Re: How does this probability thing work in MWI?

From: <hal.domain.name.hidden>
Date: Tue, 23 Nov 1999 09:20:58 -0800

Fritz Griffith, <fritzgriffith.domain.name.hidden>, writes:
> All worlds are real, whether or not they will be ours. Therefore, you
> cannot assign probabilities to how likely it is a world will exist; every
> world has a 100% probability.

But we can define probabilities for how likely it is that we, or any other
SAS, will experience a given world. These probabilities vary. Not all
worlds are equally likely to be experienced. Do you agree?

> When we
> define probabilities for worlds, we are simply saying which SAS's we are
> most likely to end up as.

We are saying more than this, we are describing which SAS's we are most
likely to START as, too. The probability says more than, given that you
start as A, how likely will you be to end up as B, C, or D? It gives a
numeric ranking to every world in the multiverse. Each world has a real
number associated with it. We sometimes call it a "measure", sometimes a
"probability", but the point is, all worlds have such a numeric ranking.

When you start as A, the reason why the probabilities to end up as
B, C, or D differ is because those worlds differ in their measures.
All the various continuations of world A have lower measures than A,
and the sum of all their measures equals the measure of A. The relative
proportions of their measures produce the variant probabilities for how
likely a SAS in A is to experience B, C, or D as its continuation.

> So you can imagine a split, which creates world A
> and world B. World A is the expected world, where we observe the universe
> to act as it should. World B is the unexpected world, where we observe the
> universe to act strangely. Both worlds are real, both exist. So whenever
> our world splits into a world we expect, there is another world, just as
> real, which for all of time acted as expected, for which we had no reason to
> expect anything different from. But all of a sudden, that world went
> haywire, leaving us baffled.

This is true, some people experience such things. The same thing happens,
BTW, in a spatially infinite universe. Somewhere someone is astonished
to see water freeze on the stove and boil in the freezer.

> The three important things to remember here are:
> 1. Both worlds are real.
> 2. The SAS's within each world are real.
> 3. Both worlds acted exactly the same for all of time until that one
> moment. Therefore, the SAS's within the unexpected world had observed the
> same physical laws, with the same degree of stability, as the expected
> world, right up until that moment. They too expected to be in the likely
> world; they had no reason to expect anything different. But, to their
> incredible surprise, they didn't end up in that world.

Sure, they are surprised.

> Given these three conditions, I see no reason why our world is any more
> likely to be one than the other.

Some worlds have higher measure than others.

Another way to think of it that some prefer, is to say that the reason
why some worlds have more measure than others is that there are multiple
copies of each one, and the worlds with higher measure have more copies.

In your example, the universe doesn't split into just A and B, it splits
into 9999999999999999999999999999999999999999 copies of A and and 1 copy
of B. Now we have 10000000000000000000000000000000000000000 SAS's and
all of them are equally real. All three of your points are valid except
instead of 2 worlds there are 1000000000000000000000000000000000000000
of them, and an equal number of SAS's. Only 1 was surprised, the others
saw business as usual.

Personally I don't find the multiple-world-copies model that helpful,
as I am happy to think of each world as having a little tag with it that
tells what its measure is. Either way, though, the important point
is that the total measure of the SAS's who see unlawful universes is
very small compared to the measure of SAS's who see lawful behavior,
and that explains why we see the universe as lawful.

Hal
Received on Tue Nov 23 1999 - 09:31:22 PST