"The wavefunction never collapses"

[javisot]

Regardless of one's objections (e.g. "the measurement problem") to generic Copenhagen-type QM:

The most obvious problem with MWI is that it is falsified by observation. Much like the assertions that the Earth is flat, or angels exist, or so forth. If there are other branches, where are they? I don't see any, no one ever has.

What is the point of saying that MWI is falsified while Copenhagen is not?

These interpretations correspond in the sense that they can explain the same experimental results. In this sense, MWI is like an analytical extension of Copenhagen (I'm speaking in an analogous sense).

 

[PeterDonis]

This is a brutal underestimate

Not necessarily. You are assuming that every single Planck scale spacetime "cell" is decohered from every other. But that's not the case. The MWI does not say that every single quantum degree of freedom is branching at every Planck time. It only says branching occurs when an interaction takes place that results in decoherence, and the only branches are the decohered ones. So, for example, in a Schrodinger's Cat experiment, there would be only two branches, "cat alive" and "cat dead", since those are the two decohered outcomes. There would not be a different branch for every single microscale interaction between the cat's atoms, since those don't decohere separate branches; they just cause the cat to behave classically in the two branches caused by the experiment, "alive" and "dead".

 

[PeterDonis]

What is the point of saying that MWI is falsified while Copenhagen is not?

These interpretations correspond in the sense that they can explain the same experimental results. In this sense, MWI is like an analytical extension of Copenhagen (I'm speaking in an analogous sense).

Please do not pursue this subthread further. What I said in post #27 is all that can be said about it in this forum.

 

[Roberto Pavani]

My estimate in #29 uses the same logic as the standard vacuum energy calculation that gives the 10¹²⁰ cosmological constant problem: counting quantum modes up to the Planck cutoff. If that counting is wrong for branching, as your correction in #32 suggests, could it be wrong for vacuum energy too? That would be interesting in itself. If instead the vacuum energy counting is legitimate, then perhaps my estimate isn't as far off as it seems.

I'm probably missing something here, but I'd be curious to understand where the two calculations diverge, if they do.

 

[PeterDonis]

If that counting is wrong for branching, as your correction in #32 suggests, could it be wrong for vacuum energy too?

If it is, I don't think it would be for the same reason, since the vacuum energy counting assumes a single universe, not many worlds. It's simply a comparison of the simple, obvious way to calculate the ground state energy of the QFT vacuum with a Planck scale cutoff, with the value we actually observe based on the acceleration of the cosmological expansion. That ground state energy is the energy of a single state in a single universe.

 

[bhobba]

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.

At our current understanding of QM, that is true. Still, some think that with future research, it may be possible to experimentally distinguish between them; for example, the experimental confirmation of Bell's theorem by Alain Aspect and others rules out a whole class of interpretations, namely those with local hidden variables. Also, to some extent, the difference between interpretations is a matter of philosophical preference rather than anything objective. Many, including me, think the difference between modern versions of Many Worlds and so-called Dechorent Histories is just the semantic difference between potentially real and actually real. See David Wallace's excellent book, The Emergent Multiverse:
https://www.amazon.com.au/Emergent-Multiverse-Quantum-According-Interpretation/dp/0199546967

Contrast it to Decoherent Histories, as explained here:
https://quantum.phys.cmu.edu/CHS/histories.html.

It must also be mentioned that ordinary QM is just an approximation to a deeper theory called Quantum Field Theory (QFT), which incorporates Special Relativity. Interestingly,y when the non-relativistic limit of QFT is taken, the result is not ordinary QM. This means that strictly speaking, interpretations of ordinary QM are just intellectual exercises. What is needed are interpretations of QFT. For one such realistic interpretation (it has a few issues, no need to go into here), see:
https://www.amazon.com.au/Fields-Their-Quanta-Quantum-Foundations/dp/303172612X/ref=tmm_hrd_swatch_0

Somewhat pricey, but it does give a different take (and one I basically agree with) than found in popular accounts.

Thanks
Bill

 

[bhobba]

Why should MWI derive it? Why shouldn't every interpretation?

Well, there is Gleason's Theorem.

However, Many World proponents seem to favour a betting-type argument, possibly because they don't want to use Gleason's non-contextuality assumption.

Anyway, this has been examined before on this forum:

Graduate Thread 'Can the Born Rule Be Derived in the Many Worlds Interpretation?'

Jul 24, 2014

I'm not 100% sure that this is the right forum to post this, but I think that the people who read the Quantum Physics forum might be interested:

Sean Carroll has written a paper explaining how it is possible to derive the Born Rule in the Many Worlds Interpretation of Quantum Mechanics. I'm not sure that it's the final word on the subject, but it does grapple with the big question of how it makes sense to use probabilities to describe a universe that evolves deterministically...

• stevendaryl
• Born rule Many-worlds
• Replies: 154
• Forum: Quantum Interpretations and Foundations

• 

Thanks
Bill

 

[PeterDonis]

the experimental confirmation of Bell's theorem by Alain Aspect and others rules out a whole class of interpretations, namely those with local hidden variables

A local hidden variable theory isn't an interpretation of QM, it's a different theory--because it doesn't (and can't) predict Bell inequality violations, and QM does. What experimentally confirming the QM predictions of Bell inequality violations did was to dash the hopes of people who were clinging to the idea that QM might end up not being quite right in this regime, and some kind of more classical-like theory would win out. No such luck.

 

[bhobba]

No, you're seeing an objection that many others (myself included) also see to the MWI.

Same here.

I am not convinced of the betting argument either.

To be fair, anyone reading this needs to see the argument and its various forms and decide for themselves. I personally stick with Gleason.

Thanks
Bill

 

[PeterDonis]

there is Gleason's Theorem.

Gleason's Theorem doesn't depend on any particular interpretation of QM: it just says that, given the basic math of QM, if you want to compute something from the quantum state that has the desired properties of a "probability", you have to use the Born rule (more precisely, you have to compute $\text{tr} \rho A$ where $\rho$ is the density operator for the state and $A$ is whatever observable you're interested in). The theorem says nothing about what the thing you compute that has the desired properties of a "probability" means physically. That's what has to be filled in by QM interpretations, and different ones of course fill it in very differently. But in this respect the MWI is not in a different position from any other interpretation--it has its own way of doing the filling in, but so do all the other interpretations.

 

[Paul Colby]

And given that infinitely many quantum events have occurred since the beginning of the universe, why do we always find ourselves in the branch where statistics match the Born rule?

Why is this any different than very large fluctuations being observed in local gas pressure in statistical mechanics? All micro-states are possible. We just don’t observe ones like these because they are just too rare.

 

[Matterwave]

So, for example, in a Schrodinger's Cat experiment, there would be only two branches, "cat alive" and "cat dead", since those are the two decohered outcomes. There would not be a different branch for every single microscale interaction between the cat's atoms, since those don't decohere separate branches; they just cause the cat to behave classically in the two branches caused by the experiment, "alive" and "dead".

Although I agree with the general gist of statements made in this post (my read: decoherence drives branching, we don't branch off of every quantum d.o.f.), I think saying there's just *two* branches for Schrodinger's cat is oversimplifying things. Decoherence is not a sharp line. You still have to define what is the sub system and what is the environment the subsystem gets entangled with. Further, the decoherence typically has a time scale through which the off-diagonal terms decay. It's not clear to me how you set a threshold for when a "full decoherence" has even happened.

Lastly of course, there's at least macroscopic states like "detector has clicked", "poison has entered the blood stream", "cat has gone unconscious" etc...

I think measuring the number of branches in MWI is quite tricky...

Further, here is a (genuine) question: do we even know MWI has a finite number of branches? I don't know if even this question is settled yet?

 

[bhobba]

The most obvious problem with MWI is that it is falsified by observation. Much like the assertions that the Earth is flat, or angels exist, or so forth. If there are other branches, where are they? I don't see any, no one ever has.

I am not a fan of many worlds, but the fact that the other branches have never been seen does not disprove it. It predicts that as part of the theory.

In my opinion, for what it is worth, it's unnecessarily extravagant. If you are attracted to MW, Decoherent Histories treats all possible outcomes on equal footing, but only one is real. The classical world is then emergent by coarse-graining:
https://www.sciencenews.org/blog/context/gell-mann-hartle-spin-quantum-narrative-about-reality

Both can be generalised to QFT, which I believe is important.

Thanks
Bill

 

[Matterwave]

This means that strictly speaking, interpretations of ordinary QM are just intellectual exercises. What is needed are interpretations of QFT.

We would generally regard QFT as only an effective field theory that approximates some deeper theory as well. QFT still suffers from a whole host of issues -- there's a millennium prize problem just to put one type of QFT on solid mathematical footing.

 

[bhobba]

Although I agree with the general gist of statements made in this post (my read: decoherence drives branching, we don't branch off of every quantum d.o.f.), I think saying there's just *two* branches for Schrodinger's cat is oversimplifying things. Decoherence is not a sharp line. You still have to define what is the sub system and what is the environment the subsystem gets entangled with. Further, the decoherence typically has a time scale through which the off-diagonal terms decay. It's not clear to me how you set a threshold for when a "full decoherence" has even happened.

Indeed:


Thanks
Bill

 

[bhobba]

We would generally regard QFT as only an effective field theory that approximates some deeper theory as well. QFT still suffers from a whole host of issues -- there's a millennium prize problem just to put one type of QFT on solid mathematical footing.

Indeed.

That is the argument against the literal realistic interpretation of QFT as found in Art Hobson's book, Fields and Their Quanta. However, the very reality of particles becomes an issue: in QFT, they are 'knots' in the quantum field. If the field is not real - gurgle, gurgle.

To the OP, there are still unresolved issues in the foundations of QFT. Ordinary QM, I am not worried about, since it is not the limiting case of QFT, so all that is needed to show it is a reasonable approximation to QFT, which it is. Start a new thread if you are interested in how to do that.

Thanks
Bill

 

[PeterDonis]

I think saying there's just *two* branches for Schrodinger's cat is oversimplifying things. Decoherence is not a sharp line.

The premise of the thought experiment is that "alive" and "dead" are two distinct, macroscopically distinguishable cat states, and that there is no third one. Of course neither of these cat states are simple, and of course the cat is not the entire universe. But the premise of the thought experiment is that there are no other macroscopically distinguishable outcomes: just "poison released, cat dead" and "poison not released, cat alive".

You still have to define what is the sub system and what is the environment the subsystem gets entangled with.

Not really, no. You don't need to have an exact accounting of which atoms are part of the cat and which are part of the environment in order to observe whether the cat is alive or dead.

Further, the decoherence typically has a time scale through which the off-diagonal terms decay. It's not clear to me how you set a threshold for when a "full decoherence" has even happened.

The heuristic answer we have now is "when macroscopic outcomes can be irreversibly distinguished". In this case, when we can tell whether the cat is alive or dead. Of course it takes a finite time for the poison, if it's released, to kill the cat. But by that time the "poison released" vs. "poison not released" decoherence has already happened; the decoherence time for that is much shorter than the time it takes for a poisoned cat to die. So actually, by the time the cat dies, in the branch where it does, a macroscopically distinguishable outcome has already occurred--the cat dying is just a further classical consequence of it.

Lastly of course, there's at least macroscopic states like "detector has clicked", "poison has entered the blood stream", "cat has gone unconscious" etc...

Which is how the MWI defines branching. See above.

I should note that there is another reason for expecting there to be more than two branches in this thought experiment that has nothing to do with any of the above, at least if we add a clock to the setup: if the clock records the time when the radioactive atom decays and causes the poison to be released, there will be a branch for each possible time that could have happened (heuristically, the granularity will be the accuracy of the clock's readings--is it accurate to 1 second, 1 microsecond, 1 nanosecond, etc.). I don't know if this angle has been considered in the literature.

 

[PeterDonis]

do we even know MWI has a finite number of branches?

In the general case, no, because not all observables have a discrete spectrum, and at least on its face, the math for observables with a continuous spectrum leads to a continuous infinity of branches. And even with observables that have a discrete spectrum, it might have a countably infinite number of possible outcomes (for example, energy levels of bound states of electrons in an atom).

 

[javisot]

In the general case, no, because not all observables have a discrete spectrum, and at least on its face, the math for observables with a continuous spectrum leads to a continuous infinity of branches. And even with observables that have a discrete spectrum, it might have a countably infinite number of possible outcomes (for example, energy levels of bound states of electrons in an atom).

Didn't you say that after message 27 we couldn't talk about this anymore and that everything had already been said?

 

[PeterDonis]

Didn't you say that after message 27 we couldn't talk about this anymore and that everything had already been said?

No. I said that about the claim that the MWI has been falsified. That's not what's being discussed in the post you quoted.

 

[Roberto Pavani]

Following #48: so the number of branches can be a continuous infinity. My estimate of 2^(10²⁴⁵) in #29 was potentially wrong, but still an underestimate.

 

[sbrothy]

Different QM interpretations say different things about wave function collapse. Roughly speaking, at a high level, there are three different general things that different interpretations say:

Some interpretations say that "wave function collapse" is something we do in the math to make correct predictions once we know the results of experiments, and doesn't reflect anything physical actually happening to an individual quantum system when it's measured. "Copenhagen" interpretations more or less take this approach (it's hard to be definite because "Copenhagen" is a very vague and general label for interpretations); so do statistical/ensemble interpretations such as the one used by Ballentine in his textbook. Intepretations in this category say that measurements do have single outcomes (unlike those in the third category below), but they offer no explanation of how that happens.

Some interpretations say that "wave function collapse" is an actual physical thing that happens to an individual quantum system when it's measured--in other words, during a measurement the actual dynamics of the wave function are not the same as the unitary dynamics it has between measurements. This is how such interpretations account for measurements having single outcomes. The main issue with this category of interpretations is that all attempts to construct an underlying model of what the dynamics would be during a measurement have failed.

Finally, interpretations like the Many Worlds Interpretation say that "wave function collapse" never actually happens, because measurements don't have single outcomes--all possible outcomes happen, each one in its own branch of the wave function. This is indeed what you get if you just apply unitary dynamics to the wave function all the time, including during a measurement. In interpretations like this, we ourselves, observing the results of measurements, have "branches" of our own wave functions, and when we think we've observed a measurement to have a single outcome, that's because "we" are just one branch of the wave function. In that particular branch, you can mathematically apply the "wave function collapse" rule to make predictions about what you, in that particular branch, will observe in the future, because the other branches will never interfere with yours.

So there is no single answer to your question; all we have are different QM interpretations that say different, mutually incompatible things.

It collapses all the way down!

EDIT: (better add a smiley here.)

 

[johntpl]

It collapses all the way down!

That’s how the bottom turtle feels…
EDIT: (better add a smiley here.)

 

[olgerm]

Following #48: so the number of branches can be a continuous infinity. My estimate of 2^(10²⁴⁵) in #29 was potentially wrong, but still an underestimate.

I think it makes more sense to talk about number of different possible arguments of wavefunction $\Psi$ than number of branches, because there is no good generally accepted way to divide given wavefunction at given time into branches.

For example in QM: if:

• you assume there are N particles (in 3D space) in "universe".
• you assume that "universe" (or our hypotetical simulated environment) is cube which linear lenght (side lenght) is L.
• you assume that "universe" (or our hypotetical simulated environment) is divided into pixels which linear lenght (side lenght) is l.

Then $\Psi$ has 3*N arguments appart of time(1 argument for each coordinate of each particle). Then $\Psi$ has 3*N arguments that have $L/l$ different possible values. Then argument of wavefunction $\Psi$ has $(L/l)^{3*N}$ possible values. For each of these possible argument values and each value of time $\Psi$ has 1 complexnumber valued value.
So if someone tried to calculate QM-model-simulation of "universe" using Schrödinger equation then at each timestep he had to renew amplitudes of $(L/l)^{3*N}$ different configurations. Amplitudes of these configurations may form blobs that could be called branches.

For example in QFT: if:

• you have fields which are described by $N_f$ real numbers in each point.
• Each of these numbers that describe fields in each point can have $N_{fv}$ different values in each point.
• you assume that "universe" (or our hypotetical simulated environment) is cube which linear lenght (side lenght) is L.
• you assume that "universe" (or our hypotetical simulated environment) is divided into pixels which linear lenght (side lenght) is l.

Then argument of waveconfiguration has 3 real valued arguments(1 argument for each coordinate). These arguments themselfs can have L/l different values. So argument of waveconfiguration can have $(L/l)^3$ different values. For each of these possible argument values and each value of time waveconfiguration has ${N_fv}^{N_{f}}$ possible different values. So waveconfiguration itself can have $({N_fv}^{N_f})^{(L/l)^3}$ possible different values. Arguemnts of wavefunction are time and waveconfiguration. So wavefunction can have $({N_fv}^{N_{f}})^{(L/l)^3}$ possible different arguemnts for each time. For each of these possible argument values and each value of time $\Psi$ has 1 complexnumber valued value.
So if someone tried to calculate QFT-model-simulation of "universe" using Schrödinger equation (chrödinger functional) then at each timestep he had to renew amplitudes of ${N_fv}^{N_{f}*(L/l)^3}$ different configurations. Amplitudes of these configurations may form blobs that could be called branches.

Schrödinger equation is $\frac{d\Psi}{dt}=-i(2\pi)H(\Psi)$, but Hamiltonian itself for example standard model is very long and complicated. I used units, where h=1. h is planckonstant.

As much as I know according to mainstream science the real universe is not divided into pixels like that (so l=0), but you can alternatively think if it was some simulation that does divide space into pixels. Real universe (not visible universe) is considered to be infinetly large (so $L=\infty$). Also in mainstream physics it is assumend that realvalued fields can have any real numbers as arguments (so $N_{fv}=\infty$). if we subsitute L for M, l for 1/M and $N_{fv}$ for M where M is some very big number we get $M^{6*N}$ different configurations in QM and $M^{N_{f}*M^6}$ different configurations in QFT.

 

[Roberto Pavani]

Let me simplify with an even cleaner example: alpha decay.
²³⁸U → ²³⁴Th + α
One nucleus. One alpha particle flies off. In which direction? Any direction in 4π steradians, a continuous space (S²).

That's it. One decay, one particle, uncountably infinite possible directions. In MWI, each direction is a separate world.
Just a single particle going somewhere on a sphere.
And yet MWI demands a distinct "world" for each point on that sphere.
That's the cardinality of the continuum ($\mathfrak{c}$) of worlds, from one atom.

Now, if you want to have fun: the observable universe contains roughly 10⁴⁹ uranium atoms. Each one independently can decay at any instant, in any direction. Since these are independent continuous degrees of freedom, the total space of possible outcomes is: (S² × ℝ⁺)^(10⁴⁹)

We can multiply this for every radioactive nucleus that exists (²³²Th, ⁴⁰K, ¹⁴C, ²²²Rn, ...) with their respective abundance, and if we want, with all possible scatterings of CMB photons with all electrons in the universe. Still
missing: all possible instants where each one of those events may occur.

 

[PeterDonis]

In MWI, each direction is a separate world.

Only if there is something that decoheres as a result of each direction. But there won't be a continuous infinity of such somethings. For example, if you put alpha particle detectors all around the sphere, each one will have a finite resolution and there will only be a finite number of them, not a continuum.

I know I said that some observables have a continuous spectrum, but actually that was something of an overstatement, since in practice no actual detector has infinite resolution, so in practice no observable with a truly continuous spectrum can be physically realized. (Note that this is already accepted by standard QM with regard to the two most obvious such observables, position and momentum--neither of them have eigenstates that are actually within the standard Hilbert space of non-relativistic QM.)

 

[PeterDonis]

Amplitudes of these configurations may form blobs that could be called branches.

Why? As has already been said, "branching" in the MWI occurs as a result of decoherence. I see nothing at all about decoherence anywhere in your post.

 

[Roberto Pavani]

But the particle doesn't need a local detector, sooner or later it will interact with something, even if it takes eons. The direction of emission determines what it will eventually hit and what momentum it transfers.
Moreover, the daughter nucleus recoils immediately at emission time, and since it's embedded in an environment (a lattice, a gas, etc.), the direction information decoheres right away through that recoil, without waiting for the alpha particle to arrive anywhere. So it seems that branching is already determined at emission time, regardless of placed detectors. Or am I missing something?

 

[PeterDonis]

the particle doesn't need a local detector, sooner or later it will interact with something, even if it takes eons.

Possibly, or possibly not. Even if it does, there aren't necessarily a continuum of things to interact with.

the daughter nucleus recoils immediately at emission time, and since it's embedded in an environment (a lattice, a gas, etc.), the direction information decoheres right away through that recoil

Yes, this is probably true since there are enough degrees of freedom involved, unless someone is running an experiment that takes particular care to isolate the daughter nucleus from the environment--but even then that can only last for some finite (and probably fairly short) time.

 

[Roberto Pavani]

Thank you for confirming the recoil decoherence. But then, since the recoil can occur in any direction on the sphere, doesn't that imply a continuum of branches after all? The environment doesn't need external detectors; the recoiling nucleus itself provides the continuous directional information that immediately decoheres.