# Can the Speed of Light be derived?

1. Feb 23, 2012

### friend

Einstein postulated that the speed of light is the same for all observers. But it seems that this speed limit applies to more than just photons. It also applies to any massless particle. So I have to wonder if there is some way of deriving the speed of light from more general principles that applies to all massless particles. For example, could more general principles hide a maximum speed of information? Any thoughts are welcome.

2. Feb 23, 2012

### Khashishi

It doesn't make much sense to derive a non-dimensionless constant. We _define_ the value of the speed of light. We don't derive it. Historically, it made sense to derive it, because we had a conventional standard for the meter. But we abandoned that standard and just define the meter based on the speed of light.

3. Feb 23, 2012

### friend

Yes, I'm sure a derivation would be in terms of other dimensionful constants like h-bar, charge of the electron, etc. So my question is whether there is some means of deriving the speed of light within the formulism that does contain other dimensionful constants.

PS. I'm not sure this thread belongs to SR&GR forum since the speed of light is assumed constant there in ALL there calculations. It seems actually deriving "c" would require a much broader theory that includes SR and GR and so would be beyond the standard model.

4. Feb 23, 2012

### elfmotat

Well, historically Maxwell used his newly-corrected Ampere law to get an electromagnetic wave equation. When solving this equation, he found that EM waves travel at a speed given by:

$v=\frac{1}{\sqrt{\mu_0 \epsilon _0}}$

, where μ0 and ε0 are the magnetic and electric constants. When he calculated this value, he found that it was the same speed that light was known to travel at, suggesting that light consisted of EM waves.

5. Feb 23, 2012

### bcrowell

Staff Emeritus
Starting from certain symmetry principles, it is possible to prove that there is a universal speed which also acts as a speed limit: http://www.lightandmatter.com/html_books/0sn/ch07/ch07.html [Broken]

Last edited by a moderator: May 5, 2017
6. Feb 23, 2012

### lugita15

But even Newton would have accepted the existence of a universal speed limit, he just thought its value would be infinite in all inertial reference frames.

Last edited by a moderator: May 5, 2017
7. Feb 23, 2012

### bcrowell

Staff Emeritus
Yes, you can consider Galilean/Newtonian spacetime as the limit of Einstein's spacetime as $c\rightarrow\infty$.

8. Feb 24, 2012

### friend

It would help if you could give a reference to where to find these "symmetry principles" in the long article that you link to.

Last edited by a moderator: May 5, 2017
9. Feb 24, 2012

### bcrowell

Staff Emeritus
7.2.1

10. Feb 26, 2012

### friend

Correct me if I'm wrong, but as I understand it, μ0 and ε0 are entities of the EM field only. This does not leave much room for confidence that other fields would propagate at a maximum speed of light.