# Different interpretations? No, different theories!

1. Feb 23, 2013

### JK423

http://rmp.aps.org/abstract/RMP/v29/i3/p454_1
on the "Relative State" Formulation of Quantum Mechanics, and i realized that this is not an interpretation experimentally equivalent to other "interpretations" like the Copenhagen.. These are different theories that give different predictions!
For example, Everett's (elegant and simple) formulation of quantum mechanics is based on the hypothesis that everything is quantum mechanical, hence the observer and apparatus are all quantum mechanical systems decribed by the deterministic Schrodinger's equation. The Copenhagen formulation of quantum theory denies that, which means that it's something testable to experiments. If someone is able to design an experiment which proves the quantum mechanical nature of an apparatus and an observer, then he disproves the Copenhagen theory, hence Everett's theory will be the correct one..

Someone may object that proving the quantum mechanical nature of the observer is mission impossible. Indeed. But is this relevant? The different predictions are there. The fact that one cannot design an experiment, for practical reasons and not of principle, to investigate these predictions is another thing. I never saw anyone calling string theory a "different interpretation" of nature (..not implying ofcourse that the degree of "impossibility" is the same in the two cases! :) ). To my understanding, we have to do with different theories and should stop calling them different "interpretations".

Last edited: Feb 23, 2013
2. Feb 23, 2013

### Fredrik

Staff Emeritus
Observers and measuring devices are obviously not classical, since their component parts aren't. This has nothing to do with Copenhagen vs. many worlds.

An experiment that "proves the quantum nature of an apparatus and an observer" is impossible to carry out in practice. But a much more relevant fact is that even if we could carry it out, it wouldn't shed any light on which interpretation is correct. The reason is that what we would use to "prove the quantum nature" of some measuring device, is another measuring device, and its necessary that this second measuring device can for all practical purposes be treated as classical when we're doing this experiment. The reason is that we couldn't possibly interpret the final state of that second measuring device as a result of the experiment unless a human observer can easily distinguish that final state from the other possible final states.

What's relevant in practice may not be relevant to a theorist or a philosopher, but what's relevant in principle certainly should be. And it's not possible in principle for the indicator component of the measuring device that's supposed to tell us the result of the experiment to behave in a way that is distinguishable from classical during the experiment, because if it did, we wouldn't consider it a measuring device.

My thoughts on Everett's idea is that it's just a crippled version of QM that fails to make any predictions at all. The problem is that he removed the Born rule, which is what we use to assign probabilities to possible results of experiments. Some people claim that the Born rule can be recovered, but that's only true if you make some other assumptions instead of it, and I think those assumptions can always be derived from the Born rule. So it seems to me that those derivations don't really tell us anything.

3. Feb 23, 2013

### JK423

What you are saying implies that an observer can be both classical and quantum mechanical at the same time, which is a contradiction. For example consider the Schrodinger's cat experiment where the cat is an observer.

1) The cat, inside the box, is doing it's own experiments collapsing wavefunctions non-unitarily. Cat=classical

2)However cat+box is a closed quantum mechanical system, for an external observer, that evolves unitarily. The latter implies that all the interactions inside the box are unitary. Cat=quantum mechanical

Since (1) and (2) should hold simultaneously, we are lead to a contradiction hence this cannot be true.

Am i right?

4. Feb 23, 2013

### Staff: Mentor

Different predictions aren't enough, we'd need different testable predictions. Sure, MWI seems to be predicting that the cat in the unopened box is alive or dead and Copenhagen seems to be predicting that the cat in the unopened box is alive and dead; but they both agree that no conceivable (in principle; it's not just a matter of practical difficulties) experiment can distinguish the two.

5. Feb 23, 2013

### JK423

In order to promote an "interpretation" to a "theory", you just need different predictions that can be tested in principle. In this thread i just want to argue that they are different theories, not different intepretations, and i don't argue on which is the correct one (because i don't know) and how to devise an experiment to prove it.. So, it doesn't matter if these predictions are testable with today's technology or not, it matters only that they are testable in principle.

6. Feb 23, 2013

### stevendaryl

Staff Emeritus
I don't agree. If you analyze people and measuring devices and the universe by the same rules of quantum mechanics that you use to analyze electrons and atoms, then it seems to me that Many Worlds is where you end up. If an electron is in a superposition of spin-up and spin-down, and a human measures its spin, then the human will enter into a superposition of "human measuring spin-up" and "human measuring spin-down". Very quickly, the Earth is in a superposition of "Earth where that human measured spin up" and "Earth where that human measured spin down". The "Many Worlds" aspect is, it seems to me, inevitable unless you impose some non-unitary evolution step that destroys some branch of a superposition.

But it's hard for me to understand what possible role there can be for a postulated Born rule if you treat macroscopic objects quantum mechanically. What does it mean to say "The experimenter has a 50/50 chance of measuring spin-up or spin-down?" if what actually happens is that he deterministically evolves into a superposition of "human measuring spin-up" and "human measuring spin-down"? It seems to me that there are only two possibilities:

1. There is something nonunitary that happens, that breaks the superposition and destroys all branches except one.
2. There is some way to understand the Born rule from the point of view of pure unitary evolution of the wavefunction.

I agree with you, that it seems that there is no noncircular way to derive Born probabilities from Many Worlds. On the other hand, if you imagine a wave function $\vert \Psi \rangle$ for the entire universe, you can mathematically decompose it into a superposition of macroscopically distinguishable states (plus maybe some junk states that can't be understood as a classical universe, at all). It seems plausible to me (although I haven't done it, and I don't know whether anyone has) that one could start with a pure theory of smooth wave function evolution and derive an "effective" theory for the evolution of "macroscopically distinguishable states of the universe" that would look a lot like Copenhagen with its Born rule and wave function collapse.

Last edited: Feb 23, 2013
7. Feb 23, 2013

### JK423

I agree with you.
I just don't like the name "Many Worlds" because i feel like extra assumptions are hidden in this name. Everett's original paper only states that everything evolves unitarily, and says nothing about "Many Worlds" and "Universes being continuously created", and personally i think that it's more safe to stay with the original paper.

8. Feb 23, 2013

### Staff: Mentor

But both Copenhagen and MWI agree that none of their different predictions are testable in principle. So I don't understand how to reconcile the first sentence of the above with the argument you're making.

9. Feb 23, 2013

### stevendaryl

Staff Emeritus
I thought I remembered reading about a clever experiment that supposedly could detect the existence of macroscopic superpositions. Quantum computing almost counts, but it's not quite macroscopic.

10. Feb 23, 2013

### Staff: Mentor

The effects of macroscopic superpositions can be observed, but AFAIK can be analyzed in either Copenhagen or MWI terms... So no help there.

11. Feb 23, 2013

### Fredrik

Staff Emeritus
They are always quantum mechanical, but interactions with the environment will make their behavior indistinguishable from classical, and because of that, we usually don't use the words "quantum mechanical" when we talk about them.

Quantum mechanical, but in a state that's practically indistinguishable from a classical superposition.

If the box can be sufficiently isolated from its environment, this is true. However, the stuff inside the box includes a particle detector and a mechanicsm that kills the cat if the detector signals that a particle has been detected. After a while, the atom will be in a superposition of "decayed" and "not decayed". You might expect that this will put the detector in a superposition of "signal" and "no signal". Let's denote those states by |s> and |n>. What will actually happen is that the detector will interact with its environment (in particular the mechanicsm that's supposed to kill the cat), and this interaction will change the state of the detector into a state that's for all practical purposes indistinguishable from a mixed state a|s><s| + b|n><n|, which is not equivalent to a superposition of |n> and |s>. So not even the cat would be correct to describe the detector as being in a superposition. And this prediction is made entirely using the unitary time evolution of quantum mechanics.

I think your argument doesn't quite work in its current form, because of the decoherence problem described above. But I think that the apparent contradiction will reemerge if you describe what's going on here in terms of state operators (mixed states) instead of in terms of wavefunctions. However, I would say that the contradiction isn't actually derived from quantum mechanics. It's derived from QM plus two additional assumptions:

1. In addition to being things that we can use to assign probabilities to possible results of experiments, states also describe what's actually happening in the real world, even at times between state preparation and measurement.
2. There's only one world.

Drop one of these assumptions (both of which are non-mathematical and unscientific), and there's no contradiction. The assumption that 1 is true and 2 is false can be taken as the starting point of a MWI. The assumption that 1 is false and 2 is true can be taken as the starting point of a Copenhagen/statistical/ensemble interpretation. Note that both can be false.

12. Feb 23, 2013

### stevendaryl

Staff Emeritus
I'm a little skeptical about the distinction that you're making. If you treat macroscopic things quantum mechanically, then there are no definite "results of experiments".

13. Feb 23, 2013

### stevendaryl

Staff Emeritus
The assumption that a macroscopic measurement collapses the wave function into an eigenstate makes a difference in interference effects. Presumably, there's a way to observe these interference effects and decide whether wave function collapse happens, or not.

I remember some kind of thought experiment involving testing bombs. The premise was that some fraction of bombs are "duds" and the only way to tell was to try to trigger them to explode using a high energy laser. But quantum mechanics allows for some weird way of testing which are duds without exploding the nonduds. The duds have a different interference pattern when you split the laser beam, send one half through the bomb, and then recombine with the other half. Considering the bomb exploding to be a special case of "measuring the presence of a photon", it makes a difference whether this measurement collapses the wavefunction or not.

I don't remember the details.

14. Feb 23, 2013

### JK423

@Fredrik
Decoherence just complicate things. For example, i could argue that decoherence has a time scale, and the external observer make measurements before decoherence destroy the superposition. However, i understand that it's difficult to devise a thought experiment to -even in principle- prove what i want to prove. (I'll think about it a little bit more)
What i cannot understand is how you can accept that everything is quantum mechanical but still refute Everett's proposal.. he says just that!

15. Feb 23, 2013

### Fredrik

Staff Emeritus
Either that, or that QM doesn't describe the real world at all, and is just something we use to assign probabilities to possible results of experiments.

This is an aspect of the "measurement problem". However, if we don't make both of the non-mathematical and unscientific assumptions that "states describe what's actually happening", and "there's only one world", I don't see a need for a second kind of time evolution. I think that this sort of "collapse" is a solution to a problem that was created not by the theory, but by two unnecessary assumptions that aren't actually part of the theory.

I think it's accurate to say that quantum mechanics doesn't have a measurement problem. The problem is with the additional assumptions that we tend to make, sometimes without even realizing that they are additional assumptions.

16. Feb 23, 2013

### Fredrik

Staff Emeritus
I didn't find anything like that in the time that I was willing to spend on it. You may however be interested in the quote below. It's similar to the argument you're making here. But I'm arguing that the problem isn't with the theory, but with the additional assumptions. (I think that I've posted another version of this argument somewhere, and that I was talking about state operators instead of wavefunctions in that one).

Last edited: Feb 23, 2013
17. Feb 23, 2013

### JK423

18. Feb 23, 2013

### stevendaryl

Staff Emeritus
I don't think that decoherence changes anything, fundamentally, except that it means that we very rapidly go from "a single object is in a superposition" to "the entire universe is in a superposition".

19. Feb 23, 2013

### stevendaryl

Staff Emeritus
I agree that the Born rule is needed to make predictions. But it seems very weird to me that it can be added as an additional assumption without assuming that some things are NOT described by quantum mechanics.

20. Feb 23, 2013

### Fredrik

Staff Emeritus
Sigh...I don't know how I managed to do this, but I was going to quote a sentence from my post #16 in a new post here, but I apparently clicked the edit button and ended up replacing the content of #16 with what I wanted to say here.

Oh well, I hope that what I had previously said in #16 wasn't very important. :)