I personally don’t really see the big deal about VSL. Even in general relativity, since one is dealing with Lorentzian manifolds, it seems pretty clear to me that the speed of light should vary from point to point depending on variations in the metric. (I think I agree with Matti here.)

It is only in flat (3,1) space ie Minkowski space, in the complete absence of matter, that the speed of light should be constant (or in places where the stress energy tensor is close to negligible, like the solar system in which we live). Or am I being just hopelessly naive?

]]>* The wording of Ellis’s points betrays some further prejudices about the mathematics being used in VSL investigations. For example, the whole set of physical equations is far too restrictive a notion for a category theorist. Causality takes us beyond the realm of mere set theory, as we have seen.*

I almost agree. If one however takes light-like 3-surfaces as fundamental objects, one obtains almost topological QFT and S-matrix as timelike entanglement coefficients defining a functor from the category of Feynman cobordisms (see my blog) to the category of operators between Hilbert spaces of positive and negative energy Hilbert spaces. Lightlikeness brings in the notion of length measurement and makes the theory physically interesting.

S-matrix need not be unitary and

unless one has HFF of type II_11 one obtains by functor property S-matrix which is thermal S-matrix. Center of mass degrees of freedom bring unavoidably in factor of type I so that one cannot avoid thermodynamics for normalizable zero energy states.

This is very nice result since thermodynamics becomes part of quantum theory rather than being a mere practical fiction of theorist. Already the possibility to assign temperature to blackholes and p-adic mass calculations suggest this possibility as also the findings about states for hyper-finite factors of type III.

S-matrices and quantum states are parametrized by complex number whose real part has interpretation as duration of experiment and imaginary part as inverse temperature. By the functor property S-matrices and thus also quantum states allow product decomposition analogous to group multiplication.

]]>I mentioned already earlier that

in many-sheeted space-time one indeed obtains different times for the propagation of photons along different space-time sheets from point A to point B because the distance is different in the induced metric for different seets. This picture is consistent with metric view about gravitation.

I agree with Carl about how dangerous it is to put hbar=1;-).

]]>“Important physics has never worked like that. Quite on the contrary. Every new major revolution in physics has shown that a certain conversion parameter was not only constant but it was meaningful to set it equal to one.”

Ah, strong induction, surely an important foundation stone of string theory.

But this sort of reasoning is considered garbage in mathematics.

]]>I wonder how the geometric algebra people over at Cambridge would answer this first point.

As you are aware, I’m convinced that I have a VSL theory where all known particles (and photons) are made up of preons that travel at a fixed speed that is approximately c\sqrt(3) in a typical astronomical reference system (i.e. the sun or earth or milky way).

So I can use the preons to define distance. Difficulties in observing them are an experimental issue, not a theoretical problem.

I agree that the rest of his points have to be addressed. And that’s why I’ve been working fairly hard (for me) on Painleve metric stuff. I’ve got the 4th order R-K numerical differentiation stuff running and it is on the web at GravitySimulation.com

One point that is missing, interestingly, is the question of what happens to the equivalence principle. I’m convinced that there is a maximum possible gravitational (i.e. not cosmological) redshift.

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