I'm going to discuss a really big number here. Bigger than the national
debt. Bigger than the distance to the farthest star in the universe. Bigger
than anything you've ever contemplated before.
It is an estimate of how many universes exist.
I believe it to be the largest number that has ever been derived from a
real-world, physical speculation. Stay close while I wring it out. Take the
math for granted. I won't dwell too awfully much on it. You only need
to recall that scientific notation, for example 106, is the easy
way of writing big numbers. In this case, it's equal to 1 followed by 6 zeroes
(1,000,000).
The "Many Worlds" interpretation (MWI) of quantum mechanics was developed
way back in 1957 by Wheeler & Everett. It says that every physically
permissible outcome that could happen in a subatomic transaction does
happen. But because the results of each potential transaction are all mutually
exclusive, they spin off their own separate, adjacent universes, therein to
fully manifest themselves.
So in consequence, there are untold new universes spinning off every
instant, in every conceivable direction, in response to every single
possibility. In some of these, Hitler won the Second World War. In others, the
digital computer was never conceived. There are many where dinosaurs still
rule the Earth, and we small mammals scuttle from one rock to another,
avoiding them.
In slightly more technical terms, in MWI all the possible outcomes of a
quantum interaction are realized. The Schrodinger wave function, instead of
collapsing at the moment of observation, carries on evolving in a
deterministic fashion, embracing all solutions that are embedded within it.
All outcomes exist simultaneously--as orthogonal vectors in Hilbert state
space--but do not interfere further with each other. Each single prior world
is split into mutually unobservable but equally real worlds.
From a recent poll taken of the leading cosmologists and quantum physics
theorists, about 60% of them believe the Many Worlds interpretation to be the
true one.
The MWI is, to date, the only logically consistent explanation of quantum
mechanics. Thinking about it more, the idea does give one some psychological
comfort. For example, it takes the edge off to think that all the unfortunate
people around you who get caught up in a bad Karmic trip in your world
have a much more benevolent universe out there in which their "true" selves
are thriving and happy.
For some utterly perverse reason, this also brings to mind the remark by
the Captain in charge of the Christian crusade against the heretical Cathars
in Beziers, in the 13th century. When asked how to distinguish the
heretics from Catholics, he replied: "Kill them all, God will know his own."
In many of the MWIs, all those poor Cathars and their Catholic neighbors
survived this merciless slaughter.
If alternate universes do actually ensue from every quantum-level
interaction, there would be a truly huge number of outcomes. I've often
wondered just how big a number that would be.
According to modern physical theory, quantum events occur on an
extraordinarily small scale. The smallest physical space possible is defined
by something called a "Planck length". This is the scale at which the universe
ceases to be a continuum and becomes "grainy". Indeed, the whole idea behind
quantum physics is that events at this level can only be described as
step-changes (quanta) of energy or mass, and not by a smooth, continuous (analogic)
function. The Plank length is the area within which quantum events
emanate--for example, "vacuum fluctuations", wherein virtual particle pairs
are spontaneously created and (normally) rejoin and self-destruct an instant
later.
The Planck length is 1.6 X 10-35 (undecillionth) meter. For a
sense of scale, that’s about 1 ten-octillionth the diameter of an atom. Tiny,
indeed!
The universe--as we know it today--is about 1026 (octillion) km
wide. The volume of a sphere this large is about 1081 (sexvigintillion)
cubic meters. You can pack 10186 (unsexagintillion) Planck-sided
cubes into this volume. So I figure that’s the size of one instantaneous
potential universal reality. Every Plank volume in the universe-sphere has a
particular state--here, I assume for simplicity a digital state, 0 or 1--and
the single unique combination of all those states represents one
"Wheeler-Everett World". (At this point, I can't resist coining an acronym for
this: WHEW!)
Of course, that’s just in one instant. The timescale of quantum events is
described by a unit called the Planck time. This is the time it would take a
photon traveling at the speed of light to cross a distance equal to the Planck
length. This is the "quantum of time," the smallest measurement of time that
has any meaning. No smaller division of time can be contemplated. This defines
what an "instant" is.
The Planck time has a duration of 10-43 (ten-tredecillionth)
seconds.
The cosmologists tell us that our "mother" universe started in a "Big Bang"
from a Planck-length-sized point, about 14 billion years ago--4 X 1018
(40 quintillion) seconds in the past. Since then, it has evolved through a
Minkowsi space-time volume that is calculated as the volume of a hypercone.
Described in this fashion, the space-time volume of our universe is on the
order of 6.2 X 10243 (octogintillion) Plank space-time "globs" big.
This describes the total number of Plank-volume potentialities existing in the
universe in every instant since the beginning of time.
If you assume that a particular overall Planck-volume state arrangement
establishes a unique universe, then an upper bound for the total number of MWI
universes that could have spun off from our Mother Universe since the
beginning of time is the factorial of the number of Planck space-time globs,
or 10243! (A factorial of a number, whose symbol is an exclamation
point, is the multiplicand of all the counting numbers up to and including it,
e.g., 10!=10 X 9 X 8 X 7...) The total of 10243! comes out to
(roughly) 10243^(10243) universes. Reduced, that equals
101,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
. . . oh heck, my finger is getting tired typing zeroes. Just imagine this
exponent carried out to 245 digits.
This number defines the total of all possible combinatory "shuffles" of
every Planck card in the universe-wide deck. For a normal deck of cards, this
would be given as 52!. But the size of the deck I'm talking about includes
all the Planck cards that have existed throughout the entirety of
Planck-time history.
The number is way too large to write out in its entirety; we can only
represent it in exponential format. There are not nearly enough trees in the
universe to make paper enough to print it out in its expanded form. Consider
that scientists estimate the total number of primary atomic particles in the
universe to be about 1080. If you assigned them each a digit, they
couldn't even come close to representing this number.
But think about this: There are 1043 Plank-time units in every
second. If there are 10186 Plank-unit volumes within the (present)
universe-volume, that comes out to 10229! (factorial of one hundred
quinseptuagintillion) universes spinning off every second. That seems
plenty enough to include at least one that embodies peace and happiness
for all Mankind.
Or maybe you can just mark me down as one of those naively unredeemable
optimists!
It's easy to technically criticize the derivation of this
number. For example, even though the vacuum at the Planck length
viewpoint is a frothing sea of instantaneously generated and
self-extinguishing "virtual" quantum events, you could suppose that most
of the Planck volumes at any given instant of time are in a "zero" or
"true vacuum" base state. One base state is probably the same as
another, so there really wouldn't be any difference in the universal
arrangements when you shuffle just the zero-state cards. These "null"
situations might actually make up most of the overall combinatory population.
Also, it's likely that most of the "non-null" shuffles aren't valid to begin
with, because many would be a product of quantum state outcomes that have
zero-probability of occurring. And to be a valid outcome, a quantum
transaction must emanate from a true and good probability wave function.
Lastly, being neither mathematically nor physically literate, my whole
methodology and calculation might just be dead wrong! Anyway, this whole
thing is just for mental kicks, right?
If there is nothing smaller than the Planck length, and nothing quicker
than a unit of Planck time, I wonder if there are no valid counting numbers
beyond the number of MWI universes resulting from these givens?
Notwithstanding the fact that you can write a larger number, or even
manipulate it mathematically (just as I can write a length shorter than the
Planck length here: 1 X 10-36 meter -- and do calculations
based upon it), the reality of those numbers is invalid and meaningless
in any physical sense. They simply don't have any enumerative
meaning. It would certainly be helpful to have a way of
eliminate terms of infinity from popping up in the results of complicated
physics calculations. I say, let infinity be equal to my
number
and be done with it!
By the laws of thermodynamics and conservation of energy as I understand
them, the total mass-energy in any given MWI universe must remain constant and
equivalent to its "mother" universe. I suppose you could envision a
valid (though highly unlikely) quantum history whereby all but one of the
Planck-length volumes in the universe evolves to a "base state" of zero energy
and zero mass (i.e., a true vacuum condition), leaving all the potential
mass-energy of that universe to pop up in the single leftover Planck volume.
It would be as if that universe contracted to a single Planck-length volume in
size. And the next vacuum fluctuation would have to happen at that one
remaining Plank volume, since quantum mechanics obeys relativity and is
governed by local, linear wave equations. (While it may be the epitome of
heresy -- undoubtedly mixed with a lot of ignorance of physics -- it seems to
me that the Minkowski light-history cone must contract as the outer Plank
volumes go to their zero mass-energy states. Remember, if those remote
states go to zero, not even a photon survives. And the universe's
history cone can't expand in the absence of light and/or other kinetic energy.
No events can happen, except within that Minkowski cone.) The kinetic
expression of all the potential mass-energy contained in the original universe
within one Planck volume would surely end up as a Big Bang, wouldn't it?
Perhaps you can get smaller, more localized Big Bangs inside any given
universe if not all, but just many of the Planck volumes in a
particular region evolve to a base vacuum state. That is, the overall
Minkowski light cone in that universe might develop a pucker. It could
happen right in your living room! (That might explain why you keep
finding the corner of your oriental carpet there turned up.) However,
it's much, much more physically likely that all the molecules of oxygen
in the room would decide to congregate in one corner of the room, resulting in
your asphyxiation...
Following are links to a few reference sites of interest. Since you
will undoubtedly get fascinated whilst reading them, and then end up surfing
deeper and farther away from here, I may as well just say goodbye now.
Thanks for coming; I'll keep the light on for you...
