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05/29/2003
Cancel Those Twins?
Last week, I wrote about the exotic concept of a “multiverse”, a
collection of universes including our own visible universe, which
extends some hundred billion trillion (10^23, a 1 with 23 zeros
after it) miles out in space in all directions. As if the very idea of
a multiverse weren’t mind boggling enough, we talked abut the
preposterous claim by a fellow named Tegmark that, out there in
some of those other universes, identical twins of you and me are
doing precisely what we’re doing at this very moment. Not only
that, but in certain of these universes the whole universe is
identical to our own at this moment.
The night that I posted the column, I awakened and couldn’t get
back to sleep, troubled by this whole idea. The more I thought
about the problem, the more I began to question the logic behind
this startling conclusion. For one thing, if our identical twins in
that identical universe are experiencing exactly the same thing
we’re experiencing here on our earth, doesn’t it mean that the
history of that universe has to have been exactly the same as our
universe’s history going all the way back to its own Big Bang?
How likely is it that another universe, over a period of some 14
billion years, would follow precisely the same path as we did?
To make his argument, Tegmark calculated how many ways the
total number of particles in our universe could be arranged. To
do this he used a simple formula: the number of arrangements is
equal to 2^n, where n is the number of particles. If this formula
scares you, let’s say we have just one particle; the number of
arrangements is 2^1 = 2. With 2 particles, the number of
arrangements is 2^2 = 4; with 3 particles, 2^3 = 8, etc. Let’s go
back to 1 particle. If we have a box with room for just one
particle, the two arrangements might be that there is a particle in
the box or there is not a particle in the box. Or, I guess we might
have a box that has just two compartments in it, each big enough
to hold just one particle. The two arrangements would be that
the particle is in one compartment or it’s in the other one.
Now, I will either make a fool of myself or make a profound
criticism of Tegmark’s approach. Let’s go back to the simplest
case of just one particle. What if our box, our universe, is
bigger? Let’s say it has 10 compartments. Now, isn’t the
number of possible arrangements 11? That is, all the
compartments could be empty or our lone particle could be in
any one of the 10 vacant slots. But wait a minute. Our really big
box, our universe, doesn’t have compartments. Our particle
doesn’t have to be in any particular spot. It can be at one spot, or
a microscopic distance off that spot. If so, how many
arrangements are possible for this one particle? Darned if I
know, but it seems like a heck of a lot more than 2!
My conclusion is that the number of possible arrangements of the
zillions of particles in the universe is vastly, perhaps infinitely,
larger than Tegmark calculates. And this is without worrying
about such things as black holes, neutron stars and the like in
which particles pack at fantastic densities. How does one fit
these into the calculations? Again, I may be na ve, and Tegmark
may have dumbed down his calculations for the Scientific
American reader. At this point, I might accept that I have an
identical twin somewhere out there in infinite space but I think
it’s highly unlikely that your twin is out there with me, let alone
reading this column! (In fairness, I should note, as I did in the
previous column, that Tegmark used 10^n instead of 2^n, in his
calculations. This does give a vastly larger number of
possibilities but he implied this approximation was just for
convenience rather than any due to any effect of the size of the
box.)
These thoughts are somewhat along the lines of those expressed
in an article in the April 12, 2003 New York Times that Brian
Trumbore called to my attention. The article, by Paul Davies,
was titled “A Brief History of the Multiverse”. Davies, a
professor of natural philosophy at the Australian Center for
Astrobiology, seems skeptical about the whole multiverse
scenario. The multiverse that we’ve been discussing is what
Tegmark calls a Level I multiverse. All the universes at Level I
have what you might term the same “knob settings”. That is, all
the forces of gravity, the size of the electrons and proton, etc. are
all the same.
Davies is more concerned with those who suggest that there are
other universes with what might be called “different knob
settings”. This addresses the concerns of those who are amazed
by the fact that we exist in a universe where all the “settings” are
just the right values to allow us to exist. Others scoff and say,
“Hey, if the settings weren’t what they are we wouldn’t be here
to question them!” Others invoke divine intervention. Some
suggest that there are other universes with different knob settings
in which life cannot exist.
Davies likens such proposals to theological discussions and calls
the multiverse a theory dressed up in scientific language but one
that ultimately requires a leap of faith. He then comes up with a
really weird multiverse, if only to show how absurd the whole
multiverse thing is. He assumes that in some of the other
universes there are more technologically advanced civilizations
than our own. These advanced techies have managed to program
computers to simulate conscious behavior. Having done that, in
the mother of all Nintendo games, they’ve simulated whole
worlds in their computers. In these virtual worlds, those little
action figures actually know what they are doing. But they don’t
know that they’re just figments of their Creator’s imagination.
Their virtual world is real as far as they’re concerned and they
may even learn how to generate robots that in turn can create
their own virtual worlds.
Could it be that all of us are just creations of some high powered
Bill Gates? Davies cautions that the multiverse concept can be a
“slippery slope”. Davies concedes there may be “some limited
form of multiverse, but if the concept is pushed too far, then the
rationally ordered (and apparently real) world we perceive gets
gobbled up in an infinitely complex charade, with the truth lying
forever beyond our ken.”
I’ve decided that someone should solve the following problem,
which is much simpler than the multiverse problem. Take a
cylindrical box that is 6 feet high and 2 feet in diameter. Now
figure out the number of atoms of hydrogen, oxygen, carbon,
iron, phosphorus, and other elements that are in my body and in
the immediately surrounding air. It shouldn’t be too hard to get a
pretty good approximation to these numbers from my weight and
taking average percentages for all the elements for humans given
in encyclopedias. Finally, take all these atoms and figure out the
total number of possible arrangements of all these atoms in this
cylindrical box. If you actually do this calculation and one of
these arrangements turns out to be me standing in a 6-foot by 2-
foot diameter box, I can almost guarantee that you will get the
Nobel Prize and will be acclaimed as the Einstein of the 21st
century.
Until such a “simple” problem is solved, I must question any
calculation that purports to show that somewhere I have a twin
who is now finishing a column questioning the existence of his
twin in another universe. Thank you for indulging my obsession
with this whole affair. I promise that next week I’ll write about
something I can comprehend.
Allen F. Bortrum
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