Undergrad The Probability Distribution and 'Elements of Reality'

[vanhees71]

Well, in contradistinction to the QT case the various philosophical interpretations of spacetime models (SR, GR) don't play much of a role within the physics community. The only impact of philosophy on relativity concerning the history of physics is that Einstein explicitly did not get his Nobel prize for his work on relativity. It's one of the few if not the only example where the Nobel diploma explicitly emphasizes that a laureat got the Nobel prize not for one of his major achievements. The "culprit" here is the very influential philosopher Henri Bergson, who could not be convinced by the physicists among them particularly Langevin and also Einstein himself that the notion of time in the theories of relativity are valid.

The philosophical quibbles with the interpretations of QT however have triggered and still trigger a lot of work also in the physics community. While before Bell it was a career-killing step to question the Copenhagen doctrine with Bohr as the pope, and Bell cautioned young colleagues not to enter the field before having secured a tenured job. Fortunately this changed when his ideas, making the philosophical speculations a la EPR and others a scientifically well-defined hypothesis which was decidable by objective observations, and then starting with the first experiments by Clauser and particularly Aspect et al a whole new branch of physics started to be created, which today we call quantum information or the like. With the development of all kinds of sources of entangled quantum systems and after most of the "thought experiments" could be realized in high-precision experiments now for a few years it has reached such a maturity that it becomes a subject of engineering, opening an entire new branch of "quantum engineering" research and development. So here the philosophers had a good impact on science and technology although some philosophers as well as physicists still seem not to be satisfied with what I call a clear answer of the question whether QT describes reality completely.

For me the answer definitely is yes with the qualification that QT is not intrinsically complete as long as there is no satisfactory description of the gravitational interaction within QT or some more comprehensive new theory. That's, however, not a philosophical but a scientific problem, which I guess won't be solved before there's clear empirical evidence of "quantum effects" of gravity (gravitons?) to guide the theorists to maybe find one day the desired theory "beyond the Standard Model".

 

[Lynch101]

For me EPR's description of physical reality is ruled out by all the very accurate Bell tests, including the most recent ones ruling out many if not all the loopholes.
...
Particularly their conclusion about the predetermination of observables that are indetermined due to quantum mechanics is ruled out, at least for the class of local hidden-variable theories a la Bell.

We need to be careful not to throw the baby out with the bathwater here. While the primary focus of the paper is on the one particular argument put forward by EPR, it is situated in the context of a broader point. The broader point was that of the complete description of the system, for which they gave their more general criterion. EPR say that their argument does not exhaust all possible arguments. Theirs is just one possible way of 'recognising an element of reality'.

That one particular argument is ruled out by Bell tests, there can be no 'local hidden variables' without (what people refer to as) 'conspiratorial common causes'. There can be no single, pre-defined value for position. But that doesn't mean that there cannot be multiple values for position, or that there is no position/location whatsoever.

The invalidation of their single, inexhaustive argument does not allow us to conclude that the statistical interpretation is, therefore, a complete description of the system. It only allows us to conclude that there are no 'local hidden variables'.

Bell's theorem appears to leave us with 3/4 options of how to explain the observed correlations:
1) non-local hidden variables
2) superdeterminism
3) [strong] anti-realism
4) [Insert alternative here]

All of these represent [potentially] complete descriptions of the system. We might not be able to determine, by way of experiment, which of them is correct, but they are potentially complete. If we reject these options but fail to provide an alternative explanation, then we are leaving ourselves with an incomplete description.

The difficulty seems to be still today that many philosophers (and also some physicists) seem not to accept what physics is telling us, i.e., that our all too classically formed intuition about how Nature behaves is flawed, and we have to adapt our intuitions to what quantum theory tells us about Nature's behavior. It's not the purpose of the natural sciences to confirm our prejudices but to learn how Nature "really" behaves, and obviously Nature's behavior is much closer to what's described by QT than by the (imho pretty vague) philosophical ideas by EPR.

I'm in full agreement that the physics doesn't need to conform to our intuitions and that we need to examine what the physics is telling us. That is precisely what I am trying to do.

Simply saying that QT doesn't conform to our intuitions isn't a complete answer nor, necessarily, is saying that the system behaves randomly. It is possible that we can draw further, necessary, conclusions about the system. We can do this by exploring what the physics is telling us and by following the consequences. By doing this we can identify precisely where nature diverges from our intuitions or more precisely, our current models of the universe. More importantly, for the purpose of completeness, we can try to establish how nature diverges from our current models.

For example, when we say the system passes through a carefully-prepared, inhomogenous magnetic field, this has certain implications according to our existing models. If the magnetic field occupies a finite region of space and the system passes through this finite region of space then, according to our existing model, we can narrow down the location of the system at some time during the experiment i.e. it must be located in the finite region of space occupied by the magnetic field.

If we deny that the system has a location somewhere in this finite region of space then we need an explanation as to why. Simply saying that nature doesn't need to conform to our intuitions is fine, but it is incomplete.

The only example, which works as a theory is the Bohmian nonlocal reinterpretation of non-relativistic QT. The problem with this is that there's no satisfactory Bohmian reinterpretation of local relativistic QFT, which is the most comprehensive theory of matter yet found.

The relativity of simultaneity [potentially] has consequences for the statistical interpretation and the application of the probability distribution. But that would be the subject of a different discussion.

 

[Fra]

That is what advocates of various QM interpretations are basically claiming: that their preferred interpretation will lead to a deeper understanding by being extrapolated or extended to a different theory that can be experimentally tested. But so far that hasn't happened.

Fair enough.

But i think it's a hard problem, and it may take still more time. And I also wonder how many that really work hard enough on this, compare to other work? After all, it's not the best way for making a living. To be honest I had expected much more from myself in this regard even, but reality is that other stuff grabs most time. So I think the lack or process is also partially a research political question. Some of the dominating research programs in foundational QM, IMO avoids some of the harder questions, so no wonder progress is slow.

/Fredrik

 

[Morbert]

Was I interpreting your statement correctly when I interpreted it as saying, QT 'does not does not completely describe the reality of [the] system' but most physicists believe that a more complete description is not possible?

These discussions can't be reduced to unqualified propositions. E.g. If I answered yes to your question above, then the proposition itself would be open to misinterpretation, especially if it was used as the starting point of some other argument. Instead we should say something like

"QM (with the usual interpretational caveats) does not completely describe the reality of the system in the sense that a quantum theory will report the likelihoods of possible events occurring, but will not single out the set of events that actually occur, and not in the sense that there is a physical state or thorough account of all elements of reality not uniquely characterised by the quantum state."

I try to make the distinction between the EPR argument and the overall aim as suggested by the title of the paper. The argument that they put forward in the paper does not, they say, exhaust all possible ways of regocognising an element of physical reality.

Ultimately, what they are calling for is a complete description of the system and their general criterion is that all elements of physical reality i.e. everything about the system should correspond to something in the mathematics. You have stated previously that the statistical (or 'anti-realist') interpretation says that the wave function does not correspond to physical reality.

I don't think we can easily divorce the aim from the argument. And ultimately we have to depart from simple terms like "elements of reality" into specifics.

 

[WernerQH]

I'm in full agreement that the physics doesn't need to conform to our intuitions and that we need to examine what the physics is telling us. That is precisely what I am trying to do.

The difficulty lies in identifying misleading intuitions (preconceptions). Before Einstein it was "self-evident" that there can be only one time throughout the universe that is the same for all observers. A similar preconception, in my opinion, is the idea that the world around us is composed of objects that are subject to definite "laws of motion".

Bell's theorem appears to leave us with 3/4 options of how to explain the observed correlations:
1) non-local hidden variables
2) superdeterminism
3) [strong] anti-realism
4) [Insert alternative here]

Physics would certainly become more intuitive, if an explanation based on familiar notions could be found. But I think a search for such explanations is futile and we should be happy to have an excellent description of those correlations. You may dislike statistical theories (e.g. the kinetic theory of gases) as "incomplete", but I think their incompleteness is an advantage. We don't become overwhelmed with details. I don't dare to imagine a theory that could predict the decay time of a particular neutron.

 

[vanhees71]

These discussions can't be reduced to unqualified propositions. E.g. If I answered yes to your question above, then the proposition itself would be open to misinterpretation, especially if it was used as the starting point of some other argument. Instead we should say something like

"QM (with the usual interpretational caveats) does not completely describe the reality of the system in the sense that a quantum theory will report the likelihoods of possible events occurring, but will not single out the set of events that actually occur, and not in the sense that there is a physical state or thorough account of all elements of reality not uniquely characterised by the quantum state."
I don't think we can easily divorce the aim from the argument. And ultimately we have to depart from simple terms like "elements of reality" into specifics.

But you can also argue, and that seems the most plausible alternative given the empirical facts, that QM completely describes the reality of the system, because the set of events that actually occurs is not predetermined but objectively random.

 

[Morbert]

But you can also argue, and that seems the most plausible alternative given the empirical facts, that QM completely describes the reality of the system, because the set of events that actually occurs is not predetermined but objectively random.

You can, but without qualifying "complete" I think it will ultimately be set against us in some future conversation.

E.g. You tell Bob that "QM completely describes the reality of the system, because the set of events that actually occurs is not predetermined but objectively random.". Bob says great and prepares a Schroedinger's cat experiment as per usual. The cat, vial, box atmosphere etc is prepared in a state ψ. After t seconds, our quantum theory of the box tells us the probability that the cat is alive is 0.5. Since bob heard you use the word complete, and he imposes his understanding of the word, he decides the reality inside the box is that the cat is suspended in some state of neither dead nor alive, and will only exhibit the reality of a dead (or living cat) with a 50% likelihood once he opens the box.

 

[vanhees71]

A physical theory is complete if it describes all known observations.

All that Bob can know about the poor cat is that it is with probability 1/2 alive and with probability 1/2 dead. There's not more to be known about the observables "dead" or "alive" before looking. That's the only "reality" there is.

 

[Morbert]

A physical theory is complete if it describes all known observations.

All that Bob can know about the poor cat is that it is with probability 1/2 alive and with probability 1/2 dead. There's not more to be known about the observables "dead" or "alive" before looking. That's the only "reality" there is.

I agree that Bob's quantum theory of the box {ψ, H} uniquely characterises all he can know about it. But he (as I'm sure you agree) should still be free to suppose that the cat really is dead or alive, regardless of whether or not he can know it.

 

[vanhees71]

You can suppose a lot of unobserved things, but that has no meaning at all. You can suppose you've chosen the right numbers in Lotto, but it doesn't help you, if other numbers are drawn next Saturday.

 

[Lynch101]

These discussions can't be reduced to unqualified propositions. E.g. If I answered yes to your question above, then the proposition itself would be open to misinterpretation, especially if it was used as the starting point of some other argument. Instead we should say something like

"QM (with the usual interpretational caveats) does not completely describe the reality of the system in the sense that a quantum theory will report the likelihoods of possible events occurring, but will not single out the set of events that actually occur, and not in the sense that there is a physical state or thorough account of all elements of reality not uniquely characterised by the quantum state."

It is essentially the emboldened claim that is being questioned namely that there is not more to be described.

I don't think we can easily divorce the aim from the argument. And ultimately we have to depart from simple terms like "elements of reality" into specifics.

The overall aim is quite different from the specific argument they make. The overall aim is to give a complete description of the system. Their argument was that they had chosen one possible way of establishing the incompleteness of the QM description. They also said it was far from exhausting all possible ways.

So, disproving their specific argument only demonstrates that QM was not incomplete in the way they had envisioned. That does not then mean that the description is complete. The purpose of this discussion is to explore the consequences of taking the statistical interpretation as complete. If there is no more to be described, then that has certain implications for how nature is.

But even starting with the position that the SI is a complete description arguably leads us to the absence of an explanation for how the system randomly assumes a single, well-defined position.

 

[Lynch101]

You can, but without qualifying "complete" I think it will ultimately be set against us in some future conversation.

E.g. You tell Bob that "QM completely describes the reality of the system, because the set of events that actually occurs is not predetermined but objectively random.". Bob says great and prepares a Schroedinger's cat experiment as per usual. The cat, vial, box atmosphere etc is prepared in a state ψ. After t seconds, our quantum theory of the box tells us the probability that the cat is alive is 0.5. Since bob heard you use the word complete, and he imposes his understanding of the word, he decides the reality inside the box is that the cat is suspended in some state of neither dead nor alive, and will only exhibit the reality of a dead (or living cat) with a 50% likelihood once he opens the box.

If you put a live cat in a box and prepare a schroedingers cat experiment, at time t, if there is a 0.5 probability that the cat is alive or dead but our description of the cat doesn't describe the cat as either alive or dead, then our description cannot be complete because the cat is either alive or dead.

Alternatively, we need to drastically re-imagine our notion of 'cats' and what it means for a cat to be 'alive' or 'dead'.Also, if we put the cat in a box but we don't know the exact position of the cat within the box, because it may be moving around, we can still narrow the location/position of the cat to within the finite region of space that the box encompasses.

 

[Lynch101]

A physical theory is complete if it describes all known observations.

All that Bob can know about the poor cat is that it is with probability 1/2 alive and with probability 1/2 dead. There's not more to be known about the observables "dead" or "alive" before looking. That's the only "reality" there is.

Our ability to know what state the cat is in has no bearing on what state the cat is actually in. The cat is either dead or alive, not suspended in some in-between state.

If we put the cat in the box and close the lid, we might not know the exact location/position of the cat, but we can narrow it down to the finite region enclosed by the box.

 

[Lynch101]

You can suppose a lot of unobserved things, but that has no meaning at all. You can suppose you've chosen the right numbers in Lotto, but it doesn't help you, if other numbers are drawn next Saturday.

We don't have to suppose one or the other. We can suppose all possible scenarios and explore their consequences.

 

[Morbert]

The overall aim is quite different from the specific argument they make. The overall aim is to give a complete description of the system. Their argument was that they had chosen one possible way of establishing the incompleteness of the QM description. They also said it was far from exhausting all possible ways.

So, disproving their specific argument only demonstrates that QM was not incomplete in the way they had envisioned. That does not then mean that the description is complete. The purpose of this discussion is to explore the consequences of taking the statistical interpretation as complete. If there is no more to be described, then that has certain implications for how nature is.

But even starting with the position that the SI is a complete description arguably leads us to the absence of an explanation for how the system randomly assumes a single, well-defined position.

If you put a live cat in a box and prepare a schroedingers cat experiment, at time t, if there is a 0.5 probability that the cat is alive or dead but our description of the cat doesn't describe the cat as either alive or dead, then our description cannot be complete because the cat is either alive or dead.

It cannot be complete in this sense yes. But it can be complete in the sense that the the state ψ is the unique physical state of the system, and there is no underlying physical state λ distinct from ψ that fully characterises the system.

 

[Lynch101]

It cannot be complete in this sense yes. But it can be complete in the sense that the the state ψ is the unique physical state of the system, and there is no underlying physical state λ distinct from ψ that fully characterises the system.

ψ is a mathematical description of the state of the system. So, we ask, what does ψ tell us about the system. In your use of Schroedinger's cat here, the 'cat in the box' is the system being described, it is the 'physical reality'.

A complete description of the system i.e. the cat in the box, would have to describe the cat as either:
1) Alive
or
2) Dead

Any description which fails to do this is, by necessity, an incomplete description of the system or of physical reality.
But again, we might not know the exact position of the cat in the box, but we can narrow its position down to within the finite region the box encapsulates.

 

[PeterDonis]

With relativity we have the Lorentzian view based on absolute simultaneity and the Einsteinian based on relativity of simultaneity.

There is not a "rich history" of exploration of alternative interpretations to what you are calling the Einsteinian one. The Lorentzian view has never had many proponents and the literature on it is almost entirely disconnected from the literature on standard relativity. That is very different from the situation with regard to quantum interpretations.

From the Einsteinian view we have all manner of interpretations from the Block Universe, the growing block universe, the Relational Block Universe, Julian Barbour's 'Platonia', to the interpretation you've written about in your insight article.

None of these are "the Einsteinian view", since they all ascribe some kind of absolute significance to one particular simultaneity convention.

 

[Lynch101]

There is not a "rich history" of exploration of alternative interpretations to what you are calling the Einsteinian one. The Lorentzian view has never had many proponents and the literature on it is almost entirely disconnected from the literature on standard relativity. That is very different from the situation with regard to quantum interpretations.

Fair enough, it may not be a 'rich history', but there is a history. You've written an insight article on it yourself.

Regardless, physicists today certainly seem to be engaging in it - as evidenced by this section of the forum.

None of these are "the Einsteinian view", since they all ascribe some kind of absolute significance to one particular simultaneity convention.

Ah, I see. Thank you for the clarification.

 

[Morbert]

ψ is a mathematical description of the state of the system. So, we ask, what does ψ tell us about the system. In your use of Schroedinger's cat here, the 'cat in the box' is the system being described, it is the 'physical reality'.

A complete description of the system i.e. the cat in the box, would have to describe the cat as either:
1) Alive
or
2) Dead

Any description which fails to do this is, by necessity, an incomplete description of the system or of physical reality.

But again, we might not know the exact position of the cat in the box, but we can narrow its position down to within the finite region the box encapsulates.

Again, in one sense yes. In another, no. See my comments in previous posts for more detail.

 

[Lynch101]

Again, in one sense yes. In another, no. See my comments in previous posts for more detail.

Noted. Incomplete in the sense of describing the [actual] physical system.

 

[Morbert]

Noted. Incomplete in the sense of describing the [actual] physical system.

No. That is too reductive.

 

[gentzen]

A physical theory is complete if it describes all known observations.

Well, of course, intuitively you would expect that this is meant by "complete". But then, how could Born and Heisenberg claim in 1927 that quantum mechanics was complete? It certainly did not describe all known observations back then, and both were perfectly aware of that. So we know that something else is meant by "complete" in those discussions. Something like "there is no hidden classical layer underneath the quantum description".

 

[Lynch101]

No. That is too reductive.

Not from the Schroedinger's cat example you gave. But that doesn't accurately represent the issue being discussed because cat's have definite, well-defined properties, whereas quantum systems don't necessarily. However, it does speak to the issue of incomplete descriptions, since the cat is either alive or dead and if the description doesn't describe the cat as one or the other, it cannot be complete.

But, as I said, that isn't representative of the issue being discussed. What is representative is the position of the cat in the box. If we imagine that Schroedingers cat is pregnant when we put it in the box and we know that, roughly, at some time t, the cat will give birth inside the box. We don't know exactly when, but we have a rough idea.

When the cat gives birth, we don't know the position of the kitten, since the cat can move around in the box and so too can the kitten. What we can do, however, is narrow down the position* of the kitten to the finite region enclosed by the box. We know that it must be inside the box.

Now, it's possible that the cat gave birth to an entire litter inside the box. We don't know. But what we can do, is narrow down the position*/location of all potential kittens to somewhere within the finite region of space enclosed by the box.

It might be that our intuitive notions about cat's giving birth are completely incorrect. There could be some random process that occurs which we have never witnessed. Regardless of this, we can still narrow down the position* of the cat/kitten system to somewhere within the finite region enclosed by the box.

*position does not have to be a single, well- pre-defined value

 

[Lynch101]

A physical theory is complete if it describes all known observations.

Not necessarily, because there may be limitations to what can be observed.

 

[vanhees71]

Whatever this is, it's not subject of the natural sciences and thus off-topic in a physics forum ;-).

 

[Demystifier]

For me QT is complete as long as nobody has found another theory compatible with all empirical facts that proves that in fact observables always take determined values.

You consider completeness as a relation between theory and experiment. People in quantum foundations consider completeness as a property of the theory itself, which does not depend on whether it agrees with experiments or not. In that sense, classical mechanics is generally agreed to be complete (even though it is in conflict with many experiments), while there is no consensus whether QM is complete (even though there is consensus that it agrees with all experiments).

The problem, of course, is that there is no generally agreed definition of completeness of a theory itself. The choice of definition is a matter of philosophy, if you will. But once a definition is chosen, it can be proved more-or-less rigorously whether a theory is complete according to that definition. One such definition was chosen by EPR, who then proved that, according to this definition, QM cannot be both local and complete. Of course, others have chosen other definitions of completeness and then proved completeness or incompleteness according to those other definitions.

 

[Morbert]

Not from the Schroedinger's cat example you gave. But that doesn't accurately represent the issue being discussed because cat's have definite, well-defined properties, whereas quantum systems don't necessarily. However, it does speak to the issue of incomplete descriptions, since the cat is either alive or dead and if the description doesn't describe the cat as one or the other, it cannot be complete.

But, as I said, that isn't representative of the issue being discussed. What is representative is the position of the cat in the box. If we imagine that Schroedingers cat is pregnant when we put it in the box and we know that, roughly, at some time t, the cat will give birth inside the box. We don't know exactly when, but we have a rough idea.

When the cat gives birth, we don't know the position of the kitten, since the cat can move around in the box and so too can the kitten. What we can do, however, is narrow down the position* of the kitten to the finite region enclosed by the box. We know that it must be inside the box.

Now, it's possible that the cat gave birth to an entire litter inside the box. We don't know. But what we can do, is narrow down the position*/location of all potential kittens to somewhere within the finite region of space enclosed by the box.

It might be that our intuitive notions about cat's giving birth are completely incorrect. There could be some random process that occurs which we have never witnessed. Regardless of this, we can still narrow down the position* of the cat/kitten system to somewhere within the finite region enclosed by the box.

*position does not have to be a single, well- pre-defined value

It is reductive because again there are two senses of completeness being thrown around. QM not selecting a history of events that occurs is not the same thing as a quantum state not completely characterising the physical state of the system. QM is incomplete in the former sense, but complete in the latter.

 

[vanhees71]

You consider completeness as a relation between theory and experiment. People in quantum foundations consider completeness as a property of the theory itself, which does not depend on whether it agrees with experiments or not. In that sense, classical mechanics is generally agreed to be complete (even though it is in conflict with many experiments), while there is no consensus whether QM is complete (even though there is consensus that it agrees with all experiments).

The problem, of course, is that there is no generally agreed definition of completeness of a theory itself. The choice of definition is a matter of philosophy, if you will. But once a definition is chosen, it can be proved more-or-less rigorously whether a theory is complete according to that definition. One such definition was chosen by EPR, who then proved that, according to this definition, QM cannot be both local and complete. Of course, others have chosen other definitions of completeness and then proved completeness or incompleteness according to those other definitions.

Is classical mechanics really intrinsically complete? Maybe Newtonian mechanics, but for sure not relativistic mechanics of point particles.

In QT I think also non-relativistic QT as a mathematical theory is complete, QFT is only partially complete in the sense of perturbation theory.

I thought the quantum foundation people deal with physics rather than with pure mathematics and thus the only meaning of completeness can be the question whether it describes all observations correctly.

Concerning EPR I think the issue is pretty much clear: Their criterion of reality and completeness is simply not realized in Nature. You know my arguments for this hypothesis.

 

[Lord Jestocost]

The problem, of course, is that there is no generally agreed definition of completeness of a theory itself. The choice of definition is a matter of philosophy, if you will.

I think that questions about the "completeness" of scientific theories have their root in a very old philosophical question and have infected physics particularly since the advent of quantum mechanis (Bohr/Einstein debate). As Harald Atmanspacher remarks in “Between Chance and Choice: Interdisciplinary Perspectives on Determinism“ (Edited by Harald Atmanspacher and Robert Bishop) regarding this fundamental philosophical question:

“Can nature be observed and described as it is in itself independent of those who observe and describe – that is to say, nature as it is “when nobody looks”? This question has been debated throughout the history of philosophy with no clearly decided answer one way or the other. Each perspective has strengths and weaknesses, and each epoch has had its critics and proponents with respect to these perspectives. In contemporary terminology, the two perspectives can be distinguished as topics of ontology and epistemology. Ontological questions refer to the structure and behavior of a system as such, whereas epistemological questions refer to the knowledge of information gathering and using systems, such as human beings.”

 

[Demystifier]

Is classical mechanics really intrinsically complete? Maybe Newtonian mechanics, but for sure not relativistic mechanics of point particles.

Sure, I meant Newtonian mechanics.

I thought the quantum foundation people deal with physics rather than with pure mathematics and thus the only meaning of completeness can be the question whether it describes all observations correctly.

Putting emphasis on agreement with observations is called phenomenology. Sure, most of work in physics in phenomenology. But foundations of physics is something else. It's neither pure phenomenology nor pure mathematics. In addition it contains some elements of philosophy, but it's not pure philosophy either.