Motif of Motives

It is said that Grothendieck, one of the greatest mathematicians of the 20th century, is now mad. A piece of evidence often cited in support of this hypothesis is his fixation with the speed of light, a mental exercise that might be recommended to many of the critics.

The arbitrary local numerical value of this quantity depends on the arbitrary old definition of the metre from Napolean’s time. After some international political wrangling, some French guys measured the meridian from Dunkerque to Barcelona in the years 1792 to 1798. If they had chosen a different geographical location the platinum metre bar would no doubt have come out slightly differently and maybe, with a little stretch of the imagination, we would not be plagued with awkward values for c today. As Einstein said in a lecture in 1921:

In order to complete the definition of time we may employ the principle of the constancy of the velocity of light in a vacuum.

With emphasis on the word may. The constancy of c was not to be taken as a fundamental consideration, but as a convenient means of defining clocks for observers in uniform motion. To assume that the constancy of c should suffice for quantum gravitational clocks is rather stupid. Fortunately people have considered alternatives. Louise Riofrio has some very pretty pictures and graphs which use a varying c to explain away the magical Dark Energy.

4 Responses so far »

  1. 1

    CarlBrannen said,

    “One story has it that Grothendieck is now convinced that the Devil is working to falsify the speed of light. Schneps ascribes his concerns with the speed of light to his anxiety about the methodological compromises physicists make. He talks constantly, however, about the Devil, semi-metaphorically, sitting behind good people and nudging them in the direction of compromise, of the fudge, of the move towards corruption. ‘Uncompromising’ is the expression Schneps favours.”

    I should probably admit that I believe in particles that travel faster than light.

    Another link:

  2. 2

    CarlBrannen said,

    Wow. That was quite a link. On the subject of the symmetry group of a point, look at the unification efforts of the 1960s in footnote #45. This really expresses the problem with assuming Poincare invariance. Yes, the devil is destroying the constancy of the speed of light. And it seems to be expressed as a QFT (i.e. point like) thingy rather than a string thingy.

  3. 3

    Kea said,

    Hi Carl

    Yes, that Cartier paper is a classic. Proposing particles that travel faster than light in a regime where no observations have yet been carried out shouldn’t be any problem at all!

  4. 4

    CarlBrannen said,

    Some papers I’ve kept around on the subject:

    But the best evidence is the centauros and the AGASA energy problem.

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