What is colour?

No doubt you have thought about this deep philosophical question at some stage(s) in your life. Why is the sky blue, why is grass green, why is blood red? What does ‘blue’ even mean? Do we see the same colours as other people? Do animals see the same colours we do? Why are there three primary colours? Are there three primary colours? Do we see three dimensions of colour because we sample three different frequencies of light? Could we see more dimensions of colour if we sampled more frequencies? Is colour real, or just a sensation in our brains?

In modern physics, colour is treated as an infinite-dimensional Hilbert space of frequencies, and the 3-dimensional colour that we see with our eyes is treated as a figment of our imagination, and not as physical reality. But how can an infinite-dimensional Hilbert space be physically real? Obviously it is useful as a mathematical tool for understanding the world, but it can’t be physically real. But a 3-dimensional world of “colour” could, just possibly, be physically real.

That at any rate is what my G2 model of physics proposes. Or, to be more precise, if space and time are real, then 3-dimensional colour is real. So if colour is not real, then space and time are not real either. You are free to choose whichever of these philosophical positions you want, but you are not allowed to mix and match. The reasons are two: first, physicists use time/distance (frequency/wavelength) to measure colour; second astronomers use colour to measure time/distance.

My G2 model says that the fundamental concept of physics is 7-dimensional, and consists of three dimensions of “space”, one of “time” and three of “colour”. These are the concepts we abstract from the dual concepts (measurements) of momentum, mass/energy and angular momentum, respectively. Mainstream physics does not distinguish adequately between momentum and angular momentum, and therefore sees the world in black and white. Einstein introduced 50 shades of grey into gravity, and Dirac introduced one colour (let us call it blue, after the sky) into quantum mechanics. After that, physics got the blues, as it persistently failed to reconcile Einstein with Dirac. (I won’t even mention how they tied themselves up in knots after they invented string.) So what makes me see red?

The short answer is that it is impossible to have just one colour. Colours only exist by contrast with other colours. Therefore you need at least two of them. But it is mathematically impossible to have two colours without having three, because each colour converts Einstein’s shades of grey (real numbers) into complex numbers, and there is no 3-dimensional number system, as Hamilton discovered in 1843, when he discovered quaternions. Quaternions, then, allow for a consistent world of three primary colours. In the version of Hamilton’s notation that I use, the primary colours are called I, J and K.

Let’s say I is green, J is blue and K is red. Or perhaps I should say I am green, I feel blue and I see red. In the second person you, J, are blue, feel red and see green. In the third person, K is red, feels green and sees blue. This is how the theory of relativity works in the G2 model. It is necessary to distinguish between what you see (with electromagnetism), what you feel (with gravity) and what you are (an insignificant dot on an insignificant dot orbiting an insignificant star on the outer edge of the Milky Way).

So, to relate this to ordinary physics, which tries to measure 3-dimensional colour with 1-dimensional time (i.e. frequency). Time is dual to energy, which is equivalent to mass, so that mass (which is very difficult to measure directly) is always measured as an equivalent frequency (which is much easier to measure accurately). The problem with this is that frequency depends on gravity, at least according to Einstein, so that measurements of mass that are actually made on Earth cannot be separated from the gravity that we feel. It is usually considered that this effect is too small to worry about, but I have demonstrated in many different ways that it is not.

Unification of the fundamental forces depends on unifying time with colour into a 4-dimensional concept. I am certainly not the first person to suggest that time should be more than 1-dimensional, and there is plenty of literature on the subject. Three is a popular choice, but I have been vacillating for many years between three and four. It seems I have now definitely decided that four is correct. (Until the next time I change my mind, of course.) You see, the question of how many dimensions of time there are is the same question as how many independent fundamental masses there are, and I have identified exactly four fundamental masses, of the proton and three generations of electron. The only thing that still worries me is whether the Koide formula might actually be correct – if it is, then it reduces the dimension of time down to three. But I am pretty sure the Koide formula is only approximate, not exact.

Now if you just take the Lorentz group SO(3,1) with one-dimensional time, and extend to four-dimensional time, you get the group SO(3,4). But of course this is not really the symmetry group of physics, because there really is a physical difference between time and colour, even if they do get mixed together in practice. The only group that is available to mix time and colour and space together in this way is G2. There is no other symmetry group available. Therefore G2 (the split version) is the symmetry group of the unified concept of space-time-colour.

If you fix the time coordinate, so that you fix mass and energy, what is left is the strong force (in particle physics) or gravity (in classical physics), with a symmetry group SL(3,R) acting on space-colour. In other words the “colour” of quantum chromodynamics is not just a metaphor, it is mathematically equivalent to the classical concept of colours of light. Therefore it is observable in practice, contrary to the assumptions of the Standard Model. And “gauge-gravity duality” is no longer just a vague feeling that the mathematics looks similar in gauge theories and in gravity, it becomes a genuine isomorphism between the symmetry groups in the two cases.

That is how to unify spacetime with colour to create a consistent theory of everything.