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?
Posted by Clara, once known as Nemo at 06:29

9 comments:

  1. Vladimir Kalitvianski2 January 2011 at 13:07

    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. Vladimir Kalitvianski2 January 2011 at 13:44

    What do you mean by "points"?

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  3. Clara, once known as Nemo2 January 2011 at 19:39

    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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  4. Clara, once known as Nemo2 January 2011 at 19:41

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

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  5. Vladimir Kalitvianski2 January 2011 at 20:36

    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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  6. Clara, once known as Nemo3 January 2011 at 12:20

    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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  7. Vladimir Kalitvianski3 January 2011 at 23:12

    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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  8. Clara, once known as Nemo4 January 2011 at 07:45

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

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  9. Vladimir Kalitvianski4 January 2011 at 11:29

    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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