MWI -- Infinite number of worlds?

[entropy1]

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]

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.

 

[entropy1]

Then it seems to me that MWI is really telling us that we can't say anything about the ontology of reality, right?

 

[DarMM]

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.

 

[entropy1]

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?

 

[charters]

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]

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]

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]

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.

 

[Dfpolis]

In Hugh Everett's 1957 paper, in which he called the MWI "the relative state formulation," he argued that the brain, like Schrödinger'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, Schrödinger cats and superimposed brain states do not exist.

 

[StevieTNZ]

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, Schrödinger 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)

 

[Dfpolis]

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]

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]

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]

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]

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?

 

[Dfpolis]

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]

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.

 

[StevieTNZ]

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]

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.

 

[eloheim]

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.

Unless you're going to modify quantum mechanics with something like GRW's spontaneous collapse theory then I'm afraid you're stuck with superposition as a general principle. And since no deviation from linearity has shown itself despite steady progress towards larger and more complex superposition experiments over the years (not to mention research into quantum computers), the onus should fall on supporters of nonlinear dynamics to prove that their theory is the correct one.

 

[Dfpolis]

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.
...

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.

I think we are in agreement -- more assumptions are needed beyond macroscopic superposition. Still, since bulk matter is bound by EEIs (A ⋅ J terms), which are quartic in ψ, it is clear that macroscopic superposition is a myth.

A linear approximation will work until the phase shift due to the nonlinear terms becomes significant. This makes the time during which linearity works dependent on the number of electrons involved and so on the mass.

 

[Dfpolis]

Unless you're going to modify quantum mechanics with something like GRW's spontaneous collapse theory then I'm afraid you're stuck with superposition as a general principle. And since no deviation from linearity has shown itself despite steady progress towards larger and more complex superposition experiments over the years (not to mention research into quantum computers), the onus should fall on supporters of nonlinear dynamics to prove that their theory is the correct one.

It is accepted physics that electrons interact with each other via the mediation of the EM field, with the relevant interactions represented by A ⋅ J, with A being the vector potential and j the current density. It is also accepted physics that j is quadratic in ψ and that A is generated by the current of the other electrons. These nonlinarities prevent an analytic solution of even the two electron problem. So, we solve the problem with perturbation theory, using a sequence of linear approximations.

It is hard to see what objection there can be to applying these well-confirmed principles to bulk matter, such as quantum detectors. Any skepticism should be laid to rest by the fact that calculations based on nonlinear dynamics, such as Hartree-Fock method and the Gross-Pitaevskii approximation, show reasonable agreement with observations -- confirming the nonlinear view.

On the other had, linearity in bulk matter, which is bound by EEIs, is an unconfirmed postulate. It is underpinned by no accepted physics other than linearity working reasonably well for isolated quanta and small samples of matter. As the phase shift induced by nonlinear EEI terms increases with time and the number of electrons involved, the observed small sample quantum behavior is fully consistent with nonlinear EEI dynamics.

Thus, the burden of proof rests on those ignoring the known physics of EEIs by postulating macroscopic quantum superposition.

Finally, we need no gratuitous or ad hoc assumptions to explain the collapse of the wave function. As long as quantum wave packets are far from bulk matter, EEIs can be safely ignored. Once the detection process begins, the incident quantum is interacting with the detector's electrons, and we can no longer ignore the nonlinear terms in the Hamiltonian. As the sum of solutions of nonlinear sets of equations is not a solution of those equations, a superpositions of states is no longer possible. So the wave function inevitably collapses.

 

[StevieTNZ]

Finally, we need no gratuitous or ad hoc assumptions to explain the collapse of the wave function. As long as quantum wave packets are far from bulk matter, EEIs can be safely ignored. Once the detection process begins, the incident quantum is interacting with the detector's electrons, and we can no longer ignore the nonlinear terms in the Hamiltonian. As the sum of solutions of nonlinear sets of equations is not a solution of those equations, a superpositions of states is no longer possible. So the wave function inevitably collapses.

So really there is no measurement problem that we need to resolve?

 

[Dfpolis]

So really there is no measurement problem that we need to resolve?

I see it a whole ensemble of problems revolving around quantum measurement, so I'm unsure what specific problem you have in mind. Knowing that detection events involve nonlinear EEIs is just one step toward a better understanding. If there is some specific problem which you consider "the measurement problem," I will try to be more specific.

 

[StevieTNZ]

I see it a whole ensemble of problems revolving around quantum measurement, so I'm unsure what specific problem you have in mind. Knowing that detection events involve nonlinear EEIs is just one step toward a better understanding. If there is some specific problem which you consider "the measurement problem," I will try to be more specific.

Collapse of the wave function, aka at which point potentiality becomes an actuality. (But nothing in regards as to, for example, spin up was the result rather than spin down.)

 

[Dfpolis]

Collapse of the wave function, aka at which point potentiality becomes an actuality. (But nothing in regards as to, for example, spin up was the result rather than spin down.)

While it's clear that the collapse occurs because of the nonlinear dynamics of detection, this leaves an open question, i. e. why the collapse always reveals an eigenvalue corresponding to a superimposed eigenstate. I suspect this has to do with the experimental design, which is always constructed to measure that kind of value. Still, I would like to be able to formulate this mathematically. A brute force solution is impossible due to the complexity of the dynamics, but perhaps a symmetry argument could show why we get the observed distribution of eigenvalues.

 

[Avodyne]

I think we are in agreement -- more assumptions are needed beyond macroscopic superposition. Still, since bulk matter is bound by EEIs (A ⋅ J terms), which are quartic in ψ, it is clear that macroscopic superposition is a myth.

A linear approximation will work until the phase shift due to the nonlinear terms becomes significant. This makes the time during which linearity works dependent on the number of electrons involved and so on the mass.

You are confusing nonlinearities in the field equations of quantum field theory with nonlinearities in the time evolution of states. They are completely different. The former exist in standard QFT, the latter do not.

 

[Dfpolis]

You are confusing nonlinearities in the field equations of quantum field theory with nonlinearities in the time evolution of states. They are completely different. The former exist in standard QFT, the latter do not.

I am well aware that the standard theory assumes that quantum states can be represented as vectors in a complex Hilbert space, and that measurable quantities can be represented by linear, Hermitian operators acting on this space. I also know that John von Neumann, who is largely responsible for this formulation in his Mathematical Foundations of Quantum Mechanics (1932), distinguished two processes in quantum mechanics: Process 1, which he believed to be non-causal and thermodynamic, described physics of measurement. Process 2, which is causal and deterministic, describes the time evolution of quanta between measurements. Only Process 2 was represented by linear, Hermitian operators acting on vectors in a Hilbert space.

While I agree that process 1 involves dynamics not seen in process 2, I see no reason to exempt it from the application of accepted physics as von Neumann did and Henry Stapp continues to do. We have widely used nonlinear models of multi-electron systems, confirmed by reasonable agreement with observations, in which EEIs are treated nonlinearly. Nonlinearity was not introduced to simplify these models, but because electrons interact via the EM field by way of A_μJ_μ terms, where A_μ is the EM four-potential and J_μ the four-current.

The Hamiltonian (the time-development generator) can only be represented by a linear, Hermitian operator if the Schrödinger equation is linear. If it involves nonlinear terms, which it must to describe EEIs, it is not possible to represent the physics using the Hilbert formalism, nor did von Neumann attempt to do so.

 

[Cten]

Could MWI run both ways in time?

Hi, all - new member; last studied quantum physics almost 50 years ago, and couldn't do a path integral to save my life (in this or any alternate reality). Have had a possibly silly question for some time, and this forum and thread seem like a reasonable place to ask. Please be gentle if what follows is already well-known, elementary, poorly expressed or just wrong...

One conceptual/aesthetic/realism issue with MWI that arises for most of us relative laypeople is the notional continuous creation (to borrow an older term) of virtually infinite mass, energy and information at every decision point. It seems that solutions to this apparent problem (presumably an artifact of limited understanding, worldview or mental complexity) tend to fall into a few attractors, like weighting of realities, or the orthogonality of all universes making the point meaningless, etc.

Discussions of MWI and variants that I've encountered focus on branching in what we perceive to be advancing time, itself an issue for some schemes. So I'm wondering:

Could each point in cosmic configuration space, or each instant's parameters of the universal wavefunction, be considered a starting point that branches backward in time through all states that could have given rise to this one? This still requires some kind of infinity at every moment, but at least the general size of the manifold is more or less constant. And who knows - it might meet at the ends, which would increase symmetry and perhaps simplify the math.

From an SF point of view, and maybe even in "real life" (to the extent that anything so abstract could be considered real), this might erase or repurpose the arrow of time, have some interesting implications for the Second Law, and offer new plot options for both time-travel and track-jumping themes. Not to mention making questions of causality and karma somewhat more interesting, as well as the notion of "self" as some kind of locus that wanders through branching paths, like Neil Gaiman's Destiny of the Endless.

Does this make any sense at all? Already been elaborated or discarded?