"The wavefunction never collapses"

[PeterDonis]

since the recoil can occur in any direction on the sphere, doesn't that imply a continuum of branches after all?

I don't know, because "any direction" might still not be a continuum, if there is not a continuum of states that the environment can be in when the recoiling atom interacts with the environment. Nobody actually writes down the detailed math for things like this; we just wave our hands and say the recoil is in some direction.

I'm not sure it actually makes a great deal of difference in practical terms whether there is only a countable infinity of branches, vs. a continuum. Either way the issue of how the Born Rule comes out of the MWI is still there.

 

[Roberto Pavani]

Fair enough, whether it's a strict continuum or a countable infinity is probably not essential to the point, and that's just for a single decay event. The key issue was whether branching occurs at emission time regardless of external detectors, and I think we agree it does. The Born Rule question is important but, as you say, it's there either way.

By the way, if branching occurs at decay time through the recoil, wouldn't that settle the Schrödinger's cat question in MWI? The cat is never in superposition from the environment's perspective.

 

[PeterDonis]

if branching occurs at decay time through the recoil, wouldn't that settle the Schrödinger's cat question in MWI?

It means the cat is already decohered into the "alive" and "dead" states as soon as the poison is released and reaches it, no matter how long the experimenter delays before opening the box. That's true independent of any interpretation of QM. The only thing particular to the MWI is the claim that both the "cat alive" and "cat dead" branches are real--both outcomes occur.

The cat is never in superposition from the environment's perspective.

"In superposition" is a bad term, because superposition is basis dependent. The correct description is what I gave above, that decoherence occurs as soon as the poison is released and reaches the cat, no matter how long the experimenter delays before opening the box. What's inside the box is already more than enough for decoherence to occur.

 

[Roberto Pavani]

Thank you for the clarification on terminology, I agree that "decoherence has occurred" is more precise than "not in superposition."
Regarding the Born Rule issue you raised earlier, here's a naive observation: consider 2 coin flips where I only able to observe the total number of heads. MWI produces 4 branches (HH, HT, TH, TT) but there are only 3 observable outcomes (0, 1, or 2 heads). Two different branches (HT and TH) map to the same observable state. The Born Rule assigns probabilities to states, but MWI creates branches, and there are more of the latter than the former. How does MWI handle this mismatch?

 

[PeterDonis]

consider 2 coin flips where I only able to observe the total number of heads. MWI produces 4 branches (HH, HT, TH, TT) but there are only 3 observable outcomes (0, 1, or 2 heads).

You're assuming that decoherence can distinguish HT from TH. If that's true, it's just an example of how different outcomes don't have to be "observable" by us humans in order for decoherence to work. Similar remarks apply to the Born Rule: if HT and TH are distinguishable by decoherence, then the Born Rule applies to each one separately, whether we humans can distinguish the information or not. (We humans would just add together the HT and TH probabilities from the Born Rule to get the probability of us observing "1 head".)

If, OTOH, you say the HT and TH outcomes can't be distinguished by decoherence, then it's not true that the MWI would produce 4 branches; it would produce only 3.

How does MWI handle this mismatch?

There isn't a mismatch; you just haven't been clear enough about exactly what the Born Rule applies to. See above.

(And of course all this assumes that by "coin flips" you actually mean quantum coin flips, e.g., something like spin measurements on qubits.)

 

[olgerm]

Regarding the Born Rule issue you raised earlier, here's a naive observation: consider 2 coin flips where I only able to observe the total number of heads. MWI produces 4 branches (HH, HT, TH, TT) but there are only 3 observable outcomes (0, 1, or 2 heads). Two different branches (HT and TH) map to the same observable state. The Born Rule assigns probabilities to states, but MWI creates branches, and there are more of the latter than the former. How does MWI handle this mismatch?

I guess it is clear anyway, but just to clarify: You probably meant some Scrödinger cat type experiment and metaphorically called it coinflip, because normal coinflips would produce only 1 branch with significant weight according to MWI and had only 1 singificantly probable outcome according to Copenhagen interpretation. It would be better to say 2 Schrödinger-cat experiments insted of 2 coin-flips. or 1 experiment that returns1 of 4 different values instead of 1 of 2 different values like classical schrödingers cat experiment.
If humans who do the experiment are only able observe the total number of heads, then they can not understand if they are in branch TH or HT after the experiment is done according to MWI.
weight of branch TT according to MWI = probability of observing TT according to copenhagen. weight of branch TH according to MWI = probability of observing TH according to copenhagen. weight of branch HT according to MWI = probability of observing HT according to copenhagen. weight of branch HH according to MWI = probability of observing HH according to copenhagen. Weight of branch HT plus weight of branch TH according to MWI = probability of "getting into" a branch where 1 head was observed after the experiment is done according to MWI = brobability of obesrving 1 head according to Copenhagen.

 

[Roberto Pavani]

Fair point, let me sharpen the example. Replace the two coins with two entangled qubits (singlet state). Now the combinatorially possible branches at measurement are 4 (↑↑, ↑↓, ↓↑, ↓↓), but entanglement restricts the outcomes to only 2 (↑↓ and ↓↑). Does MWI create 4 branches and then eliminate 2? Or does it only create 2? If only 2, what determined, before measurement, which 2? This seems to require either a "collapse" (4→2) or a hidden variable (it was already decided).

 

[PeroK]

Fair point, let me sharpen the example. Replace the two coins with two entangled qubits (singlet state). Now the combinatorially possible branches at measurement are 4 (↑↑, ↑↓, ↓↑, ↓↓), but entanglement restricts the outcomes to only 2 (↑↓ and ↓↑). Does MWI create 4 branches and then eliminate 2? Or does it only create 2? If only 2, what determined, before measurement, which 2? This seems to require either a "collapse" (4→2) or a hidden variable (it was already decided).

MWI is an interpretation of QM. There is only one entangled state here and only two possible measurement outcomes.

 

[Roberto Pavani]

Agreed, only 2 outcomes. But when did the branching occur? At preparation or at measurement? If at preparation, then the result was already determined before anyone measured, which is a hidden variable. If at measurement, whose measurement? Alice's or Bob's?

 

[PeroK]

Agreed, only 2 outcomes. But when did the branching occur? At preparation or at measurement? If at preparation, then the result was already determined before anyone measured, which is a hidden variable. If at measurement, whose measurement? Alice's or Bob's?

You haven't understood MWI. MWI is just regular QM without the single outcomes. It's very simple.

Decoherence is complicated to get from a microscopic to a macroscopic picture. That applies to most interpretations.

 

[PeroK]

Here's how I look at the Schrodinger cat experiment. There are two questions:

Why did the atom appear to do one thing or the other and not a superposition of both? This is the measurement problem.

MWI explains this by saying that there are in fact two main branches, not one.

Why was the food, water, oxygen, state of decomposition etc consistent with the cat dying immediately or being alive all the time? This is explained by decoherence.

 

[Roberto Pavani]

I'm not questioning what MWI is. My question is physical: if the branching occurs at different spacetime locations for Alice and Bob, then there must be a moment where Alice has already branched but Bob has not (and viceversa). What is the state of the system in that intermediate moment? It seems to be a mixed state, partially branched, partially not, which is exactly the kind of indefiniteness MWI was supposed to eliminate.

 

[Roberto Pavani]

That's exactly my point, there is no global "instant," so different observers see the branching in different orders. Observer 1 sees Alice branch(decohere) first, observer 2 sees Bob branch(decohere) first. Both descriptions are equally valid in SR. But then, which branching tree is the real one? MWI needs the branches to be ontologically real, yet their structure is frame-dependent.

 

[javisot]

That's exactly my point, there is no global "instant," so different observers see the branching in different orders. Observer 1 sees Alice branch(decohere) first, observer 2 sees Bob branch(decohere) first. Both descriptions are equally valid in SR. But then, which branching tree is the real one? MWI needs the branches to be ontologically real, yet their structure is frame-dependent.

The individual experience of an observer in many worlds is indistinguishable from Copenhagen.

 

[Roberto Pavani]

let me believe in MWI: I will add observer C who receives results from both A and B. In MWI, when exactly do the worlds branch for C? When A measures? When B measures? When C receives the information? And how many worlds does C inhabit before receiving all the information?

 

[javisot]

let me believe in MWI: I will add observer C who receives results from both A and B. In MWI, when exactly do the worlds branch for C? When A measures? When B measures? When C receives the information? And how many worlds does C inhabit before receiving all the information?

Perhaps the correct thing to do would be to start another specific thread about MWI with this comment, and have Peter Donis answer directly.

 

[olgerm]

That's exactly my point, there is no global "instant," so different observers see the branching in different orders. Observer 1 sees Alice branch(decohere) first, observer 2 sees Bob branch(decohere) first. Both descriptions are equally valid in SR. But then, which branching tree is the real one? MWI needs the branches to be ontologically real, yet their structure is frame-dependent.

If you do SR( aka poincare group aka lorennz) tranfsformation on coordinate system, then it affects whole wavefunction $\Psi$. You can not do SR frame-of-refence trasformation to only some of branches. If in frame of refence 1 arguments of $\Psi1$ are coordinates of particles given by numbers that give particle locations if these are multiplied with some base-vectors from base-vector-list 1, then in another frame of refence 2 arguments of $\Psi2$ are coordinates of particles given by numbers that give particle locations if these are multiplied with some base-vectors from base-vector-list 2. if arguments of $\Psi1$ multiplied to base-vectors from base-vector-list 1 == same location as arguments of $\Psi2$ multiplied to base-vectors from base-vector-list 2, then arguments of $\Psi1$ and arguemnts $\Psi2$ describe same location. Since physical realitymust be same in all frames of refence, then amplitude of configuration described by these numbers and base vecotrs must be same. so amplitude of $\Psi1$ with its arguments and amplitude of $\Psi2$ with its arguments must be same.
You could also do some complex number phase transformation of wavefunction where only modul of ampplitude stays same, but that also can be applied to whole wavefunction not to just some of branches..

 

[PeroK]

let me believe in MWI: I will add observer C who receives results from both A and B. In MWI, when exactly do the worlds branch for C? When A measures? When B measures? When C receives the information? And how many worlds does C inhabit before receiving all the information?

I don't see how MWI complicates this. It doesn't explain non-locality, but neither does it complicated the question of entangled states.

 

[Roberto Pavani]

I don't see how MWI complicates this.

I'm not saying MWI complicates it, I'm asking a simple question within MWI: when do the worlds branch(decohere) for observer C? This should have a straightforward answer if MWI is "just regular QM." Could you specify: is it when A measures, when B measures, or when C receives the information?

 

[PeroK]

I'm not saying MWI complicates it, I'm asking a simple question within MWI: when do the worlds branch(decohere) for observer C? This should have a straightforward answer if MWI is "just regular QM." Could you specify: is it when A measures, when B measures, or when C receives the information?

It must be when the entangled state interacts with a measuring device and decoherence takes place.

 

[Roberto Pavani]

It must be when the entangled state interacts with a measuring device and decoherence takes place.

Thank you. Let me make it concrete: A and B each send a radio signal to C with their result. The entangled state can only interact (decohere) at A's device or B's device, not at C, who just receives classical information. So:
does the branching occur at A's measurement, at B's measurement, or at both independently? And if both, in which order? (Since they are spacelike separated, the order is frame-dependent.)

 

[PeroK]

Thank you. Let me make it concrete: A and B each send a radio signal to C with their result. The entangled state can only interact (decohere) at A's device or B's device, not at C, who just receives classical information. So:
does the branching occur at A's measurement, at B's measurement, or at both independently? And if both, in which order? (Since they are spacelike separated, the order is frame-dependent.)

The branching is not a physical process. It's the usual evolution of probability amplitudes. Without decoherence, it's simple state evolution - albeit with non-locally-realistic entanglement.

With decoherence it looks like a classical either-or scenario.

The wavefunction itself is almost infinitely complicated, but one branch (collapse theories) and two branches (MWI) stand out. In the later case, the branches evolve effectively separately, following the mathematics of decoherence.

MWI can't work in a locally realistic way, because QM is not locally realistic. You are trying to force a locally realistic process into the scenario.

As per entanglement, A B and C all end up correlated. MWI or not. No one can give you a locally realistic step-by-step process for that.

 

[Roberto Pavani]

The branching is not a physical process.

Thank you for the honesty. But if "the branching is not a physical process", in what sense are the branches real?

 

[olgerm]

Agreed, only 2 outcomes. But when did the branching occur? At preparation or at measurement? If at preparation, then the result was already determined before anyone measured, which is a hidden variable. If at measurement, whose measurement? Alice's or Bob's?

There is no good generally accepted method how to divide given wavefunvtion at given time into branches. If you have quantum computer with 2 entangeled qbits. And some output of this computer that makes output value understandable for human user Alice. Since this computer creates many branches according to MWI it is non-deterministic according to Copenhagen and looks non-deterministic from lookers who assume non-quantum physics. At beginning (time t0) there is wavefunction $\Psi$ that describes this system that includes this quantum computer and human Alice who use it. Time-evolution of this system is determined by Schrödinger equation $d\Psi/dt(t,q)=-i(2\pi)*H(t,\Psi,q)$ this equation alone is sufficent to describe time-evolution of this system. This wavefunction $\Psi$ has high aplitude values for times that are bigger than t0 and where configuration q describes situation, where human Alice who uses this quantum computer is looking at various possible output values.
If someone Bob who knows the wavefunction(that contains the quantum computer and human Alice, who uses it) and configuration of the system at time t0, wants to predict what will happen in that system at times bigger than t0, then Bob can use Schrödinger function to calculate it. While data is still processed inside the quantum computer Bob must use full wavefunction $\Psi$, where physical things such ase volatage on capacitors can be in superposition of multiple values, to calculate time-evolution of the system that contains the quantum computer. But AFTER time (in Bob's simulation) when the quantum computer has outputed the result to humans to make Bob's calculations(reduce his simulation timecomplexity) easier and get approximate values Bob CAN divide his calculted wavefunction into parts $\Psi=\Psi1+\Psi2+\Psi3+\Psi4$ that do not affect each other's time-evolution significantly. It can be done because if you fix time-argument $\Psi$ then confguration space has evolved into such form that it contains blobs, where aplitudes of $\Psi$ are high. And these blobs are separated by areas in configuration-space where aplitude of $\Psi$ is low. Also these blobs are very "decohered". In each of this part there is only 1 significant value for output value of the quantum computer. To explain how he makes his system futur prediction calulations easier making approximation trick in his calculations Bob can use different terminologies(interpretation).
If he decides to use MWI he says:
"To make calculating easier and get approximate values. I can divide $\Psi$ into parts. and calculate probaility of only those parts that contain those configurations of system that interest me. Lets make approxiation that these parts do not affect eachother's time-evolution at all. Lets call the blobs that are assumed in approximation not to influence eachothers time-evolution at all branches. To calculate time-evolution of only 1 of these blobs I overwrite all other blobs in my calculation-Psi with 0-aplitude. And then continue calculate time-evolution of my renewed calculation-Psi using Schrödinger equation."

If he decides to use Copenhagen intepretation he says:
"To make calculating easier and get approximate values. I can divide $\Psi$ into parts. and calculate probaility of only those parts that contain those configurations of system that interest me. Lets make approxiation that these parts do not affect eachother's time-evolution at all. To calculate time-evolution of only 1 of these blobs I overwrite all other blobs in my calculation-Psi with 0-aplitude. While looking at some 1 selected blob lets say that wavefunction has collapsed to configuration of that is in this blob in configuration space. And then continue calculate time-evolution of my renewed calculation-Psi using Schrödinger equation. I call total probility of each blob probability that system will have the configuration described by this blob. "

Both ways to describe the approximation are equal and give same predictions.
Of at what time of his calculation(simulation) Bob says "now blobs of high aplitude are so separated and decohered that those time-evolution can be calculated separately" depends of how accurate simulation he needs. interactions between these blobs rapidly decreases (and blobs rapidly decoher) apporimately at time when machine puts its output into human-readable form.

My question is physical: if the branching occurs at different spacetime locations for Alice and Bob, then there must be a moment where Alice has already branched but Bob has not (and viceversa). What is the state of the system in that intermediate moment?

There is no good generally accepted method how to divide given wavefunvtion at given time into branches. Also branching does it does not have some specific spacetime location and it would not make sense to define it, because it would not correspond to anything intuitive. Brancing is process that happens to whole wavefunction $\Psi$ . You did not describe what is the setup/thought-experiment where Alice and Bob are involved, but if it experiment where "alices" nor "bobs" are not created nor destroyed(number of alices and bobs remains same all the time), then there is no alice-branch nor Bob-branch, but branches where Bob and Alice see different results and react differently. How can branching occurs at different spacetime locations for Alice and Bob?

That's exactly my point, there is no global "instant," so different observers see the branching in different orders. Observer 1 sees Alice branch(decohere) first, observer 2 sees Bob branch(decohere) first. Both descriptions are equally valid in SR. But then, which branching tree is the real one? MWI needs the branches to be ontologically real, yet their structure is frame-dependent.

There is no global "instant" of what?

 

[PeroK]

Thank you for the honesty. But if "the branching is not a physical process", in what sense are the branches real?

In MWI everything is real, so to speak.

In fact, the mathematics of decoherence, treating the detector as a QM system, leads naturally to two branches. That's why the proponents of MWI are so enthusiastic. A collapse interpretation has to get rid of one branch. How does the other branch disappear?

 

[Roberto Pavani]

In MWI everything is real, so to speak.

I'm not defending Copenhagen, I'm happy to analyze that too. But let's finish with MWI first: you said the branching is "not a physical process," yet "everything is real." How does something real come into existence without a physical process?

 

[PeroK]

I'm not defending Copenhagen, I'm happy to analyze that too. But let's finish with MWI first: you said the branching is "not a physical process," yet "everything is real." How does something real come into existence without a physical process?

In MWI, the wavefunction is all there is. It is the reality.

 

[Roberto Pavani]

In MWI, the wavefunction is all there is. It is the reality.

If the wavefunction is the reality and branching is not a physical process, then the branches were always there, nothing is ever "created." But then the outcomes were predetermined in the wavefunction from the start. How is this different from a hidden variable theory?

 

[olgerm]

I'm not defending Copenhagen, I'm happy to analyze that too. But let's finish with MWI first: you said the branching is "not a physical process," yet "everything is real." How does something real come into existence without a physical process?

wavefunction $\Psi$ is real. Wavefunction contains detectors and humans watching detectors. and all configurations that have non-0 amplitude according to the wavefunction are real. There may be wavefunction that gives high amplitude for configuration that describes experiment with detector and humans waching it at time t0, but detector has not yet outputed value. At time t1 wavefucction may have evolved to such that it gives high amplitude for 2 separated blobs in configuration space. 1 of these blobs is in area of configuration-space that describes detector showing output 0, humans reading the value 0 and reacting to it. 2. of these blobs is in area of configuration-space that describes detector showing output 1 and humans reading the value 1 and reacting to it. both of these branches are "real". But humans IN both of these blobs may think that only their branch is real. And that the other branch does not exist at all. That after branching of the blobs other branches ,in which they are not in, do not exist at all.

 

[PeroK]

If the wavefunction is the reality and branching is not a physical process, then the branches were always there, nothing is ever "created." But then the outcomes were predetermined in the wavefunction from the start. How is this different from a hidden variable theory?

I don't really understand the comparison. We still measure correlations that cannot be explained by local variables. The wavefunction itself is not a local variable.