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From: Stathis Papaioannou <stathispapaioannou.domain.name.hidden>

Date: Sat, 17 Jul 2004 20:46:48 +1000

I have been wondering about the possibility that all possible worlds exist,

but sequentially rather than simultaneously, under a conservative cosmology

with assumptions as follows:

1. There exists one, and only one, real, physical universe;

2. While it is possible to simulate any subset of this universe, including

conscious beings, with a computer program, this program must be implemented

on a physical computer, or on a virtual machine (or series of such) which is

itself implemented on a physical computer;

3. The universe has a finite age and is comprised of a finite amount of

matter/space/energy, but it is expanding and cooling and will continue to do

so forever;

4. Some single world interpretation of quantum mechanics is correct.

My understanding is that the above assumptions, which I have deliberately

chosen as being contrary to many of the ideas discussed on the Everything

List, still allow for the possibility of fantastically unlikely events, such

as the spontaneous formation of an exact and stable copy of our solar system

from the random motion of particles in interstellar space, or from vacuum

fluctuations posited by the Uncertainty Principle.

Let p(t) = probability that an event P will occur somewhere in the universe

during the next year, t years from the present. The probability that P will

NOT occur at some time between the present (t=0) and (t=a+1) is then given

by the product:

[1-p(0)]*[1-p(1)]*[1-p(2)]...*[1-p(a)]

As a-> infinity this becomes an infinite product, representing the

probability that P will NEVER occur. It is easy to see that this infinite

product diverges to zero in the special case where p(t) is constant for all

t; in other words, that P, however unlikely, will definitely occur at some

point in the future if the probability that it occurs during a unit time

period remains constant over time. The same conclusion applies if p(t)

increases with increasing t: the infinite product diverges to zero, more

quickly than in the case of constant p(t).

Things get more difficult, however, if p(t) decreases over time. A Google

search for "infinite product" brought up some very complicated expressions

for even rather simple p(t), and it is by no means obvious (to me, anyway)

whether the product will converge or diverge.

Now, my question is, what happens to p(t) over time? I would have guessed

that as the universe expands, chemical and nuclear reactions are less likely

to occur, in the same way as chemical reaction rates are proportional to the

concentration the reagents. On the other hand, it is not clear to me how

more exotic processes such as spontaneous appearance of particles out of the

vacuum are affected by the expansion, which after all results in "more

vacuum" - doesn't it?

I'm sure the above is a gross oversimplification - I'm not a physicist - but

I would welcome people's thoughts on it.

Stathis Papaioannou

_________________________________________________________________

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Received on Sat Jul 17 2004 - 06:49:26 PDT

Date: Sat, 17 Jul 2004 20:46:48 +1000

I have been wondering about the possibility that all possible worlds exist,

but sequentially rather than simultaneously, under a conservative cosmology

with assumptions as follows:

1. There exists one, and only one, real, physical universe;

2. While it is possible to simulate any subset of this universe, including

conscious beings, with a computer program, this program must be implemented

on a physical computer, or on a virtual machine (or series of such) which is

itself implemented on a physical computer;

3. The universe has a finite age and is comprised of a finite amount of

matter/space/energy, but it is expanding and cooling and will continue to do

so forever;

4. Some single world interpretation of quantum mechanics is correct.

My understanding is that the above assumptions, which I have deliberately

chosen as being contrary to many of the ideas discussed on the Everything

List, still allow for the possibility of fantastically unlikely events, such

as the spontaneous formation of an exact and stable copy of our solar system

from the random motion of particles in interstellar space, or from vacuum

fluctuations posited by the Uncertainty Principle.

Let p(t) = probability that an event P will occur somewhere in the universe

during the next year, t years from the present. The probability that P will

NOT occur at some time between the present (t=0) and (t=a+1) is then given

by the product:

[1-p(0)]*[1-p(1)]*[1-p(2)]...*[1-p(a)]

As a-> infinity this becomes an infinite product, representing the

probability that P will NEVER occur. It is easy to see that this infinite

product diverges to zero in the special case where p(t) is constant for all

t; in other words, that P, however unlikely, will definitely occur at some

point in the future if the probability that it occurs during a unit time

period remains constant over time. The same conclusion applies if p(t)

increases with increasing t: the infinite product diverges to zero, more

quickly than in the case of constant p(t).

Things get more difficult, however, if p(t) decreases over time. A Google

search for "infinite product" brought up some very complicated expressions

for even rather simple p(t), and it is by no means obvious (to me, anyway)

whether the product will converge or diverge.

Now, my question is, what happens to p(t) over time? I would have guessed

that as the universe expands, chemical and nuclear reactions are less likely

to occur, in the same way as chemical reaction rates are proportional to the

concentration the reagents. On the other hand, it is not clear to me how

more exotic processes such as spontaneous appearance of particles out of the

vacuum are affected by the expansion, which after all results in "more

vacuum" - doesn't it?

I'm sure the above is a gross oversimplification - I'm not a physicist - but

I would welcome people's thoughts on it.

Stathis Papaioannou

_________________________________________________________________

Find love today with ninemsn personals. Click here:

http://ninemsn.match.com?referrer=hotmailtagline

Received on Sat Jul 17 2004 - 06:49:26 PDT

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