Theory of nothing

Multiple
universes and why there is something instead of nothing

by Marcus Loane

31^{st}
March 2012

You may want
to read my article “In the beginning” first.

Imagine a
library of books which contains every possible book containing 1000,000 letters
or less (plus numbers / spaces / punctuation). This is the Library of Babel.
This library would have books containing every possible ordering of letters.
Most of the books would not make any sense as only certain sequences of letters
form words and only certain sequences of words form
meaningful sentences. Most of the books in this library would contain nonsense
but the library would also contain every book ever written such as the works of
Shakespeare, the bible, the Koran and the articles on my website. It would also
contain these works with minor variations and improvements and with random
mistakes and nonsense sections. A simple computer program can generate the
library of Babel but the number of books is so large that the entire history of
the universe is too short for it to make much of a dent in the huge task of
generating every book. The computer program works basically as a counting
program using letters, so the first book would be a million 'a's in a row. The second book would be 999,999 'a's followed by a 'b'. The third
book would be 999,998 'a's followed by b and then an a. Every combination can be systematically churned
out and the number of books while very large is not infinite. In fact the
number of books can be calculated quite easily – it would be (26+4) to the
power of 1000,000 assuming we used 4 different types of punctuation such as a
comma, semi colon, space and a period. If I have done my sums correctly that
would equal a 1 followed by 1.5 million zeroes books in the library of Babel.

**Macbeth**

Now imagine
two versions of reality.

One is the
reality where all that exists is Shakespeare's Macbeth. Let us call it the
Macbeth reality (universe).

The second
version of reality is one where all that exists is the Library of Babel. Let us
call it the Babel reality. Note the Library of Babel will of course contain
Macbeth. The Babel reality contains the Macbeth universe.

Now let us
suppose that we have the task of describing or modeling the contents of either
reality. What is surprising is that it is easier, shorter and simpler to
describe the Babel reality than it is to describe the Macbeth universe. To
fully describe the Babel reality we just need the short computer program or my
brief description above to generate everything that exists in the Babel
universe (which could be described as a multiverse of
books). However to describe a Macbeth reality (universe) we need to type every
letter in the work of Macbeth which takes up much more space than the program
or description which generates every possible book including Macbeth in a Babel
universe.

What this
shows, and I will return to it later, is that multiple entities can actually be
simpler and less complex than a single entity. It will become apparent that
multiple universes could be simpler than a single universe.

**The types of parallel
universes.**

Many physics
theories today have the startling side effect of predicting or suggesting
various types of other universes in addition to the observable space-time
bubble we find ourselves in (the Hubble volume, a sphere many billions of light
years across). The Hubble volume is what we have traditionally called our
universe.

It should be
appreciated that the extra universes are a side effect of the theories which
are used to explain something else which we can measure. It is not as if we
went out of our way to find these parallel universes. It is just that they keep
popping out of the successful theories used to describe and predict behaviour in the experiments which we *can* do. There are different varieties of parallel universes all of
which can coexist. The classification scheme below is used by Max Tegmark.

**Level I parallel universes –
infinitely big universe**

This type of
parallel universe is uncontroversial and is a generic prediction of
cosmological inflation. It exists if our own space-time bubble is infinite in
spatial extent (or very very large) and the current
data suggests that it is, ie. space
is flat on large scales. Our Hubble volume, that is our observable universe,
contains approximately 10^118 sub-atomic particles within it. That is a large
number, a one followed by 118 zeroes, but it is a finite number. It follows
that there is a finite number of arrangements that these particles can be in.
The point is that there are only so many ways our observable universe could be
arranged, given consistent laws of physics. There is a
very large but limited number of *states *it
can be in. Now if our universe is infinite as the data suggests then there are
an infinite number of Hubble volumes within it. This would mean that every
possible arrangement of particles, every state, would occur somewhere in the
universe. In fact every possible state would occur an
infinite number of times. This means that there would be multiple copies of our
own observable patch of universe including you and also copies of you with
slight variations where you made different life decisions or got some rare
disease or won the lottery. The laws of physics are the same in these regions
but each of them can have different initial conditions.

It is
possible to calculate how far away on average an exact copy of you would exist
in this infinite universe and it would be 10^10^29 metres,
which is a one followed by 100 billion billion billion zeroes metres. That is a
very great distance away so you are very unlikely to ever encounter your
nearest copy unless we invent faster than light travel. A copy of our entire
observable patch of universe would be repeated on average every 10^10^118 metres. If our universe is infinitely big as the data
suggests then it is inevitable that everything which can happen (given the laws
of physics) *will* happen somewhere in
this infinite universe. That means there would be many versions of you, the
earth, and your observable patch of universe which are just as real as you feel
yourself to be and none of this requires any new physics!

A common
question is how can the universe be infinite if our
Hubble volume was once compressed into a tiny volume at our big bang 13.7
billion years ago. We only get to see out as far as light could have traveled
in this time. The answer is that all of this infinite space was still infinite
13.7 billion years ago and all of it was compressed. Therefore any observer
such as us in an infinite universe will be able to observe a Hubble volume
around them now when they peer through their telescopes. Their Hubble volume
would also have been compressed to a tiny point 13.7 billion years ago and all
the points would have been adjacent - they are all part of the same space. To visualise this just imagine an infinitely large very dense
volume made of rubber for the sake of argument. Then imagine it expanding
everywhere so that it becomes lighter and less dense everywhere.

The level 1
parallel universes do not require any new physics. In
fact they are not really parallel or separate from our observable universe, they are just further away within the same space.
They are a logical consequence if our own 'little' Hubble volume is part of an
infinite space. The laws of physics remain constant across these Level I
parallel universes.

**Level II parallel universes – bubble
universes (String theory)**

The level II
parallel universes are a prediction of String theory or something like it. In
String theory it is suggested that our universe has local *effective* laws of physics which are derived from more *fundamental* laws of physics. Our local *effective* laws of physics contain such
values as physical constants (eg. charge on the
electron, strength of gravity), number of dimensions and number and types of
particles. It is suggested by String theory that different regions of space can
exhibit different *effective* laws of
physics derived from the same underlying *fundamental*
laws of physics. This means that all these observed physical constants and
local physics can be different in different regions. These can be thought of as
*bubble* universes where new universes
are bubbling up out of quantum chaos (multiple big bangs),
each bubble having its own initial conditions and parameters even though the
underlying mechanism is the same. A level II (bubble) universe could be an
infinitely large level I universe. There is no problem in that there can be
multiple infinitely large universes - the mathematics of this is understood.
Also not every level II universe will be infinitely big so level I universes
are a subset of level II universes.

Level II
parallel universes help us with the fine tuning puzzle. When we look at the
physical constants in our universe it seems to be very finely tuned to allow
the formation of galaxies and planets and life like us. If we changed some of
these constants such as the strength of the charge on an electron by a small
amount then the universe would not develop into one which allows carbon
chemistry and biology and the evolution of humans. If the laws of physics are
much more fundamental such as in String theory, then we do not need to specify
these values. Instead many variations of these constants will be automatically
“tried out” creating a plethora of universes with a huge number (approximately
10^500) of different local (effective) physics. Some of these will have extra
dimensions or stronger gravity or a different zoo of particles from the ones we
detect in particle accelerators. Only some of these universes will be suitable
for life and of course we must find ourselves to be in one suitable for life.
This gets rid of the fine tuning problem and disposes of the question “why this
particular physics and not another type”.

This brings
me back to the __Library of Babel__. You will remember
that it was simpler to have a description or model or method of generating
every possible book than it was of generating one particular book only, such as
Macbeth. It is the same with the level II “bubble” parallel universes. It is
simpler to have a mechanism for generating multiple universes with different
settings than it is to have one generating our observed universe with its
particular fine tuned settings.

It has been a
pattern in the history of science that the simpler and more general theories have
tended to be the most successful. This has resulted in our constant demotion in
the scheme of things. First we learned that the earth was not the centre of the
universe and that we were moving around the sun. Then we learned that even the
sun was not special. It was just another ordinary star out of billions. Then we
learned that even our galaxy of 100 billion stars was not alone and that there
were at least 100 billion galaxies. Now it may be that not even our universe
(space-time bubble) is unique, but is one of many.

And it
doesn’t end there….

**Level III parallel universes – quantum
weirdness**

This type of
parallel universe comes from quantum mechanics which is a very successful theory
for explaining the behavior of the very small. It has been shown to be accurate
to 10 decimal places. This type of parallel universe is the most difficult for
laymen and even some physicists to accept due to its perceived “weirdness”. In
quantum experiments particles are in more than one place at once until they are
“observed” and this has led to much debate and interpretation about what is
going on.

There is the
“wave collapse” (Copenhagen) interpretation which states that the particles are
in more than one place at once until we *observe*
them and then there is an instantaneous wave collapse which puts them into one
place. This agrees with experiment but the problem is how do you define an
“observer”? Is it a person, a dog or an instrument cluster? Also an instant
collapse of anything breaks our known laws of physics where nothing travels
faster than light.

The more
widely accepted interpretation amongst those working in the field is the Many
Worlds Interpretation which also agrees with experiment. It states that the
particle is in more than one place at once in separate parallel ‘worlds’. These
parallel universes are splitting off all the time and sometimes recombining so
that there is a whole ensemble of universes. It is more useful to visualise this as the universe splitting itself into ever
thinner slices. For example this splitting would occur when a photon strikes
detector A or detector B (it does each in a separate parallel universe). These
level III parallel universes sometimes interfere with each other and this has
been demonstrated in experiments for many decades. There is a lot of current
work looking into harnessing the parallel universes for quantum computing which
could have incredible powers. See David Deutsche. The quantum parallel universes
exist within the level I and level II parallel universes so any particular
level I/II universe will also be splitting over time.

In a quantum
experiment, from the point of view of an observer (eg.
a person) a photon may be observed to randomly choose whether to hit detector A
or detector B with a probability of 50%. This means that if the experiment is
run repeatedly, half of the time detector A is triggered and half of the time
detector B is triggered. However it is impossible to predict what the result
will be of any particular run. This is the fundamental uncertainty and
randomness built into the universe which caused Einstein to remark that God
does not play dice. However if we take a God’s eye view of the whole ensemble
of branching parallel universes the experiment loses its randomness and appears
deterministic (it runs like clockwork). Each time the experiment is run, in one
universe detector A is triggered and in the other universe detector B is
triggered. Meanwhile the experimenter will have been duplicated so that there
is a copy in one universe reading the A result and a copy in the other universe
reading the B result. When they each run the experiment again there is a
further splitting so there will be four experimenters in four universes with
the result A then A, B then B, B then A, and A then B. From our God’s eye view
of the multiverse (collection of universes) there is
no randomness but from the point of view of most experimenters there appears to
be randomness with an overall probability of 50:50 over time.

The many
worlds interpretation is actually the most elegant one and leads to the least
problems. It means we don’t have to start inventing what wave collapse
equations might look like or how we define the vague notion of observer. It
even explains the mysterious randomness in our observed universe. It does have
the rather disturbing effect of us having to come to terms with the idea of our
identities splitting over and over and our lives following multiple different
paths. However each copy of you will only experience his/her own path even
though their history was shared up to the point of branching off. This is quite
consistent and does not lead to any paradoxes.

So far we
have seen three types of parallel universes. It is very suggestive that
different areas of physics have independently predicted parallel universes.

**Is there evidence for
multiple universes?**

Level I

There is
evidence for our universe being infinitely large so that means level I multiple universes exist. New data could refute this but
our best current models suggest an infinitely large universe.

Level II

If we get
evidence for supersymmetric particles in the latest
collider experiments, this would be supporting evidence for string theory and
Level II universes. There are also some cosmological observations which would
strengthen the case for string theory.

Level III

A simple
working quantum computer has been built and this is evidence for level III
parallel universes - the quantum calculation got done in the other universes.
It is only when we can build them such that they can perform calculations which
would be impossible using the resources available in our own universe alone
that people will really sit up and take notice. It is, after all, difficult to
change your whole conception of reality without strong evidence, even for
scientists. Good scientists can hold multiple competing models of reality in
their heads at once and assign each model different probabilities as
experimental results unfold, strengthening or weakening the case for each
model.

**Level IV parallel universes – other
mathematical structures**

The level IV
parallel universes is a more speculative idea but it
has the tantalising prospect of offering us an answer
to the ultimate question:

“Why is there something instead of nothing?”

It has been
noted in the past that mathematics seems unreasonably effective at describing
how our universe works. Everything from the motion of the planets to the motion
of sub-atomic particles seems to be governed by mathematics. All the forces
such as gravity and electromagnetism are described by mathematics. The change
in the quantum state of a physical system is described by the Schrodinger
equation and by Richard Feynman’s path integral formulation.

Max Tegmark has championed a bold proposal which is that
different *mathematical structures* are
realised as universes so not only would the parallel
universes described above exist, but also other mathematical structures
(actually a subset which is computable). These make up the level IV parallel
universes which can have radically different physics. This may seem strange but
it does make a kind of sense after further thought. We think our universe is
solid and “real” but what does that mean? The more we know the more we realise that solidity is an illusion. We cannot walk
through walls because of forces connecting particles together so our evolved
minds have labeled our bodies and the walls “solid” to capture that concept.
Particles have zero volume so how can they be solid? However even particles are
not the little points we used to visualise and they
may be modeled by vibrating strings. Note I said “modeled by” and not “made of”
strings. In physics now most entities are described as fields such as the
electromagnetic field and “particle physics” has become quantum *field* theory. Where this is heading is
that

*at**
the heart of reality there seems to be nothing solid or real at all
except mathematical structure and
information,*

neither of which are physical as
traditionally understood.

What is a
mathematical structure? It is a set of abstract objects with relations between
them.

The multiverse rather than being *described by* mathematical structures could be *equivalent to* mathematical structures. This could solve some
puzzles.

One puzzle
is:

Why does this particular set of equations
describe

our universe/multiverse and why not some other set of
equations?

One answer is
that this particular set of equations describes a structure which allows conscious
observers like us so we must find ourselves to be in such a universe. However
then we might ask why should a universe/multiverse
capable of having conscious observers exist if other types of mathematically
described universes without observers might not exist?
The answer could be that all such universes *do*
exist. Again it is simpler and more economical and more symmetrical to generalise and have multiple entities.

Stephen
Hawking once asked what breathed the fire into the equations to make them into
a “real” universe. The answer could be that no fire is required and that the
only things existing are mathematical structures. With this view our universe *is* a mathematical structure whose
details we have been exploring for centuries with the scientific method. Its
solidity and “realness” would be impressions from our human consciousness which
is itself based on mathematical structures. Our brains are physical objects
whose sub-atomic constituents are ultimately mathematical entities.

“Mathematical
structures as universes” looks like it can answer our deepest question of,

*Why is there something
instead of nothing?*

Mathematical
structures are often described as being *discovered*,
not invented. In other words they already exist before we understand them.
Alien civilisations would discover the same
mathematical structures. They might use different symbols and notation but they
would be describing the same mathematical objects and relations between them.
The mathematical objects exist whether or not we find them and describe them.
Mathematical truths and structures do not need a physical substrate and they
are not created. They *just exist*
independently. They are abstract, timeless, spaceless and *just
are*. Therefore they must exist and if Max Tegmark’s
proposal is correct therefore universes must exist and that is why there is
something instead of nothing!

--

Marcus Loane

Note: Level I,II and III parallel universes would be a subset of level IV
parallel universes. All the parallel universes can exist as one huge universe
ensemble. Some of the parallel universes are connected to others causing
interference effects and some are isolated. As time is an internal property of
some of the universes, the ‘outside’ view of the whole ensemble could be
thought of as one giant static (ultimately mathematical) structure with our
subjectively experienced lives and branched-off parallel lives ‘forever’ (if
that even makes sense without an external time) embedded within it.

Many
physicists have been brought to this position where what appears to be more
fundamental is abstract, timeless and spaceless and emphasises *information*.
Matter, energy and even time and space are emergent phenomena from the underlying
mathematics. In my opinion this position also makes consciousness a little
easier to understand. Many people have trouble accepting that consciousness
arises from processes occurring in “physical stuff” but this physical stuff is
less physical than we first thought. The physical stuff is, at its heart,
mathematical structure (abstract objects with relations between them) which
makes it seem less physical. It seems somehow easier to imagine consciousness
as depending on mechanisms in an abstract space. Most functionalists accept
this anyway where the abstract space is at a much higher level such as the
abstract space where software runs on a computer. However it is pleasing
aesthetically that this software abstract space is running on brain hardware which
when examined at a fine-grained enough level, the level from sub-atomic down to
the Planck length or lower, would also be constructed
out of abstract objects (mathematical objects).

Perhaps Level
IV universes can only ever be *implied,* but multiverses with conscious
beings can be experimented upon by the conscious beings and thus gain a
different ontological status.

Max Tegmark’s explanation of the multiple universe levels in __Scientific American__.

Max
Tegmark’s __more technical paper__ on the
mathematical universe.

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