When Quantum Mechanics is thrashed by non-physicists #1

[vanhees71]

You cannot do further measurements with the photon, but you can do further measurements with the atom which absorbed the photon. The claim that your new state is an atom in an excited state can also be expressed in terms of a collapse.Of course there is. You can prepare the state to be $\sigma_z=+1/2$, or you can prepare the state to be $\sigma_z=-1/2$. In the first case you can say that the state collapsed to $|+1/2>$, while in the second case you can say that the state collapsed to $|-1/2>$. If you do not use the word "collapse", then what would you say, how did the state come to one of these two states? Certainly not by unitary evolution governed by the Schrodinger equation!

Nothing has collapsed in my SG example. There was just unitary time evolution of one particle beam into two spatially separated particle beams with (FAPP) determined spin-$z$ components (one has $\sigma_z=1/2$, the other $\sigma_z=-1/2$). Nowhere did I envoke non-quantum dynamics, let alone an instantaneous action at a distance, to explain that I have well-separated beams with determined spin-$z$ components, and that's very important, because a collapse would be an unphysical process envoked as an "explanation" for a physical process, and that's not physics but esoterics!

The same with the photon part. Here you have a single atom as "detector" and a photon to begin with. Then you look at the case where a photon gets absorbed by the atom which is excited after that. Great, but no collapse either. The absorption of the photon can be well described with quantum dynamics (at least perturbatively).

 

[Demystifier]

This example also shows that from a scientific point of view it's more fruitful to try to attack the real open problems of contemporary physics than to ponder "cold cases" like the "collapse" or the "measurement problem".

How do you distinguish the "real" open problems from the "cold" ones? Most lists of the most important open problems in physics, such as this one
http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics (see 1.9 Other problems),
include the collapse and measurement problem. Even Weinberg in his recent book admits that this is one of the most important open problems in physics.

 

[Demystifier]

There was just unitary time evolution of one particle beam into two spatially separated particle beams with (FAPP) determined spin-zz components (one has σz=1/2\sigma_z=1/2, the other σz=−1/2\sigma_z=-1/2).

If your initial beam contains only one particle, the experiments show that there are no two separated beams, but only one! How can you explain that, by unitary means without a collapse?

 

[zonde]

The same with the photon part. Here you have a single atom as "detector" and a photon to begin with. Then you look at the case where a photon gets absorbed by the atom which is excited after that. Great, but no collapse either. The absorption of the photon can be well described with quantum dynamics (at least perturbatively).

Wait, but what about (irreversible) amplification of signal? Single excited atom won't work as detector.

 

[stevendaryl]

The reason is simply that on the one hand from a scientific point of view, there's no problem with quantum theory

Yes, that's part of what is confusing and frustrating about QM, and intractable about ending the interpretation debates: There is no problem to be solved, in the sense of having an experiment whose result we are unable to predict (at least probabilistically). On the one hand, conceptually, there is lots of things that we don't understand about quantum mechanics, but on the other hand, there's no empirical guidance from unexplained results. It seems to me that if there is a solution to the interpretation problem for QM, we already have enough information to solve it--we're just not smart enough, maybe.

 

[stevendaryl]

Even if it is true that the preferred basis can be derived from the working of memory, the point is that somehow the existence of a preferred basis can be derived. The paper we discuss in this thread can also be viewed as a derivation of its existence.

Yes, I think that a preferred basis might very well be derivable. My suggestion, which I don't know whether anyone has looked into it, is that the preferred basis isn't inherent in the physics of particles and fields, but instead comes from the human need to be able to remember past observations. The physics doesn't care about one basis versus another, but WE do.

 

[Demystifier]

It seems to me that if there is a solution to the interpretation problem for QM, we already have enough information to solve it--we're just not smart enough, maybe.

Yes, that's why many physicists try to solve it without making new experiments or even without making new measurable predictions.

 

[Demystifier]

Yes, I think that a preferred basis might very well be derivable. My suggestion, which I don't know whether anyone has looked into it, is that the preferred basis isn't inherent in the physics of particles and fields, but instead comes from the human need to be able to remember past observations. The physics doesn't care about one basis versus another, but WE do.

Yes, some variants on MWI already look into that direction.

 

[vanhees71]

If your initial beam contains only one particle, the experiments show that there are no two separated beams, but only one! How can you explain that, by unitary means without a collapse?

The "beam" can consist of single particles. By assumption the location of the particle at the 2nd Stern-Gerlach apparatus is enough to be sure that there enters a particle with definite $\sigma_z$.

Of course, to test the predictions of QT you always need "beams" in the sense that you have to perform the experiment with single particles often enough to collect "enought statistics" to have a large enough confidence level to confirm disconfirm the probabilistic prediction. That's why this point of view is usually called "(Minimal) Statistical Interpretation" or "Ensemble Interpretation".

 

[Demystifier]

The "beam" can consist of single particles. By assumption the location of the particle at the 2nd Stern-Gerlach apparatus is enough to be sure that there enters a particle with definite $\sigma_z$.

Of course, to test the predictions of QT you always need "beams" in the sense that you have to perform the experiment with single particles often enough to collect "enought statistics" to have a large enough confidence level to confirm disconfirm the probabilistic prediction. That's why this point of view is usually called "(Minimal) Statistical Interpretation" or "Ensemble Interpretation".

Ah, now I think I finally see what interpretation of QM do you have in mind. In the ensemble interpretation, the wave function does not represent individual measured objects, but only statistical properties of the ensemble. With that view, you don't need collapse.

That's fine, but then, instead of a collapse, you need something else. Since the individual measured objects are not wave functions, it follows that there is something which is not a wave function. But then what it is? Are you (like Ballentine) agnostic about that question, or do you believe in some sort of hidden variables such as the Bohmian ones?

 

[vanhees71]

I'm agnostic about this question. As long as there's no clear evidence against standard QT, there seems not to be a chance to find a more comprehensive theory.

 

[Ilja]

I've never heard or read a convincing argument for the necessity of a collpase. The naive collapse is unphysical, and it doesn't help to call it epistemic. I have minimally interpreted quantum theory without a collapse, and that's all what's needed by experimentalists and theorists alike to describe quantitative observations with a high accuracy. So again: What do I need a collapse for?

Strange. I have never heard about a minimal version without collapse.

The point is very simple: Measurements play a double role. First, they measure A of something, which is in a state with wave function \psi=\sum a_i\psi_i. The minimal interpretation tells us that with probability a_i^2 the result is the \lambda_i which is defined by A \psi_i=\lambda_i\psi_i. Fine, this part we can manage without introducing a collapse. But then there is the second part, state preparation. If we prepare a state in \psi_i, what do we have to do? To make a measurement, and wait until the measurement result is \lambda_i. This prepares the state as being \psi_i. You cannot make a minimal interpretation without such a rule for state preparation. And Nature does not know if the measurement is made for getting a result or for preparing a state. Thus, this double role is sufficient to require that the measurement transforms the initial state \psi=\sum a_i\psi_i with probability a_i^2 into the final state \psi_i. But this is the collapse.

 

[Demystifier]

I'm agnostic about this question. As long as there's no clear evidence against standard QT, there seems not to be a chance to find a more comprehensive theory.

But you do admit that probably there is something which is not the wave function (otherwise you would need either the collapse or many-worlds), even if you don't care what exactly that something might be. Am I right?

 

[Ilja]

It seems to me that if there is a solution to the interpretation problem for QM, we already have enough information to solve it--we're just not smart enough, maybe.

I think "smart" is not the problem. Most are not ready to accept the hypothesis that relativistic symmetry is not fundamental, not even as a working hypothesis, which one accepts for the sake of the argument, to have a look at how it fails, no, it is rejected out of hand, without any discussion. Like here, where even to discuss the Lorentz ether interpretation vs. Minkowski interpretation is forbidden (BTW with a completely wrong argument that there is no difference in the predictions, in a situation where one can derive Bell's inequalities only in the Minkowski interpretation, but not in the Lorentz interpretation, which allows hidden causal influences, SCNR).

And this prejudice, of course, severely damages all realistic interpretations of QT, because they all require (because of Bell's inequality) a preferred frame.

 

[Ilja]

With such a more common terminology, their theorems say that the physical content of QM is not basis independent. But this claim is not new at all. This is nothing but a restatement of the preferred basis problem appearing in one way or another in all interpretations of QM.

Where do you see the preferred basis problem in the de Broglie-Bohm interpretation?

 

[bhobba]

Strange. I have never heard about a minimal version without collapse.

Its pretty well known eg
http://en.wikipedia.org/wiki/Wave_function_collapse
On the other hand, the collapse is considered a redundant or optional approximation in:
the Consistent histories approach, self-dubbed "Copenhagen done right"
the Bohm interpretation
the Many-worlds interpretation
the Ensemble Interpretation

In the ensemble interpretation state and preparation procedure are the same thing. If you have a filtering type observation all you have done is prepared the system differently. I suppose to some extent if that's the same as collapse or not depends on what you mean by collapse. I side with it isn't because it's consistent with the Bohmian interpretation and it doesn't have collapse. Indeed in Ballentine's original paper some say its really BM in disguise. I don't think it is, but he did express it a bit poorly in that paper - and it has been corrected in his textbook.

Thanks
Bill

 

[Demystifier]

Where do you see the preferred basis problem in the de Broglie-Bohm interpretation?

As you know, the position basis has a preferred role in dBB, which some people consider to be a problem. You will probably agree with me that this is not a problem for non-relativistic QM, but a generalization of dBB to relativistic quantum field theory is much more problematic. Does the preferred basis fixes a preferred Lorentz frame? If yes, which one? Should the preferred basis be associated with particles or fields? If it is fields, then what about fermions? If it is particles, then what about Unruh effect and curved spacetime? These are all non-trivial questions and neither of the proposed answers (including yours and mine) is without problems.

 

[vanhees71]

But you do admit that probably there is something which is not the wave function (otherwise you would need either the collapse or many-worlds), even if you don't care what exactly that something might be. Am I right?

Within quantum theory there's nothing else than the mathematical setup to define it, including the Born rule. If you want a deterministic theory with hidden variables, then there's more and according to the violation of Bell's inequality it'll be a non-local model.

At the moment, however, I don't see the necessity for such a deterministic theory, because quantum theory never has been disproven by any experiment. In my opinion there are more urgent true problems to solve like: What's dark matter? How can we understand the smallness of "dark energy"? What's a consistent quantum theory of gravity? I don't see any urgent demand for a solution of the pseudo-problem of interpretation of quantum theory.

 

[stevendaryl]

I think "smart" is not the problem. Most are not ready to accept the hypothesis that relativistic symmetry is not fundamental, not even as a working hypothesis, which one accepts for the sake of the argument, to have a look at how it fails, no, it is rejected out of hand, without any discussion. Like here, where even to discuss the Lorentz ether interpretation vs. Minkowski interpretation is forbidden (BTW with a completely wrong argument that there is no difference in the predictions, in a situation where one can derive Bell's inequalities only in the Minkowski interpretation, but not in the Lorentz interpretation, which allows hidden causal influences, SCNR).

I don't completely agree with this. You're right, that giving up relativity (as the Bohm-DeBroglie interpretation does) is a way out, but it isn't a satisfying way out because there is no experimental justification for such a leap. There is absolutely no experimental support for the existence of a preferred frame.

[Note: some people consider the frame in which the background radiation from the Big Bang is isotropic to be a "preferred frame" of sorts. It gives a standard of "rest" for every point in the universe. If you consider that a "preferred frame", then my claim could be amended to: there is absolutely no experimental evidence that this frame is special for quantum mechanical processes.]

 

[Demystifier]

Within quantum theory there's nothing else than the mathematical setup to define it, including the Born rule. If you want a deterministic theory with hidden variables, then there's more and according to the violation of Bell's inequality it'll be a non-local model.

At the moment, however, I don't see the necessity for such a deterministic theory, because quantum theory never has been disproven by any experiment. In my opinion there are more urgent true problems to solve like: What's dark matter? How can we understand the smallness of "dark energy"? What's a consistent quantum theory of gravity? I don't see any urgent demand for a solution of the pseudo-problem of interpretation of quantum theory.

You didn't answer my question, probably because you missed my point entirely. So let me try to explain my point (and my question) again.

First, I didn't talk about determinism, so why do you talk about it? I talked about ontology.

The point is the following. According to the statistical ensemble interpretation, which you said you accept, the wave function does not describe an individual observation, but only a statistical ensemble. Do you agree?

On the other hand, individual observations do exist. Do you agree with that too?

Now, if you agree with both claims above, then logically you must accept that something (individual observation) exists which is not a wave function. Q.E.D.

So to condense all these questions into one: Do you agree that statistical ensemble interpretation of QM requires that something which is not a wave function must exist?

--------------------------------------

Or if you still don't get it, here is a yet another way to put it. In individual observations we observe something. That something is either wave function or something else. So let us explore both possibilities:

1) If it is wave function, then the statistical ensemble interpretation is wrong. In that case one needs either the collapse or many worlds.

2) If it is not wave function, then, obviously, there is something which is not wave function.

 

[TrickyDicky]

At the moment, however, I don't see the necessity for such a deterministic theory, because quantum theory never has been disproven by any experiment. In my opinion there are more urgent true problems to solve like: What's dark matter? How can we understand the smallness of "dark energy"? What's a consistent quantum theory of gravity? I don't see any urgent demand for a solution of the pseudo-problem of interpretation of quantum theory.

Well, you cannot discard a link between those problems and QM incompleteness-interpretations.

 

[rubi]

I talked about ontology.

The point is the following. According to the statistical ensemble interpretation, which you said you accept, the wave function does not describe an individual observation, but only a statistical ensemble. Do you agree?

On the other hand, individual observations do exist. Do you agree with that too?

Now, if you agree with both claims above, then logically you must accept that something (individual observation) exists which is not a wave function. Q.E.D.

I don't think that follows. One has to distinguish nature and its mathematical description. Ontology is concerned with nature itself. It tries to answer questions like: "What is the real nature of the things that we - as humans - perceive? What is beyond perception?" On the other hand, we have a mathematical description of nature, which includes mathematical objects like wave functions, fields or trajectories. None of these things exist in the way ontology talks about existence. A ball for example might exist in one way or the other or it might not, but it is not a trajectory, because a trajectory is just a certain string of symbols written on a piece of paper (for example the string $x(t)=-\frac{1}{2}gt^2$ is a trajectory). Obviously, a ball that you can see in front of you is never the string of symbols $x(t)=-\frac{1}{2}gt^2$ and neither is it any other string of symbols, so a ball is definitely not a trajectory. Neither is it a wave function. I still don't know what the ball "is", but I definitely know that it is not identical with its mathematical description. Even in classical mechanics, we strictly can't know what the right ontology is to interpret it. The difference between CM and QM is just that there are no interpretational difficulties with the standard ontology of CM (which postulates the existence of tiny little balls or something like that), so nobody worries about it. But still, if we prefer to accept only analytical arguments, having a classical (mathematical) description of physics doesn't tell us anything about ontology. So having a list of individual observations doesn't tell us anything about the (ontological) existence of "something". For example, I can easily build a measurement apparatus that measures something that most definitely doesn't correspond to something that onologically exists: Take a piece of paper and write "5" on it. Whenever you look at it, it reveals the number 5. It even has a classical and a quantum observable corresponding to it (a constant function $f(x,p)=5$ or the identity operator multiplied by 5). So I don't think it is possible to analytically conclude the ontological existence of "something" (whatever it is) from having a recorded list of measurement results.

 

[Demystifier]

So I don't think it is possible to analytically conclude the ontological existence of "something" (whatever it is) from having a recorded list of measurement results.

Are you saying that, even if nothing exists in the ontological sense, it is still logically possible to have measurement results?

 

[bhobba]

None of these things exist in the way ontology talks about existence.

Would all philosophers agree with you on that? For example would Penrose agree with that - he believes the mathematics is the only reality - what we experience is just a platonic shadow of that reality.

A ball for example might exist in one way or the other or it might not, but it is not a trajectory, because a trajectory is just a certain string of symbols written on a piece of paper

So the path traced out by a ball is just a string of symbols on a bit of paper. Actually it can be modeled by all sorts of things.

I think discussion of such philosophical issues is best taken up on a forum dedicated to such - not one discussing science.

Thanks
Bill

 

[rubi]

Are you saying that, even if nothing exists in the ontological sense, it is still logically possible to have measurement results?

I'm not adressing that situation, because obviously, something exists ("I think, therefore I am"). I'm basically arguing that the word "existence" can refer to different things and we should not mix them. On the one hand, we have the mathematical meaning of existence, which can be rigorously defined in mathematical logic and it is mainly a syntactic notion that has no inherent meaning. On the other hand, there is the ontlogical meaning of the word "existence", which talks about a loosely defined philosophical idea. My claim is that either notion of "existence" doesn' tell us anything about the other notion, respectively. So there are two things that we can't conclude analytically:
1. From having a list of measurement results that exists in an ontological way (I can see it), we can't conclude anything about the (syntactic) existence of mathematical objects that describe them.
2. From having a mathematical descrption of nature using (syntactically) existing mathematical objects, we can't conclude anything about ontological existence.

 

[bhobba]

From having a mathematical descrption of nature using (syntactically) existing mathematical objects, we can't conclude anything about ontological existence.

Actually I agree with that. Physics is a mathematical model - what relation it has to this 'ontology' thing is best left to the subject that analyses such - philosophy.

Thanks
Bill

 

[Demystifier]

I'm not adressing that situation, because obviously, something exists ("I think, therefore I am"). I'm basically arguing that the word "existence" can refer to different things and we should not mix them. On the one hand, we have the mathematical meaning of existence, which can be rigorously defined in mathematical logic and it is mainly a syntactic notion that has no inherent meaning. On the other hand, there is the ontlogical meaning of the word "existence", which talks about a loosely defined philosophical idea. My claim is that either notion of "existence" doesn' tell us anything about the other notion, respectively. So there are two things that we can't conclude analytically:
1. From having a list of measurement results that exists in an ontological way (I can see it), we can't conclude anything about the (syntactic) existence of mathematical objects that describe them.
2. From having a mathematical descrption of nature using (syntactically) existing mathematical objects, we can't conclude anything about ontological existence.

You are making good points!

So, would you say that the fight between "physicists" and "philosophers" on the meaning of quantum theory is to a large extent caused by the fact that they are not aware that they talk about two different types of "existence"?

 

[vanhees71]

You didn't answer my question, probably because you missed my point entirely. So let me try to explain my point (and my question) again.

First, I didn't talk about determinism, so why do you talk about it? I talked about ontology.

I think if it comes to "ontology" it means that you need determinism, but that's perhaps another topic.

The point is the following. According to the statistical ensemble interpretation, which you said you accept, the wave function does not describe an individual observation, but only a statistical ensemble. Do you agree?

Yes, that's the very point of quantum theory with Born's rule, and Born's rule is crucial. As is marvelously demonstrated in Weinbergs textbook, Lectures on Quantum Mechanics, it's a postulate independent of the others.

On the other hand, individual observations do exist. Do you agree with that too?

Sure, otherwise I couldn't measure any individual system, which one definitely can (nowadays even single elementary particles or photons).

Now, if you agree with both claims above, then logically you must accept that something (individual observation) exists which is not a wave function. Q.E.D.

First of all: QT is incomplete if you insist on wave functions. You can live with wave function alone only in (part) of non-relativistic QT. I don't know, why individual observations should be beyond quantum theory. The only constraint by QT compared to classical theory (CT) is that about individual observations you can in general make only probabilistic statements, even if you have complete knowledge about the system (i.e., if you know in which pure state it has been prepared).
[/QUOTE]

So to condense all these questions into one: Do you agree that statistical ensemble interpretation of QM requires that something which is not a wave function must exist?

I think, that's answered now, right?

 

[vanhees71]

Well, you cannot discard a link between those problems and QM incompleteness-interpretations.

I don't think that any physical theory is complete. It's great. So there's still enough left to be discovered for us and hopefully many future generations of scientists :-).

 

[Demystifier]

I think, that's answered now, right?

Not at all, but maybe the right answer lies in post #117.