"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.