Does quantum mechanics partially supply its own interpretation?

[Physics Monkey]

I will try to keep things brief. I am trying to understand what is considered interpretation.

Imagine we have a totally isolated and complex quantum system in a fixed initial state which we can prepare with essentially perfect fidelity. Suppose that this system is macroscopic in which small subsystems are totally decoherent and classical and life exists.

If we now make measurements on this system, then according to the usual prescription we will find a variety of outcomes. For example, if a living being inside the system measures a spin 1/2 particle in their world and we then measure them, then we would find that sometimes they found spin up and sometimes spin down. In this sense the same state describes two different experiences for the living being.

Except for the absurd level of control and isolation being assumed here, can we all agree that this is what quantum mechanics predicts? (Quantum mechanics here including the usual measurement rule that describes so well what occurs in our laboratories.)

My real question is this: where does interpretation come in? Is it just a matter of calling the state vector "really real" versus a "statistical description" versus ... or is there something more to it? If we are the living being and we believe our isolated world is described by a unitarily evolving state vector, then doesn't quantum mechanics (if we take it completely seriously) force us to conclude that the state of the world describes multiple possible experiences for beings similar to us? Is this trivial observation what it usually called "many-worlds"?

 

[JamesOrland]

An interpretation is what you think those pretty numbers you get as results mean, in the real world. The main concern is, really, the wavefunction collapse problem.

In Q.M. you have pretty numbers that say a lot of things about the system which is observed. But what they actually mean, in the real world, depends on the interpretation.

For instance, the Copenhagen interpretation says that when the wavefunction collapses upon measurement, then all other possible outcomes of a measurement do not exist anymore. When this collapse happens, we do not know, but it does.

The Many-Worlds interpretation says that there is no collapse, and that each possible existence given by the wavefunction is real. That is, there are different versions of you, each one having measured a different spin.

Check my other thread, the poll about the Interpretations of Q.M. and see the list of interpretations of the poll. Read up on a few of them so you will see what we're talking about.

Wikipedia gives a good explanation of what an interpretation is supposed to do, and the list I got was off the wiki, too.

 

[Fredrik]

Imagine we have a totally isolated and complex quantum system in a fixed initial state which we can prepare with essentially perfect fidelity. Suppose that this system is macroscopic in which small subsystems are totally decoherent and classical and life exists.

If we now make measurements on this system, then according to the usual prescription we will find a variety of outcomes. For example, if a living being inside the system measures a spin 1/2 particle in their world and we then measure them, then we would find that sometimes they found spin up and sometimes spin down. In this sense the same state describes two different experiences for the living being.

Except for the absurd level of control and isolation being assumed here, can we all agree that this is what quantum mechanics predicts?

I don't know decoherence well enough to be sure that what I'm about to say is right, but I think the assumption in your first paragraph ensures that the state of this "system" will be indistinguishable from a classical superposition.

My real question is this: where does interpretation come in? Is it just a matter of calling the state vector "really real" versus a "statistical description" versus ... or is there something more to it?

There are many things one can mean by "interpretation". To some people, an interpretation is defined by the mathematical axioms and correspondence rules that define the theory. (The correspondence rules tell us how to interpret the mathematics as predictions about results of experiments). I would say that axioms and correspondence rules define theories, not interpretations, that QM is a theory, rather than a piece of mathematics that needs to be interpreted, and that the words "interpretation of QM" should refer to non-scientific speculation about what the theory we call "QM" really means.

Some would say that the concept of "really real" that you mentioned is nonsense, since it's untestable. I think those people are missing the point. It's certainly unscientific, but that doesn't make it nonsense. The concept of "being real" is as fundamental as anything can get (certainly more fundamental than the set theories that we take as the foundation of mathematics), so physics (which is based on mathematics) can't really shed any light on what that concept means.

If we are the living being and we believe our isolated world is described by a unitarily evolving state vector, then doesn't quantum mechanics (if we take it completely seriously) force us to conclude that the state of the world describes multiple possible experiences for beings similar to us? Is this trivial observation what it usually called "many-worlds"?

In my opinion, yes. To say that the state vector describes the system, or to say that it represents all the properties of the system (rather than the properties of an ensemble of identically prepared systems) is to advocate an MWI. I have made this argument myself in this forum.

Edit: However, Everett's MWI is something more (or maybe I should say less) than this. It's based on the idea that you can drop the Born rule from the list of axioms, and then derive it from the others. This is almost certainly impossible if you don't make any additional assumptions. So Everett's MWI simply hasn't been developed to the point where it can be called an interpretation of QM, in any sense of the word. It's just a failed idea. Of course, that doesn't imply that there aren't many worlds.

 

[JamesOrland]

In my opinion, yes. To say that the state vector describes the system, or to say that it represents all the properties of the system (rather than the properties of an ensemble of identically prepared systems) is to advocate an MWI. I have made this argument myself in this forum.

Edit: However, Everett's MWI is something more (or maybe I should say less) than this. It's based on the idea that you can drop the Born rule from the list of axioms, and then derive it from the others. This is almost certainly impossible if you don't make any additional assumptions. So Everett's MWI simply hasn't been developed to the point where it can be called an interpretation of QM, in any sense of the word. It's just a failed idea. Of course, that doesn't imply that there aren't many worlds.

Some people claim to have derived the Born rule, including Everett himself. I am uncertain about this, but whichever way, just because the Born rule hasn't been derived yet doesn't mean it's not derivable. One should not underestimate human ingenuity.

 

[Whovian]

I have one tiny little thing to point out. The system can't be closed if we observe this living thing that's measured a particle's spin.

 

[JamesOrland]

Once we observe it, no, of course it's not. But I believe he meant that the system was closed up until we observed the living thing.

 

[Physics Monkey]

Thanks for the replies so far.

James,
I understand the general idea of an interpretation, but I don't understand many of the words within various interpretations. For example, when you say that Copenhagen declares that unrealized outcomes don't exist, what does that mean? Does it mean that there is no local unitary transformation (e.g. time evolution in reverse) that would formally take the state of the world after the measurement back to the state of the world before the measurement? If we accept that the state of the system before we look at it is a complicated superposition like (spin up and being sees up) + (spin down and being sees down), would we say, as textbooks often do for isolated spins, that the spin/being system is both up and down?

Fredrik,
Although I was using "really real" half in joking, I do agree with you that it is not nonsense and am happy to think about it. Mostly I just don't know what such a thing is supposed to mean even apart from scientific considerations.

Whovian,
I did have in mind that the system was isolated up until the time when we measure it.

Regarding the Born rule, in many ways I feel that it should be obvious that it can be derived from unitary evolution. I say this because I believe a unitarily evolving state vector can describe beings like us who assign probability according to the Born rule. Thus with the proper definition of being, etc. it should be possible to show in the context of unitary evolution that such beings will use the born rule. But perhaps this argument is too meta.

In other words, given a definition of classical beings, analyzing the unitary evolution of complex composite systems should reveal a notion of probability, etc.

 

[Fredrik]

Regarding the Born rule, in many ways I feel that it should be obvious that it can be derived from unitary evolution. I say this because I believe a unitarily evolving state vector can describe beings like us who assign probability according to the Born rule. Thus with the proper definition of being, etc. it should be possible to show in the context of unitary evolution that such beings will use the born rule. But perhaps this argument is too meta.

Sounds like what we'd find this way isn't that the Born rule must hold, or an explanation of what the probabilities mean. We would only be able to show that there are people who believe in the Born rule.

 

[The_Duck]

Regarding the Born rule, in many ways I feel that it should be obvious that it can be derived from unitary evolution. I say this because I believe a unitarily evolving state vector can describe beings like us who assign probability according to the Born rule. Thus with the proper definition of being, etc. it should be possible to show in the context of unitary evolution that such beings will use the born rule. But perhaps this argument is too meta.

I've not read much about this, but it sounds like you're arguing that you should be able to show that predictions that use the Born rule to assign probabilities will turn out most accurate in the long run. But for any finite number of trials, there's always a finite probability that the Born rule will look completely wrong, and I don't see how you can argue that this probability is small unless you first (circularly) assume the Born rule.

 

[JamesOrland]

Thanks for the replies so far.

James,
I understand the general idea of an interpretation, but I don't understand many of the words within various interpretations. For example, when you say that Copenhagen declares that unrealized outcomes don't exist, what does that mean? Does it mean that there is no local unitary transformation (e.g. time evolution in reverse) that would formally take the state of the world after the measurement back to the state of the world before the measurement? If we accept that the state of the system before we look at it is a complicated superposition like (spin up and being sees up) + (spin down and being sees down), would we say, as textbooks often do for isolated spins, that the spin/being system is both up and down?

Copenhagen assumes a non-unitary, non-local, all in all magical process called collapse that happens when something undefined that they call an observation happens. They mean that, once a measurement is made, there is no longer any superposition. Before we look, superposition alright. After observation, the superposition is gone.

Many-Worlds states that the superposition is never gone, it just starts holding a larger number of things in it; in this case the person who measured the spin is in a superposition of states, too.

---

Now, the Born rule is a problem. It has been shown, I think, that a conscious observer would derive the Born rule, but it's still a challenge to prove that the Born rule actually exists.

 

[Fredrik]

Copenhagen assumes a non-unitary, non-local, all in all magical process called collapse that happens when something undefined that they call an observation happens. They mean that, once a measurement is made, there is no longer any superposition. Before we look, superposition alright. After observation, the superposition is gone.

I know that this is what "everyone" says that the Copenhagen interpretation says, but I think this is just how it was defined by people who have misunderstood it. It's like when creationists define the big bang theory as "first there was nothing, and then it exploded". I don't think this definition is logically consistent, and I don't think there's evidence that Bohr thought that this is how the world works. If there is, I haven't seen it.

I like this quote from Asher Peres:

There seems to be at least as many different Copenhagen interpretations as people who use that term, probably there are more. For example, in two classic articles on the foundations of quantum mechanics, Ballentine (1970) and Stapp (1972) give diametrically opposite definitions of “Copenhagen.”​

The quote is from this article (page 6). Peres goes on to explain how he thinks the Copenhagen interpretation should be defined.

I believe that Bohr's idea was essentially just that QM should be viewed as a way to calculate probabilities of possible results of measurements, rather than as a description of what's actually happening. This would mean that his view is an ensemble interpretation, regardless of whether he said that explicitly or not.

This is by the way the reason I didn't answer that poll. There's no consensus about how the interpretations should be defined, or even about what an interpretation is. I don't want to put a label on my views of QM when I know that different people would interpret that label differently.

 

[Demystifier]

Some people claim to have derived the Born rule, including Everett himself. I am uncertain about this, but whichever way, just because the Born rule hasn't been derived yet doesn't mean it's not derivable. One should not underestimate human ingenuity.

The Born rule is derivable, and several derivations of it are already known. But the point is that all derivations rest on some ADDITIONAL ASSUMPTIONS. What different people disagree is whether the specific assumptions (in a given derivation) are appealing or not.

 

[Hurkyl]

The central feature of the Copenhagen interpretation is wave-function collapse. As far as I tell, the main variations are whether you take that at face value (as I was originally taught was meant by the phrase "Copenhagen interpretation", and still often seen it defined as), or you interpret it as ignorance about an unknown hidden variable theory.

I know I'm being a bit glib, but since no details of the hidden variable theory are supplied, there really isn't any difference between the two variations, except in the amount of leeway it gives people to rationalize away criticism.On an unrelated point, if Peres is really giving a fair representation of Bohr, then Bohr was being rather silly on at least one point. (i.e. the "argument" that experiments must be described in classical terminology, which consists of nothing more than an assertion that experiments must be described in classical terminology)

 

[Fredrik]

The central feature of the Copenhagen interpretation is wave-function collapse. As far as I tell, the main variations are whether you take that at face value (as I was originally taught was meant by the phrase "Copenhagen interpretation", and still often seen it defined as), or you interpret it as ignorance about an unknown hidden variable theory.

Peres's article about the CI doesn't even contain the word "collapse" or its synonym "reduction", so I doubt that he would agree. But I suppose that if almost everyone in physics believes that collapse as a physical process is a part of the CI, then maybe we should define it that way. This is like reluctantly admitting that "nucular" (nuke-you-lurr) is now an acceptable way to pronounce the word "nuclear", just because the mistake is so common.

If this collapse is assumed to be exact rather than approximate, it would probably make the CI logically inconsistent (it seems to contradict the unitary time evolution), so this would make the CI a nonsense interpretation. If it's approximate, then we're just talking about decoherence, which is already a part of the theory. So if the CI is defined by an assumption of "collapse", it's either nonsense or a bunch of words that don't actually say anything.

On an unrelated point, if Peres is really giving a fair representation of Bohr, then Bohr was being rather silly on at least one point. (i.e. the "argument" that experiments must be described in classical terminology, which consists of nothing more than an assertion that experiments must be described in classical terminology)

I don't understand this objection. Science requires us to test the predictions of our theories, so we obviously have to do experiments that have (classical) results. How else would we know if the theory has passed the test or failed it?

 

[martinbn]

Fredrik, I don't agree. I don't think that the collapse is viewed as a physical process in CI, and I don't think that's what Hurkyl meant. Also, I don't see any inconsistency in having two different ways in which the evolution is described, one the unitary and the other the non-unitary projection.

 

[Fredrik]

Fredrik, I don't agree. I don't think that the collapse is viewed as a physical process in CI, and I don't think that's what Hurkyl meant. Also, I don't see any inconsistency in having two different ways in which the evolution is described, one the unitary and the other the non-unitary projection.

It's pretty common to claim that collapse as a physical process is an essential part of the CI. See post #10 for example. I think almost all the attempts to explain what the CI says that I've seen have said something similar.

It's true that there's no obvious contradiction between unitary and non-unitary time evolution. Isolated systems evolve unitarily, and non-unitary time evolution is something that happens to systems that interact with their environments. However, if collapse is supposed to be something different from decoherence, then I think a contradiction is unavoidable, but it's of course impossible to prove that without a definition of "collapse".

So what is a collapse? Isn't it supposed to be the process that allows us to think of QM as a description of what actually happens, without having to accept that there are many worlds? If it is, then collapse is not decoherence, because decoherence doesn't eliminate unwanted worlds. It just puts quantum systems into states that are indistinguishable from classical superpositions.

The stuff I said in the quote below is also relevant. I have changed my mind about one thing since I wrote it. I wouldn't say that the CI is defined as in this quote, because now I understand that everyone means something different by that term.

The main assumption of the CI is that state vectors can be identified with physical systems, i.e. that each state vector describes all the properties of the system it represents. Let's label that assumption (1). I said that if we add this on top of QM, we get a contradiction, but that's not quite right. What we get is many worlds. So QM+(1) contradicts the assumption that there's only one world. Let's label that assumption (2). Obviously, (2) should also be considered part of the definition of the CI.

So I'm not going to argue that QM+(1) is logically inconsistent, I'm going to argue that CI=QM+(1)+(2) is. The argument can't be made rigorous, since the assumptions (1) and (2) aren't mathematical statements. An informal argument is the best anyone can do.

The Schrödinger's cat thought experiment has taught us that the linearity of the SE implies that if microscopic systems can be in superpositions, then so can macroscopic systems. The details of this part of the argument are included both in Ballentine's 1970 article and in his more recent textbook. (Section 9.2).

(A calculation that includes decoherence effects would change the argument somewhat, but not enough to solve the problem).

Suppose that we prepare a large and complicated system, e.g. a system that includes you, in a state like |this>+|that>, where |this> and |that> describe two different experiences you can have in there. Now the problem is that (1) says that |this>+|that> is a complete description of the physical system. Clearly this means that neither |this> nor |that> can be a complete description of the physical system, and this means that what you actually experience as a part of that system is no more than half the story. If the complete description includes both of your possible experiences, then so does reality. Otherwise it wouldn't be a complete description.

Therefore QM+(1) implies that there are many worlds. This means that QM+(1)+(2) is inconsistent.

 

[ParticleGrl]

I like Ballentine's interpretation, personally. We note that quantum mechanics doesn't let us make predictions for single experiments, only for ensembles of experiments. So the obvious thing to do is to take the wavefunction as predicting probability distributions. Taking on experiment is taking one sample from the distribution.

No collapse, no extra worlds. Its a very minimal interpretation.

 

[Fredrik]

I like Ballentine's interpretation, personally. We note that quantum mechanics doesn't let us make predictions for single experiments, only for ensembles of experiments. So the obvious thing to do is to take the wavefunction as predicting probability distributions. Taking on experiment is taking one sample from the distribution.

No collapse, no extra worlds. Its a very minimal interpretation.

In his 1970 article that defines the interpretation, Ballentine is assuming that every particle has a well-defined position at all times* (in particular, each particle in a double-slit experiment goes through one of the slits, we just don't know which one). I prefer to not make that assumption. If we don't, what we have left is just the idea that QM is a way to calculate probabilities of possible results of experiments, and not a description of what's actually happening. This is an "ensemble interpretation", but I don't know if I really want to call it an "interpretation", since it tells us nothing at all about what's actually happening to the particle between state preparation and measurement.

*) I used to think that this contradicts QM, but it doesn't, if we can tolerate that particles behave in a very strange way. There's some discussion about this in this thread.

 

[mwalmasri]

QM is an approximation tool but strong in the same time, the philosophical implications to QM is much harder to be described to us by our life experience, we have two explanations to QM, one is CI and second is Many Worlds interpretation, I suggested the following title
http://arxiv.org/abs/quant-ph/0101077, 100 Years of the Quantum Theory By Wheeler, Tegmark
as start point ,
Bos-einstein Condensation is an overlap Wave-Functions at the same state, which make us very close to Real World.
I think we can not be able to understand all the quantum world and its behaves without have theory unified all the forces in the nature.

 

[Mark M]

QM is an approximation tool but strong in the same time, the philosophical implications to QM is much harder to be described to us by our life experience, we have two explanations to QM, one is CI and second is Many Worlds interpretation, I suggested the following title
http://arxiv.org/abs/quant-ph/0101077, 100 Years of the Quantum Theory By Wheeler, Tegmark
as start point ,
Bos-einstein Condensation is an overlap Wave-Functions at the same state, which make us very close to Real World.
I think we can not be able to understand all the quantum world and its behaves without have theory unified all the forces in the nature.

mwalmasri, there are far more than just those two interpretations. Look at this chart:

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

 

[martinbn]

Fredrik, I still disagree, but as you said there isn't a single version of CI, and I am not so familiar with any CI, so you might be right. But I would be very surprised if you can quote Bohr saying that the collapse is a physical process.

 

[Physics Monkey]

I take it that even the so-called copenhagen interpretation means different things to different people, yet I am sympathetic with the idea that calling for literal "collapse" is excessive (or even in principle flat wrong). I think we know enough about the dynamics of composite quantum systems to say that the process would look like "collapse" even without actually doing anything besides unitary evolution. But then I wonder again in what sense copenhagen is really an interpretation at all? I have a similar feeling about many worlds as I understand it.

Suppose that the world is a unitarily evolving state vector. I think we can agree that because of decoherence, etc. this world world would look very much like a classical superposition of different classical histories. The beings in anyone history never see more than one outcome (essentially by definition), yet wouldn't it be strange for them to say that the other possibilities don't exist anymore because e.g. there is a unitary that undoes any "measurement"?

 

[Fredrik]

Fredrik, I still disagree, but as you said there isn't a single version of CI, and I am not so familiar with any CI, so you might be right. But I would be very surprised if you can quote Bohr saying that the collapse is a physical process.

I obviously don't think Bohr ever said anything like that, but that's one of the points I've been trying to make. What people are calling the CI today, especially here at Physics Forums, doesn't resemble Bohr's views. The CI seems to have been redefined by people who have misunderstood it.

 

[Hurkyl]

Peres repeatedly emphasizes the claim that the result of experiment must be described "in classical terms". This implies collapse, because classical terms don't include any way to talk about an uncollapsed state, or even an approximately collapsed state.

I am using "collapse" slightly more generally, to include classical probability distributions.

However, "classical terms" usually include the interpretation of probability distributions as quantifying ignorance, and thus seems to imply either total collapse down to a single outcome, hidden variables, or fundamental non-determinism.

I don't understand this objection. Science requires us to test the predictions of our theories, so we obviously have to do experiments that have (classical) results. How else would we know if the theory has passed the test or failed it?

You're begging the question. Experiments have to be described in classical terms because experiments have to be described in classical terms!

What is true^* is that experiments must be described in terms of things in the domain of validity of classical mechanics. This is a very different claim from asserting the description must actually be classical.For comparison, how often do you see people insisting that the empirical evidence regarding Special Relativity must be described in pre-relativistic terms? I don't think I've ever seen such a thing! What we actually require is pretty much the exact opposite: we insist that Special Relativity be able to explain the empirical evidence regarding pre-relativistic mechanics!*: This may be debatable, but that would be off-topic

 

[Fredrik]

How am I begging the question? I'm just saying that the definition of "measurement" includes the requirement that measurements have results. That's precisely what distinguishes measurements from other interactions between the system and its environment.

 

[Hurkyl]

How am I begging the question? I'm just saying that the definition of "measurement" includes the requirement that measurements have results. That's precisely what distinguishes measurements from other interactions between the system and its environment.

No, you're further asserting that it is impossible to suitably interpret the phrase "measurements have results" in quantum terms.

 

[zonde]

What is true^* is that experiments must be described in terms of things in the domain of validity of classical mechanics. This is a very different claim from asserting the description must actually be classical.


For comparison, how often do you see people insisting that the empirical evidence regarding Special Relativity must be described in pre-relativistic terms? I don't think I've ever seen such a thing! What we actually require is pretty much the exact opposite: we insist that Special Relativity be able to explain the empirical evidence regarding pre-relativistic mechanics!

Description of experimental results must actually be classical.
To do it otherwise would be just more sophisticated form of begging the question fallacy i.e. we would ask to accept the theory to be tested in order to test it.

 

[Fredrik]

No, you're further asserting that it is impossible to suitably interpret the phrase "measurements have results" in quantum terms.

I still don't understand your objections. A human can't possibly interpret the state of the measuring device at the end of the measurement as a "result" unless it's a state that can also be described classically. The classical description would of course only be an approximation, but it would be an absurdly excellent one.

A measurement is by definition an interaction between the system and its environment that puts a part of the environment (like a needle) into one of at least two possible final states that a human can distinguish between. If a human can distinguish between the possible final states, then he has no reason to not think of them in classical terms.

To do it otherwise would be just more sophisticated form of begging the question fallacy i.e. we would ask to accept the theory to be tested in order to test it.

This is a very good point. I didn't even think of that.

Since we can test classical theories without first accepting their validity, we should perhaps avoid the word "classical" in statements such as the one I just made about what a measurement is. If a human can distinguish between the different final states, he can think of them in terms that are much simpler than any of the classical theories. He only has to think of each distinguishable states as a unique piece of information. Theories of physics don't really enter into it.

Of course, things that are much simpler than classical theories can of course also be described classically, so it's not wrong to say that we can describe the final states of a measuring device classically.

 

[Hurkyl]

I still don't understand your objections. A human can't possibly interpret the state of the measuring device at the end of the measurement as a "result" unless it's a state that can also be described classically. The classical description would of course only be an approximation, but it would be an absurdly excellent one.

I think it's because you're actually saying the things I'm saying.

A key word here is can. Not "must be described classically" but "can also be described classically". You even admit the possibility that a classical interpretation of our ideas about measurement may be merely approximate!

Now, I don't know whether Peres is accurately representing Bohr. While Peres emphases the point implied by the usage of 'must' in the quote of Bohr's

The necessity of using a classical terminology was
emphasized by Bohr (1949) whose insistence on this point was very strict

it might turn out that Bohr was just stating the fact that quantum mechanics had not yet developed to the point where it could host a suitable interpretation of our notion of 'experiment' (and due to various no-go theorems, it seemed impossible that it could). Or he might have even been using the word 'classical' in such a broad sense as to be effectively meaningless. However, barring evidence otherwise, I have to assume Bohr means what he says.

That Bohr is begging the question is evident when the quote is trimmed down:

The account of all evidence must be expressed in classical terms. The argument is that we must provide an account of the evidence, and therefore we must use classical terms.​

Everything else in the quote is just fluff -- things like a more wordy description of 'provide an account of the evidence'. In particular, no clarification on 'therefore' is provided; it's just asserted.


The implication simply doesn't hold water (unless 'classical' is being used in a meaninglessly broad sense). Yes, experiments must^* involve us seeing outcomes, telling others what we have done, and explaining what we have learned. But each of those concepts -- e.g. 'outcome', 'seeing outcome', 'telling others' -- could, in principle, be interpreted in terms other than classical terms .

*: Again, I'm accepting this for the sake of argument.