I MWI -- Infinite number of worlds?

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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.)
 
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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

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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.
 
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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 AμJμ terms, where Aμ is the EM four-potential and Jμ the four-current.

The Hamiltonian (the time-development generator) can only be represented by a linear, Hermitian operator if the Schrodinger 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.
 
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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?
 
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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.
MWI does not say this happens. In MWI, the wave function is the reality, and there is only one wave function. It doesn't split. The appearance of multiple "worlds" comes from picking out particular terms in the wave function in some chosen basis and calling them "worlds". But there is only one wave function, and it always evolves unitarily in time, and unitary evolution can't create or destroy anything.
 

Lord Jestocost

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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?
Yes! There is no single reality, which is essentially equivalent to no reality.
 
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MWI does not say this happens. In MWI, the wave function is the reality, and there is only one wave function. It doesn't split. The appearance of multiple "worlds" comes from picking out particular terms in the wave function in some chosen basis and calling them "worlds". But there is only one wave function, and it always evolves unitarily in time, and unitary evolution can't create or destroy anything.
Helpful - thanks! First learned (a very little) about Everett and his work in the 1960s, and apparently been carrying around a distorted mental picture ever since.
 

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