A Understanding Barandes' microscopic theory of causality

[Morbert]

Why will this be the case?

Equation (56) from this paper is an example of a subsystem's transition matrix divisible at $t'$. The transition matrix $\Gamma^\mathcal{S}(t\leftarrow t')$ on the left hand side will have the form (as per equation 1)$$\Gamma^\mathcal{S}_{ij}(t\leftarrow t') = p^\mathcal{S}(i,t|j,t')$$In a quasiclassical context, these conditional probabilities encode our quasiclassical expectations, and are how Barandes's formalism recovers quasiclassical physics at the appropriate limit, analogous to the way Everettian quatum mechanics recovers it with quasiclassical, decoherent branches. E.g. The probability that it will rain presently where you are, given there are no clouds where you are, is 0. The earth subsystem will not spontaneously evolve into a configuration where it will in fact immediately start to rain.

I suspect what Albert is doing is considering the transition matrix of the entire universe modeled as an isolated system, which does not contain any division events, and hence the standalone probability does not constrain any quasiclassical evolution. The mistake here is that standalone probabilities, are epistemic, not dynamical/nomological. It is only the directed conditional probabilities that make up transition matrices that are dynamical.

 

[gentzen]

I don't understand this paragraph

Division events will give rise to more than probability distributions. They will give rise to directed conditional probabilities that make up the dynamics of the theory. And these directed conditional probabilities will prohibit the world from jumping from branch to branch.

Barandes is free to clarify this, if he wants. Perhaps he wants the minimal version, where each division event is global, and has the same status as t=0. Then t=0 would be just one division event among many. And as a further clarification, give time a clear direction, so that each division event is only important for what happens in its future (and not its past), until the next division event happens.

 

[Morbert]

Barandes is free to clarify this, if he wants. Perhaps he wants the minimal version, where each division event is global, and has the same status as t=0. Then t=0 would be just one division event among many. And as a further clarification, give time a clear direction, so that each division event is only important for what happens in its future (and not its past), until the next division event happens.

See this timestamp, where he distinguishes the dynamical conditional (transition) probabilities from the epistemic standalone probabilities.

 

[Morbert]

Since quantum mechanics is non-local, any attempts to "fix" that is bound to be unsatisfactory.

"Bound to be unsatisfactory" needs to be unpacked. There are objective conditions of a good interpretation of quantum mechanics: Empirically adequate, unambiguous, generalizeable to all quantum theories (e.g. QFT). A good few interpretations meet these conditions.

Then there are subjective conditions: Must be realist, must be deterministic, must be local. These subjective conditions are where things become "unsatisfactory".

 

[gentzen]

See this timestamp, where he distinguishes the dynamical conditional (transition) probabilities from the epistemic standalone probabilities.

Are you sure you have the correct timestamp? It doesn't clarify the points where David Albert sees the incompleteness. But I could even find anything where he would distinguish "dynamical conditional" from "epistemic standalone" probabilities.

 

[gentzen]

A good few interpretations meet these conditions.

And some sometimes claim to be local, for example MWI. But this claim risks to make MWI "unambiguous", and hence no longer satisfying all "objective conditions of a good interpretation". Why? Because before that claim, MWI was just a wavefunction in Hilbert space which evolves according to the Schrödinger equation. But such claim that MWI would be local refer to papers where the Heisenberg picture is used instead. It remains unclear whether this is still the same MWI or not.

Then there are subjective conditions: ..., must be local.

And this last one is bound to cause trouble.

 

[PeterDonis]

such claim that MWI would be local refer to papers where the Heisenberg picture is used instead

Can you give any specific references?

 

[gentzen]

Can you give any specific references?

Bell on Bell’s theorem: The changing face of nonlocality
Harvey R Brown, Christopher G Timpson
https://arxiv.org/abs/1501.03521

In our view, the significance of the Bell theorem, both in its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz covariant version of quantum theory, free of action-at-a-distance, can be articulated in the Everett interpretation.

So here we have a claim that MWI is local, at least that is how David Marcus interpreted that paper here. Not sure how they argue themselves, but they certainly cite and comment on
Rubin, Mark A. 2001. Locality in the Everett Interpretation of Heisenberg Picture Quantum Mechanics. Foundations of Physics Letters, 14, 301–322.
Deutsch, David, and Hayden, Patrick. 2000. Information Flow in Entangled Quantum Systems. Proceedings of the Royal Society of London A, 456, 1759–1774.

We also had a thread "How Does the Many-Worlds Interpretation Address Nonlocality?" recently, with examples of claims that MWI is a "local interpretation":

To follow up, David Deutsch argues for a local interpretation here. I note this is an old paper. https://arxiv.org/pdf/quant-ph/9906007

Many "Oxford Everettians" (Deutsch, Wallace, Vaidman et al) hold a local (in the sense of no spooky action) account of MWI.

(I don't think that Vaidman himself is an "Oxford Everettian", but maybe one of his "et al" coauthors was.)

 

[PeterDonis]

here we have a claim that MWI is local

By "local" here is meant "free of action-at-a-distance", which, if you unpack further based on what's said in section 9 of the paper, means that the dynamics is derived from a Hamiltonian that only includes point interactions. But in the very next sentence, the paper says that the fundamental states of the theory are non-separable, due to entanglement--which is exactly where things like correlations that violate the Bell inequalities come from.

In other words, the claim the MWI is local is based on picking a definition of "local" that makes it true. But that might not be the definition of "local" that other people actually care about. Much of the argument in the literature about this, and indeed about QM interpretations in general, is based on different people picking different definitions of a key term and then talking past each other.

 

[RUTA]

From SEP on Many-Worlds (written by Vaidman):

Although the MWI removes the most bothersome aspect of nonlocality, action at a distance, the other aspect of quantum nonlocality, the nonseparability of remote objects manifested in entanglement, is still there. A “world” is a nonlocal concept. This explains why we observe nonlocal correlations in a particular world.