# What is this equation?

1. May 2, 2010

### thecow99

$$c = \frac{1}{\sqrt{\varepsilon \mu}}$$

I'm not familiar with all the symbols. I was looking into why the speed of light is "c". Why not faster or slower? What are the determining factors behind it's value?

2. May 2, 2010

### bcrowell

Staff Emeritus
http://en.wikipedia.org/wiki/Vacuum_permittivity

http://en.wikipedia.org/wiki/Vacuum_permeability

The speed of light has a defined value, because the meter is defined as the distance light travels in a certain time. http://en.wikipedia.org/wiki/Speed_of_light#Numerical_value.2C_notation_and_units

FAQ: Is the c in relativity the speed of light?

Not really. The modern way of looking at this is that c is the maximum speed of cause and effect. Einstein originally worked out special relativity from a set of postulates that assumed a constant speed of light, but from a modern point of view that isn't the most logical foundation, because light is just one particular classical field -- it just happened to be the only classical field theory that was known at the time. For derivations of the Lorentz transformation that don't take a constant c as a postulate, see, e.g., Morin or Rindler.

One way of seeing that it's not fundamentally right to think of relativity's c as the speed of light is that we don't even know for sure that light travels at c. We used to think that neutrinos traveled at c, but then we found out that they had nonvanishing rest masses, so they must travel at less than c. The same could happen with the photon; see Lakes (1998).

Morin, Introduction to Classical Mechanics, Cambridge, 1st ed., 2008

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51

R.S. Lakes, "Experimental limits on the photon mass and cosmic magnetic vector potential", Physical Review Letters 80 (1998) 1826, http://silver.neep.wisc.edu/~lakes/mu.html

3. May 3, 2010

### jeppetrost

That is the value of the speed of an electromagnetic wave (light) predicted by Maxwell's equations.