Recent content by victorvmotti

Answer provided by Ted Shifrin: You don't push forward forms, of course. Here's the idea: Cover ##M## by open sets ##U_\alpha## over which the frame bundle ##P## is trivial, and let ##s_\alpha\colon U_\alpha\to P## be sections for all ##\alpha##. Define the projection ##\psi_\alpha\colon...

I am following [this YouTube lecture by Schuller][1] where he finds the appropriate formalism for the quantum mechanics in the physical curved space. Everything makes sense to me but at the very end I see that we find the pull backed connection one-form on the base manifold. He says to the end...

So back again to your point earlier. It is impossible, logically, to know if the speed of light was different in the past or not!

Actually, I meant that the Standard Model of cosmology and its metric to be used, only that we pick a specific definition for the scale factor as suggested.

Consider the FLRW metric. We pick a specific definition for the scale factor as suggested bellow. Suppose we have a hypothetical metric having the scale factor defined by ## a(t)=\sin(t) (1+ \text {sgn}(\sin(t)) +\epsilon ## Does this make sense, mathematically (and physically)? Like having...

Yes, that is what I was looking for. More precisely, do you mean by the entire concept of spacetime not be valid that a continuous smooth (differentiable) 4D manifold does not make sense and spacetime, or the metric field, has to be discrete?

After reading the responses here and elsewhere, and noting the repeated emphasis on the fine structure constant by the Physics Forums community mentors, I'd say we can measure it in the past indirectly. So, assuming that other dimensionful constants involved in this particular ratio known as...

Now fully clear, if in the present the speed of light is one light-second per second then in the past it was again one light-second per second. No different!

So you use the "present" speed of light in the present to compute a distance and then compute the speed of light, having used the speed of light, by canceling out the time! Isn't this meaningless? Also, where did you compare with the past, when the same distance could have been travelled in...

I cannot follow, how about showing/writing the calculation you are doing so that I see what is cancelling out?

I believe that I get it now. So speed of light is actually a strcutural constant of the spacetime geometry. And the unit of measurement of distance, meter, is actually defined using this constant which relates time to space. So logically it does not make sense to say if the speed of light was...

So you are saying that we do not need a test, and it can be shown logically, but how, that is the question, any hint, still not clear, why it is logically impossible to say that the speed of light was either smaller or larger in the past than the current measurment?

The constancy of the speed of light is a fundamental principle in modern physics, and it is supported by a wide range of current experimental evidence. There is no evidence to suggest that the speed of light was different in the past, and the idea that it could have been different is at odds...

Still a little confused here that a cut off time is not needed. So suppose we go much further back than last scattering. With very high energies and fluctuations of the quantum field, we could have very high or powerful gravitational waves, right? That means fluctuations of spacetime itself will...

It looks like I have the answer myself. Given this definition of ##w## dimension it is not actually an extra dimension. Instead it is some scaled time dimension and drops from the five dimensional metric that I was looking for.