifier]

This philosophical paper is indeed completely incomprehensible to me.

Is it a statement about the paper or a statement about you?

 

[vanhees71]

I agree, unfortunately, Van Fraassen's rational paper is hard to read (unless perhaps for a trained philosopher). Ironically, he says the same thing as you, that we have a successful working theory and we have to listen to it (but he recognizes that to make QM local, we must give up causal explanations of QM's perfect correlations).
Lamentably, we cannot communicate with each other, or maybe you did not read what I wrote before carefully enough. If you want to argue for quantum locality you have to explain why ordinary quantum mechanics' objective nonlocal predictions are indeed local, not simply declare their local character. This, in principle, has nothing to do with the Bell inequality or realism.
I think that it would be wise to end the discussion right here and accept that QM interpretation is a hard problem.

My problem is to understand, why people think relativistic quantum field theory were not local although it's local by construction. There are long-ranged correlations in situations as described by the two-photon Bell states where the single photons' properties are measured at space-like separated events. Within standard relativsitic QFT there cannot be any "spooky action at a distance" influencing the outcome of one of these measurements through the other. Nevertheless standard QFT describes all observations perfectly right. My conclusion from this simply is that we just have to take the quantum state as what it tells us: The probabilities for the outcomes of measurements. In the Bell states the single-photon observables (e.g., polarization which is usually used to demonstrate the quantum features) are maximally indetermined (i.e., the reduced statistical operators describing the single-photon properties are maximum-entropy statistical operators) but at the same time there are strong correlations between the outcomes of measurements. E.g., in the polarization-singlet state, the probability that A finds a H-polarized photon then B must necessarily find a V-polarized photon etc. These strong correlations are then due to the preparation procedure of the photon pair (anyway, operationally it's most plausible to interpret quantum states as a description of the outcome of preparation procedures), i.e., the photon pair has these strong correlations from the very beginning of their creation and, as long as they don't interact with something else on their way to the measurement devices, this correlations are not destroyed.

Of course, there is no causality problem within QM, which is non-relativstic, where actions at a distance are the standard description of interactions anyway. There you can have all kinds of instantaneous-interaction interpretations you like, though for the said photon experiments it's way outside of the realm of its applicability, because, of course, photons cannot be described in any way with a non-relativistic theory.

 

[vanhees71]

Is it a statement about the paper or a statement about you?

About me, of course. I can't even figure out whether I agree or disagree with the author.

 

[vanhees71]

But there is randomness, and it appears to be nonlocal. Why? Because the randomness only occurs when the entangled particles are measured, and you can compare the random outcomes of the spatially separated measurements later to confirm that they are not independent.

The important point is that you can confirm the correlations ONLY later! From an operational/instrumental point of view the locality of relativistic QFT implies the cluster decomposition principle excluding any possibility of faster-than-light communication. So to confirm the correlations "Alice and Bob" have to compare their measurement protocols by exchanging the corresponding information, which is only possible with at most the speed of light.

 

[martinbn]

My problem is to understand, why people think relativistic quantum field theory were not local although it's local by construction.

In my opinion, it is because the terms "local" and "nonlocal" have more than one meaning. Which changes from paper to paper, and even within one paper. What I don't understand is why people refuse to use a more clear language! Sometimes I think it is on purpose so that the can push their agenda. Sometimes I think it is because they are really bad at philosophy, despite the fact that they put philosophy on a high pedestal.

 

[WernerQH]

Tumulka (https://arxiv.org/pdf/1501.04168.pdf) also discusses many of these assumptions.

Has anyone tried to deny the Reichenbach common cause principle to avoid denying locality? I'm trying to think how that would go...I suppose one could argue that the correlation between two phenomena is just a brute fact with no underlying cause.

I'm wedded neither to locality nor the Reichenbach principle. I think it is futile to seek "explanations" of Bell-type correlations. Rather we should learn to accept them as a fundamental feature of reality, just like we have learned to accept the counter-intuitive constancy of the speed of light. Of course it is a compelling idea that the correlations are caused by "photons" traveling from the source to the detectors. (As compelling as the idea that light waves cannot propagate without an ether!) But it is misleading to think of a photon as an object. It is neither a wave spreading out into space, nor a traveling particle. The only meaning I can give to the term photon is as a pair of short-lived localized currents, which we can call emission and absorption events. I consider myself a realist, but I reject as unreal photons in the sense in which this term is frequently used. What I do think is real are the currents and their statistical tendency to be parallel. That's what photon polarization is about. Also electrons should not be thought of as "objects". Already Heisenberg rejected the notion of an electron's world-line. I think it is more appropriate to think of an electron as a track of short-lived current events in space-time, and of QED as a theory describing the correlations between such events.

Of course there is a strong psychological force against such a world-view. We are very good at detecting correlations, and they can take on a life of their own. Instead of the food, Pavlov's dog reacted to the sound of the bell! Likewise we perceive motion where there are just correlated events. And we assume continuity where there are discrete atoms. To interpolate, we construct continuous fields where there are only discrete events. A gravitational field can make Newton's action at a distance more palatable. Locality is a feature of such fields, but not of the underlying reality. I don't think locality can have a fundamental theoretical status.

PS: Thank you for the reference to the Tumulka paper. I was delighted to read about the GRW "flash" model, and to discover that already John Bell had likened a piece of matter to a "galaxy of events". I'm still not a fan of GRW, because I find it too ad hoc. But it might converge with an effort of interpreting QFT as a statistical theory of events and the correlations between them.

 

[RUTA]

I never understood these arguments. We have a working local theory, relativistic QFT, violating Bell's inequality in all observed cases.

QM is not Lorentz invariant, i.e., QM is the "non-relativistic" limit of QFT, yet it predicts the observed violations of the Bell inequality. Whether or not the parent theory QFT is Lorentz invariant or not is irrelevant. That in a nutshell is the issue.

 

[RUTA]

The situation is worsened by the introduction of meaningless assumptions like CFD that only contribute to the general confusion,

There is a very good reason for talking about counterfactual definiteness (CFD) when discussing the "mystery" of entanglement. Simple hidden variable models will accommodate the correlated outcomes for the same measurements (Mermin's "case (a)"), so the real "mystery" resides in the correlations found in different measurements (Mermin's "case (b)"). And that "mystery" comes from assuming the simple hidden variable account responsible for the case (a) outcomes obtains counterfactually for case (b), i.e., the quantum state doesn't "know" how it will be measured, so it has to be ready for case (a). But being ready for case (a) then does not yield the correct correlations for case (b) if there is no superluminal communication between measurement events. That's Mermin's presentation.

 

[facenian]

Thanks for the reference, it is facinating! However I was strictly talking about CFD as used to derive the Bell inequality.

 

[facenian]

QM is not Lorentz invariant, i.e., QM is the "non-relativistic" limit of QFT, yet it predicts the observed violations of the Bell inequality. Whether or not the parent theory QFT is Lorentz invariant or not is irrelevant. That in a nutshell is the issue.

I would add that Lorentz invariant does not imply a velocity limit. That only works the other way around.
That QFT is local by construction sounds very dubious to me. It is only Lorentz invariant by construction.

 

[Demystifier]

I would add that Lorentz invariant does not imply a velocity limit. That only works the other way around.
That QFT is local by construction sounds very dubious to me. It is only Lorentz invariant by construction.

Indeed, there are many effective non-local Lorentz invariant QFT theories, such as those involving $\Box^{-1}$ in the action.

 

[vanhees71]

I'm wedded neither to locality nor the Reichenbach principle. I think it is futile to seek "explanations" of Bell-type correlations. Rather we should learn to accept them as a fundamental feature of reality, just like we have learned to accept the counter-intuitive constancy of the speed of light.

In addition, we have a perfect "explanation" (I'd rather say "theoretical description") of Bell-type correlation: Quantum theory. I also don't know, whether Reichenbach's ideas help much. I've the impression they make already special relativistic classical physics more complicated than necessary.

 

[Lynch101]

My problem is to understand, why people think relativistic quantum field theory were not local although it's local by construction.

My conclusion from this simply is that we just have to take the quantum state as what it tells us: The probabilities for the outcomes of measurements.

From reading and listening to various viewpoints (here and elsewhere) it seems to me that there are two levels to the discussion which can lead to people talking past each other. To my mind, the issue lies in the question of 'completeness'.

Those that argue that QM or QFT must be non-local seem to be taking the position that a complete description of physical reality, in the broader sense meant by EPR, must be non-local to explain how the observed correlations occur i.e. what underlying mechanism gives rise to such correlations.

While QFT might be local by design, if the mathematics only gives us 'the probabilities for the outcomes of measurements', then it can't be a complete description of physical reality.

This is what Lee Smolin has said about 'going beyond the statistical predictions of QM'.

 

[vanhees71]

But the local explanation of how the observed correlations occur is given by Q(F)T: It's due to the preparation of the system.

You also cannot conclude from the fact that Q(F)T gives "only" probabilities for the outcomes of measurments, that it must necessarily be an incomplete theory. It may well be that Nature really behaves inherently probabilistic. We don't know this, of course, but there is no empirical evidence for determinism.

 

[Lynch101]

But the local explanation of how the observed correlations occur is given by Q(F)T: It's due to the preparation of the system.

You also cannot conclude from the fact that Q(F)T gives "only" probabilities for the outcomes of measurments, that it must necessarily be an incomplete theory. It may well be that Nature really behaves inherently probabilistic. We don't know this, of course, but there is no empirical evidence for determinism.

But, if Q(F)T only gives probabilities for the outcomes of measurments then, by definition, the mathematics doesn't describe the system prior to measurement. This would mean that it cannot be a complete description of physical reality.

 

[vanhees71]

But it describes the system prior to measurement. Knowing the quantum state doesn't imply that all observables take predetermined values. According to all observations known, particularly those very precise ones with Bell states, that's really the case.

 

[martinbn]

But, if Q(F)T only gives probabilities for the outcomes of measurments then, by definition, the mathematics doesn't describe the system prior to measurement. This would mean that it cannot be a complete description of physical reality.

You are making assumptions on how reality should be. If you prepare a system and make a measurment, and you do that many times in the exact same way, but get differnt results, how can you expect to predict anything more than probabilities? Of course it may be that the preparations were not identical, but we don't know, so your demand for more is based on an assumption. Also the fact that decades of refining and improveing the expariments have shown no improvement for the probabilities, say what used to be 50-50 now is 51-49, is a good indication that may be nature is like that and you cannot complete the theory in that direction.

By the way that is not what EPR meant by incompletenes.

 

[Lynch101]

But it describes the system prior to measurement. Knowing the quantum state doesn't imply that all observables take predetermined values. According to all observations known, particularly those very precise ones with Bell states, that's really the case.

It doesn't require that all observables take pre-determined values, but if the mathematics gives us the probability distribution for the outcome of a position measurement, it doesn't tell us where it was prior to measurement.

While it might be a classical bias to expect a definite value for position, prior to measurement, the system in question must be somewhere as it cannot be nowhere. If the mathematics doesn't describe this 'somewhere' it cannot give a complete description of physical reality.

Some interpretations ascribe an ontology to the wave function which attempts to describe this 'somewhere', which make them [an attempt at] a complete description of physical reality. Any interpretation that only gives probabilistic predictions for the outcomes of measurements cannot be said to describe the location of the system prior to measurement. Since the system must be somewhere - even if that doesn't imply a definite location - such an interpretation/theory cannot be said to be a complete description of physical reality.

 

[vanhees71]

No, it doesn't tell us where it was prior to measurement, but not because it's an incomplete description, but because indeed the position was indetermined. Then the probabilistic description is complete. I still don't know your definition of "physical reality".

 

[Lynch101]

You are making assumptions on how reality should be. If you prepare a system and make a measurment, and you do that many times in the exact same way, but get differnt results, how can you expect to predict anything more than probabilities? Of course it may be that the preparations were not identical, but we don't know, so your demand for more is based on an assumption. Also the fact that decades of refining and improveing the expariments have shown no improvement for the probabilities, say what used to be 50-50 now is 51-49, is a good indication that may be nature is like that and you cannot complete the theory in that direction.

By the way that is not what EPR meant by incompletenes.

According to EPR, a complete theory is one in which 'every element of the physical reality must have a counterprart in the physical theory.

Quantum systems must be located somewhere [in the universe] prior to measurement, since they cannot be 'nowhere'. If the mathematical formalism only gives the probabilities for observing the quantum system at a given location after interacting with a measurement device, then it does not describe the location of the system prior to that. Since it must be located 'somewhere', any such interpretation/theory cannot be considered a complete description of physical reality.

 

[martinbn]

According to EPR, a complete theory is one in which 'every element of the physical reality must have a counterprart in the physical theory.

Quantum systems must be located somewhere [in the universe] prior to measurement, since they cannot be 'nowhere'. If the mathematical formalism only gives the probabilities for observing the quantum system at a given location after interacting with a measurement device, then it does not describe the location of the system prior to that. Since it must be located 'somewhere', any such interpretation/theory cannot be considered a complete description of physical reality.

That is not EPR, it is your statement. EPR say that if you can predict with 100% certainty the outcome of a measument, then a complete theory must accout for that, the observable must have a value before the measurement. What you are saying is that the system must be somewhere (because it cannot be nowhere), therefore any complete theory must have values for positions at any time.

 

[Lynch101]

No, it doesn't tell us where it was prior to measurement, but not because it's an incomplete description, but because indeed the position was indetermined. Then the probabilistic description is complete. I still don't know your definition of "physical reality".

I'm referencing the "physical reality" of the EPR paper. I take it to mean 'the Universe' or 'how the universe is'.

The system must be located somewhere in the universe prior to measurement. If it were not, then it couldn't interact with the measurement device in the first place. If all we have is the probability of observing the system in a given location after its interaction with the measurement device, then we lack a description of where the system is located prior to measurement. It may not necessarily require a definite value, but it does require a description for a theory to be considered a complete description of physical reality.

 

[Lynch101]

That is not EPR, it is your statement.

Whatever the meaning assigned to the term complete, the following requirement for a complete theory appears to be a necessary one: every element of the physical reality must have a counterpart in the physical theory. We shall call this the condition of completeness.

EPR paper

EPR say that if you can predict with 100% certainty the outcome of a measument, then a complete theory must accout for that, the observable must have a value before the measurement.

Yes, EPR did say that, but they also said that was just one possible way, not the only possible way.

It seems to us that this criterion, while far from exhausting all possible ways of recognizing a reality, at least provides us with one.

What you are saying is that the system must be somewhere (because it cannot be nowhere), therefore any complete theory must have values for positions at any time.

I'm not suggesting the theory must have definite values, but it must have some description of its location - whatever form that may take.

A theory/interpretation which only gives the probability of a location after interacting with a measurement device does not, by definition, describe the location prior to measurement. Thus making it, by definition, an incomplete description of physical reality.

 

[WernerQH]

The system must be located somewhere in the universe

It is a natural assumption that a "system" is alwas there. But it still is an assumption. It is silly to question it in the case of the moon. At least in some sense it is always there. But it is it an irrefutable fact in the case of "objects" like electrons and photons?

H.G. Wells wrote:
"It may be that we exist and cease to exist in alternations, like the minute dots in some form of toned printing or the succession of pictures on a cinema film."
(Science and Ultimate Truth, 1931)

Wells obviously had a more general notion of "system".

 

[vanhees71]

That quantum systems are located somewhere is described by QT in the sense that the probability that the particle is somewhere is 1 (supposed it is sure that it is indeed still there and not annihilated with some antiparticle).

 

[Lynch101]

That is not EPR, it is your statement. EPR say that if you can predict with 100% certainty the outcome of a measument, then a complete theory must accout for that, the observable must have a value before the measurement. What you are saying is that the system must be somewhere (because it cannot be nowhere), therefore any complete theory must have values for positions at any time.

Yes, EPR did say that, but they also said that was just one possible way, not the only possible way.

It seems to us that this criterion, while far from exhausting all possible ways of recognizing a physical reality, at least provides us with one.

It is a natural assumption that a "system" is alwas there. But it still is an assumption. It is silly to question it in the case of the moon. At least in some sense it is always there. But it is it an irrefutable fact in the case of "objects" like electrons and photons?

H.G. Wells wrote:
"It may be that we exist and cease to exist in alternations, like the minute dots in some form of toned printing or the succession of pictures on a cinema film."
(Science and Ultimate Truth, 1931)

Wells obviously had a more general notion of "system".

If the system ceases to exist, how can it interact with the measurement device? Does the system spontaneously comes into existence at the precise moment we would expect it to interact with the measurement device? Does the system, which is made of 'something' disappear into complete 'nothingness' i.e. go from existing to not-existing? Equally does it physically manifest out of complete nothingness?
If so, this would seem to be more 'spooky action' that needs explaining or describing.

 

[Lynch101]

It is a natural assumption that a "system" is alwas there. But it still is an assumption. It is silly to question it in the case of the moon. At least in some sense it is always there. But it is it an irrefutable fact in the case of "objects" like electrons and photons?

H.G. Wells wrote:
"It may be that we exist and cease to exist in alternations, like the minute dots in some form of toned printing or the succession of pictures on a cinema film."
(Science and Ultimate Truth, 1931)

Wells obviously had a more general notion of "system".

If the system ceases to exist, how can it interact with the measurement device? Does the system spontaneously comes into existence at the precise moment we would expect it to interact with the measurement device? Does it just randomly come into existence at the locations where measurement devices just happen to be located? Does the system, which is made of 'something' disappear into complete 'nothingness' i.e. go from existing to not-existing? Equally does it physically manifest out of complete nothingness?
If so, this would seem to be more 'spooky action' that needs explaining or describing.

 

[Lynch101]

That quantum systems are located somewhere is described by QT in the sense that the probability that the particle is somewhere is 1 (supposed it is sure that it is indeed still there and not annihilated with some antiparticle).

Can it be anywhere?

 

[vanhees71]

It's described by the position-probability distribution, which tells you for any region in space what the probability is to find it there when looking.

 

[Demystifier]

You also cannot conclude from the fact that Q(F)T gives "only" probabilities for the outcomes of measurments, that it must necessarily be an incomplete theory. It may well be that Nature really behaves inherently probabilistic.

You are missing the point. In the first sentence, the emphasis is not on "probabilities". The emphasis is on "measurements". If a theory only predicts outcomes of measurements (irrespective of whether those predictions are probabilistic or deterministic), then the theory is incomplete. A complete theory (according to this philosophy, which you are not obliged to accept) should describe things at the microscopic level without referring to measurements. Quantum theory in its standard minimal form cannot consistently talk about probabilities without talking about measurements. If a probabilistic theory is complete, then this complete theory should talk about probabilities without measurements. Standard minimal QM does not do that.

 

[Demystifier]

It's described by the position-probability distribution, which tells you for any region in space what the probability is to find it there when looking.

Yes, when looking. But according to people who argue that minimal QM is incomplete, the complete theory should say something about probabilities even in the absence of looking.

 

[Lynch101]

It's described by the position-probability distribution, which tells you for any region in space what the probability is to find it there when looking.

This is an explanation of what it means to give the probability of measurement outcomes. What we need is a description of the system prior to measurement.

If we drill down into the statement however, we can try to see if it tells us anything about the system prior to measurement.

We always measure the system to be in a definite location and the probability distribution tells us the likelihood of measuring a definite position for the system, at the given location. Does this mean that the system always has a definite location but due to a lack of information we can only predict the probability of that definite location?

If not, then what does it mean, in our universe, to not have a definitive position but to still be located somewhere in the universe?
Does it mean:
- the system is located in more than one place at a time?
- the system pops in an out of existence?
- [insert other possible questions].If the answer is that it only allows us to make probabilistic predictions as to the definite location of the system, after it interacts with a measurement device, then, by definition, it is an incomplete description of physical reality.

 

[facenian]

I believe that trying to "prove" the incompleteness issue as a mathematical theorem is not the correct approach. It could lead to endless unproductive discussions. You either postulate its truth or reject it. It is an epistemological possion.
EPR tried to prove it but Einstein did not like it. That is a very important point. We should listen to Einstein, not to EPR. In my opinion, EPR produced much confusion introducing unnecessary metaphysical elements.
Einstein "proved" incompleteness by assuming locality (through his separation principle). That means that completeness and locality cannot go together when we assume a given notion of locality.
One of the important things that the Bell theorem tells us when it is correctly interpreted is that to keep locality we must change its usual meaning and replace "Local Causality" with "No-signaling". That is one way, that locality and completeness can get along together.
I do not agree with those who cheerfully declare that quantum theory is local by construction. That explains nothing.
Not to mention the absurd claim that QM is local because the Bell inequality is a classical result.

 

[Demystifier]

I do not agree with those who cheerfully declare that quantum theory is local by construction. That explains nothing.

Indeed. If one looks carefully at the QFT axioms, one can see that some axioms are local in a certain sense by construction, but some are not. In particular, the Born rule axiom is not local by construction (here I'm not saying that it is nonlocal by construction). So one must look carefully at consequences of all axioms together to see whether the theory as a whole is local or not. Depending on how exactly one defines locality of theory as a whole, one obtains that the theory is local in one sense and nonlocal in another. Which definition of locality is more relevant or makes more physical sense is a matter of philosophy.

 

[WernerQH]

Does the system, which is made of 'something' disappear into complete 'nothingness' i.e. go from existing to not-existing? Equally does it physically manifest out of complete nothingness?

Yes. Why not? (It was obviously conceivable for Wells.)

Your addition "which is made of 'something'" indicates a metaphysical belief that the universe is made from some "stuff". Feel free to seek a description of Nature that conforms more closely to your intuition.

 

[Lynch101]

Yes. Why not? (It was obviously conceivable for Wells.)

I would question how conceivable it actually is. How does 'something' cease to exist?

EDIT: or the more difficult age old question, how do you get 'something' from 'absolutely nothing'?

Your addition "which is made of 'something'" indicates a metaphysical belief that the universe is made from some "stuff". Feel free to seek a description of Nature that conforms more closely to your intuition.

'Something' is simply the bluntest descriptor we can use for existence. We know that there is existence because there is experience. Whatever it is that exists we apply the label 'something' to it. Whatever exists is made of 'something' - you might call it 'stuff'. It can't be made of 'nothing' because 'nothing', by definition, does not exist.

It's not possible for 'something' i.e. existence to come from 'nothing' i.e. non-existence - at least not without some 'spooky action'.

Equally, how 'something' could suddenly cease to exist would require similar 'spooky action'.

 

[vanhees71]

You are missing the point. In the first sentence, the emphasis is not on "probabilities". The emphasis is on "measurements". If a theory only predicts outcomes of measurements (irrespective of whether those predictions are probabilistic or deterministic), then the theory is incomplete. A complete theory (according to this philosophy, which you are not obliged to accept) should describe things at the microscopic level without referring to measurements. Quantum theory in its standard minimal form cannot consistently talk about probabilities without talking about measurements. If a probabilistic theory is complete, then this complete theory should talk about probabilities without measurements. Standard minimal QM does not do that.

Then no physics is realistic or complete, because all of physics describes or predicts observations and thus, in quantified form, the outcome of measurements. How do you want to describe anything if not by referring to the phenomena we can observe about it?

 

[vanhees71]

Yes, when looking. But according to people who argue that minimal QM is incomplete, the complete theory should say something about probabilities even in the absence of looking.

If I never look, I can't check any predicted probabilities.

 

[vanhees71]

This is an explanation of what it means to give the probability of measurement outcomes. What we need is a description of the system prior to measurement.

If we drill down into the statement however, we can try to see if it tells us anything about the system prior to measurement.

We always measure the system to be in a definite location and the probability distribution tells us the likelihood of measuring a definite position for the system, at the given location. Does this mean that the system always has a definite location but due to a lack of information we can only predict the probability of that definite location?

If not, then what does it mean, in our universe, to not have a definitive position but to still be located somewhere in the universe?
Does it mean:
- the system is located in more than one place at a time?
- the system pops in an out of existence?
- [insert other possible questions].If the answer is that it only allows us to make probabilistic predictions as to the definite location of the system, after it interacts with a measurement device, then, by definition, it is an incomplete description of physical reality.

As I repeatedly said, the description of the system prior to measurement is given by the quantum state (statistical operator) at the initial time (after the "preparation" is finished). In classical mechanics it's given by the point in phase space at the initial time.

What does it mean not to have a definite position is clear: You cannot predict with certainty to find the particle in a given region in space but you can give only the probability to find the particle in any given region. That's all we know given the quantum state of the particle, and according to all observations today that's also all we can know in principle.

 

[vanhees71]

Indeed. If one looks carefully at the QFT axioms, one can see that some axioms are local in a certain sense by construction, but some are not. In particular, the Born rule axiom is not local by construction (here I'm not saying that it is nonlocal by construction). So one must look carefully at consequences of all axioms together to see whether the theory as a whole is local or not. Depending on how exactly one defines locality of theory as a whole, one obtains that the theory is local in one sense and nonlocal in another. Which definition of locality is more relevant or makes more physical sense is a matter of philosophy.

Can you specify more clearly, what you mean by the Born rule were not local? I have no clue, how the Born rule may be considered as local or non-local at all.

 

[Lynch101]

you can give only the probability to find the particle in any given region.

What does this tell us about the system?

We can only predict, with probability, that we will find the particle in any given region. Yet, when we measure the particle, we always measure it with a definite location. Does this mean that the particle always has a definite location but, due to missing information, we can only predict [with probability] where this definite location will be?

That's all we know given the quantum state of the particle, and according to all observations today that's also all we can know in principle.

There is a distinction to be made, as you have here, between all that we can know in principle and all there is to know. The latter would constitute a complete description of physical reality. It's possible that no more complete theory is possible but that would not mean that the given theory is a complete description of the univervse.

 

[PeterDonis]

The system must be located somewhere in the universe prior to measurement. If it were not, then it couldn't interact with the measurement device in the first place.

QM has no such requirement. In QM it is perfectly possible for systems that do not have definite positions to interact. In fact, since in QM states with definite positions (eigenstates of the position operator) are not even normalizable, they are not realizable physically, so strictly speaking, nothing in QM ever has a definite position. Yet things interact in QM just fine.

 

[PeterDonis]

I'm not suggesting the theory must have definite values, but it must have some description of its location - whatever form that may take.

A theory/interpretation which only gives the probability of a location after interacting with a measurement device does not, by definition, describe the location prior to measurement. Thus making it, by definition, an incomplete description of physical reality.

Again, QM has no such requirement. See my previous post just now.

 

[PeterDonis]

We always measure the system to be in a definite location

No, we don't. All measurements of position have finite error bars; it is impossible to measure position with infinite precision.

 

[vanhees71]

QM has no such requirement. In QM it is perfectly possible for systems that do not have definite positions to interact. In fact, since in QM states with definite positions (eigenstates of the position operator) are not even normalizable, they are not realizable physically, so strictly speaking, nothing in QM ever has a definite position. Yet things interact in QM just fine.

Yes, and indeed that implies that positions are always to a certain extent "uncertain". A $\delta$-distribution is indeed not a square-integrable function!