From: Glenn Morton (glennmorton@entouch.net)
Date: Wed Jul 02 2003 - 22:20:38 EDT
Hi Richard, you wrote in the last message:
>How Tegmark ever got his article past peer review is beyond me. When I
first looked at
>his basic claim, I knew it was false. It took only minutes to prove it
false.
I have done some very simple research. Tegmark has gotten his ideas past
peer review. A more technical article will appear in Science and Ultimate
Reality: From Quantum to Cosmos, honoring John Wheeler's 90th birthday,
J.D. Barrow, P.C.W. Davies, & C.L. Harper eds., Cambridge University Press
(2003)
Having been involved in trying to get an article published in such a volume,
I know they are peer-reviewed. The article can be found at:
http://arxiv.org/PS_cache/astro-ph/pdf/0302/0302131.pdf
If you are correct, then I would challenge you to write a letter or article
to a PEER-REVIEWED physics journal pointing out the simple and supposedly
stupid error that Tegmark made. It would be good for you to go through the
same peer review so that we can be sure that your criticisms are valid.
You further wrote in this message:
>-----Original Message-----
>From: asa-owner@lists.calvin.edu [mailto:asa-owner@lists.calvin.edu]On
>Behalf Of Richard McGough
>Sent: Wednesday, July 02, 2003 5:52 PM
>Glen,
>
>You seem to be repeating Tegmark's mistake. The fact that there
>are a finite number of eigenstates corresponding to an energy less
>than 10^8k does not mean that there is not an infinite number of
>distinct physical configurations corresponding to linear
>superpositions of said eigenstates. You failed to address my
>points and my calculations. If a single electron can exist in a
>continuous infinity of states, do you really think a tiny little
>finite number like 2^10^118 really represents all the physical
>configurations possible in a Hubble volume with 10^50 interacting
>particles? I repeat, Tegmark's calculations are patently absurd.
Gee, then I guess, G.F.R. Ellis, a 'minor' figure in cosmology today, makes
the same mistake. His views, explaind by George Gale, are as follows:
"The simplest spatial MWT is developed in a series of papers by G. F. R.
Ellis and various colleagues. In these articles Ellis has defended the idea
that the observational evidence suggests that we live in a low density,
hyomogeneous, open and infinite universe. In the most recent article, he
and Brundrit consider the possibilities of life in such a universe. On the
assumption that we take seriously the conditions specified, especially
homogeneity and infinity, then 'we can obtain non-zero probabilities for
occurrences of conditions within any specified finite neighborhood of [-=
with any specified degree of similarity to] those on earth.' Indeed the
similarity collapses to identity, since 'it is highly probable that there
exist infinitely many worlds on whcih there are 'duplicate' populations to
that on our own world.'" George Gale, "cosmological Fecundity, Theoreis of
Multiple Universes," in Modern Cosmology and Philosophy, ed. by John Leslie
(another minor figure in cosmology), (Amherst: Prometheus Books, 1998),
p.201
And so dows
>
>Re: Peer review. Ooops, I didn't realize sciam was not peer
>reviewed. Of course, the general principle implied by peer review
>is really what I had in mind, which is that somebody who knew
>first year quantum physics should have mentioned that physical
>states generally involve infinite superpositions of eigenstates.
Well I have had first year quantum physics. And what I read doesn't agree
with what you are saying. there is only an infinite summation if there are
an infinite number of different states for the system. If there are a finite
set of states then the summation is finite, e.g., a electron two-slit
experiment which has only two states. indeed the pattern seen is due to the
superposition of exactly 2 states. The summation is finite. Thus, I suspect
you are assuming what you wish to prove, i.e. you assume there are an
infinity of states and then criticise others for not accepting your
assumption.
I would quote Eisberg and Resnick,
"Just as we are accustomed to adding wave function (E1+E2=E) for two
superposed electromagnetic waves whos resultant intensity is given by E^2,
so we shall add wave functions for two superposed matter waves (psi1 +psi2
=psi) whose resultant intensity is given by psi^2. That is, a principle of
superposition applies to matter as well as to radiation." Robert Eisberg and
Robert Resnick, "Quantum Physics of Atoms, Molecules, Solids, Nuclei, and
Particles, ((New York: John Wiley and sons) p. 64
Note that the summation was finite, not infinite. And also remember from
first year quantum the concept of distinguishability? If two protons are in
the same quantum state, they are indistinguishable? What Tegmark did was
count the distinguishable states. Here is what he says:
"This is an extremely conservative estimate, simply count-
ing all possible quantum states that a Hubble volume can have
that are no hotter than 10^8K. 10^115 is roughly the number of
protons that the Pauli exclusion principle would allow you
to pack into a Hubble volume at this temperature (our own
Hubble volume contains only about 10^80 protons). Each of
these 10^115 slots can be either occupied or unoccupied, giving
N = 2^(10^115) 10^(10^115) possibilities, so the expected distance to
the nearest identical Hubble volume is N^1/3~10^(10^115)
Hubble radii 10^(10^115) meters. Your nearest copy is likely to be
much closer than 10^(10^29) meters, since the planet formation
and evolutionary processes that have tipped the odds in your
favor are at work everywhere. There are probably at least
1020 habitable planets in our own Hubble volume alone." Max Tegmark,
"Parallel Universes," in Science and Ultimate Reality: From Quantum to
Cosmos, honoring John Wheeler's 90th birthday, J.D. Barrow, P.C.W. Davies, &
C.L. Harper eds., Cambridge University Press (2003)
I would also point out that a first year quantum book speaking of a system
of particles (which most assuredly our region of the observable universe is)
does not engage in an infinite summation of wave functions. David Saxon,
Elementary Quantum Mechanics, (Cambridge:Holden Day, 1968), p. 245 says:
"We return now to the consideration of the properties of a system of A
identical particles. Such a system is described by the Hamiltonian
H = sum(i=1->A) P[i]^2/2m + sum(i=1->A) V(x[i]) + sum(i=1->A)Vbar(x[i]-x[j])
where V(x) is the common external potential in which each and every particle
moves and Vbar(x[i]-x[j]) is the common mutual interaction potential of each
and every pair of particles. To determine the symmetry characteristics of
the states of such a system we must examine the properties of the exchange
operators P[ij]. Now we have said before, P[oj] necessarily coomuutes with
H for every pair of particles, and hence the states of the system may be as
much as A!-fold degenerate under exchange, corresponding to the A!
permutations of the order in which the A particles can be labeled in
writing the state function."
Now this applies to describing the A=10^80 particles in our observable
universe. The state function summation is not infinite! What Tegmark is
pointing out is that if the state function of our observable universe is
identical with the state function of another Hubble volume, then the two are
indistinguishable. Which answers Debbie's question about whether or not we
would be identical with our doppelganger (more below).
(For those who know that my library has been in storage for the past 3
years, it is good to have it back again).
But I will stand corrected if someone like George or Howard correct my
understanding.
>
>As for your lack argumentative competence, I fear you may have
>proven your point with your own comment.
Perhaps, but I am not ready to agree to my incompetence yet. So far you have
been mistaken in your knowledge of Sciam's status, and have been less than
aggressive in finding out that Tegmark has had his paper go through peer
review. So, what is the case, Howard?, George?
I might also re-comment to one of Debbie's points about would our
doppelgangers be identical to us. According to Tegmark, they would:
"VB: if there are
indeed many copies of "you" with identical past lives and
memories, you would not be able to compute your own
future even if you had complete knowledge of the entire
state of the cosmos! The reason is that there is no way
for you to determine which of these copies is "you" (they
all feel that they are). Yet their lives will typically begin
to differ eventually, so the best you can do is predict
probabilities for what you will experience from now on.
This kills the traditional notion of determinism." Max Tegmark, "Parallel
Universes," in Science and Ultimate Reality: From Quantum to Cosmos,
honoring John Wheeler's 90th birthday, J.D. Barrow, P.C.W. Davies, & C.L.
Harper eds., Cambridge University Press (2003)
Now, Richard, put your money where your mouth is. Submit your criticisms to
a peer-review process and correct Tegmark. In that way, you can show
everyone that you are correct and he is a hopeless incompentent.
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