Lightspeed as a curvature scalar

Why c (the speed of light) is the value that it is (~3x10^8 m/s) is
sort of a non-question because we would ask the same regardless of its
value. It's just a universal parameter. But some generalization
opens up the possibility that it may be a scalar artefact of the
curvature of space, and that different curvatures may feature
different values of c.

Standard cosmology models that the space manifold is flat. Given that
spherical and hyperbolic manifolds are self-consistent, it seems most
remarkable that space should be flat, i.e., that the degree of
curvature should be precisely zero (neglecting perturbations). My
idea is that there is an observer component to this, that any observer
perceives his own space to be flat. I think all will agree that in
the presence of (say) a large black hole, any observer falling through
the event horizon will still see his local space to be flat.

So my notion is that our perception of the flatness of the universe is
because we see our local space to be flat because of the same
observer-dependent dynamic that exists in quantum physics. and
currently we assume this flatness, i.e., particular value of
curvature, to perpetuate wherever we look.

Next, a point about hyperbolic space of which not all are acutely
aware, and that is that in hyperbolic space distant things are closer
than in flat space. This is because the shells of space are larger
than 4*pi*R^2, and are in fact arbitrarily large depending on how
hyperbolic the space is. Thus light dissipates accordingly and
everything looks the same but when you travel there it turns out to be
closer than in flat space, so you get there faster. It is as though
the speed of light was faster.

Given this, it could then be extrapolated to the first moment of the
universe when we can posit that the universe was almost infinitely
hyperbolic with everything everywhere at once. Thus so-called
"inflation" was simply a consequence of the hyper-hyperbolic space
allowing quick action over a vast volume. As the universe grew its
curvature lessened and so did c. Thus today's value of c is just
where we are now as the universal manifold continues to trend more
spherical as the universe grows. I don't necessarily believe this
model to be true, but it seems a reasonable mechanism by which the
Standard model can work without any need for the "magic" of inflation.


Thus by this view, light speed and the curvature of space are
intimately connected -- light speed is simply a scalar expression of
the curvature of space.

20 years ago I put forth the proposition that the Copenhagen
interpretation of physics should be embraced in an extreme way, where
the observer is fundamentally linked to physical law. This -- that
any observer sees his own local space as flat -- is an example
consequence. And I'll stop there, cheers.

It's worth mentioning as a postscript to the OP, that universal
expansion may not be necessary if spatial curvature is simply decaying
with time, as follows.

Model a universe bounded by an N-dimensional sphere of constant
radius. At t=0. its internal spatial curvature is C(0) which is some
high enough value that the universe is essentially contiguous
everywhere, i.e. maximum distance is arbitrarily close to zero.

In this model, spatial curvature decays with time using the standard
exponential decay function C(t) = C(0)*e^(-kt). Lightspeed (c)
consequently decreases in tandem with the spatial curvature as
outlined in the OP.

This model thus provides a mechanism both for inflation (the very high
spatial curvature in early times which solves the flatness problem)
and redshift (as e.g., light at z=1 hails from a time when c was twice
the speed, and so the slowed light is naturally redshifted).

So it's a simple model. Possibly there's not even a singularity. As
for reverberations, no I don't see where those would come from. Ugly
facts can be such a nuisance...

cheers,
Eric Flesch