# Light Speed Question

1. Jul 24, 2013

### jacassidy2

Hey folks, My first post. I'm a retired guy who liked physics in college, but couldn't quite get my head around calculus, so I was never able to confirm the things I learned through mathematical equations. I read primary lit., but I don't have the math skills to understand it. Physics became a lifelong avocation - I love cosmology and quantum mechanics and the internet opens doors to learning. As physics becomes more complex, further away from direct sensory perception, our ability to create understandable and recognizable metaphors (tools for the masses like me who don't have the math skills) becomes almost impossible. I hope this sight can be my savior.

I do have a more complete academic background in metaphysics and epistimology. I find myself looking at recent physics discoveries and using the laws of identity and causality to explore basic assumptions. So here's one.

I'm not asking why light speed is the limit - I understand the law of causality, can't see it before it occurs. I want to know why it isn't a little more or a little less - what truth gives light it's specific speed? It must have something to do with the nature of waves or the environment through which they travel. Einstein's equation, E=MC2, implies that the answer lies in the square root of the inverse relationship between matter and energy. But the result of an equation is not always "THE" answer. (Many current scientists just took a quick deep breath.) Mathematics is the science of measurement, and measurement is not an entity in the universe. Mathematics is a system to confirm aspects of entities -that is, measurement works with the law of identity.

Am I correct that gravitation (space-time curvature) can effect the path of the wave, but not the absolute speed? The answer to this last question will guide my subsequent questions.
TXS, Jack

2. Jul 24, 2013

### Staff: Mentor

You can calculate the speed of light in a vacuum from Maxwell's equations of electrodynamics, discovered in the middle of the nineteenth century. The argument for the speed of a light as a limit comes from requiring that the laws of physics (including Maxwell's) are not affected by motion at a constant speed. To understand more, you You could do worse than read Einstein's 1905 paper "On the electrodynamics of moving bodies" as a starting point. It's easy to find online via Ggoogle.

"Absolute speed" has no generally accepted meaning. You might want to google around for "spacetime interval", "proper time", and "Minkowski", but you really want to get these concepts down cold in flat spacetime using Special Relativity before you move into the effects of curvature.

3. Jul 25, 2013

### tom.stoer

The basic idea is the following: all field equations describing wave propagation for fields without mass term (Maxwell, Yang-Mills, Dirac, Klein-Gordon, linearized GR for gravitational waves) must have a certain property for their differential operator called hyperbolicity. The simplest example is an operator

$c^2 \partial_0^2 - \nabla^2$

Non-hyperbolicity means that we are not really talking about a wave equation (but e.g. about diffusion) or that we do not have something like 3-dim. space and 1-dim. time (but e.g. 4 space dimensions and no time at all). An example for a non-hyperbolic differential operator would be to replace the "-" with a "+".

b/c all above mentioned wave equations should respect (local) Lorentz invariance there must be one universal constant called c which applies to all these theories (and that's why the "speed of light" is missleading b/c it does not explain why gravitational waves propagate with the same speed). So having different constants c, c', ... in wave equations for different fields means that all theories with c' ≠ c (where c is the constant in the Lorentz transformation) necessarily violate Lorentz invariance.