Will There Ever be a Definitive Answer to the Quantum Interpretation Debate?

[confusedashell]

Ever since QM was introduced in the very early 20th century, the debate on which interpretation got it right has been ongoing for just as long as it's development up to the present.
Do you EVER think any interpretation will satisfy all minds beyond doubt?

PS: not including solipsists here :tongue2:

 

[Hurkyl]

I assume by "got it right", you mean aesthetically or pedagogically; they are, of course, empirically indistinguishable. Multiple approaches to a theory are frequently useful; no single viewpoint should be studied to the exclusion of all others.

That said, I do think there is far too much reluctance to actually learn quantum viewpoints, instead preferring to wedge QM into classical viewpoints.

 

[Usaf Moji]

I think the only interpretation that has a chance of ever satisfying all minds is the simple acceptance that there will always be the unknown - the unknown as an intrinsic feature of reality just as uncertainty is intrinsic to subatomic particles. If you take away the unknown, you destroy reality.

Just as an electron can exist in countless superimposed states, no single state being the one true state, so the various interpretations coexist, no one being the absolute truth. I think eventually people will come to accept that we live in a world of models and arguments and that absolute truth is meaningless.

John Gribben has a nice discussion of this in Schrodinger's Kittens.

 

[confusedashell]

I agree, I doubt we'll ever know everything, that means ALL the details.
But, I mean more generally the big picture.
That we'll know whethr or not there's parallel univeres splitting all the time, or a single universe.
If there's a objective reality, or that the quantum doesn't exist unless we observe it.

Those type of questions, ever think we'll get teh answer?

 

[Usaf Moji]

I agree, I doubt we'll ever know everything, that means ALL the details.
But, I mean more generally the big picture.
That we'll know whethr or not there's parallel univeres splitting all the time, or a single universe.
If there's a objective reality, or that the quantum doesn't exist unless we observe it.

Those type of questions, ever think we'll get teh answer?

My personal belief (for what it's worth) is a soft "yes". I think eventually humanity will figure out the real picture (as far as real can be real using the human tools of logic and observation). But, I think that at that point, we will realize just how insignificant the real is - kind of like mastering every video game only to find shortly thereafter that you've wasted your life playing video games.

My belief (and sincere hope) is that we will, one day, understand reality, and this understanding can be found by following the rules of reality - and, more importantly, that it will mark the exit from reality and the entrance into what we, as living creatures, really want, beyond space and time, and beyond physics and logic.

Just one guy's opinion.

 

[Lord Ping]

I mentioned in another thread recently that I'm fond of Huw Price's "backward causation" interpretation. We can retain hidden variables, locality and one-world provided we are prepared to accept that our measurements causally influence the state of the system in the past. I'm not sure if it fully works but it sounds nice, doesn't it?

The "Copenhagen" interpretation suffers terribly from the Schrodinger's Cat problem, and I don't think the "many worlds" interpretation is useful. The problem with many worlds is that:

(1) It actually doesn't give an interpretation of probability in QM. You could say "well what's most probable is what happens in the biggest region of the world-space" or something - but that requires a (circular) assumption that the worlds are all equiprobable.

(2) It's metaphysically reckless. It needs concepts like worlds "splitting" into "infinities of equally real worlds"... the fact you can say these things doesn't mean they have coherence or content.

(3) It challenges basic assumptions about rational belief. Intuitively, it's not rational to bet your life on a game of roulette. But, since there are always many worlds in which you win the game, you're bound to stay alive somewhere, and in those worlds you'll be very rich. So what should you do - base rationality on what happens in "most" worlds? See problem 1.

 

[Hurkyl]

I don't think the "many worlds" interpretation is useful.

Don't forget that MWI is one of the few interpretations that doesn't require unitary evolution to be violated.

(1) It actually doesn't give an interpretation of probability in QM.

What do you mean by that? In most interpretations, the quantum state space can be factored into Hilbert spaces, state vectors written in a measurement basis, and probabilities assigned to the components through some rule, such as the Born rule. And, if I recall, with a mild assumption of continuity, this is consistent with the frequentist interpretation of probabilities.

And, incidentally, there is no reason why the rule needs to be derivable from whatever your favorite set of 'first principles' is. (But, anyways, I think the Born rule is derivable from the fact that we want the probabilities to be consistent with the "expected value" interpretation of the application of an operator to a quantum state)

(2) It's metaphysically reckless. It needs concepts like worlds "splitting" into "infinities of equally real worlds"... the fact you can say these things doesn't mean they have coherence or content.

Is your complaint about the state space description of the universe, or simply the words that people who study MWI have chosen to describe states? (or something else entirely)

(3) It challenges basic assumptions about rational belief.

I agree that, to someone who refuses to consider anything violating his preconceived ideas about the universe, something that violates his preconceived ideas about the universe won't be useful. But that doesn't mean it's useless to the rest of us!

(Incidentally, I really don't see why you think it challenges the notion of "rational belief", rather than merely challenging our ideas about the nature of the universe)

 

[Lord Ping]

Sorry this has turned out long...

Don't forget that MWI is one of the few interpretations that doesn't require unitary evolution to be violated.

You're talking about interpretations that claim QM is a complete picture? I don't think it is a complete picture.

What do you mean by that? In most interpretations, the quantum state space can be factored into Hilbert spaces, state vectors written in a measurement basis, and probabilities assigned to the components through some rule, such as the Born rule. And, if I recall, with a mild assumption of continuity, this is consistent with the frequentist interpretation of probabilities.

And, incidentally, there is no reason why the rule needs to be derivable from whatever your favorite set of 'first principles' is. (But, anyways, I think the Born rule is derivable from the fact that we want the probabilities to be consistent with the "expected value" interpretation of the application of an operator to a quantum state)

Well the main thing is that we're agreed probability does need an interpretation. You suggest a frequentist interpretation. I don't quite see how that works. Take the claim (1): "There is a probability of 0.9 that, when I take my measurement, that nucleus is going to be found to have decayed".

How do we account for this with a frequentist interpretation? We can't. It is a single instance. To make things worse, suppose that it is the only nucleus of its kind currently in existence. There is no actual-world "frequency" to appeal to.

A common strategy is therefore to appeal somehow to what would happen if the measurement were to be repeated in identical circumstances (even if this is impossible in practice). I think this is best called a propensity interpretation. The nucleus has a real, physical, indeterministic propensity of 0.9 to decay. Articulating the idea of a propensity has proved tricky, but in any case it can't work for MWI.

MWI claims that each world is a deterministic world, so the propensity interpretation as articulated above can't work here. In @, it is already determined that the nucleus must decay (a propensity of 1) or that it must not decay (a propensity of 0). We don't know which, but, objectively speaking, the outcome is predetermined.

A response available to the advocate of MWI is to talk about subjective probabilities. On this view a probability is a rational degree of belief. They then say that this subjective probability for the decay is equal to the total proportion of all worlds (of the "many") in which the decay occurs. Now, sentence (1) means something like: "It is rational for me to believe with 90% confidence that the nucleus will be found to have decayed."

Sounds good... or does it?

First problem: Under MWI, there are many worlds in which the nucleus will be found have decayed, and many worlds in which the nucleus will be found to have not decayed. And each of those different real worlds contains a different real me doing the observing. Does it make sense for me to talk about my rational degree of belief? Well maybe. After all, I am ignorant as to which world the post-measurement me will find itself in, so perhaps my degree of belief is rational in my position of ignorance (applying a "principle of indifference").

Second problem: Suppose that, in some kind of freakish Schrodinger's cat setup, I die if the nucleus decays. Now, after measurement, there will only be a me in the worlds where the nucleus does not decay. So what's my rational degree of belief now? 0? After all, I am certain that I will end up in a world in which the nucleus hasn't decayed!

So I think this interpretation of probability fails too. MWI fails with it, if we insist that the idea of probability must make sense in QM. As ever with philosophy, different people will take have different views. I think MWI is unforgivably wacky, though I can see it inspiring some great sci-fi.

Is your complaint about the state space description of the universe, or simply the words that people who study MWI have chosen to describe states? (or something else entirely)

I mean that no one can provide an adequate account of "splitting". But I think there might be versions of MWI that don't mention splitting.

I agree that, to someone who refuses to consider anything violating his preconceived ideas about the universe, something that violates his preconceived ideas about the universe won't be useful. But that doesn't mean it's useless to the rest of us!

(Incidentally, I really don't see why you think it challenges the notion of "rational belief", rather than merely challenging our ideas about the nature of the universe)

I think you probably (haha) misunderstood my use of "rational belief" there - I hope my mention of it in the context of interpretations of probability cleared that up.

 

[Hurkyl]

Consider this:
We have a system of (n+1) qubits, with a chosen basis of |0>, |1>.
We have a suite of "indicator" measurements X_p,q whose action on basis states is given by:
$$X_{p,q} (|x\rangle \otimes \varphi) = \begin{cases} |1 - x\rangle \otimes \varphi & p \leq \chi(\varphi) \leq q \\ |x \rangle \otimes \varphi & \mathrm{otherwise} \end{cases}$$
where $\chi(\varphi)$ is the number of 1's in the (n-bit) basis state.


Let $| \psi \rangle = a |0\rangle + b |1\rangle$. You can compute the following "transition probability"

$$\left( \langle 1 | \otimes \langle \psi |^{\otimes n} \right) X_{p,q} \left( | 0 \rangle \otimes | \psi \rangle^{\otimes n} \right) = P(p \leq Z \leq q)$$

where Z is a binomially distributed random variable for n trials with a success probability of |b|².

In particular, if we project down the first coordinate, I believe we have a purely mixed state with a probability |a|² of being |0> and |b|² of being |1>.


I assert that the operator $X_{p,q}$ adequately corresponds to the experiment "Observe n copies of the state $| \psi \rangle$, and record a success if there were between p and q ones."


Furthermore, I observe interesting things like the fact we can use these indicators to build operators corresponding to experiments like "Do n trials, and check if the proportion of ones is within epsilon of the proportion r". Let $\theta_{n, \epsilon, r}$ denote the corresponding (mixed) result state for this experiment. Then, the limit state is actually pure:

$$\lim_{n \rightarrow +\infty} \theta_{n, \epsilon, r} = \begin{cases} |1\rangle & r = |b|^2 \\ |0\rangle & r \neq |b|^2$$

I assert that if this calculation is at all meaningful, it demonstrates that |b|^2 is the frequentist probability of measuring the state a|0> + b|1> and seeing |1>.

 

[Lord Ping]

I'd prefer it if you specifically answered the single-case example.

You have one nucleus, one measurement. I think a committed frequentist following the principle you just suggested has to say it makes no sense to talk of a single nucleus's probability of being found to have decayed in a single measurement.

 

[Hurkyl]

I'd prefer it if you specifically answered the single-case example.

You have one nucleus, one measurement. I think a committed frequentist following the principle you just suggested has to say it makes no sense to talk of a single nucleus's probability of being found to have decayed in a single measurement.

I don't think that's quite accurate -- I would think that any scheme for assigning probability distributions to (infinitely many) observations would conform to the frequentist interpretation, as long as the appropriate limits turn out correct.

 

[Hurkyl]

Incidentally, I always understood "splitting" as simply being a qualitative description of the trajectory of the state through Hilbert space. For one particular example, points in the Hilbert space L₂(R) can be drawn as a probability distribution on R -- if the time evolution of that probability distribution transitions from a unimodal to a bimodal distribution, that could be described as a "splitting". A discrete examples could happen when watching the state of a qubit, represented not as a point on the Bloch sphere, but as a pair of probabilities of our favorite basis states occurring.

I suppose I could be wrong in my understanding.

 

[Lord Ping]

I don't think that's quite accurate -- I would think that any scheme for assigning probability distributions to (infinitely many) observations would conform to the frequentist interpretation, as long as the appropriate limits turn out correct.

A frequentist intepretation talks about actual sequences, or the limits of actual sequences. As I see it, the problem is that the idea makes no sense for a single instance that does not fit any general class of instances (i.e. the single nucleus [of a new element] example).