Theory of nothing

Multiple universes and why there is something instead of nothing

by Marcus Loane

31st March 2012

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

The Library of Babel

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!

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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.