A Many-Timelines Interpretation of Quantum Mechanics

A Many-Timelines Interpretation of Quantum Mechanics

What can be called the "Many-Timelines" (MT) interpretation of quantum mechanics is given by the following:

(1) all the information about the universe is given by ontologically existing information-bearers

(2) to the extent an object (information-bearer) is ontologically distinct, it evolves according to its own ontologically distinct timeline

Normally the timelines will be correlated, but distinct. Unlike other interpretations of quantum mechanics, MT is inspired by philosophical considerations that are prior to quantum mechanics itself. I collect a few arguments in favor of (2).

The first argument is the odd behavior of mathematical theories of time. Let b₁ and b₂ be ontologically existing information-bearers... [cf. previous post] ...I conclude there is an aspect of time that is ineffable (incommunicable). I stress this argument is not intended to speak to the presentism/eternalism debate, nor the A-series/B-series debate, only ineffability.

The second is another under-appreciated fact. Alpha Centauri is about 4 lightyears away. It's physically impossible to communicate to aliens who live on Alpha Centauri what it's like to exist now on Earth, because for all we know Alpha Centauri exploded 3 years ago, and we won't even know it for another year.

The third is the often noted fact that temporal flow has a qualitative character, and qualia are ineffable.

The fourth is that things exist at particular times, and existence is supposed to be a 2^nd-order phenomenon.

By (1), there is an aspect of time that is ontologically ineffable.

Different things evolving on different timelines has radical implications. If b₂ evolves on it's own ontologically distinct timeline, then, for b₁, there is never "a time" at which b₂ has a particular state. b₁ and b₂ evolve independently in their respective timelines. By (1) there is no objective time, or objective fact of the matter, about the state of both b₁ and b₂. As a result, at any given b₁-time, the maximum amount of information (i.e. all the possible states of interaction of b₁ with the rest of the universe) is a function of b₂ along all its b₂-times, and vice versa. They evolve in a correlated but ontologically independent way until they physically interact, become one ontological system, and thereby evolve according to one and the same time-parameter. Only then can one talk about "the state" of b₁ and b₂.

Suppose b₁, b₂, and b₃ are three systems that feel a force from the other two systems. There are six relational values of the force R_bibj. Classicaly, the three systems carve out a worldline in the 7-dimensional manifold {t}cross{R_bibj}, with a single state for everything at time t. If they evolve in a universe where time has ineffable aspects, they each have a timeline, t_bi. There is no fact of the matter about the forces R_bibj at a single objective time. Instead one has the three 3-dimensional manifolds {t_bi}cross{R_bibj}, j ≠ i. If they are part of the same universe (ontology), there will be 2^nd-order relations among the t_bi, for a total of 12 dimensions. At any given b_i-moment t_bi all the information that there is in the universe, for b_i, is given by the collection of possible states of b_j at times t_bj, and the possible states of b_k at times t_bk, i ≠ j ≠ k. The upshot is that, for b_i(t_bi), the system (b_j, b_k) doesn't evolve in {b_j}sum{b_j} but instead {b_j}cross{b_j}. The obvious conjecture is

(3) systems that evolve in their own timelines behave quantum mechanically with respect to each other, and otherwise they behave in terms of a classical theory such as General Relativity