Quantum Mechanics without Hilbert Space

[Fredrik]

Many said that the state vector and collapse is just our knowledge of the system. But in the double slit, the detector indeed collapse the wave function even if you don't do calculations. So collapse exists independently from your knowledge. What do you say about this?

I have never liked the claim that a wavefunction represents the observer's knowledge of the system. What does that even mean? I think that this is just a less accurate way of saying that a wavefunction is something mathematical that's used to calculate probabilities of possible results of experiments. If that's what it's supposed to mean, then why not just say it that way? There really is no need to dumb it down to a statement the meaning of which is unclear.

This could mean that people who use that phrase really mean something else, but I don't see how it can mean something different unless it comes with a definition of the term "knowledge".

Some of my earlier posts about the topics you brought up ("collapse" and "observers"): 1, 2, 3.

 

[Varon]

I have never liked the claim that a wavefunction represents the observer's knowledge of the system. What does that even mean? I think that this is just a less accurate way of saying that a wavefunction is something mathematical that's used to calculate probabilities of possible results of experiments. If that's what it's supposed to mean, then why not just say it that way? There really is no need to dumb it down to a statement the meaning of which is unclear.

This could mean that people who use that phrase really mean something else, but I don't see how it can mean something different unless it comes with a definition of the term "knowledge".

Some of my earlier posts about the topics you brought up ("collapse" and "observers"): 1, 2, 3.

So if they meant a wavefunction is something mathematical that's used to calculate probabilities of possible results of experiments. So does the electron have classical trajectory to either left or right slit and we just don't know what it is? Or doesn't it have trajectory? Or in Copenhagen, do they just try to suppress this fact by pretending the electron and slits are not really there physically?

What bothers me is decoherence. Since collapse (as most commonly believed) is supposed to be only our knowledge of the system during observation. But we never observe decoherence.. so in your view.. is decoherence just purely mathematical? I want to have a physical picture of decoherence in Copenhagen. Can I imaginine that when I walk in the street.. billions of particles in the street are physically entangling with my body. Can I imagine waves interfering with my body waves (and it actually occurring). But since the wave function is supposed to be just knowledge of the observer and not ontological. Then in Copenhagen view. There isn't any actual waves interfering in decoherence but just a math trick? But could it be merely math when my body atoms really entangled with the environment. This bothers me for many months and probably years now. Hope we can settle this. What do you think? Let's just focus on the Copenhagen for now as I just want to understand how this is understood by mainstream physicists (not what we'd like it to be and how much some of us dislike it but how it is understood by others. Because it is by knowing how it is commonly understood that we can know what is really wrong. Let's also avoid Many worlds for this discussion as Many worlds is simply an easy way out and if this world is only one world. Many worlds is escaping from reality).

 

[Fredrik]

So if they meant a wavefunction is something mathematical that's used to calculate probabilities of possible results of experiments. So does the electron have classical trajectory to either left or right slit and we just don't know what it is? Or doesn't it have trajectory?

I would say that it's the latter, but for the last few weeks, I've been really baffled by the fact that Ballentine's 1970 article on the statistical interpretation suggests that particles with wavefunctions that aren't sharply peaked can have definite but unknown positions. I'm going to have to take the time to read that article one of these days, to find out if I have misunderstood something fundamental. (This suggestion seems completely wrong to me, so I really want to know).

What bothers me is decoherence. Since collapse (as most commonly believed) is supposed to be only our knowledge of the system during observation. But we never observe decoherence.. so in your view.. is decoherence just purely mathematical?

In a double-slit experiment with C70 molecules moving through air, the interactions between the molecules and the air destroy more of the interference pattern the higher the air pressure is. This is decoherence in action, so it's definitely not purely mathematical.

I want to have a physical picture of decoherence in Copenhagen. Can I imaginine that when I walk in the street.. billions of particles in the street are physically entangling with my body. Can I imagine waves interfering with my body waves (and it actually occurring).

Yes. The surrounding air is going to have a much larger effect on you than on a single C70 molecule.

But since the wave function is supposed to be just knowledge of the observer and not ontological. Then in Copenhagen view. There isn't any actual waves interfering in decoherence but just a math trick? But could it be merely math when my body atoms really entangled with the environment. This bothers me for many months and probably years now. Hope we can settle this. What do you think?

This isn't something we can settle. It's conceivable that QM assigns probabilities to possible results of experiments with fantastic accuracy without giving us a detailed description of what's "actually happening" to the system at all times. It's also conceivable that the reason why those probability assignments are so accurate is that there is a description of what's "actually happening" somewhere in QM, that we just don't understand.

 

[Varon]

I would say that it's the latter, but for the last few weeks, I've been really baffled by the fact that Ballentine's 1970 article on the statistical interpretation suggests that particles with wavefunctions that aren't sharply peaked can have definite but unknown positions. I'm going to have to take the time to read that article one of these days, to find out if I have misunderstood something fundamental. (This suggestion seems completely wrong to me, so I really want to know).


In a double-slit experiment with C70 molecules moving through air, the interactions between the molecules and the air destroy more of the interference pattern the higher the air pressure is. This is decoherence in action, so it's definitely not purely mathematical.



Yes. The surrounding air is going to have a much larger effect on you than on a single C70 molecule.


This isn't something we can settle. It's conceivable that QM assigns probabilities to possible results of experiments with fantastic accuracy without giving us a detailed description of what's "actually happening" to the system at all times. It's also conceivable that the reason why those probability assignments are so accurate is that there is a description of what's "actually happening" somewhere in QM, that we just don't understand.

Using all your knowledge of Hilbert space and QM. Please let me know if the following scenerio is possible. Got it from Peter Ryser article:

"Everett considers the many worlds as real, in an ontological sense. However, it is not necessary to adopt this assumption. Following Squires (1991) I will consider the many worlds as possibilities or, as Popper (1977) described it, as ‘propensities’. I will assume that a single universal mind experiences only one of the many possible realities. In terms of the Copenhagen Interpretation this would mean: A single universal mind collapses the universal wave-function. In this picture there is no local wave-function collapse and no artificial distinction between classical and quantum systems. There is only the universal wave function and a universal mind that moves along one of the many branches of this function. I will also assume that the universal mind can, to a certain degree, ‘choose’ which branch is realized."

~~~~~~~~~~~~~~~~~~~

How much should you alter QM mathematics and conceptual foundations to make this scenerio possible where the other Everett branches are not real worlds but just possibilities. And if it was not chosen by the single universal mind, the branches cease to exist. Only the branch chosen becomes real. This scenerio differs from standard Many Worlds where all the worlds are real. What kind of alteration must you do to the mathematics of QM to make this only one branch becoming real possible? You may say this is weird.. well.. standard Collapse theory is just as weird, and Many worlds all real is equally weird (or strange) too. So we must not reject any theory on the basis of weirdness. Let's be open to all possibilities.

 

[Fredrik]

Using all your knowledge of Hilbert space and QM. Please let me know if the following scenerio is possible. Got it from Peter Ryser article:

"Everett considers the many worlds as real, in an ontological sense. However, it is not necessary to adopt this assumption. Following Squires (1991) I will consider the many worlds as possibilities or, as Popper (1977) described it, as ‘propensities’. I will assume that a single universal mind experiences only one of the many possible realities. In terms of the Copenhagen Interpretation this would mean: A single universal mind collapses the universal wave-function. In this picture there is no local wave-function collapse and no artificial distinction between classical and quantum systems. There is only the universal wave function and a universal mind that moves along one of the many branches of this function. I will also assume that the universal mind can, to a certain degree, ‘choose’ which branch is realized."

Is this "single universal mind" named YHWH by any chance? This is a science forum, not a religion forum.

If it's observing at all times, then no system would be isolated from its environment and QM would fail completely. There wouldn't be any superpositions at all.

What kind of alteration must you do to the mathematics of QM to make this only one branch becoming real possible?

I don't see any other way than to just add what you just said as an additional assumption on top of QM.

You may say this is weird.. well.. standard Collapse theory is just as weird, and Many worlds all real is equally weird (or strange) too. So we must not reject any theory on the basis of weirdness. Let's be open to all possibilities.

The problem isn't that it's weird. It's that the assumption is completely unjustified and doesn't change any of the theory's predictions. It's like adding an invisible blue giraffe that doesn't interact with matter to the axioms of special relativity.

I don't know if there is such a thing as "standard collapse theory". I assume that this would describe how "collapse" is a physical process. I'm not familiar with anything like that.

 

[Fredrik]

No. According to Ryser. "Individual minds can only influence the indeterminacy that
has its origin in their brains while the indeterminacy of the environment belongs to the realm of the universal mind." Hence the realm of superpositions don't belong to the universal mind but to individual mind (but with zero probability of effects occurring outside the brain lest we can control superpositions).

This sounds like crackpot stuff. Do you have a reference to a peer-reviewed physics journal? If he hasn't been able to publish, it doesn't seem worthy of any deeper analysis.

We need a radical idea.

I don't think we do. We may just have to lower our expectations about what a good theory can tell us.

Any idea that's good enough to improve on the current situation would be a new theory, not an interpretation of QM.

Copenhagen is already getting outdated as you agreed.

Did I agree to that? Maybe you just confused me with Fra (the guy who signs his posts /Fredrik). My view on "the Copenhagen interpretation" is that the term is useless, because there's no standard definition of the term. (There isn't even a standard view of what an interpretation is). And I think that the idea that QM is just a set of rules that assigns probabilities to possible results of experiments is a "Copenhagenish" interpretation. It includes most of the ideas that people tend to slap the Copenhagen label on. The main detail that's left out is the idea that a wavefunction is a complete description of all the features of the system, but I don't know if Niels Bohr really held that view.

 

[Fredrik]

I still don't think that the article is worth the time it would take to read it.

 

[Varon]

I still don't think that the article is worth the time it would take to read it.

Ok let's just ignore it then. In Copenhagen. There is collapse. In Many worlds there is none. By putting Collapse back to Many worlds. It's redundant. So I guess "Copenhagen Many Worlds' interpretation is thus refuted. So at the end of the day. There is a million Fredriks after all. I hope none of my billion other copies have shot Obama because I sometimes dreamt of it and uncomfortable thinking my other copy has done it.

 

[Varon]

I would say that it's the latter, but for the last few weeks, I've been really baffled by the fact that Ballentine's 1970 article on the statistical interpretation suggests that particles with wavefunctions that aren't sharply peaked can have definite but unknown positions. I'm going to have to take the time to read that article one of these days, to find out if I have misunderstood something fundamental. (This suggestion seems completely wrong to me, so I really want to know).

What are you baffled with this. It's written in 1970 so maybe outdated already and refuted?

http://www.kevinaylward.co.uk/qm/ballentine_ensemble_interpretation_1970.pdf

Bohr proposed that in the absence of measurement to determine its position, the electron has no position. It probably exists as ghostly mist in Hilbert Space with no definite basis. In the ensemble interpretation (which I presume is identical with the statistical interpretation). It's like the electrons are brownian motion of gas? But why did they have wave characteristic. Can't we even refute such differences using experiments?

Anyway. Here's how someone refutes it as wiki:

http://en.wikipedia.org/wiki/Ensemble_interpretation

"Criticism

Arnold Neumaier finds fault with the applicability of the ensemble interpretation to small systems.


"Among the traditional interpretations, the statistical interpretation discussed by Ballentine in Rev. Mod. Phys. 42, 358-381 (1970) is the least demanding (assumes less than the Copenhagen interpretation and the Many Worlds interpretation) and the most consistent one. It explains almost everything, and only has the disadvantage that it explicitly excludes the applicability of QM to single systems or very small ensembles (such as the few solar neutrinos or top quarks actually detected so far), and does not bridge the gulf between the classical domain (for the description of detectors) and the quantum domain (for the description of the microscopic system)". (spelling amended) [5]"

In a double-slit experiment with C70 molecules moving through air, the interactions between the molecules and the air destroy more of the interference pattern the higher the air pressure is. This is decoherence in action, so it's definitely not purely mathematical.



Yes. The surrounding air is going to have a much larger effect on you than on a single C70 molecule.


This isn't something we can settle. It's conceivable that QM assigns probabilities to possible results of experiments with fantastic accuracy without giving us a detailed description of what's "actually happening" to the system at all times. It's also conceivable that the reason why those probability assignments are so accurate is that there is a description of what's "actually happening" somewhere in QM, that we just don't understand.

 

[yoda jedi]

I have never liked the claim that a wavefunction represents the observer's knowledge of the system. What does that even mean?

that the reality is more than what we see.


.

 

[strangerep]

[Ballentine, Statistical Interpretation was] written in 1970 so maybe outdated already and refuted?

No.

BTW, it's not a good look for anyone to pass assessments (positive or negative)
on material they haven't studied properly. :-)

 

[Varon]

No.

BTW, it's not a good look for anyone to pass assessments (positive or negative)
on material they haven't studied properly. :-)

That is why there is a question mark.

So in the Statistical Interpretation, the electron has position and trajectory at all times? How does this differ to Bohmian Mechanics. How come the latter has to propose a separate real wave function and quantum potential to push the particle while in the Statistical Interpretation )SI), these two extra ingredients are not necessary? Hope experts in the SI can share how Bohmian is identical to SI and how SI differs to de Broglie/Bohm Mechanics. Thanks.

 

[strangerep]

Hope experts in the SI can share how Bohmian is identical to SI and how SI differs to de Broglie/Bohm Mechanics.

They are not at all identical -- as anyone who has actually studied them would know.
But there's no need for me (or anyone else) to write a tutorial on SI here,
since Ballentine has already written a good paper and a good textbook.

But I'm happy to discuss specific points in either his paper or the textbook,
with anyone who has conscientiously studied them.

 

[Fredrik]

But I'm happy to discuss specific points in either his paper or the textbook,
with anyone who has conscientiously studied them.

I started to read the article a couple of days ago. I have only read a few pages a day, so I haven't made it to the end yet. There's definitely a lot of good stuff in there. For example, the discussion of the uncertainty relations is the best I've seen. But there are a few specific points that I disagree with. If I still think he's wrong about those things when I get to the end of the article, I will start a thread about it.

 

[Varon]

They are not at all identical -- as anyone who has actually studied them would know.
But there's no need for me (or anyone else) to write a tutorial on SI here,
since Ballentine has already written a good paper and a good textbook.

But I'm happy to discuss specific points in either his paper or the textbook,
with anyone who has conscientiously studied them.

I have read the paper although not 100% because I don't understand all the math. We who delve in Many worlds and Copenhagen or even Bohmian would love any interpretation that has promise of a resolution of the measurement problem with least assumptions. So the Statistical Interpretation would be promising if it were true. But it didn't appear to be. Although Bohmian can describe individual system where the particle is push by pilot wave or quantum potential by a real wave function located in some configuration space. Statistical interpretation is only valid for ensemble of similarly prepared experiments. Now here is where its weakness lies according to this site:

http://implications-of-quantum-physics.com/qp24_ensemble-interpretation.html

"24. The Ensemble or Statistical Interpretation.

Summary

The ensemble or statistical interpretation is unsatisfactory because it is vague and does not take advantage of all we know about quantum physics.

There are interpretations (championed by Einstein) in which it is assumed that quantum physics gives only statistical information. It is assumed that there is a collection, or ensemble, of copies of the physical system and our perceived world corresponds to only one of them. The wave function then gives statistical information about which one of these copies corresponds to our actual world.

But such interpretations do not say what the actual world is ‘made of.’
And they do not explain why the copies change in time in a way that is consistent with the changes in the wave function. That is, the dynamics of the actual copies of the physical world are not specified. In my opinion, these schemes are not well-formulated enough to say whether or not they constitute a valid interpretation."

Also note in http://en.wikipedia.org/wiki/Bell_test_experiments that bell test experiments only started in 1972 (2 years after the article was written) so it didn't take into account that Bell's Thorem is violated categorically especially in light of Alain Aspect more rigorous experiment. So Statistical Interpretation is not designed to totally explain the correlation of Bell's theorem. It only mentions at the end of the 1970 Ballentine paper that it mentioned that it departed from the formalism of quantum theory but there was no subsequent updated work that would make it explain the correlation of Bell's Theorem.

I also read elsewhere about Einstein similar idea of Statistical interpretation which he presented at the 1927 Solvay Congress but he and many didn't push thru with it because it couldn't describe individual system or even a single atom. That is.. it couldn't explain a single atom electronic behavior hence Einstein didn't completely support it.

So it is more likely that the Statistical Interpretation is not representative of reality at all. Or it is very incomplete. Or if it could be model of reality, Neumaier approach may extend where it left off... that is if Neumaier was right. But Neuameir stated that the 430 atom buckyball simply vanish after it reach the detector or become smeared as wave... this doesn't seem to make sense.

 

[StevieTNZ]

This sounds like crackpot stuff. Do you have a reference to a peer-reviewed physics journal? If he hasn't been able to publish, it doesn't seem worthy of any deeper analysis.

Try http://www.neuroquantology.com/journal/index.php/nq/index - it says its peer-reviewed, and its also a journal on physics.

 

[Fredrik]

So the Statistical Interpretation would be promising if it were true. But it didn't appear to be.

What makes you say that? The statistical interpretation is really just quantum mechanics with no additional assumptions. (I've read enough of the article now to see that he doesn't actually assume that every particle has a well-defined position and momentum at all times. He just claims that this wouldn't contradict QM. Maybe he's right, maybe he's wrong. Either way, it doesn't affect the statistical interpretation, since that claim isn't a part of its definition). So how could the statistical interpretation be wrong? Is your point that QM is wrong?

Now here is where its weakness lies according to this site:

You should probably select your sources more carefully. It's actually against the forum rules to post links to questionable material. This guy rejects just about everything except the idea that a mind isn't physical. (It gets funny when he rejects particles because of "no evidence", but doesn't require evidence for his claim about minds).

But such interpretations do not say what the actual world is ‘made of.’

So? What makes him think that there's a version of QM that can tell us that?

Also note in http://en.wikipedia.org/wiki/Bell_test_experiments that bell test experiments only started in 1972 (2 years after the article was written) so it didn't take into account that Bell's Thorem is violated categorically especially in light of Alain Aspect more rigorous experiment.

He was certainly aware that QM violates Bell inequalities. The experiments only confirmed that reality does too. So the experiments weren't that relevant.

So it is more likely that the Statistical Interpretation is not representative of reality at all. Or it is very incomplete.

Right, but if that's true, then the same can be said about QM itself (since the statistical interpretation is just QM without additional assumptions), so that problem can't be solved by another interpretation.

 

[strangerep]

I have read the [Ballentine] paper although not 100% because I don't understand all the math. [...]

Fredrick has already responded appropriately to most of your post.
I'll just say two things...

(1) Try to acquire more understanding of the math so you can understand such
papers completely. Worry a bit less about intepretation until you've done so.

(2) Regarding the following quote:

Also note in http://en.wikipedia.org/wiki/Bell_test_experiments that bell test experiments only started in 1972 (2 years after the article was written) so it didn't take into account that Bell's Thorem is violated categorically especially in light of Alain Aspect more rigorous experiment. So Statistical Interpretation is not designed to totally explain the correlation of Bell's theorem. It only mentions at the end of the 1970 Ballentine paper that it mentioned that it departed from the formalism of quantum theory but there was no subsequent updated work that would make it explain the correlation of Bell's Theorem.

One need only read Ballentine's much more recent textbook to see that this is rubbish.

 

[Fra]

I didn't follow the cascade of threads about interpretations lately, but here is one comment to Varon, connecting loosely to some previously threades before the cascade.

To speak for myself, as long as we talk about the small subsystem abstraction, and complex observer - ie the cases where the statistical ensemble can in fact the realized in some principal sense, then then ensemble view is pretty close to my view. I think it's good.

But IMHO, the obvious problem is that the, the general case (ie. think cosmological models, or intrinsic measurement theory where the observer is EMBEDDED IN the much more complex system it's trying to observe), then this abstraction fails.

What I seek is the generalization, where the statistical enterpretation corresponds to one limiting case.

In cosmological models, you switch from "statistics" of similarly prepared system, to "statistics" of many measurements perhaps of the same system... but what is lacking is a coherent abstracting on this that makes sense in the general case - in particular are we switching from descpritive views to a decition theoretic view where we do not have acces to the limiting cases of "perfectly known ensembles" to beeing forced to evaluate the action based upo incomplete but rational "counting of evidence"; without reference to ensembles (because they only exists in the limiting sense, and the limit isn't at hand in cosmologilca or inside views).

My motivation is taht we need to understand this general case to solve the open issues of unification/theory scaling and QG.

/Fredrik

 

[Varon]

What makes you say that? The statistical interpretation is really just quantum mechanics with no additional assumptions. (I've read enough of the article now to see that he doesn't actually assume that every particle has a well-defined position and momentum at all times. He just claims that this wouldn't contradict QM. Maybe he's right, maybe he's wrong. Either way, it doesn't affect the statistical interpretation, since that claim isn't a part of its definition). So how could the statistical interpretation be wrong? Is your point that QM is wrong?


You should probably select your sources more carefully. It's actually against the forum rules to post links to questionable material. This guy rejects just about everything except the idea that a mind isn't physical. (It gets funny when he rejects particles because of "no evidence", but doesn't require evidence for his claim about minds).

Oh. I just saw that single web page. I didn't see the main index or other parts so didn't know he is a crackhead.

So? What makes him think that there's a version of QM that can tell us that?


He was certainly aware that QM violates Bell inequalities. The experiments only confirmed that reality does too. So the experiments weren't that relevant.


Right, but if that's true, then the same can be said about QM itself (since the statistical interpretation is just QM without additional assumptions), so that problem can't be solved by another interpretation.

I thought in the Solvay congress in 1927. Einstein already saw the weakness in the Statistical Interpretation (I was reading a history of the debate). Maybe Ballentine's formulation is an update. Anyway. In a single 430 atom-buckyball at a time double slit experiment.. how does the single buckyball move from the emitter to the detector? Did the Statistical Interpretation answer this or doesn't it know? If it doesn't know. Then it is not an explanation. It just smears it into ensemble of 'don't knows', isn't it.

 

[Varon]

Here's Gary Bowman take on the Statistical Interpretation in his book "Essential Quantum Mechanics":

"Most texts adopt—implicitly or explicitly—the so-called Copenhagen interpretation
of quantum mechanics. Like other, conflicting interpretations, Copenhagen is an attempt to tell us what’s really “going on”—to inform us of the quantum world beyond the formalism itself.

By contrast, the statistical interpretation arguably is not an interpretation, but a broad framework that describes how quantum mechanics works in actual practice. You may worry that by learning quantum mechanics from this perspective, you’ll be at a disadvantage. On the contrary, the statistical interpretation provides an understanding one can have confidence in: because it’s “just” a framework, it remains compatible with other approaches, such as Copenhagen, while avoiding many conceptual puzzles
that arise within them.

But what is the statistical interpretation? In a sense, it simply amounts to the following edict: take seriously what quantum mechanics does tell us, and don’t take seriously what quantum mechanics doesn’t tell us."

~~~~~~~~~~~~~~~~~~~~~

I wonder if there are many variants of the Statistical Interpretations (like Many worlds or Copenhagen which have many variants) or there is only one SI which came from Ballentine. Can anyone confirm?

So Statistical Interpretation is simply a framework. Not really an interpretation. It is the pragmatist framework. This means it is compatible with all interpretations and if you are serious about knowing what made QM tick at the very heart, you still have to entertain other interpretations after accepting the Statistical I. Framework. Agree??

 

[strangerep]

[...] take seriously what quantum mechanics does tell us, and don’t take seriously what quantum mechanics doesn’t tell us. [...]

Your post was reasonable up to this point.

But then...

[...] if you are serious about knowing what made QM tick at the very heart, you still have to entertain other interpretations after accepting the Statistical I. Framework.

No, the opposite is true. You don't need to waste any brain energy at all on fictional stories that have become grafted onto the exterior of QM theory.

 

[Fredrik]

I thought in the Solvay congress in 1927. Einstein already saw the weakness in the Statistical Interpretation (I was reading a history of the debate). Maybe Ballentine's formulation is an update.

I don't think so. As far as I know, he only rejected the unnecessary and unjustified assumption that a wavefunction describes all features of a single system. Ballentine takes that rejection as the definition of the statistical interpretation.

In a single 430 atom-buckyball at a time double slit experiment.. how does the single buckyball move from the emitter to the detector? Did the Statistical Interpretation answer this or doesn't it know? If it doesn't know. Then it is not an explanation. It just smears it into ensemble of 'don't knows', isn't it.

That's right. (Close enough anyway). But why would you think that QM actually contains an explanation of that sort? This isn't implied by anything that's known for sure.

I agree with Strangerep's comments in the post above this one.

 

[Varon]

What makes you say that? The statistical interpretation is really just quantum mechanics with no additional assumptions. (I've read enough of the article now to see that he doesn't actually assume that every particle has a well-defined position and momentum at all times. He just claims that this wouldn't contradict QM. Maybe he's right, maybe he's wrong. Either way, it doesn't affect the statistical interpretation, since that claim isn't a part of its definition). So how could the statistical interpretation be wrong? Is your point that QM is wrong?

I found out Ballentine specifically claimed that a particle has a well defined position and momentum at all times! Here's the relevant quotes. Don't you agree with him? Why?

Page 8.

"This statement is often supported by one or both of the following arguments:

(i) A measurement of q causes an unpredictable and uncontrollable disturbance of p, and vice versa. [This was first proposed by Heisenberg (1927) and is widely repeated in textbooks].

(ii) The position and momentum of a particle do not even exist with simultaneously and pefectly well defined (though perhaps unknown) values (Bohm, 1951, p.100)"
<snip>
"Argument (ii) is easily seen to be unjustified"
<snip>
"Using de Broglie's relation between momentum and wavelength, p = h / wavelength, it is then asserted that a particle cannot have definite values of both position and momentum at any instant. But this conclusion rests on the almost literal identication of the particle with the wave packet (or what amounts to the same thing, the assumption that the wave function provides an exhaustive description of the properties of the particle)."
<snip>
"A consistent application of the Statistical Interpretation yields the correct conclusion that the division of the wavepacket yields the relative probabilities for transmission and reflection of particles. But there is no justification for assertion (ii)"

You should probably select your sources more carefully. It's actually against the forum rules to post links to questionable material. This guy rejects just about everything except the idea that a mind isn't physical. (It gets funny when he rejects particles because of "no evidence", but doesn't require evidence for his claim about minds).


So? What makes him think that there's a version of QM that can tell us that?


He was certainly aware that QM violates Bell inequalities. The experiments only confirmed that reality does too. So the experiments weren't that relevant.


Right, but if that's true, then the same can be said about QM itself (since the statistical interpretation is just QM without additional assumptions), so that problem can't be solved by another interpretation.

 

[Varon]

Ballentine paper assumes all particles have positions at all times. This means in Bell's Theorem. He indeed believed that the particles were connected with superluminal link? In Ballentine 1989 textbook which I studied, he mentioned:

Are the experiments conclusive?
If we accept the theoretical arguments that quantum mechanics is incompatible with locality, the next question is whether the experiments are adequate for ruling out locality. We have already seen that, strictly speaking, they are not, because of inefficiencies of the detectors and other instrumental problems. However, the fact that those photon pairs that are detected are correlated in the manner predicted by quantum theory is certainly strong evidence for the correctness of those predictions. Although it is possible to devise local models that would obey Bell’s inequality for ideal detectors, but which agree with quantum theory for the imperfect instruments presently available, such models seem rather contrived. This is especially true in view of the fact that the effect of the various systematic errors that experimentalists have studied is to reduce the coincidence detection rate. But quantum theory predicts a
coincidence rate that is greater than is permitted by Bell’s inequality.

Question. Anything wrong by assuming entangled particles exist at all times even 100 billion light years away and since Bell's Theorem is violated, they really are connected with superluminal link? This is the consequence of Ballentine's Statistical Interpretation.

Bohr arguments was the particles attributes like position didn't exist before measurements, so there was no non-local link because the particles wasn't there at all.

 

[Fredrik]

I found out Ballentine specifically claimed that a particle has a well defined position and momentum at all times!

In section 5, titled "Joint probability distributions", he says

...quantum theory is not inconsistent with the supposition that a particle has at any instant both a definite position and a definite momentum, although there is a widespread folklore to the contrary. Of course we are not compelled either to accept or reject this supposition, but it is of interest to explore it on a tentative basis.​

So he isn't really claiming that particles have well-defined positions and momenta at all times. He's just saying that they might have well-defined positions and momenta at all times. I'm not convinced that this is true. However, if he's wrong, it doesn't have any implications for the statistical interpretation, since this assumption isn't part of its definition.

 

[Varon]

In section 5, titled "Joint probability distributions", he says

...quantum theory is not inconsistent with the supposition that a particle has at any instant both a definite position and a definite momentum, although there is a widespread folklore to the contrary. Of course we are not compelled either to accept or reject this supposition, but it is of interest to explore it on a tentative basis.​

So he isn't really claiming that particles have well-defined positions and momenta at all times. He's just saying that they might have well-defined positions and momenta at all times. I'm not convinced that this is true. However, if he's wrong, it doesn't have any implications for the statistical interpretation, since this assumption isn't part of its definition.

maybe not the statistical interpretation but he mentioned that when using the capital Statistical Interpretation, it's his string of ideas. So maybe we must distinguish them in the future by using smaller or capital letters when mentioning this particular interpretation to denote general or Ballentine version.

 

[Fredrik]

I don't think it would be helpful to have two different definitions of "statistical interpretation" and "Statistical Interpretation".

I read section 1.3 again. It bothers me a lot that he says

In contrast, the Statistical Interpretation considers a particle to always be at some position in space, each position being realized with relative frequency |\psi(\vec r)|^2 in an ensemble of similarly prepared experiments.​

This bothered me just as much the first time I read it, but when I got to the part (section 5) where he says that it's not necessary to assume that particles always have well-defined positions and momenta, I sort of forgot how strong the statement in section 1.3 is.

What bothers me the most is that section 1.3 is supposed to be the one that defines the statistical interpretation. This means that the statistical interpretation does include the assumption that particles always have well-defined positions. I find this very strange. The main idea is to reject an unnecessary assumption, and then he goes and makes another unnecessary assumption!?

Edit: On the other hand, in section 1.2, he says

Although there are many shades of interpretation (Bunge, 1956), we wish to distinguish only two:

(I) The Statistical Interpretation, according to which a pure state (and hence also a general state) provides a description of certain similarly prepared systems, but need not provide a complete description of an individual system.

(II) Interpretations which assert that a pure state provides a complete and exhaustive description of an individual system (e.g. an electron).
​

So he's sort of contradicting himself. Section 1.3 says that the statistical interpretation includes the assumption that particles have well-defined positions at all times. Section 5 says that there's no need to assume that. And yet, section 1.2 talks about "the" statistical interpretation, as if there's only one. It would have made more sense to talk about "statistical interpretations".

 

[strangerep]

I read [Ballentine, SI of QM paper] section 1.3 again. It bothers me a lot that he says

In contrast, the Statistical Interpretation considers a particle to always be at some position in space, each position being realized with relative frequency |\psi(\vec r)|^2 in an ensemble of similarly prepared experiments.​

[...]

What bothers me the most is that section 1.3 is supposed to be the one that defines the statistical interpretation. This means that the statistical interpretation does include the assumption that particles always have well-defined positions.

No it doesn't. Ballentine said "some position", not "well-defined position".

Edit: On the other hand, in section 1.2, he says

Although there are many shades of interpretation (Bunge, 1956), we wish to distinguish only two:

(I) The Statistical Interpretation, according to which a pure state (and hence also a general state) provides a description of certain similarly prepared systems, but need not provide a complete description of an individual system.

(II) Interpretations which assert that a pure state provides a complete and exhaustive description of an individual system (e.g. an electron).
​

So he's sort of contradicting himself. Section 1.3 says that the statistical interpretation includes the assumption that particles have well-defined positions at all times.

He's not contradicting himself. That quote from sect 1.2 is about sharply distinguishing different classes of interpretations of QM. And as I said above, sect 1.3 doesn't say what you said it does.

 

[Jaisonsc]

Im May, 7, Chopin sad: In addition to using a Hilbert state to describe a particle at a position, you can use it to describe a particle with a certain charge, or a certain momentum, or even something more abstract like which slit a particle goes through in the double-slit experiment.

Somebody know's how is possible to do the idea that I put in italics types?
Some article ou so on...
Thanks!