Different interpretations? No, different theories

[Demystifier]

I need you to give me a clear definition of what CI is.. Can you?

I'm not sure that this is clear enough, but here it is:
https://www.physicsforums.com/showpost.php?p=2319553&postcount=1

 

[bhobba]

There is no definition of the CI that wouldn't make a lot of people go "hey, CI doesn't say that".

Oh boy aren't that the truth as a number of 'discussions' I have had about it show.

Even the MSI I hold to has variations - it seems part of the landscape that within most if not all interpretations you have different schools of thought.

Thanks
Bill

 

[atyy]

What I said is the objection. The argument is circular. It's roughly like this:

QM with the Born rule → the rules for propositional systems → QM without the Born rule + tensor products → QM with the Born rule​

What Zurek did is perhaps the ultimate proof of that last implication. But the relevant implication

QM without the Born rule → QM with the Born rule​

has never been proved, and I don't think it can be done.

But you do have "QM without the Born rule + tensor products → QM with the Born rule", so if one were happy to start at "QM without the Born rule + tensor products" it wouldn't be circular.

 

[bhobba]

But the relevant implication

QM without the Born rule → QM with the Born rule​

has never been proved, and I don't think it can be done.

Hmmmm.

That depends on what you mean by QM without the Born rule.

If that includes non contextuality then Gleasons Theorem implies the Born rule.

What I think it is fairer to say is the observable axiom (ie the eigenvalues of a Hermition operator give the possible outcomes of an observation) is not sufficient by itself to derive the Born rule - however some reasonable added assumptions such as additivity of expectations or non contextuality are.

Thanks
Bill

 

[Fredrik]

Hmmmm.

That depends on what you mean by QM without the Born rule.

And that depends on what I mean by "the Born rule". I consider it to be not just the formula, but the statement that the probabilities it assigns correspond to measurement results.

If that includes non contextuality then Gleasons Theorem implies the Born rule.

Gleason's theorem tells us that probability measures on the lattice of closed linear subspaces of the Hilbert space correspond bijectively to state operators, and that the formula for that bijection is a generalized version of the formula that makes up the purely mathematical part of the Born rule. So when we drop the Born rule, what we're really dropping isn't the formula, but the assumption about in what way the subspaces of the Hilbert space are significant.

 

[Maui]

I would give it a lot of thought if that was the case, but as you can see from the posts above, it's not. Copenhagen interpretation does not say that the observer is non-quantum mechanical. For CI, an observer is quantum if he is being observed but something else if he is observing. All this is so vague that i am not sure what CI is about, and i don't know what to prove! In order to prove something, i need to know the rules.. and the rules seem so vague in CI.

That's because you after a classical explanation of quantum behavior. Of course this can't be done and no such explanation exists except fancy, religious ideas like the MWI.

As usual, most of the mystery is reflected and highlighted in the double slit experiment - esp. the one done with large molecules like C60. This experiment is the best evidence to date that the observed classical properties and behavior at our scales(of table and chairs and walls) are JUST a manifestation of an underlying reality.

You may continue to imagine a billion different worlds and magical guiding waves that have access to the SE, but the truth is only one - classical behavior is a completely contextual secondary manifestation.

http://www.uam.es/personal_pdi/ciencias/jcuevas/Teaching/double-slit-C60.pdf

Quantum interference experiments with large molecules
Olaf Nairz, Markus Arndt, and Anton Zeilinger
Institut fur Experimentalphysik, Universitat Wien

 

[stevendaryl]

That's because you after a classical explanation of quantum behavior. Of course this can't be done and no such explanation exists except fancy, religious ideas like the MWI.

Calling it "religious" is pretty ridiculous. You might as well call it "poopy-headed" for all the information it conveys.

 

[Fredrik]

But you do have "QM without the Born rule + tensor products → QM with the Born rule", so if one were happy to start at "QM without the Born rule + tensor products" it wouldn't be circular.

Yes, I think that last part is correct. But now I think that my statement that "QM without the Born rule + tensor products → QM with the Born rule" isn't accurate enough. I think that the real problem with Zurek's derivation is that it relies not only on "QM without the Born rule + tensor products", but also on an assumption about how the probabilities assigned by the formula correspond to measurement results.

 

[stevendaryl]

That's because you after a classical explanation of quantum behavior. Of course this can't be done and no such explanation exists except fancy, religious ideas like the MWI.

MWI is about as far from a "classical explanation" as you could possibly get. Really, your comment makes no sense whatsoever. In my opinion.

 

[Maui]

Calling it "religious" is pretty ridiculous. You might as well call it "poopy-headed" for all the information it conveys.

Religious dogma is usually defined as something that is taken on faith without experimental evidence. Like the MWI. Sorry if i hurt religious feelings about the trillion worlds.

MWI is about as far from a "classical explanation" as you could possibly get. Really, your comment makes no sense whatsoever. In my opinion.

Your commment makes no sense either, as I didn't say that the MWI was a classical explantion, but that JK423 seemed to be intent on reducing the CI to a complete account of classical behavior, whereas as Bohr himself stated - the role of physics is what we can say about nature, not how nature is. The purpose of the CI is not to make sense to you or to JK423, but to provide the best framework for making predictions. Yes, it doesn't make sense classically, but neither do the other so called "interpretations".

 

[stevendaryl]

Yes, I think that last part is correct. But now I think that my statement that "QM without the Born rule + tensor products → QM with the Born rule" isn't accurate enough. I think that the real problem with Zurek's derivation is that it relies not only on "QM without the Born rule + tensor products", but also on an assumption about how the probabilities assigned by the formula correspond to measurement results.

On odd days, I agree with you that the Born rule must be added as an additional hypothesis. However, the weird thing about the Born rule is that you can push its application off indefinitely. What I mean by that is this: Suppose you are interested in measuring the spin of an electron that is in a superposition of states $\vert \Psi \rangle = \alpha\ \vert +\frac{1}{2}\rangle + \beta\ \vert -\frac{1}{2}\rangle$. You could

1. Say that the spin-measuring apparatus has a probability $\vert \alpha \vert^2$ of measuring spin-up
2. Treat the apparatus quantum mechanically, so there is no definite result of the measurement until an experimenter comes along and observes the apparatus, in which case the human has a probability of itex]\vert \alpha \vert^2[/itex] of observing the apparatus to be in the state of having measured an electron in the state spin-up.
3. Treat the experimenter quantum mechanically, so there is no definite result for his observation until a different observer comes along and reads his lab write-up.
4. Treat the second experimenter quantum mechanically...
5. Etc.

There is no need for the Born rule until the last step of however many steps you want to include in the list. And the last step could be pushed off until the far future, where our great-great-great-great-grandchildren read about the whole history of the human race.

 

[stevendaryl]

Religious dogma is usually defined as something that is taken on faith without experimental evidence. Like the MWI. Sorry if i hurt religious feelings about the trillion worlds.

You're using words ("religion" and "dogma") in a way that conveys no information except your own feelings.

 

[stevendaryl]

Your commment makes no sense either, as I didn't say that the MWI was a classical explantion

You said:

...you [are] after a classical explanation of quantum behavior. Of course this can't be done and no such explanation exists except fancy, religious ideas like the MWI.

I interpreted "no such explanation exists" as "no classical explanation of quantum behavior exists", and I interpreted the word "except" to mean that MWI is an exception. Which would imply that "MWI is an exception to the claim that no classical explanation of quantum behavior exists".

I guess I shouldn't try to interpret your words as conveying meaning, as opposed to pure scorn, which is how they were intended.

 

[Maui]

You said:
I interpreted "no such explanation exists" as "no classical explanation of quantum behavior exists", and I interpreted the word "except" to mean that MWI is an exception. Which would imply that "MWI is an exception to the claim that no classical explanation of quantum behavior exists".

I will modify my initial statement so that no confusion arises, though from the context it seems obvious what my motivation was:

"you [are] after a classical explanation of quantum behavior. Of course this can't be done and no such explanation exists except fancy, religious attempts like the MWI""attempts" here does not equal classical explanation within physics, though it probably does within religion.

I guess I shouldn't try to interpret your words as conveying meaning, as opposed to pure scorn, which is how they were intended.

So if i react to scorn being thrown at the CI(a minimalist, no nonsense interpretation of experimental results) by showing the same amount of dismay at the religious proposition of MWI, it suddenly makes my words meaningless? I guess you haven't read my posts or your motivation is different from addressing the point being made but the author who made the point(basically an ad homimnem attack).

You're using words ("religion" and "dogma") in a way that conveys no information except your own feelings.

...towards beliefs that rest on no experiemental evidence whatsoever.

 

[stevendaryl]

So if i react to scorn being thrown at the CI(a minimalist, no nonsense interpretation of experimental results) by showing the same amount of dismay at the religious proposition of MWI, it suddenly makes my words meaningless?

I would say yes, your claims are pretty devoid of anything but scorn.

 

[Nugatory]

no such explanation exists except fancy, religious attempts like the MWI

The thread, taken as a whole, appears to my support my position (which I believe to be widely shared) that there are a number of interpretations that cannot be falsified experimentally. Therefore:
1) the idea suggested in the thread title can be rejected; interpretations are not theories.
2) there's not a lot of point in arguing about which interpretation is "right", nor whether an interpretation is being accepted for aesthetic or religious or other reasons. (Me, I choose mine based on aesthetics).

 

[Fredrik]

...towards beliefs that rest on no experiemental evidence whatsoever.

The MWI is essentially just the idea that QM is not just an assignment of probabilities to possible results of experiments, but also a description of what's actually happening. There's no evidence for that statement, but there's also no evidence for its negation. So I think it would be hard to justify the claim that the defining assumption of the MWI is religion and its negation is not.

I think of interpretations the way I think of Venn diagrams for set theory. They aren't part of the theory. They are tools that can help us develop some intuition about the theory.

 

[JK423]

You've got me really confused!
Demystifier, indeed the OP seems to be impossible even in principle, i have to think about this a little bit more, and i will post in the future if i think of something.
Right now i am quite "obsessed" with the simplicity of MWI and the non-circular derivations of Born's rule. So, i would like to ask you all a question.

Say, that, tomorrow a paper appears on arXiv where Born's rule has been derived non-circularly and without inserting probabilities "by hand" in any way; assume that everything comes out naturally. What will be the meaning of this result? Will it mean that MWI is correct and infinite copies of the world exist simultaneously? I don't know why, but i have a feeling that the statement "simultaneous existence" involves hidden assumptions that require more than just deriving Born's rule.

 

[Fredrik]

Right now i am quite "obsessed" with the simplicity of MWI and the non-circular derivations of Born's rule.

You may want to take a look at Gleason's theorem then. I think it's a much better way to obtain the probability formula than what Zurek did. It even provides the motivation for the definition of state operators in QM.

Say, that, tomorrow a paper appears on arXiv where Born's rule has been derived non-circularly and without inserting probabilities "by hand" in any way; assume that everything comes out naturally. What will be the meaning of this result? Will it mean that MWI is correct and infinite copies of the world exist simultaneously?

Even without that result, the MWI can (probably) be viewed as a plausible description of what is happening to the universe. With that result, it can also be viewed as an explanation of why QM is a good theory.

 

[Demystifier]

You've got me really confused!
Demystifier, indeed the OP seems to be impossible even in principle, i have to think about this a little bit more, and i will post in the future if i think of something.
Right now i am quite "obsessed" with the simplicity of MWI and the non-circular derivations of Born's rule. So, i would like to ask you all a question.

Say, that, tomorrow a paper appears on arXiv where Born's rule has been derived non-circularly and without inserting probabilities "by hand" in any way; assume that everything comes out naturally. What will be the meaning of this result? Will it mean that MWI is correct and infinite copies of the world exist simultaneously? I don't know why, but i have a feeling that the statement "simultaneous existence" involves hidden assumptions that require more than just deriving Born's rule.

If there was a way to derive Born's rule non-circularly, I would still not be satisfied with MWI due to the following objection:
https://www.physicsforums.com/blog.php?b=4289

 

[JK423]

If there was a way to derive Born's rule non-circularly, I would still not be satisfied with MWI due to the following objection:
https://www.physicsforums.com/blog.php?b=4289

I need to study the paper, but my immediate response at this point is:
Aren't the interactions taking care of defining the subsystems? Can you give me an example of the ambiguity you mention?

 

[Fredrik]

If there was a way to derive Born's rule non-circularly, I would still not be satisfied with MWI due to the following objection:
https://www.physicsforums.com/blog.php?b=4289

I consider that a good reason to reject the idea that a preferred basis identifies the worlds, but not a good reason to reject the idea of many worlds. See e.g. my post #33.

Aren't the interactions taking care of defining the subsystems? Can you give me an example of the ambiguity you mention?

The universe can be decomposed into "you + everything else" or "you and the chair you're sitting on + everything else".

 

[Demystifier]

I need to study the paper, but my immediate response at this point is:
Aren't the interactions taking care of defining the subsystems? Can you give me an example of the ambiguity you mention?

Defining subsystems in terms of interactions looks like another circularity. Namely, a priori, all you have is a total Hamiltonian, not a split of the Hamiltonian into the "free" and "interacting" part. If you choose some splitting of the whole system into subsystems then you can also (at least to some extent) see what is the interacting part of the Hamiltonian. But then it is circular to use the interacting part to identify the subsystems again.

The explicit examples of ambiguity are presented in the paper.

 

[Demystifier]

I consider that a good reason to reject the idea that a preferred basis identifies the worlds, but not a good reason to reject the idea of many worlds. See e.g. my post #33.

Fine. But then, as the author says in the Conclusions, we deal with
"... Many Many Worlds Interpretation (because each of the arbitrary more complicated factorizations tells a different story about Many Worlds [7])."

 

[Fredrik]

Fine. But then, as the author says in the Conclusions, we deal with
"... Many Many Worlds Interpretation (because each of the arbitrary more complicated factorizations tells a different story about Many Worlds [7])."

Ooh, now I think I have to read the conclusions, and check out reference 7.

 

[Fredrik]

I had a quick look. What he called "many many worlds" is the idea that decompositions are arbitrary, but then there's a preferred bases selected by decoherence or something. I guess what I'm advocating would be "many many many worlds" then, because I'm suggesting that decompositions are arbitrary, and that the basis is arbitrary. (The basis selected by decoherence is still "preferred", but not in the sense that it identifies the worlds; it just identifies worlds that are more interesting than most).

 

[JK423]

I read the paper and it, indeed, presents a serious problem. This problem seems to be relevant to classical physics as well, not just quantum.

Consider the Earth and Sun, where the Sun stands still and the Earth goes around it in circles. The Hamiltonian of the system is
${H_1} = {H_{{r_{Earth}}}} + {H_{{r_{sun}}}} + {H_{{\mathop{\rm int}} }},$
and the equations of motion show that an object (the earth) is moving in circles.
As we know, a change of coordinates to center of mass R and relative position r uncouples the system,
${H_2} = {H_R} + {H_r}$,
and the new equations of motion gives two static objects (or at least one of them -R- moving in constant motion).
If this system was all there is in the universe, then we would not be able to tell which description is the "real one" because they are mathematically equivalent. This holds for classical physics as well.
However, in practice when we (the observer) look at the system we see the first case -the Earth going around in circles- and not the second -two objects standing still. That's because the observer interacts specifically with the r_Earth and r_Sun, and not with R and r. The paper suggests now, that if we put the observer in the description and consider the system "earth+sun+observer" all there is in the universe, then the Hamiltonian describing the whole system can be expressed in various different bases and there is ambiguity in which interpretation is "the real one".

My objection:
I agree that only the postulate of the wavefunction seems not to be enough, it leads to the aforementioned 'paradoxa'. My first thought is to postulate spacetime; if we do that, the previous ackward situation disappears. In the postulated spacetime basis, all the interactions (in the global Hamiltonian) take their well-known form (which is also postulated) and this solves (?) the subsystem ambiguity. Now, Schwindt -in that paper- presents this idea of postulating spacetime to solve the problem (in page 8), but he argues that it's not enough, but to be honest i cannot understand why. He defines a new space in order to make his argument, but this new space is not related to the previous (postulated one) via a Lorentz transformation as it should, so his argument seems really weird. If you understand it, please explain.

In conclusion, i think that postulating
1) a spacetime basis (plus Lorentz transformations)
2) the interactions (which take the particular known local form in the postulated spacetime basis plus they are invariant under Lorentz transformations),
solves the problem.
For example, in the particular situation with Earth+Sun the postulated space basis involves r_Earth and r_Sun, and the transformed coordinates R and r that we later get are not related with a Lorentz transformation to the postulated ones.

Now, one may ask; how do you know which to postulate, r_Earth & r_Sun, or R & r? Hmmm. This system came about from an initial quantum state. If we also postulate an initial quantum state of the universe, together with the spacetime basis and interactions, then the later formation of Earth+Sun would (probably) involve r_Earth & r_Sun.

 

[JK423]

You may want to take a look at Gleason's theorem then. I think it's a much better way to obtain the probability formula than what Zurek did. It even provides the motivation for the definition of state operators in QM.

Hmm, i don't think so.. Gleason's theorem involves projection operators that act on states. You cannot use the projection operator formalism in the case of the quantum state of the universe, because you will need an extra system outside of the universe to do the job.

 

[Fredrik]

Hmm, i don't think so.. Gleason's theorem involves projection operators that act on states. You cannot use the projection operator formalism in the case of the quantum state of the universe, because you will need an extra system outside of the universe to do the job.

I assume that you mean that it's impossible to do an experiment in which the entire universe is being "measured". This is of course true. But this also makes the Born rule irrelevant to such experiments.

Gleason's theorem is relevant to all situations where the Born rule is relevant.

 

[JK423]

Agreed, i just want to point out that you cannot use Gleason's theorem to prove the probability formula in the context of MWI. For example, if the state of the universe is
$\left| {{\Psi _{{\rm{universe}}}}} \right\rangle = a\left| + \right\rangle \otimes \left| \uparrow \right\rangle + b\left| - \right\rangle \otimes \left| \downarrow \right\rangle$. How would you make sense of a and b? Gleason's theorem, in this case, uses projection operators on $\left| {{\Psi _{{\rm{universe}}}}} \right\rangle$ to deduce the probability formula. In MWI this cannot be, since nothing else exists to measure this state. Zurek's derivation is based on symmetry considerations and not on projection operators, so it's applicable in MWI. What I'm trying to say is, that, we cannot treat Zurek's work and Gleason's theorem on the same footing regarding this issue.