Undergrad QM objects do not have properties until measured?

[zonde]

The problem is either the classicality condition or the locality condition. I (and most physicists) would blame the classicality condition, since locality is probably the most successful heuristic we have in physics and dropping it would generate more problems than it solves, while dropping classicality seems to generate no intrinsic problems apart from being unintuitive. But of course everyone is free to choose their own conclusion, as long as they acknowledge that such a choice exists.

Nobody (I hope) is considering dropping locality as there is no philosophical framework for such a way of thinking. "Non-locality" of QM just means that QM approximates some physical mechanism that violates speed of light limit.

 

[rubi]

Well, I won't defend Maudlin that far. I'm not a big fan of arguing from EPR. I prefer to just define classical local causality. I will say Maudlin is not a crackpot, and overall his message is not very far from what everyone agrees with: QM is local by no signalling, and not local by classical local causality.

Well, I think Maudlin wants us to believe that his argument is watertight and he doesn't need an extra assumption like a simplicial state space. Otherwise he would just have admitted that he uses that assumption, after Werner pointed it out to him. See this quote from Werner: "Whether or not assuming classicality is a good choice is not the issue here. Therefore, at the end of the introduction of my comment I said: “Of course, I now have to say what this C is. I can only hope to do it
well enough that Maudlin will say: ’Yes, we assume that, of course’.” His reply shows beyond doubt that I failed." A honest scientist wouldn't try to hide his assumptions, so I can't take Maudlin seriously.

But is there really something between (1) and (2) that operational QM satisfies?

You need to draw a two-dimensional picture here with the axes "classicality" and "locality". (1) assumes no classicality but is a bit local. (2) is fully classical and fully local. However, quantum theory can be fully local but not classical at all, so it's not "between (1) and (2)".

There is a notion, but as far as I know, the notion is empty in operational QM. Looking at the other article by Zukowski and Brukner you linked to in post #20, they basically say locality should be defined as no superluminal signalling. Maudlin explicitly says QM is local if one defines it as no superluminal signalling.

I don't think the notion is empty. At least in the Bell situation, one can consistently supplement QM with a non-empty causality relation. I don't know about the general case. This is simply very unexplored terrain. Zukowski and Brukner are also not sure about their conclusion. The point is that until someone proves the incompatibility of a non-empty causality relation with QM, one can't claim that (1) is the only option.

Also, it seems (according to Maudlin) that Werner says that QM is local if we take the epistemic state to be the physical state. Isn't that problematic? How is that different from saying that the wave function is real, which as you agreed does make QM nonlocal?

I don't get this conclusion from Werner's articles. I think Maudlin misunderstands him. As long as the state is not a physical object, everything is fine.

I am trying to understand what Werner means by "assumption of simplex state space".
I found this:
"According to Maudlin, Bell makes no assumption of “realism” or (as I called it in my reply) of “classicality” (in short “C”), or a hidden-variable description."
And this:
"The first issue is the explanation of classicality “C”. I gave a technical definition, the simplex property, ... "

So as I understand "simplex state space" is basically the same as "hidden-variable description", right?

No, hidden-variable theories can also be modeled on non-simplicial state spaces. The assumption that the state space is a simplex just means that all observables are modeled as random variables on one single probability space.

Nobody (I hope) is considering dropping locality as there is no philosophical framework for such a way of thinking. "Non-locality" of QM just means that QM approximates some physical mechanism that violates speed of light limit.

A violation of the speed of light limit is a violation of locality. Locality is a well-defined concept in relativity theory. It is dropped for example in Bohmian mechanics.

 

[zonde]

No, hidden-variable theories can also be modeled on non-simplicial state spaces. The assumption that the state space is a simplex just means that all observables are modeled as random variables on one single probability space.

So you are saying that Werner gave two different definitions for the same thing?

 

[rubi]

So you are saying that Werner gave two different definitions for the same thing?

I don't know how you come to this conclusion? I certainly didn't say this. Werner states his definition precisely in his paper: "In a classical theory this convex set is a simplex, meaning that any state has a unique decomposition into extreme points, so can be understood as statistical mixture of dispersion free states: equivalently, any two measurements (POVMs, or decompositions of one into positive affine functionals) are the marginals of a joint measurement. We take these properties as a definition of classicality and it is this property I referred to as C in the introduction."

 

[Quandry]

Well, for instance non-classicality implies that a particle can't have both a position and a momentum. How do you interpret this? Mathematically, it is not a problem, but I don't think it is intuitive.

I hope I do not misunderstand this, but I regard it as quite intuitive. Momentum is directly proportional to the velocity, which is a measurement of change of position. A particle at any instant in time has a position, but no velocity.

 

[N88]

Well, I won't defend Maudlin that far. I'm not a big fan of arguing from EPR. …

Just like Einstein one year later, shouldn't we all be arguing against EPR (written by Podolsky in 1935)? Favouring the statistical interpretation, Einstein writes (J. Franklin Institute, 1936, V.221, p.376): "Such an interpretation eliminates also the paradox recently demonstrated by myself and two collaborators [ie, EPR], …."

As I see things developing here, it seems to me that EPR went for partial naive realism ["if we can predict with certainty"] and Bell (relatedly) worked on full naive realism (see post #44 above): and both variants of naive realism are rendered inapplicable by QM and Bell-tests.

That seems to put me firmly in the camp of those who reject the classicality in EPR-Bell in favour of locality.

See also next post from me re Maudlin and Zeilinger.

 

[N88]

… See also next post from me re Maudlin and Zeilinger.

As a matter of interest. In Musser's book (2015) - "Spooky Action at a Distance" - p.116: "When Maudlin ended [his talk, circa 2011, Dresden], Zeilinger raised his hand. … … and merely reasserted his conclusion: 'This inference of nonlocality seems to be based on a rather realistic interpretation of information. If you don't assume this, you don't need nonlocality.'"

 

[stevendaryl]

As I see things developing here, it seems to me that EPR went for partial naive realism ["if we can predict with certainty"] and Bell (relatedly) worked on full naive realism (see post #44 above): and both variants of naive realism are rendered inapplicable by QM and Bell-tests.

But my difficulty is that I have no idea what it means to reject realism. I can certainly understand what it means for a specific theory not to be realistic--it means that whatever notion of state is the subject of that theory is not to be taken to be a description of the physical world, but of our information about the physical world. For example, classical probability theory interprets probabilities as reflecting our ignorance about the world, and are not to be understood as facts about the world itself. If I split up a pair of shoes, and put each into a separate box, and send one shoe to Alice, and the other shoe to Bob, then Alice would describe the situation before she opens the box as: "P(Alice has a left shoe) = 50%, P(Bob has a left-shoe) = 50%". After opening the box, this situation would instantaneously change to either "P(Alice has a left shoe) = 0%, P(Bob has a left shoe) = 100%" or vice-versa. You don't have to worry about how Alice's action made Bob's probability change instantaneously, and whether that violates special relativity, because probabilities aren't physical quantities. They don't exist in the world, they exist inside Alice's head, and that's where the change takes place. So these probabilities are non-realistic--they don't reflect objective physical facts about the world.

But this notion of "realistic" is not about the world, it's about a theory. The theory is either realistic or not. It doesn't make any sense to me to say that the world is not realistic. Sort of by definition, "realistic" means to me "having to do with reality--that is, having to do with the real world". I can understand what it means to interpret the wave function realistically or not, but I really don't understand what it means to reject realism. Maybe it means that the best possible theory about the world is non-realistic?

On another topic:

People have been using the words "simplicial" and "non-simplicial" in this thread without defining them. rubi says that Bell's assumption about the existence of a parameter \lambda is equivalent to the assumption that the underlying theory is simplicial. I take that to mean that for every situation, there is a "best", most-informative description of the situation? Or what does it mean? (I know what a simplex is, but how simplices relate to Bell's argument is unclear).

 

[atyy]

You need to draw a two-dimensional picture here with the axes "classicality" and "locality". (1) assumes no classicality but is a bit local. (2) is fully classical and fully local. However, quantum theory can be fully local but not classical at all, so it's not "between (1) and (2)".

I don't think the notion is empty. At least in the Bell situation, one can consistently supplement QM with a non-empty causality relation. I don't know about the general case. This is simply very unexplored terrain. Zukowski and Brukner are also not sure about their conclusion. The point is that until someone proves the incompatibility of a non-empty causality relation with QM, one can't claim that (1) is the only option.

Yes, there are notions between (1) and (2) but at least at present, they are not used in the derivation of a Bell inequality. At present there are 2 important routes to a bell inequality, and they use (1) and (2). In using (1) we have to supplement it with another assumption, eg. no randomness, while in using (2) there is no need for any additional assumption. So when people say they are giving up something to preserve locality, at present, they mean locality in the sense of (1). Maudlin doesn't dispute this.

There are things like consistent histories, but it is unclear whether this is an example of preserving "locality" by giving up "something", since consistent histories claims to preserve something like Einstein locality, whereas the locality that can be preserved by giving up something is merely no superluminal signalling.

I don't get this conclusion from Werner's articles. I think Maudlin misunderstands him. As long as the state is not a physical object, everything is fine.

Apparently Werner writes "Naturally, I have taken “physical state" here in the sense of the operational approach, as the quantity which allows us to determine the probabilities for all subsequent operations and measurements (“epistemic" rather than “ontic")."

If the epistemic state is taken to be the physical state, isn't that the same as taking the wave function to be physical?

 

[atyy]

As a matter of interest. In Musser's book (2015) - "Spooky Action at a Distance" - p.116: "When Maudlin ended [his talk, circa 2011, Dresden], Zeilinger raised his hand. … … and merely reasserted his conclusion: 'This inference of nonlocality seems to be based on a rather realistic interpretation of information. If you don't assume this, you don't need nonlocality.'"

At the end of the day, the important point that Maudlin is trying to make is that there is a measurement problem. One can certainly assert that it doesn't need to be solved. On the other hand, most physicists including Dirac and Weinberg, and all who suspect that MWI or consistent histories could be correct, have believed that there is a measurement problem.

 

[atyy]

People have been using the words "simplicial" and "non-simplicial" in this thread without defining them. rubi says that Bell's assumption about the existence of a parameter \lambda is equivalent to the assumption that the underlying theory is simplicial. I take that to mean that for every situation, there is a "best", most-informative description of the situation? Or what does it mean? (I know what a simplex is, but how simplices relate to Bell's argument is unclear).

In both classical and quantum state space, the pure states are those that are not a statistical mixture of anything else (which is why we can consider the quantum state to be real, with the pure state being the state of a single system). In classical physics, each mixture is a unique statistical mixture of pure states (ie. state space is a simplex, where pure states are the pointy things). In quantum physics, a mixed density matrix can arise from more than one statistical mixture of pure states (state space is not a simplex, more like a sphere).

 

[rubi]

I hope I do not misunderstand this, but I regard it as quite intuitive. Momentum is directly proportional to the velocity, which is a measurement of change of position. A particle at any instant in time has a position, but no velocity.

A classical particle with a differentiable trajectory has a both a position and a velocity at each instant of time.

But my difficulty is that I have no idea what it means to reject realism.

Personally, I don't like the word "realism". I think Werner's term "classicality" is much better. It essentially means that it is in principle possible to simultaneously assign real numbers to all observable quantities. It's of course plausible apriori that this should be possible, but QM and experiment teaches us that this must be given up at least in some situations (such as different spin directions of a particle). So for me it's not a big leap to give it up for the remaining situations.

People have been using the words "simplicial" and "non-simplicial" in this thread without defining them. rubi says that Bell's assumption about the existence of a parameter \lambda is equivalent to the assumption that the underlying theory is simplicial. I take that to mean that for every situation, there is a "best", most-informative description of the situation? Or what does it mean? (I know what a simplex is, but how simplices relate to Bell's argument is unclear).

Since we're discussing Werner's reply, I'm using the definition Werner gave in his paper, which I quoted in post #64. However, it is equivalent to the requirement that all observables can be modeled as random variables on one probability space.

Yes, there are notions between (1) and (2) but at least at present, they are not used in the derivation of a Bell inequality. At present there are 2 important routes to a bell inequality, and they use (1) and (2). In using (1) we have to supplement it with another assumption, eg. no randomness, while in using (2) there is no need for any additional assumption. So when people say they are giving up something to preserve locality, at present, they mean locality in the sense of (1). Maudlin doesn't dispute this.

A locality notion that applies to QM shouldn't be able to prove Bell's theorem, since QM violates the inequality, so it's no surprise that none such notion is used in any proof of the theorem. I don't think people preserving locality mean notion (1). They mean that there is no spooky action at a distance, i.e. all causal influences travel at most at the speed of light.

Apparently Werner writes "Naturally, I have taken “physical state" here in the sense of the operational approach, as the quantity which allows us to determine the probabilities for all subsequent operations and measurements (“epistemic" rather than “ontic")."

If the epistemic state is taken to be the physical state, isn't that the same as taking the wave function to be physical?

No, the wave function acts only as a container of information. It's as physical as the probability distribution $p_i=\frac{1}{6}$ for the throw of a die. There is no thing out there, called probability, such that if you measure it, you will get the value $\frac{1}{6}$.

 

[atyy]

A locality notion that applies to QM shouldn't be able to prove Bell's theorem, since QM violates the inequality, so it's no surprise that none such notion is used in any proof of the theorem. I don't think people preserving locality mean notion (1). They mean that there is no spooky action at a distance, i.e. all causal influences travel at most at the speed of light.

But then one needs the notion of a non-real cause.

If one thinks of Maudlin's claim that the world is non-local, it is hard to criticize him for not stating a reality assumption. The world is real in common language, so he is just saying that reality is nonlocal. So the reality assumption is clearly stated.

 

[rubi]

But then one needs the notion of a non-real cause.

One just needs the notion of a cause. It's a perfectly valid concept on all Lorentzian spacetimes, independent of the geometry of the state space.

If one thinks of Maudlin's claim that the world is non-local, it is hard to criticize him for not stating a reality assumption. The world is real in common language, so he is just saying that reality is nonlocal. So the reality assumption is clearly stated.

The word "real" is just a placeholder for a technical condition. Rejecting it doesn't mean that the world is not real (whatever that means), but rather that the technical condition is not satisfied. Moreover, this technical condition is rejected by most physicists, so accepting it is non-standard and must be pointed out clearly. Here is a quote from Maudlin's paper: "Unfortunately, many physicists have not properly appreciated what Bell proved: they take the target of his theorem—what the theorem rules out as impossible—to be much narrower and more parochial than it is. Early on, Bell’s result was often reported as ruling out determinism, or hidden variables. Nowadays, it is sometimes reported as ruling out, or at least calling in question, realism. But these are all mistakes. What Bell’s theorem, together with the experimental results, proves to be impossible (subject to a few caveats we will attend to) is not determinism or hidden variables or realism but locality, in a perfectly clear sense. What Bell proved, and what theoretical physics has not yet properly absorbed, is that the physical world itself is non-local."
Maudlin is provably wrong. It has been pointed out to him by an expert. But not even in his reply, he acknowledges that he must assume classicality. It is completely clear that he thinks that this assumption is not needed. Why else wouldn't he just admit it instead of responding polemically to criticism?

 

[atyy]

One just needs the notion of a cause. It's a perfectly valid concept on all Lorentzian spacetimes, independent of the geometry of the state space.

OK, I'll stop discussing Maudlin, since we aren't getting anywhere.

But let's discuss this point - how do you get the notion of a local common cause when the Bell inequalities are violated?

 

[N88]

But my difficulty is that I have no idea what it means to reject realism. … … Sort of by definition, "realistic" means to me "having to do with reality--that is, having to do with the real world". ...

Like you, I have no idea what it means to reject realism! And again, like you: "realistic" means to me "having to do with reality - that is, having to do with the real world". So I trust you are not reading "reject realism" in anything that I have written?

In my experience, most suggestions linking "reject" and "realism" refer to a qualified realism, and sometimes the qualifier is incomplete!

Thus, believing that we live in a quantum world, I reject classical realism. I reject the partially naive realism in EPR. I reject the naive realism on which Bell's theorem is based (see Bell's endorsement of d'Espagnat's naive realism in post #44 above). I therefore reject the local realism [SIC] associated with Bell's theorem: BUT, in this case, the qualifier is incomplete. I am in fact maintaining locality and rejecting the "naive realism" in the (properly qualified) local naive realism of Bell and d'Espagnat.

In post #67 above, Zeilinger rejects a "rather realistic interpretation of information" - by which I guess he agrees with me that Maudlin's view is "rather naively realistic"; like naively accepting that a mirage in the desert is a real lake; like accepting that the local naive realism of EPR, Bell and d'Espagnat is fully realistic.

 

[zonde]

I don't know how you come to this conclusion?

In post #59 I gave two quotes of Werner (http://arxiv.org/abs/1411.2120):

"According to Maudlin, Bell makes no assumption of “realism” or (as I called it in my reply) of “classicality” (in short “C”), or a hidden-variable description."
And this:
"The first issue is the explanation of classicality “C”. I gave a technical definition, the simplex property, ... "

Clearly Werner in the text after first quote is using words "classicality", "realism", "hidden variables" interchangeably.
And then he defines "C" as a simplex property of a state space (technical definition).
So for him it's the same. But not for you.

EDIT: And another quote of Werner:
"The point he thus missed in my explanation is that any description in terms of properties, thought to pertain to the system itself, and independent of the experimental arrangement and the choice of subsequent measurement, presupposes C. Using classical random variables, ontic states, hidden variables, and especially conditional probabilities based on those, presupposes C. And all these things are quite easy to find in the EPR and Bell arguments."

 

[zonde]

As I see things developing here, it seems to me that EPR went for partial naive realism ["if we can predict with certainty"] and Bell (relatedly) worked on full naive realism (see post #44 above): and both variants of naive realism are rendered inapplicable by QM and Bell-tests.

You are missing some details in EPR argument. Phrase: "if we can predict with certainty" does not refer to some form of realism but to prediction of QM. It's QM that says you can predict with certainty outcome of measurement of other entangled particle given measurement result of first entangled particle under the same measurement settings.

 

[N88]

You are missing some details in EPR argument. Phrase: "if we can predict with certainty" does not refer to some form of realism but to prediction of QM. It's QM that says you can predict with certainty outcome of measurement of other entangled particle given measurement result of first entangled particle under the same measurement settings.

I miss no details in EPR's argument. EPR defined their "elements of physical reality" with a qualifying IF: If, under QM's "prediction with certainty" (which I fully accept). I took their definition to be "partial naive realism" because they made no mention of "elements of physical reality" in the absence of that certainty.

Thus EPR have "elements of physical reality" corresponding to an outcome in the case of certainty (partial naive classicality) whereas (by way of comparison), Bell-d"Espagnat have "naively realistic" elements of physical reality under all conditions (total naive classicality), QM certain or QM uncertain.

 

[Quandry]

A classical particle with a differentiable trajectory has a both a position and a velocity at each instant of time.
##.

Probably not on topic here - but you have defined the particle as having differentiable trajectory and therefore you have defined it as having velocity. Take a particle about which you know nothing (therefore cannot presume velocity). Velocity is defined as the rate of change of position over a period time. If you determine the exact position of a particle at an instant of time there is no period of time and no change of position therefore no velocity.
Classically you can determine an average velocity between two positions over a defined period of time, but you can never know the velocity at any specific point in time

 

[atyy]

Probably not on topic here - but you have defined the particle as having differentiable trajectory and therefore you have defined it as having velocity. Take a particle about which you know nothing (therefore cannot presume velocity). Velocity is defined as the rate of change of position over a period time. If you determine the exact position of a particle at an instant of time there is no period of time and no change of position therefore no velocity.
Classically you can determine an average velocity between two positions over a defined period of time, but you can never know the velocity at any specific point in time

A non-relativistic quantum particle can have a trajectory with position and velocity - what it cannot have is position and canonically conjugate momentum. This just means the equation of motion is different from that in Newtonian physics.

 

[rubi]

how do you get the notion of a local common cause when the Bell inequalities are violated?

Let me try:
Let $\Psi$ be the quantum state. Let $X_A$ be an observable localized in the region $A$ and $P$ be a projector of it. Let $x\in A$. We say that $y\sim_P x$ ("$y$ causes $x$ to have the property $P$"), if there is a Lorentz transform $\Lambda$ such that $\Lambda A\subseteq I^-(A)$ and $y\in\Lambda A$ and for $P_\Lambda := U(\Lambda) P U(\Lambda)^\dagger$, we have that $\neg (P_\Lambda \Psi = \Psi) \Rightarrow \neg (P \Psi = \Psi)$.

Now you can say that there is a common cause for $x$ having the property $P_x$ and $y$ having the property $P_y$, if there exists $z$ such that $z\sim_{P_x} x$ and $z\sim_{P_y} y$.

In post #59 I gave two quotes of Werner (http://arxiv.org/abs/1411.2120):Clearly Werner in the text after first quote is using words "classicality", "realism", "hidden variables" interchangeably.
And then he defines "C" as a simplex property of a state space (technical definition).
So for him it's the same. But not for you.

EDIT: And another quote of Werner:
"The point he thus missed in my explanation is that any description in terms of properties, thought to pertain to the system itself, and independent of the experimental arrangement and the choice of subsequent measurement, presupposes C. Using classical random variables, ontic states, hidden variables, and especially conditional probabilities based on those, presupposes C. And all these things are quite easy to find in the EPR and Bell arguments."

Werner gave a perfectly fine technical condition for $C$ that I quoted earlier. This is the condition one needs. It also includes the way Bell defined his hidden variables. However, one can of course add hidden variables to a non-simplicial theory without making the state space a simplex. One just can't represent them on a single probability space.

 

[zonde]

I miss no details in EPR's argument. EPR defined their "elements of physical reality" with a qualifying IF: If, under QM's "prediction with certainty" (which I fully accept). I took their definition to be "partial naive realism" because they made no mention of "elements of physical reality" in the absence of that certainty.

Thus EPR have "elements of physical reality" corresponding to an outcome in the case of certainty (partial naive classicality) whereas (by way of comparison), Bell-d"Espagnat have "naively realistic" elements of physical reality under all conditions (total naive classicality), QM certain or QM uncertain.

Ok, I now understand that emphasis was on word "partial". But then the rest does not make sense. You said:

As I see things developing here, it seems to me that EPR went for partial naive realism ["if we can predict with certainty"] and Bell (relatedly) worked on full naive realism (see post #44 above): and both variants of naive realism are rendered inapplicable by QM and Bell-tests.

That seems to put me firmly in the camp of those who reject the classicality in EPR-Bell in favour of locality.

EPR arrives at this partial naive realism based explanation in EPR under condition of locality ["without in any way disturbing a system"]. Obviously rejecting "locality" renders EPR reasoning inapplicable (without rejecting realism).

On the other hand realism (in it's proper philosophical sense) can't be rejected if we hold on to scientific approach, as realism (in it's proper philosophical sense) is fundamental to science. Or more specifically science aims to explain reproducible certainty. And we favor such explanations over other types of explanations.
So we (should) favor non-local explanation of reproducible certainty over local non-explanation of reproducible certainty.

 

[rubi]

On the other hand realism (in it's proper philosophical sense) can't be rejected if we hold on to scientific approach, as realism (in it's proper philosophical sense) is fundamental to science. Or more specifically science aims to explain reproducible certainty. And we favor such explanations over other types of explanations.
So we (should) favor non-local explanation of reproducible certainty over local non-explanation of reproducible certainty.

You are confusing a loose philosophical concept ("realism") with a sharp technical condition ("classicality") on the mathematical description of reality. Just because we reject a certain mathematical way to describe reality, it doesn't mean that we reject reality in the philosophical sense (whatever that means).

 

[atyy]

Let me try:
Let $\Psi$ be the quantum state. Let $X_A$ be an observable localized in the region $A$ and $P$ be a projector of it. Let $x\in A$. We say that $y\sim_P x$ ("$y$ causes $x$ to have the property $P$"), if there is a Lorentz transform $\Lambda$ such that $\Lambda A\subseteq I^-(A)$ and $y\in\Lambda A$ and for $P_\Lambda := U(\Lambda) P U(\Lambda)^\dagger$, we have that $\neg (P_\Lambda \Psi = \Psi) \Rightarrow \neg (P \Psi = \Psi)$.

Now you can say that there is a common cause for $x$ having the property $P_x$ and $y$ having the property $P_y$, if there exists $z$ such that $z\sim_{P_x} x$ and $z\sim_{P_y} y$.

But wouldn't this work even if we take the wave function to be real?

 

[rubi]

But wouldn't this work even if we take the wave function to be real?

This definition of course only applies to quantum objects. If the wave function itself is a real classical object, then the classical definition applies to it. (By the way, I don't really know what the idea of a real wave function is supposed to mean if the you don't have a quantum system consisting of one particle. Already in the case of 2 particles, the wave function depends on 7 coordinates ($t, x_1, y_1, z_1, x_2, y_2, z_2$) and not on 4 as it would have to if it were supposed to be a field on spacetime.)

 

[atyy]

This definition of course only applies to quantum objects. If the wave function itself is a real classical object, then the classical definition applies to it. (By the way, I don't really know what the idea of a real wave function is supposed to mean if the you don't have a quantum system consisting of one particle. Already in the case of 2 particles, the wave function depends on 7 coordinates ($t, x_1, y_1, z_1, x_2, y_2, z_2$) and not on 4 as it would have to if it were supposed to be a field on spacetime.)

In what you wrote, is $\Psi$ a pure quantum state (ie. a ray in Hilbert space)?

The wave function is always in Hilbert space. If one wants to, one can attach a copy of Hilbert space to every point on a spatial slice of spacetime (won't make any change to the predictions, but will make collapse manifestly nonlocal). So when one is saying that the wave function is real, one regards Hilbert space as real.

Edit: in fact, since the wave function is always in Hilbert space, it is always manifestly nonlocal.

 

[Quandry]

A non-relativistic quantum particle can have a trajectory with position and velocity - what it cannot have is position and canonically conjugate momentum. This just means the equation of motion is different from that in Newtonian physics.

True, but it does not change the fact that at any point in time ΔT = 0

 

[rubi]

In what you wrote, is $\Psi$ a pure quantum state (ie. a ray in Hilbert space)?

Yes.

The wave function is always in Hilbert space. If one wants to, one can attach a copy of Hilbert space to every point on a spatial slice of spacetime (won't make any change to the predictions, but will make collapse manifestly nonlocal). So when one is saying that the wave function is real, one regards Hilbert space as real.

If a copy of wave function at some time $t$ is a physical object attached at each point of space, then I should be able to access it completely from every point of the universe, so by performing an experiment here in front of my computer, I can get all information I want about the state of the Andromeda galaxy (since a copy of all that information is supposed to be available here). That sounds very strange to me.

 

[atyy]

If a copy of wave function at some time $t$ is a physical object attached at each point of space, then I should be able to access it completely from every point of the universe, so by performing an experiment here in front of my computer, I can get all information I want about the state of the Andromeda galaxy (since a copy of all that information is supposed to be available here). That sounds very strange to me.

And by doing a measurement, Alice can instantly change the wave function at Bob's location, even though they are spacelike-separated. So if a pure quantum state is the complete information about the state of a system (eg. the entangled particles of Alice and Bob), then the quantum formalism is manifestly nonlocal.