> language? In the latter "probably" just means "likely to happen" but
> if EVERYTHING happens then how can the concept make sense? I guess it
> must be two different concepts, then?
No, not necessarily.
There are two ways that probability can play a "real" role in MW.
This is no different from how it plays a role in other interpretations
of quantum physics, though.
First would be real-world probability. Take an electron cloud. We
can say that the probability that the electron appears in a certain
range is, say, 90%. This is a real probability that guides our
expectation. If we measure a bunch of electrons we expect to find
around 90% of them in that range, and when we measure them, we do. In
MW this is like saying that 90% of worlds consist of that particular
electron being in that range. There are an infinite number of places
that electron could be, and an infinite number of places it could not
be. But there's still a 90% chance of it being in the specified
range. So we can...in a sense...think of 90% of the possible worlds
being in that range.
If you're confused it's probably in part because of a lack of
understanding in the shift from finite to infinite. Infinite numbers
don't operate under the same rules than finite numbers do, just like
negative numbers operate differently than positive numbers. I could
explain this but it would take a few hours of expounding on set theory
to get you there. Just know that infinite sets are compressible and
manipulable in ways that finite sets aren't. For example, we can pair
up the squares of all natural numbers with the set of all natural
numbers one-to-one: 0 = 0, 1 = 1, 2 = 4, 3 = 9... and so on, so that
no number in either set is unpaired. This is possible even though the
odds of selecting a perfect square arbitrarily out of the natural
numbers is 0%, because as you approach infinity, 0% of all natural
numbers are squares. Newton took this to mean than reasoning about
infinity was absurd, but this was because he didn't understand the
difference between the cardinality and the ordinality of numbers.
Second, we can talk about what it means for something to have
virtually no chance of happening. We should always expect things that
are beyond reason not to happen, even though an infinite number of
such worlds must exist. A cow could appear directly in front of me
right now due to quantum effects, but the odds are virtually zero so I
do not expect the occurrence. In these cases a mathematician would
say that "almost all" worlds obey a certain property that precludes
the appearance of the cow. "Almost all" has a technical meaning in
mathematics, but it means that the chance of something occurring is
too minute to put in terms of a real number.
> Another thing I wonder about: Are your understandings of MW purely
> mathematical, or can you imagine or "see" the MW universe before your
> eyes? In particular: Can you "see" the probability aspect of it? And
> in that case, can you describe it in a simplified way for a dummy like
> me?
I can envision it somewhat, but it's an abstract idea, yes. Just
think about an electron cloud, for one example. It's a cloud of
probability...but the electron isn't totally bound by it. It's just
less and less likely to be further and further away from the main
portion of the distribution.
Anna
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Received on Thu Nov 06 2008 - 20:26:24 PST