Monday, 22 July 2019

spacetime - How can the permittivity & permeability of the vacuum work as a viscosity term for the speed of light?


I've often read that the speed of light more about the speed of events than light specifically. I wonder if this implies that spacetime has some base viscosity, or mathematically similar mechanic.


To restate, I'm not really asking if there is a literal, physical viscosity. For a simulation, I am considering whether or not I can relate the cosmological constant to a viscosity property with some special treatment in a similar algorithm to what's used for handling refraction depending on type/density of materials.


The main goal is to get a pretty accurate speed of light as an emergent property rather than a hardcoded limit.



Answer




It is the permittivity and permeability of vacuum that determine the speed of light. Those two come from how strong an electric field is created by charge in vacuum and similarly a magnetic field. C is the inverse square root of those two multiplied. Nowadays those are considered simply part of defining the units one uses, with c more basic.


See in Wikipedia at https://en.m.wikipedia.org/wiki/Maxwell%27s_equations


In materials those are typically larger and the equivalent effective speed of light then goes down.


If ones of those were 0, or both, which makes no sense, infinite electric or magnetic fields would be induced in an electromagnetic wave and it would propagate infinitely fast, which of course makes no physical sense, only that's what Maxwells equations would lead to.


So in essence the speed of light is the best measure of how resistant the vacuum is to creating electromagnetic waves. Maybe this could represent your undefined viscosity, but it won't do anything to explain why c is what it is, and the fact that it is finite. It's that if it was infinite all effects in the universe would be instanataneous, there would be no localization.


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