Re: Everett and probability

[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.

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Everett and probability

[John Clark]

On Tue, Apr 26, 2022 at 9:12 PM Bruce Kellett  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 ClarkSee what's on my new list at  Extropolis


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