"The wavefunction never collapses"

[jbergman]

As far as their claims about "what is really happening", yes. Of course they all make the same predictions for what we can test by experiment, but they don't limit themselves to that.

For example, the MWI says measurements have all possible outcomes, but other interpretations say measurements have single outcomes. Those are incompatible statements; they can't both be true. They both make the same predictions for what we can test by experiment, but their claims go beyond what we can test by experiment, and they do so in incompatible ways.

I would say, "their claims go beyond what we can test by experiment now". For instance with MWI, one could conceivably devise an experiment to measure the gravitational effect of the different worlds which would prove or it. But of course. We don't believe we have a complete theory of gravity compatible with QM so there is your out.

 

[PeterDonis]

with MWI, one could conceivably devise an experiment to measure the gravitational effect of the different worlds

No, you couldn't, because any such effects would just end up being entangled with everything else, and in any given branch, there would be just one gravitational effect, and the branches are decohered so they don't interfere with each other, so there's no experiment that could detect the presence of more than one branch.

 

[Roberto Pavani]

Let me clarify: either
(a) the outcome was already assigned to each branch before measurement; natural, but operationally a hidden variable;
(b) the branches form at measurement and "decide" their outcomes at that moment, correlated with each other (one gets 0 because the other gets 1).
In case (b), this seems like an "entangled" collapse.
I don't see a third option, but I'm open to one.

 

[javisot]

But we are always observers inside one branch, and from that perspective, it is operationally indistinguishable from a hidden variable.

A change to this paragraph:

"we are always observers inside one branch, and from that perspective, it is operationally indistinguishable from Copenhagen."

and, Copenhagen≠hidden variable

 

[PeterDonis]

(a) the outcome was already assigned to each branch before measurement; natural, but operationally a hidden variable;

I don't even know what this means.

(b) the branches form at measurement

In the sense that the measurement interaction is what entangles the particles with the measuring devices and the environment, and that entanglement, spreading among a very large number of untrackable degrees of freedom in the environment is what leads to decoherence, yes.

and "decide" their outcomes at that moment, correlated with each other (one gets 0 because the other gets 1).

No, there is no "decision" involved. The wave function already contains all the outcomes and the correlations between them. There's nothing to decide.

I don't see a third option, but I'm open to one.

I think you need to stop waving your hands and write down some actual math. If you write down the actual math, the things I've been saying should be obvious, and it should also be obvious why things like your a) are just meaningless noise, since as far as I can see your a) doesn't correspond to anything in the actual math.

 

[Matterwave]

If nothing in the theory determines which branch you end up in, yet you end up in one, isn't that precisely the definition of "incomplete" in the EPR sense?

I would recommend you to actually read the original EPR paper! It is eminently readable!

In EPR they define a necessary (not sufficient) condition for completeness as "...every element of the physical reality must have a counterpart in the physical theory."

But they are quite specific on what they mean by "element of reality" as it pertains to that paper. A sufficient (not necessary) requirement is: "If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity."

They were quite focused on position and momentum as their "element(s) of reality" which QM had no "corresponding object" -- (I.e. standard QM has only a probability distribution for them before any measurement is made and can not tell you what they "really are" in the sense of a hidden/extra variable). It was later Bohm who expanded the EPR to spin to make the example easier to deal with.

Same as PeroK, I see no way where MWI branching fits this definition of aspect of reality and therefore I see no way to directly use EPR argument to say MWI is incomplete.

 

[PeterDonis]

you end up in one

No, you end up in all branches. You do not end up in just one. So there can't be any "hidden variable" that "determines" that you end up in a certain branch--because you don't.

 

[Roberto Pavani]

Thank you for clarifying that it is (b). I accept the correction on EPR.

But I still have a question about the mechanism in (b): you said "the wave function already contains all outcomes and correlations, there is nothing to decide."

If everything was already there before the measurement, what does the measurement actually do? Does it spawn two worlds, one with 0 and one with 1? And from the perspective of World_0: wasn't the outcome already determined? This brings me back to the same question, just without the EPR label.
Sorry for my naive quesitons but i'm trying to be as much rigorous as i can in order to understand the process.

 

[PeterDonis]

If everything was already there before the measurement, what does the measurement actually do?

It entangles the measured system with the measuring device and the environment, as I said in post #125. And this would be obvious to you if you looked at the math.

i'm trying to be as much rigorous as i can

No, you're not, if you're not looking at the actual math. Please go do that before posting any further in this thread.

 

[Roberto Pavani]

Thank you, I'll study the math and will do some simulations with qiskit. I appreciate everyone's patience with my questions.

 

[PeterDonis]

will do some simulations with qiskit

Please note that you should not require any simulations in order to see the basic idea in the math; for a simplified scenario like measuring two entangled qubits, which is what we've been discussing, everything can be written out in closed form and doesn't require any numerical analysis.

 

[bhobba]

for a simplified scenario like measuring two entangled qubits, which is what we've been discussing, everything can be written out in closed form and doesn't require any numerical analysis.

It can be found in Lenny Susskind's book on QM:
https://www.amazon.com.au/Quantum-Mechanics-Theoretical-Art-Friedman/dp/0465062903

Thanks
Bill

 

[Roberto Pavani]

MWI has no satisfactory answer for the Born rule, except where the branching is equally likely.

That's why almost all presentations of MWI assume a simple 50-50 branch.

Thank you for suggesting I look at the math. Revisiting the thread and PeroK's comment #10, it occurred to me that this might connect to information theory. So I did some calculations (possibly wrong, I studied Shannon 40 years ago, so please correct me if needed).

For a process with $p \neq \frac{1}{2}$ and $N$ measurements, Shannon's Asymptotic Equipartition Property states that the "typical" sequences (those consistent with the Born Rule) number only $2^{N H(p)}$ out of $2^N$ total possible sequences, where

$H(p) = -p\log_2 p - (1-p)\log_2(1-p)$

is the binary entropy. The fraction of typical sequences is therefore

$\frac{S}{2^N} \approx 2^{-N(1-H(p))}$

which goes to zero exponentially with $N$.

For example, with $p = 1/8$: $H(p) \approx 0.544$ , so the typical fraction $\approx 2^{-0.456\,N}$.

If MWI branch counting treats all $2^N$ sequences as equally real branches, then picking one observer from a random branch, the probability of finding him with a Born-Rule-compatible sequence goes to zero exponentially. Yet we always observe Born-Rule-compatible statistics.

If the above calculations do apply, it seems to me that (A) equal branch counting is incompatible with Shannon's AEP. Or (B) we are simply always lucky enough to find ourselves in the exponentially rare branches that happen to be consistent with the Born Rule, and the longer the experiment, the luckier we are (exponentially so)
I have nothing further to add on this point. I'll limit myself to answering specific questions about this last post.

 

[Matterwave]

If the above calculations do apply, it seems to me that (A) equal branch counting is incompatible with Shannon's AEP. Or (B) we are simply always lucky enough to find ourselves in the exponentially rare branches that happen to be consistent with the Born Rule, and the longer the experiment, the luckier we are (exponentially so)
I have nothing further to add on this point. I'll limit myself to answering specific questions about this last post.

You have to be careful with branch counting and then assigning them probabilities. Branches in MWI are not given uniform probability. In fact, you use a probability measure that matches exactly the Born rule. Everett derives the Born rule as the only measure satisfying his additivity and phase invariance requirements.

See my screenshot. Page 71 in Everett's original thesis.

Now to address your specific concern about violation of Born rule, see this quote from the thesis:

Thus, in particular, if we consider the sequences to become longer
and longer (more and more observations performed) each memory sequence
of the final superposition will satisfy any given criterion for a randomly
generated sequence, generated by the independent probabilities aiai' ex-
cept for a set of total measure which tends toward zero as the number of
observations becomes unlimited. Hence all averages of functions over
any memory sequence, including the special case of frequencies, can be
computed from the probabilities aiai' except for a set of memory sequen-
ces of measure zero. We have therefore shown that the statistical asser-
tions of Process 1 will appear to be valid to almost all observers de-
scrlbed by separate elements of the superposition (2.6), in the limit as
the number of observations goes to infinity.

(aiai' is the square amplitude, process one is Copenhagen wave function collapse. Everett is saying here that his setup reproduces the predictions of Copenhagen except for within a set of branches of measure zero. So we are not "lucky", we just don't occupy one of the branches in this set of measure zero)

Now, what this probability measure really means in MWI is a difficult question. One which I am not equipped to answer satisfactorily.

 

[Roberto Pavani]

Now, what this probability measure really means in MWI is a difficult question. One which I am not equipped to answer satisfactorily.

Thank you, this is very helpful. I agree that for p = 1/2, branch counting and Born Rule coincide.

I note that with p = 1/2, the "set of measure zero" are the extremes (all-0 and all-1 sequences).

But for p ≠ 1/2, Shannon's AEP tells us the scenarios invert: with branch counting, it is the Born-Rule-compatible sequences that become the exponentially rare set.

As you honestly noted, "what this probability measure really means in MWI is a difficult question."
One way to restore agreement is to assign a different number of copies to each outcome, so that the probability of picking a Born-Rule-compatible branch matches the expectations. But then the number of copies for each outcome is itself determined by the Born Rule,
which is the quantity we were trying to derive. I'm not saying that this is the case, it could be there are other possibilities.

 

[Matterwave]

I think you are implicitly imposing a frequentist viewpoint into the branching and assuming we can resolve things via counting.

The mathematics in my post shows that instead you need to assign a probability measure to the (branching of the) wave function which is in direct agreement with the Born rule. And this means that given enough observations "almost every branch" *with respect to this probability measure* obeys the born rule.

It doesn't say anything about *number of branches* (as far as I can tell).

Note also that just because I have difficulty in interpreting such a probability measure does not mean there's something actually wrong with it. I am not a strong MWI proponent myself.

MWI proponents often bring up self-locating probability and decision theory to "explain" or "interpret" (what have you), this probability measure. You may want to look into that if it interests you.

 

[jbergman]

No, you couldn't, because any such effects would just end up being entangled with everything else, and in any given branch, there would be just one gravitational effect, and the branches are decohered so they don't interfere with each other, so there's no experiment that could detect the presence of more than one branch.

That assumes a working model of quantum gravity that we don't have today. You can easily do an experiment with say a boulder that can go left or right based on some quantum coin flip. It's not clear at all why the gravitation effects wouldn't be impacted by both versions of the boulder which you could measure in either world.

After doing some research, it looks like I was wrong. This experiment was performed and the results were as Peter described which kills the idea of semi-classical gravity. I wonder why this result is not more widely cited as a justification for Quantum Gravity.

I guess the answer is that there is still the possibility that MWI is incorrect. So we are left with the implication MWI -> Gravity is Quantum.

Or alternatively if Gravity isn't Quantum, MWI isn't correct.

https://doi.org/10.1103/physrevlett.47.979

 

[PeterDonis]

That assumes a working model of quantum gravity that we don't have today.

Which would be necessary in order to apply the MWI at all to the scenario you pose. I agree we don't have such a working model, but what I described is how such a model is currently expected to work. And as you note, we have at least one experiment that gives indirect evidence for such a model.

 

[jbergman]

Which would be necessary in order to apply the MWI at all to the scenario you pose. I agree we don't have such a working model, but what I described is how such a model is currently expected to work. And as you note, we have at least one experiment that gives indirect evidence for such a model.

I don't agree with this point completely. If Gravity was semi-classical you still could postulate a MWI theory but it just wouldn't make sense.

Editing to restate my opinion more clearly. I think this is a fundamental difference between other QM interpretations and MWI, the requirement that Gravity is Quantum. In fact Penrose, I believe argues that it isn't and is responsible for wave function collapse. I think it is worth emphasizing this fact.

 

[PeterDonis]

If Gravity was semi-classical you still could postulate a MWI theory but it just wouldn't make sense.

I'm not sure what this means. But...

I think this is a fundamental difference between other QM interpretations and MWI, the requirement that Gravity is Quantum.

Actually, in the paper you referenced, the opposite point is made: the "semiclassical gravity" theory requires that all branches of the wave function for the matter are real in order for it to predict different results from the "gravity is quantum and gravitational fields get entangled with everything else" theory. In other words, the "semiclassical" theory, not the "quantum gravity" theory, is the one that requires the MWI (for all non-gravitational degrees of freedom) in order to work!

 

[PeterDonis]

Penrose, I believe argues that it isn't and is responsible for wave function collapse.

Yes, but note that this is a very different hypothesis from the one that is tested in the experiment in the paper you referenced.

 

[jbergman]

I'm not sure what this means. But...


Actually, in the paper you referenced, the opposite point is made: the "semiclassical gravity" theory requires that all branches of the wave function for the matter are real in order for it to predict different results from the "gravity is quantum and gravitational fields get entangled with everything else" theory. In other words, the "semiclassical" theory, not the "quantum gravity" theory, is the one that requires the MWI (for all non-gravitational degrees of freedom) in order to work!

Ballentine has a rebuttal which argues that the previous paper is incorrect on that point. The TLDR for me is that combining QM and gravity is subtle.

https://ui.adsabs.harvard.edu/abs/1982PhRvL..48..522B/abstract

 

[bhobba]

That assumes a working model of quantum gravity that we don't have today.

https://websites.umass.edu/donoghue/research/quantum-gravity-and-effective-field-theory/

My understanding is that, since Wilson, all theories are considered 'only' effective up to about the Planck scale, e.g., the Landau pole issue.

Sure, we don't have a theory of gravity beyond the Planck scale, but the standard model seems to have the same issue.

Thanks
Bill

 

[PeterDonis]

we don't have a theory of gravity beyond the Planck scale, but the standard model seems to have the same issue.

There's a difference, though. We know how to quantize everything that isn't gravity: just use the standard framework of quantum field theory, as in the standard model. But we only know how to do QFT that way on a fixed background spacetime geometry.

Quantum gravity would require a theory that can handle superpositions of different spacetime geometries, with amplitudes for each one. Our whole standard framework for QFT goes out the window in that case. So we have to figure out something else, some way of capturing the spacetime geometry degrees of freedom in the same general framework as all of the others. That's not an issue of having only an effective theory that breaks down above a certain energy scale; that's an issue of not having a theoretical framework at all.

 

[javisot]

Quantum gravity would require a theory that can handle superpositions of different spacetime geometries, with amplitudes for each one.

I've had a question for some time about the superposition of spacetime geometries. We have a quantum object in superposition; let's suppose that this quantum object has a certain spacetime geometry associated with it. Being in superposition, it has a superposition of geometries.

Ultimately, this superposition of geometries involves a calculation and defining an effect on the quantum object.

My question is, can the result of that calculation, and therefore the effect on the quantum object, be null?

 

[PeterDonis]

can the result of that calculation, and therefore the effect on the quantum object, be null?

Without an actual theoretical model to use to do the calculation, this question is not answerable.

 

[bhobba]

Quantum gravity would require a theory that can handle superpositions of different spacetime geometries, with amplitudes for each one.

Yes.

What is done is to show that linearised gravity in flat space-time results from quantised gravity (at least in the accounts I have seen), and that the gauge symmetry is infinitesimal coordinate transformations, with particles moving as if space-time had infinitesimal curvature. Ruffini, in Gravitation and Spacetime, then shows, assuming the principle of general invariance (not covariance as Einstein used, which has no actual content, as I seem to recall Einstein eventually agreed with), that GR results. This would seem a neat trick to sidestep your issue. Like you, I think it needs to be addressed.

Thanks
Bill

 

[haushofer]

I have wondered about this. Are they really mutually incompatible? They all share the same math and the same experimental predictions. So nature doesn’t seem to view them as incompatible.

Perhaps not yet. But geocentric models with arbitrary epicycels also is arbitrarily empirically precise and equivalent to heliocentric models of our solar system. Of course, modern cosmology doesn't make sense from a geocentric point of view. We need a similar breaktrough for quantum mechanics.

That's why I never get the "The interpretations are empirically similar, so why care"-argument. Of course nature "views them as incompatible"; our current theories are just not yet able to distinguish them.

 

[loop quantum gravity]

Maybe it is quantum mechanics that collapses.

Eventually both QP and GR are not the end of the story of physics.
And we are bound to have a new theory that it's not QP and not GR, only at a suitable limits it behaves like them. I guess it would be called semiclassical gravity. One neads to synthsize methods from Condensed matter physics particle physics and astrophysics to one coherent big theory... d'you know how many heavy books one needs to read to make such a theory even plausible....

 

[PeterDonis]

This would seem a neat trick to sidestep your issue.

Not really, no. The massless spin-2 field QFT approach, which is what you're describing, still has to start with an assumption of some fixed background spacetime, because it's still just doing QFT in the standard way, the same as the standard model. In the usual approach, the fixed background is Minkowski spacetime.

The approach ends up concluding that the field equation of your massless spin-2 field is the Einstein Field Equation, meaning that the classical limit of the massless spin-2 QFT is standard classical GR. Which is all very nice, but it still does not address the issue of superposition of different spacetime geometries. The fixed background spacetime geometry that you assumed to start with becomes unobservable in principle--the spacetime geometry you actually observe is the one described by whatever solution of the classical EFE you are using--but that fixed background spacetime geometry is still an assumption that you can't discard, and it limits the theory.

What we really need is a theory in which "spacetime geometry" is not built into the foundations at all, but emerges from something else. That's what, for example, loop quantum gravity is trying to do. (String theory? Not really. It still assumes a background--it's just a background with 10 or 11 or 26 or whatever dimensions instead of 4. It doesn't discard the concept completely at the foundational level.)