2 January 2011

Where to search?

If grand unification, supersymmetry, higher symmetries, higher dimensions, string theory and loop quantum gravity are dead alleys, where do we have to search for a theory of everything? Nobody knows. If nobody knows, what can be done? To think. Let me try. No prejudices means
  • There are 3 dimensions.
  • There are no points.
  • There are no other gauge groups.
What does this imply? I have no clue. The hardest problem seems to be the lack of other gauge groups. Where do gauge groups come from? Nobody knows. A few think that U(1), SU(2) an SU(3) come from the complex numbers, the quaternions and the octonions. But how? And why three dimensions?

9 comments:

  1. Why should we search for a TOE? For the sake of fame? Isn't it better to learn first to describe known things without conceptual and mathematical contradictions?

    Electrodynamics formulated in terms of field strengths E and B does not contain any gauge group. It is the "potential" formulation that has it. If your equation is written like F=0, you do not see any group. And if your equation is written like A-D=0, you have a freedom to increment A and D by the same value so there is a renormalization or gauge group, whatever. As soon as physical results do not depend on gauge, it is not physical matter but a question of convenience.

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  2. Gauge groups appear only in quantum mechanics. They do not appear in classical electrodynamics. But it is a fact that we need quantum physics to understand electrodynamics fully. And it is a fact that the three gauge groups U(1), SU(2) and SU(3) describe the three interactions.

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  3. A TOE is interesting to understand the origin of the number 1/!37.03599...

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  4. The number alpha does not come "alone". There some other dimensionless factors like ln(m/omega), for example, in the perturbation theory. And I am afraid we do not understand electrodynamics fully even with QED.

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  5. Indeed, as long as we do not understand the value and the running of alpha, we do not understand QED. Your questions was: Why a TOE? I just wanted to say: because of alpha.

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  6. OK, what kind of answer do you expect? For example, there is a dimensionless ratio of masses: M_e/M_p = 1/1836 or so. Something like this? Then alpha = v_0/c.

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  7. I have no idea! Who has? See my new post ...

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  8. I have a model, simplified but still realistic, where the coupling constant is the mass ratio between in a compound system. See http://arxiv.org/abs/0811.4416

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