# Mathematics, Substance, Consciousness

## by Martin Clewett

There are hundreds of theoretical physicists thinking about how to properly construct a mathematical description of the universe consistent with all the measurements we have so far made of it. Properly means the mathematical description must produce new predictions that can be checked.

There are two accepted mathematical descriptions. They are known as The Standard Model and General Relativity. The Standard Model is a mathematical description of how all known elementary particles interact with one another and it describes particles as excited states of underlying quantum fields. These fields extend through space, changing with time. The theories do not explain gravitational interaction. The Standard Model is Quantum Mechanical and describes all possible particle interactions for any given scenario simultaneously.

Probabilities for the outcomes of those interactions can be calculated. But, strangely, only one outcome can actually be observed.

General Relativity is a mathematical description of gravity. This is where the energy of matter, the energy of radiation and the energy of non-gravitational fields together shape the curvature of space-time. Anything in this curvature affects space-time and appears to accelerate: for example falling objects, or objects in orbit.

# Let us take a step back

Consider the philosophical implications of the preceding paragraph. I was careful to use the term mathematical description: something real in the universe is being described by mathematical physics.

To replace the term mathematical description with the term mathematical model is to assert something like this:

I don’t have any idea of what is out there in the world, all I have is a model of it in my mind that allows me to interact successfully with it

But if I can interact with the world successfully, then I must know something about it. Therefore, it is safe to make statements about the world and so, to describe the world. We can confidently say that our mathematical models are also mathematical descriptions (at least in the domain of physics) – unless of course we have good reason to doubt them.

One example of this is when Copernicus put forward a mathematical model of the solar system with the sun at the centre. We have now come to accept his view as an accurate description of reality – although there are still a few flat earth diehards out there.

# Is the universe mathematical?

But there are physicists who actually think mathematical ideas are reality itself. Max Tegmark’s Mathematical Universe Hypothesis is an example of this. According to Tegmark, mathematical theories are not a description of reality, but actual reality itself.

However, as theoretical physics advances the mathematics it uses changes. Logically, then, if it were true that mathematics were reality then reality would change when mathematics changed. The response from mathematecists is to say that all mathematics is an approximation of the actual mathematics of the universe in which we all reside.

And if we regard all mathematical theories as only approximations then these can be understood as mathematical descriptions of a deeper, universal mathematics, a reality which physicists like Tegmark claim is reality itself.

But the question remains: at what point does a mathematical theory transition from being a description of reality into being reality itself?

#### “at what point does a mathematical theory transition from being a description of reality into being reality itself?“

Worse still, if we ever reach the ultimate universal mathematics, we face a paradox: the ultimate mathematics would be a subset of itself, popping out of its own equations. According to Gödel’s incompleteness theorem an ultimate mathematics of the universe is unachievable as, in the end, all mathematical theories are inconsistent, or incomplete. None of this is satisfactory to physicists.

# The substance of the universe

An elegant mathematics that makes accurate predictions about measurements should not be arrogantly considered to be the ultimate reality, but neither should it be completely dismissed as meaningless. Successful mathematical descriptions of the universe are suggestive of the content of reality. In the same way, maps of mountains are suggestive of mountains.

Substance itself, rather than mathematics, is a better basis for reality. There are many very similar types of substances.  Firstly, there are the substances described by the Standard Model’s quantum fields. They exist everywhere and these substances must also be the source of the energy described in General Relativity that curves the space-time in which it exists.

#### “Substance rather than mathematics is a better basis for reality.“

Secondly, there is the substance of space-time itself which, by definition again, is every-when, and everywhere and contains everything.  If theoretical physicists wish to write a theory that includes all these substances then presumably this theory would result in a description of a substance that exists every-when, everywhere and as everything.

Thales of Miletus said water was the fundamental substance of the physical world. Unfortunately, water is not a fundamental substance.

Nevertheless Thales’ idea sets the stage for the possibility that there may actually be a fundamental substance. Modern theoretical physicists desire to bring theories together into a master theory that is the mathematical description of a singular substance.

The word to describe everything in terms of one substance is Monism. The mathematical description of particle interactions describes multiple simultaneous outcomes for a singular particle interaction setup.  As I said in the third paragraph: strangely only one outcome can be observed. What is actually observed when measured is a subset (of one) of these outcomes.

#### “Modern theoretical physicists desire to bring theories together into a master theory that is the mathematical description of a singular substance.“

Interestingly, if we repeat the setup, we get a different measurement, although it will still be one of the outcomes predicted mathematically by the theory. The weighting for each outcome corresponds to the probability of the outcome; this can be verified by experimental repetition.

This raises the question: if the description of the substance includes all possible outcomes co-existing, then what happens to all the rest of the outcomes when we perform a measurement?  Why is there only one measurement outcome observed when the description includes many?

For some, the quantum field is not real. Rather, it is a tool for making predictions. Another approach to this problem is to say that there is something missing from the description: since observation requires consciousness then perhaps consciousness is removing all other outcomes except for one. Maybe consciousness controls the physical universe. This kind of magical thinking is the starting point for many self-help philosophies.

#### “The process of decoherence was worked out as part of the mathematical landscape of quantum mechanics in 1969″

Actually, if we simply allow for the fact that the mathematical description of what is happening should also include the observer then this, coupled with a technical process called decoherence, is enough to explain why only one outcome is observed.

The process of decoherence was worked out as part of the mathematical landscape of quantum mechanics in 1969 and it occurs irrespective of interpretation. When we include the observer itself within the mathematical description decoherence ensures that from the perspective of each of the observed outcomes none of the other outcomes can be observed.