Everett and probability

[John Clark]

On Tue, Apr 26, 2022 at 9:12 PM Bruce Kellett <bhkel...@gmail.com> wrote:

> The distinctive feature of Everettian Many worlds theory is that every possible outcome is realized on every trial. I don't think that you have absorbed the full significance of this revolutionary idea. There is no classical analogue of this behaviour

It's not perfect, no analogy is, but classical thermodynamics can provide a pretty good analogy. There is an initial condition microstate for the room that I'm in right now that, at the macrostate level, looks pretty much like any other  macrostate; however, just due to the laws of classical physics that particular microstate is such that in 30 seconds all the air in the room will gather in a one square foot volume in the lower left corner of the room, and as a result I suffocate to death. 

The particular microstate that would cause that to happen is no more unlikely to occur than any other microstate, but it is VASTLY outnumbered by microstates in which it doesn't happen. So the odds that the room that I'm in right now just happens to be in that one particular microstate are ridiculously low, but they are not zero. So if you were a bookie you could probably make quite a lot of money by betting that John Clark will not suffocate in the next 30 seconds, but there is a very small chance you will not. The difference with the classical is that in the Everettian view every possible outcome is realized, so there is a world it which Bruce Kellett makes different life choices in his youth and decides to become a bookie and John Clark suffocates to death and bookie Bruce Kellett loses money, but that world is VASTLY outnumbered by worlds in which other things happen.

John K Clark    See what's on my new list at  Extropolis

[George Kahrimanis]

On Wednesday, April 27, 2022 at 2:55:37 PM UTC+3 johnk...@gmail.com wrote:

It's not perfect, no analogy is, but classical thermodynamics can provide a pretty good analogy.[...] but that world is VASTLY outnumbered by worlds in which other things happen.

You mean, statistical mechanics.

Counting worlds, then? I remember as a young student, the "equal probabilities" argument based on sheer ignorance of the microstate made me depressed. A much better explanation is based on the sort of agument known by the name "arbitrary functions", started by Jules Henri Poincaré. Here is an example of mine.

Whatever the microstate is (among those compatible with what we know), let us focus on the box in which the gas is contained. It has been constructed with some procedure, of which we can obtain (with good approximation) probability density functions of errors. For example, if we aim to make the height to be 4 meters exactly, then we know that the method of construction will give us 4 meters plus some error of known distribution. Therefore the dimensions of the box are random variables -- even if we assume for the time that the surfaces are perfectly flat and it is perfectly orthogonal. Every time a gas molecule hits a wall, its future trajectory becomes randomised, as well as that of every other molecule it bounces with. Soon a probabilistic description of the gas-in-the-box is all we can do, but these probabilities are well grounded on the errors in the construction of the box.

(If, instead of errors of construction, you prefer to deal with errors of measurement, we shall be mired by the controversy in the foundation of statistics. Therefore I suggest that we just consider construction.)

George K.