I A variation of the Multiple World Interpretation

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Buzz Bloom

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Summary
The thread discussion
https://www.physicsforums.com/threads/improbability-of-the-many-worlds-interpretation.906532/
has reminded me of a variation of the MWI a coworker explained to me about 15-20 years ago. I am wondering it anyone at PF knows of any publication that discusses anything like this variation. I tried to find one searching the Internet, but I had no luck.

Details of the MWI variation are below.
The multiple worlds are not real, but instead they are contingent. This mean that each of the various possible combinations of all of the possible future measurements or relevant interactions that change the probabilities, that could possibly happen according the wave function of everything, define one possible contingent world. When a measurement or relevant interaction occurs, the single real universe becomes constrained to have it's wave function of everything reconfigured to have new initial conditions consistent with the new measurement or interaction. The collection of all the contingent universes are also reduced to just those which are consistent with the new measurement or interaction and the revised initial conditions.
 
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This just looks like a standard collapse interpretation.
 

Buzz Bloom

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This just looks like a standard collapse interpretation.
Hi Peter:

I am a little puzzled by your quoted response above. I am OK with the idea that this MWI variation might be seen as a collapse interpretation, but based on what I have been told recently in the thread cited below, the word "standard" seems inappropriate.

In the thread
in posts #14, #16, #17 #21, #23, #31, and #35,
the discussion seems to be saying that there is a specific difference between standard collapse and the alternative MWI. The following are quotes from these posts.

#14: The mathematical formalism of quantum theory has nothing to say regarding the actual outcome of a single measurement event; such questions are not answered by the minimal statistical interpretation as long as one doesn't confuse the minimal statistical interpretation with the ensemble interpretation: There is no mechanism which can be proposed for the occurrence of an actual outcome of a single measurement event, no algorithm for it can be given and no causal description is possible. Thus, in order to relate the mathematical formalism of quantum theory to our perceived reality – actual outcomes of single measurement events – the wave-packet reduction postulate has to be put in “by hand” as part and parcel of quantum physics. Period!​
#16: I think I understand and find useful your message, except for the metaphor "by hand". I would appreciate your elaboration about the physics meaning of this metaphor in this context.​
#17: The dynamical evolution itself will not give the state of the wavefunction after a measurement. You have to notice the measurement outcome yourself and "by hand" update the state.​
#21: What I think I understand that what you are saying is that the wavefunction can dynamically represent state changes with respect to time, including interactions, except it does not continue to correctly do this when measurements occur. When a measurement occurs, in order to get the wave function to continue to dynamically represent changes over time, someone must specifically manually rewrite the wavefunction initial conditions to include the data from the measurement. Do I have this right?​
#23: Yes, that's the state reduction postulate.​
#31: I tried to find an authoritative explanation of the state reduction postulate online, but the best I could find is​
Is this postulate an alternative name for "wave function collapse"?
Of the five QM interpretations in​
which ones include this postulate? My guess is that it is just the following one:​
Statistical ensemble interpretation:​
Individual measurement outcomes exist, but QM has nothing to say about them. Therefore QM is complete.​
#35: It's commonly used in textbooks as an alternative name for wave function collapse as you said. It's a common element of the practical application of the theory, so all interpretations have it. They just don't agree on its status (i.e. is it fundamental) and nature (i.e. is it a physical process or a calculational aid).​

I see the MWI variation as saying that the wavefunction is a mathematical object. That means it has some kind of existence (conceptual?) without the need of a mathematician to write it down, in a similar manner as a theorem is a mathematical truth before any mathematician proves it, or even writes it down as something to be proved, or even thinks about it.

The state reduction postulate, which is a "standard" part of wavefunction collapse interpretation, says that the wavefunction does not have any existence related to a measurement until the revised wavefunction is written down (by a person) with the appropriate new initial conditions based on the measurement result.

The MWI variation has multiple contingent worlds, each corresponding to a contingent measurement with a specific value made at a specific place and future time. Whn the actual measurement ius made in the real world, then the contingent world which corresonds to the measurement time, place, and value instantly becomes the real universe. This seems to me to violate the state reduction postulate, and therefore makes the MWI variation NOT a standard wave function collapse interpretation.

Regards,
Buzz
 
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I see the MWI variation as saying that the wavefunction is a mathematical object.
It's a mathematical object that corresponds exactly to a real thing, the real quantum state of the system (which, taken to its logical conclusion, has to be the entire universe), which evolves in time purely by unitary evolution.

The state reduction postulate, which is a "standard" part of wavefunction collapse interpretation
No, it isn't, it's a standard part of the mathematical machinery of QM that is needed to make predictions at all, independent of any interpretation. We humans have to update the wave function we use in our math after we observe a measurement result in order to correctly predict the results of future measurements. That does not commit us to any interpretation at all; it's just part of the rules we have to follow to make predictions.

The MWI variation has multiple contingent worlds
"Contingent worlds" as it is being used here just means "worlds that don't exist". In the interpretation you are describing, only one world exists before the measurement, and only one world exists after the measurement, and the wave function in the one world after the measurement is the one that corresponds to the observed measurement result. That means the wave function in the one world that exists has to change non-unitarily from before the measurement to after the measurement. And that is the standard collapse interpretation--not collapse as a mathematical tool to make predictions, but collapse as a statement about what actually happens in the one world that exists. "Multiple contingent worlds" is just poorly chosen terminology that is confusing you about what the interpretation you are describing actually says.
 

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