I MWI -- Infinite number of worlds?

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If we would, for sake of argument, adopt the MWI interpretation, then are there wavefunctions (like for instance position) that have a continuous probability spectrum, and will MWI then propose that there are an infinite number of actual universes that each represent a position in that probability spectrum?

In other words: can a single measurement require an infinite number of resulting universes?
 

DarMM

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In the modern form of MWI there are an infinite number of worlds. Even in cases with a finite amount of outcomes.

Basically when you go to do an experiment with even just two outcomes ##a## and ##b## with probabilities 40% and 60% each then prior to the experiment there are an infinite number of worlds and after the experiment 40% of them have developed the ##a## outcome and 60% the ##b## outcome.
 
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Then it seems to me that MWI is really telling us that we can't say anything about the ontology of reality, right?
 

DarMM

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Then it seems to me that MWI is really telling us that we can't say anything about the ontology of reality, right?
No, MWI lays out the ontology pretty clearly. Getting that ontology to match experiment is a bit difficult, but the "picture of the world" in MWI is pretty clear.
 
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No, MWI lays out the ontology pretty clearly. Getting that ontology to match experiment is a bit difficult, but the "picture of the world" in MWI is pretty clear.
So if we have an infinite number of universes, there is always another infinite number of universes that wasn't taken into account, but should have been, it seems to me in the case of a continuous probability spectrum. What do I overlook?

Does a position never have an exact value? Even if it is measured?
 
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Worlds in MWI are emergent after decoherence and continuously branching, so it doesn't make sense to discuss how many there are in absolute terms. See section 6 here: https://arxiv.org/abs/1111.2189
 

DarMM

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So if we have an infinite number of universes, there is always another infinite number of universes that wasn't taken into account, but should have been, it seems to me in the case of a continuous probability spectrum. What do I overlook?

Does a position never have an exact value? Even if it is measured?
No there's just a "volume" of coarse-grained quasi-classic worlds. In a given dichotomic experiment a portion develop one way and another portion develop another way.

Worlds in MWI are emergent after decoherence and continuously branching, so it doesn't make sense to discuss how many there are in absolute terms. See section 6 here: https://arxiv.org/abs/1111.2189
That's unfortunately one of the features that effects Wallace's own proof of the Born rule as it ruins two of axioms. The fact that decoherence isn't exact allows worlds to develop tails out of a given reward subspace.
 

Vanadium 50

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will MWI then propose that there are an infinite number of actual universes
No.

In MWI there are not many worlds. There is only one world.
 

DarMM

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No.

In MWI there are not many worlds. There is only one world.
Well there is only one quantum universe in MWI. However usually in Many Worlds the phrase "World" refers to a large scale quasi-classical branch of which there are many.
 
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In Hugh Everett's 1957 paper, in which he called the MWI "the relative state formulation," he argued that the brain, like Schrodinger's cat is a superposition of states -- after observing a quantum experiment with two possible results, A and B, the brain would be in a superimposed state with the wave function representing the knowledge of A superimposed on that representing the knowledge of B.

Thus, in the original version, the "many worlds" were ontologically one world of superimposed states neurally representing alternate quantum results. I know of no argument for ontologically many worlds.

Everett's argument is impressive and logical valid, but unsound. It is based on the unconfirmed premise that bulk matter, like isolated quanta, is subject to linear dynamics.

This is assumption is not made by physicists actually dealing with with many-electron systems, for example in the Hartree-Fock Method for many-body quantum systems and the Gross-Pitaevskii approximation for Bose condensates. Instead, these theories, which are approximate but confirmed, recognize that electron-electron interactions (EEIs), which bind bulk matter, are nonlinear. Since bulk matter has nonlinear dynamics, the sum of two solutions is not a solution. Thus, the superposition principle fails for bulk matter such as quantum detectors and brains. In other words, Schrodinger cats and superimposed brain states do not exist.
 
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Everett's argument is impressive and logical valid, but unsound. It is based on the unconfirmed premise that bulk matter, like isolated quanta, is subject to linear dynamics.

This is assumption is not made by physicists actually dealing with with many-electron systems, for example in the Hartree-Fock Method for many-body quantum systems and the Gross-Pitaevskii approximation for Bose condensates. Instead, these theories, which are approximate but confirmed, recognize that electron-electron interactions (EEIs), which bind bulk matter, are nonlinear. Since bulk matter has nonlinear dynamics, the sum of two solutions is not a solution. Thus, the superposition principle fails for bulk matter such as quantum detectors and brains. In other words, Schrodinger cats and superimposed brain states do not exist.
That's odd - how did all those macroscopic objects go into superposition before decoherence took over? (eg the diamond experiment back in 2011: https://www.nature.com/news/entangled-diamonds-vibrate-together-1.9532)
 
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That's odd - how did all those macroscopic objects go into superposition before decoherence took over? (eg the diamond experiment back in 2011: https://www.nature.com/news/entangled-diamonds-vibrate-together-1.9532)
Thank you for commenting.

Entanglement (which depends on conservation laws and so ultimately on symmetry), does not require linear EEIs. All interactions, linear or nonlinear, are subject to symmetry constraints, and so conservation laws and entanglement.

The entangled diamond experiment of Walmsley et al., which you cite, is not looking at the electron wave function, but at a different mode of oscillation, viz. phonons, which are sound waves, i.e., vibrations of atomic positions. While such phonon are quantized, they are not electron wave functions. So, nonlinear EEIs can co-exist with linear sound waves. Nor does the nonlinearity of EEIs prevent the phonon-electromagnetic interactions that produce Stokes photons.
 

DarMM

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Everett's argument is impressive and logical valid, but unsound. It is based on the unconfirmed premise that bulk matter, like isolated quanta, is subject to linear dynamics.
You also have to add the assumption that the wavefunction is ontic to get Many Worlds.
 

A. Neumaier

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No there's just a "volume" of coarse-grained quasi-classic worlds. In a given dichotomic experiment a portion develop one way and another portion develop another way.
What happens upon a position measurement? Exact measurement seems impossible, since the associated eigenstates are not normalizable. Thus what is branching and how?
 

DarMM

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What happens upon a position measurement? Exact measurement seems impossible, since the associated eigenstates are not normalizable. Thus what is branching and how?
It doesn't really depend on eigenstates. Just whatever basis ##e_{i}## is selected out by decoherence each element of the basis is taken to give a class of worlds.

In a position measurement typically a coarse-graining of the position basis is selected out.
 

A. Neumaier

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It doesn't really depend on eigenstates. Just whatever basis ##e_{i}## is selected out by decoherence each element of the basis is taken to give a class of worlds.

In a position measurement typically a coarse-graining of the position basis is selected out.
Since the coarse-graining depends on who specifies the details, it is a partially subjective setting.
This means that the ''worlds'' cannot have any reality content.

What were the worlds before there was any physicist doing measurements?
 
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You also have to add the assumption that the wavefunction is ontic to get Many Worlds.
I am unsure that this would be adequate. As I said earlier, I know of no argument for ontological as opposed to epistemological, multiplicity. On the other hand, the nonlinearity of EEIs is accepted physics and provides a simple explanation for the quantum-classical transition. We can even use it estimate the relation between transition time and object mass.
 

DarMM

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Since the coarse-graining depends on who specifies the details, it is a partially subjective setting.
This means that the ''worlds'' cannot have any reality content.

What were the worlds before there was any physicist doing measurements?
Physicists do actually create additional worlds in measurements and yes it is the physicists who select the device which via decoherence picks out the basis and thus the class of worlds.

It's not a view I hold, but that's the description of it. It's biggest problem remains the derivation of the Born Rule.

I am unsure that this would be adequate. As I said earlier, I know of no argument for ontological as opposed to epistemological, multiplicity. On the other hand, the nonlinearity of EEIs is accepted physics and provides a simple explanation for the quantum-classical transition. We can even use it estimate the relation between transition time and object mass.
What I'm saying is that macroscopic objects being in superposition is not enough on its own for Many Worlds. You need Macroscopic superposition and the quantum state to be ontic (as well as some other assumptions)

This is simply standard Quantum Foundations.
 
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Thank you for commenting.

Entanglement (which depends on conservation laws and so ultimately on symmetry), does not require linear EEIs. All interactions, linear or nonlinear, are subject to symmetry constraints, and so conservation laws and entanglement.

The entangled diamond experiment of Walmsley et al., which you cite, is not looking at the electron wave function, but at a different mode of oscillation, viz. phonons, which are sound waves, i.e., vibrations of atomic positions. While such phonon are quantized, they are not electron wave functions. So, nonlinear EEIs can co-exist with linear sound waves. Nor does the nonlinearity of EEIs prevent the phonon-electromagnetic interactions that produce Stokes photons.
Thank you for that elaborate explanation. :)
 

almostvoid

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Worlds in MWI are emergent after decoherence and continuously branching, so it doesn't make sense to discuss how many there are in absolute terms. See section 6 here: https://arxiv.org/abs/1111.2189
thank you for that link. I write sci-fi and do try to get facts. This is indeed invaluable. Appreciated.
 

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