# Is the speed of causality $c$ or $\frac{c}{\epsilon}$?

Is the speed of causality $c$ or $\frac{c}{\epsilon}$ where $c$ is the speed of light in vacuum and $\epsilon$ is the dielectric constant of the medium?

I searched the net but could not find a good and relevant answer. There was this but it did not address the main concern.

So, will an electron travelling at $0.99c$ in water, where the speed of light is actually $\frac{c}{1.33}$, violate causality?

It's always c. But in dielectrics the photons interact (scattering etc) with the media and sort of zigzag before going out (that's a simplistic way of saying all those interactions take extra time). So it seems they go slower. Anything that has fewer interactions will go faster, eg neutrinos.

Nothing will go faster than c. There is no causality issue.

• So the electron will not violate causality, but rather cause cherenkov radiation. Am I right? – SchrodingersCat Mar 12 '17 at 6:35
• @SchrodingersCat Yes. – Bob Bee Mar 12 '17 at 6:37

To add to Bob Bee's Answer: to understand this situation, it helps to divorce light from special relativity and take an Ignatowskian approach to the latter, as I discuss further here. There is a universal signal speed limit $c$, and, experimentally light is found to move at that speed, or at least the two speeds are mighty near one another. That latter, experimental, result can be taken as asserting that light is mediated by something with zero rest mass.

So now, anything else to do with light - speeds in media and so forth - is simply not relevant to the causality issue, which arises wholly from the relativity from symmetry alone standpoint conceived by Ignatowski. The issue with $c$ is that relative speeds greater than $c$ can reverse the time-ordering of events for different observers, which is a real problem for a notion of causality if the two events in question are causally related: such as my switching on my gas ring and sometime later eating the boiled eggs that I have cooked. So, we simply postulate no faster than $c$ travel to keep our notions of causality in accordance with what we observe.

• LThe universal speed limit c comes from Special Relativity (SR). It is from SR that one can understand causality issues that come from going faster, such as arriving before you left. There's a lot of evidence that c is the speed of light and massless particles. The speed of light in media is, in between interactions, exactly c. Any change of light speed, from c, would be an issue in causality, violate SR and quantum field theory. We don't postulate no faster than c, lots of evidence, both theoretical and experimental, for it. Postulating causality as c sounds like math, not physics – Bob Bee Mar 12 '17 at 21:29
• @BobBee of course; the OP's issue seems to be telling apart aspects of light that bear on relativity and those that don't. Your explanation of interaction delays between motion at $c$ is a good way to do that. I'm simply trying to complement that with the understanding that the causality issue can be discussed from a purely geometric formulation of SR, whence experimental light speed Lorentz invariance connects light to this formulation. Postulates to make theory in keeping with everyday observations and ... – WetSavannaAnimal Mar 13 '17 at 2:06
• .. which are then testable are the essence of the scientific method, no? – WetSavannaAnimal Mar 13 '17 at 2:06
• Understand your point. Thanks. Interesting point. We've measured speed of light, how would we measure speed of causality? Ie, how do we test the difference between the two? If it was faster than the speed of light how to measure it, we'd never observe anything happening faster, at least with light. It would mean that light speed is not Lorentz invariant, and we measured it is (to some accuracy). So I'm guessing that's then your experimental confirmation. Ok, cool. – Bob Bee Mar 13 '17 at 2:17