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.


24 Responses to “What is colour?”

  1. Robert A. Wilson Says:

    If I am green, is it possible for me to feel red and see blue, rather than feel blue and see red? In physics this is a question of chirality, but in human consciousness it’s the difference between summer and winter. Or you might say that K, on holiday in the sun, is red (sunburnt) and sees blue (sea and sky) and feels green (with envy? why?). Surely K must feel anti-green? But what do you (J) or I know? We are not K. The difference between K feeling green or anti-green is a matter for K’s conscious self to determine.

    Did I just mention consciousness? Did I just suggest that consciousness is related to the chirality of colour? Did I just propose a physical basis for consciousness? Well, I’m talking mainly in metaphors, but perhaps there is some truth in it? Perhaps colour cannot be perceived by any physical object that is not conscious? Perhaps it is the physical nature of colour that is the key to understanding the physical nature of consciousness?

    Or perhaps I’ve been out in the sun too much. Or drunk too much pivo. Or looked at too many impressionist paintings. Well, the impressionists at least understood the importance of the relationship between colour and consciousness. And their works were treated then in much the same way that mine are being treated now. Perhaps in time my work will be appreciated as much as theirs is now.

  2. Robert A. Wilson Says:

    Well now, there’s an interesting thought. Is it the strong force that defines consciousness? Does consciousness consist of a mixture of feelings consisting of red, anti-red, blue, anti-blue, green and anti-green? The metaphors are certainly different in different languages, but in English the three colours are angry, sad and envious, and their opposites peaceful, happy and tolerant, say. Of course, consciousness is 3-dimensional, so much more complicated than these few words can suggest. But the colours describe how the real world is, and the anti-colours describe utopia, nirvana or heaven. Is this the source of the difference between particles and antiparticles?

    Time then relates to colours via a scale of interesting/boring. Interesting times (as the Chinese curse would have it) have plenty of red, green and blue. Boring times are characterised instead by the anti-colours.

    Well, it’s early days, and I wouldn’t call this a theory of consciousness yet. But it shows some promise, so I’ll think about it, and let you know how I get on in due course.

  3. Robert A. Wilson Says:

    This idea provides an interesting take on the “Free Will Theorem” – that says, roughly, that if we have free will then so do elementary particles. There are various different ways of interpreting this theorem, of which the most plausible is that the theory used to prove it (quantum mechanics) is incorrect. But QM is not falsified by any experiment, so an alternative interpretation is that we do not have free will. But there is a third possibility: perhaps elementary particles actually *do* have free will?

  4. Zsat Says:

    Ain’t physics great? You are free to unload all that bunk for free. And then of course your can change your mind about your “theories” whenever you want. Bet you were not able to get away with it in your field so had to beat it.

    • Robert A. Wilson Says:

      Perhaps I shouldn’t have filed this under “physics”, since it clearly isn’t. I suppose I need to create a new category of “philosophy”. In any case, a blog is not a serious academic outlet, and I don’t pretend it is. My serious papers in physics are starting to be published in respectable journals, just as my serious papers in mathematics were, and still are. In both subjects, serious advances start with crazy ideas. If you don’t have a crazy idea, you get nowhere. If you do have a crazy idea, you have to know when to abandon it and try another crazy idea. Automatically categorising all crazy ideas as “bunk” is illogical and stupid, and guarantees a complete lack of any progress at all.

    • Robert A. Wilson Says:

      I find it strange that you think the freedom to change your mind is a luxury. In the academic world I lived in, the luxury few could afford was the luxury *not* to change one’s mind. That luxury was enjoyed by only a small elite. The rest of us were forced to change our minds frequently, whether we wanted to or not. Those of us who did not comply with orders to change our minds were dealt with forcefully. In many ways, in can be said that the problems in physics are largely due to it being run by people who enjoy the luxury of not having to change their minds. They already “know” the answer, so they don’t have to change their minds. The rest of us, who realise that we do not know the answer, are changing our minds constantly.

      • Zsat Says:

        You seem to oscillate easily between this answer’s apparent humbleness to a more frequent arrogance in your entries about your latest “theory of everything” and your complaints that every other scientist in their idiocy won’t take your magic words seriously. Of course you can write whatever you want in your blog so apologies if my remarks sound somewhat snide. I certainly like crazy ideas(as a matter of fact is out of interest on some of them and agreeing about many of the pitfalls of mainstream physics that I follow your blog and comment here) and changing my mind, all the time. But I just don’t think that mix es well with bragging about new theories and implying everyone else is stupid for not acknowledging their greatness, regardless how unserious a blog may be.

    • Robert A. Wilson Says:

      Ah well. I’m a human being, not a machine.

    • Robert A. Wilson Says:

      So I play games and have fun. Not everyone appreciates my sense of humour, of course. That has always been clear.

    • Robert A. Wilson Says:

      Arrogance and humility are both essential prerequisites for these games, so I apologise for neither. One cannot begin without the arrogance to criticise Einstein, and to say he was wrong if he was. One cannot continue without the humility to criticise oneself, and to admit one is wrong when one is. Oscillating easily between these two is an essential part of the work I am doing, and therefore I do not accept criticism for it. They may not “mix well” in your eyes, but mix they must, or the project is doomed.

  5. Mark Thomas Says:

    I ‘ve always been leary of theories of consciousness and reductionist information theory to objects like binary or qubits. Information is loaded down the line with more information that one cannot see. Maybe, you have a colour space theory of information as a network that connects classical with quantum. Then maybe not. A lot of physicist talk of consciousness reminds one of “nailing jelly to a wall”.It just has to be more than their assumptions. Here is something I have never really understood which shows that there is something fundamental lacking. When a person dies how is the information of experience and memories from their brain able to be recreated because of physics reversibility ? The only activity that could be detected would be thermal (long wave photons) from a cooling skull. How is this different from the black hole paradox? In the case of the deceased where is the information that could be obtained from such an emission as the brain acts similarly as a radiating black body.
    Anyway just my thoughts. Here is something recent about a new theory of consciousness based on relativity frames and measurement by our brains.

    • Robert A. Wilson Says:

      I also find the information-theoretic approach to consciousness unconvincing. It may ultimately be right, but it isn’t yet convincing. Part of the problem as I see it is that the theory of quantum mechanics does not appear to contain the correct amount of information. Depending on your particular approach to the paradoxes of measurement and entanglement, the theory either contains too much or too little information. That is why the focus of my approach is always to try and get the amount of information right. Most of my models also contain either too much or too little information, just like every other model. There is only one that appears to me to contain just the right amount of information, and that is the model based on the group algebra of the binary icosahedral group.

      The model on which this post is based (a G2 model) probably does not contain enough information, so that what I have written here is not supposed to be taken as “fact”, or even as a statement of my “opinion”, just as food for thought.

  6. Robert A. Wilson Says:

    I don’t like changing my mind. It is uncomfortable, and disruptive. I assume most people don’t like changing their minds. I may be wrong, of course, but I think the evidence is in my favour. I don’t like making up my mind – because if I do, I might have to (or want to) change my mind later, and that would be uncomfortable (and disruptive). I like to keep an open mind, as I believe a scientist should.

    That does not mean that all hypotheses should be treated as equally likely, or equally valid. But a mathematician can work on a variety of different hypotheses and investigate the consequences of each one, without necessarily “believing” in any of them. That is what mathematicians are trained to do. I always assumed that researchers in all disciplines did this as well, but I suppose it is possible that there are exceptions.

    The point, I suppose, is to investigate as many plausible hypotheses as you can, in order to make up your mind (!) which one fits the evidence best. That is what I try to do. The standard hypotheses in physics are not plausible, and therefore I try others. When investigating a particular hypothesis, one has to believe in it (or, to use the technical term, suspend one’s disbelief), or else one’s mind is not on the job. But when that hypothesis becomes too implausible, one has to be flexible enough to change one’s mind.

    • Robert A. Wilson Says:

      For example, if a mathematician is investigating a conjecture to decide if it is true or false, the traditional advice is to try to prove it on Mondays, Wednesdays and Fridays, and to try to disprove it on Tuesdays, Thursdays and Saturdays. Not everyone finds it easy to change their mind every day of the week, however.

  7. Robert A. Wilson Says:

    In physics, of course, one can never prove that a theory or model is correct. The best one can hope for is to fail to prove it is incorrect. I don’t really believe in the G2 model discussed here, which is why I am trying to disprove it. What I am reporting on is essentially my failure to disprove it. So far, it seems to model everything I want it to model, in a way that seems to be consistent with experiment, at least as far as I can tell.

    The next test of the model is whether it can describe polarisation of light correctly. In the standard approach to polarisation, one fixes the direction of motion of the photon or photons under discussion, so reducing the Lorentz group to SO(2,1). Then one uses the helicity of SO(2,1) to define the helicity of the photon. This is fine for circularly polarised photons, but not so good for linearly polarised ones. To describe linear polarisation, one has to take complex linear combinations of the two helicities. As a mathematical trick, this seems to work, but as a physical description of what is actually happening, it does not.

    The G2 model has SL(2,R) in place of SO(2,1). These two groups have the same Lie algebra, but behave very differently in physical terms. If I rotate through 90 degrees in SL(2,R) I reverse the polarisation of the photon. The corresponding element of SO(2,1) rotates through 180 degrees, and does not change the polarisation. Which do you think is a better description of how photons actually behave in the real physical universe? Experiment is quite clear: SL(2,R) describes polarisation of photons correctly, and SO(2,1) does not.

    Failed again! I simply cannot disprove this G2 model!

  8. mitchellporter Says:

    “So here you have another illustration of the necessary trinity of nature. Blue is existence. It is darkness seen through light; a contrasting of existence and nothingness. Yellow is relation. In yellow light we see the relation of objects in the clearest way. Red is feeling. When we see red, we are thrown back on our personal feelings….”

    (The alien philosopher Corpang, in David Lindsay’s novel, “A Voyage to Arcturus”)

    • Robert A. Wilson Says:

      Ah, the necessary trinity of nature…three in one, and one in three…this is how to do unification…not three plus one equals four. I was wrong. Einstein was wrong. Everyone was wrong.

  9. Robert A. Wilson Says:

    The G2 model describes the massless bosons via the adjoint representation (14 dimensions), and splits them into adjoint SL(3,R) (the 8 gluons) plus 3+3′ (the photons, a.k.a. the electromagnetic field). All these have spin 1 in the Standard Model, but here we have no Lorentz group to define the spin. We still have SO(3), which splits the gluons into 3 spin 1 and 5 spin 2. We therefore get our spin 2 graviton, but more generally gluons and gravitons are now the same thing.

    We also have left-handed and right-handed copies of SU(2), which define different types of spin or isospin. Both split adjoint G2 into three scalars, one spin 1 triplet, and a 4-dimensional complex spinor. In the right-handed case, the spinor is irreducible (spin 3/2), while in the left-handed case it splits into two 2-dimensional (spin 1/2) spinors. This vital distinction does not appear in the Standard Model, where the spin 3/2 representation is not used. But it is used in my discrete model, in much the same way as it is used here: to give mass to the three generations of electrons.

    As I have been saying for several years (three or four, at least), this spin 3/2 representation is essential for the modelling of mass. Why is no-one interested in the spin 3/2 representation? It is what the Dirac spinor should be, but isn’t. Without it, you can’t get a spin 2 graviton for quantum gravity, and you can’t understand the three generations of fermions. It’s not rocket science, it’s just basic representation theory.

    • Robert A. Wilson Says:

      As a representation of SO(4), or SO(2,2), adjoint G2 splits as the direct sum of (a) a left-handed 3, (b) a right-handed 3, and (c) a left-handed 2 times a right-handed 4. It is (c) where electro-weak unification takes place. But in the Standard Model the 4 is split into a left-handed half (identified with the left-handed 2) and a right-handed half (not identified with anything). Therefore the machinery of electro-weak unification is a nightmare, that makes no sense either physically or mathematically. The left hand simply doesn’t know what the other left hand is doing!

  10. Robert A. Wilson Says:

    I don’t suppose there is much point in reiterating here that the Lorentz group does not accurately describe physics as she is observed in real life. No-one will listen to this argument, since their prejudices forbid them from questioning the “fact” handed down from Einstein in tablets of stone, that the Lorentz group is one of the ten commandments. But we must listen to experiment, even more than we listen to Einstein.

    The first argument is polarisation of light: the Lorentz group is incompatible with experimental properties of polarisation. The second argument is gravity: the flyby anomaly is a decisive refutation of general relativity, to add to all the other astronomical refutations which fill a vast literature. It isn’t the physical assumptions of GR that are the problem, it is the mathematical assumptions – especially the Lorentz group.

    Why does no-one listen when I try to replace the Lorentz group, which doesn’t work, by SL(3,R), which does work?

    • Robert A. Wilson Says:

      Sometimes I feel that physics has taken the ten commandments from Exodus chapter 34 instead of Deuteronomy chapter 5. There seems to be more emphasis on ensuring that leavened bread is not sacrificed along with animals, and that a kid should not be boiled in its mother’s milk, rather than avoiding murder, adultery and theft. On the other hand, perhaps it would be useful to take more notice of the commandment prohibiting the worship of gods made of metal.

      The Lorentz group is, to me, unleavened bread. It needs some leavening. The commandment to keep the kid and its mother’s milk completely separate sounds to me like the Coleman-Mandula theorem, to keep the gauge groups and the Lorentz group separate – once of enormous practical importance, but of purely symbolic significance today.

    • Zsat Says:

      Maybe more people would listen if you gave something more than purely blanket statements as your arguments for the mathematical invalidity of the Lorentz group ( most people agree GR is ultimately not right but it doesn’t follow necessarily that it is because of the Lorentz group being wrong, and in which of you papers is shown the incompatibility of polarisation and SR?) so it doesn’t simply looks like a shot in the dark.

      • Robert A. Wilson Says:

        I do give more: see for example https://robwilson1.files.wordpress.com/2021/03/lorentz5s.pdf where I explained the reasons why I thought at that time SL(3,R) did a better job than SO(3,1). The incompatibility of polarisation and SR (as interpreted by Dirac) is not something I need to prove – it is self-evident. Einstein pointed this out in 1935, and no-one has ever provided a satisfactory solution.

        It may look like a shot in the dark, but it is ten years of looking at the problem from dozens of different viewpoints, and always coming back to the same fundamental issues, and the same fundamental physical problems, regardless of what mathematics I am trying to use. Polarisation of light is not understood. At all. Anyone who denies this is a liar.

      • Robert A. Wilson Says:

        I hope to be able to provide a new paper with higher quality arguments shortly. There are just a few loose ends to tie up first.

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