# Speed of light

1. Feb 15, 2004

### piercas

Where does the speed of light (~300000km/sec in vacuum) come from
Is this the rotational speed of an electron. Up to Einstein a photon has no mass once it is in movement.
Is the absence of mass the reason why speed of light cannot be modified ?

2. Feb 15, 2004

### Integral

Staff Emeritus
From Maxwell's equations we have :

$$c = \sqrt { \frac 1 {\mu_0 \epsilon_0}}$$

Where
The permeability of free space is
$$\mu_0 = 1.26 x 10^{-6} \frac H m$$
and the permittivity of free space is
$$\epsilon_0 = 8.85x10^{-12} \frac F m$$

These 2 constants are fundamental properties of space.

3. Feb 15, 2004

### FUNKER

What do you mean by "the fundamental properties"?

4. Feb 15, 2004

### piercas

I know speed of light can be slowed down (ex.water) but what is the origin of that 300000km/sec and why lightspeed is constant. Is there a physical reason for that

5. Feb 15, 2004

### chroot

Staff Emeritus
The speed of light is arbitrary. Why? Because the units we use to measure it are arbitrary.

It is 300,000 km/sec simply because of the way we defined the kilometer and the second.

We can make c equal to any number we like, if we select appropriate units. If we choose to work in units of years and light-years, for example, c is 1. Many people use this convention to simplify their calculations.

- Warren

6. Feb 15, 2004

### GRQC

Just a personal opinion, but I think "simplifying calculations" short-chanegs the notion of natural units. They actually make the physical theory geometrically intiutive and elegant, which hints at a deeper mechanism which is at work.

7. Feb 15, 2004

### Chi Meson

The speed of light is not really slowed down in water. It takes more time for light to get through water (and all other transparent objects) due to the fact that the photons are forced to interact with the atoms and molecules of the substance. Light still travels at the same "c" in the space between each atom.

One way to think about what the limit is due to has to do with the aforementioned permeability and permittivity constants:

$${\epsilon_0}$$ and $${\mu_0}$$

The first is a property of space that indicates "the ability for an electric field line to establish itself across a vacuum." THe second is the same thing for a magnetic field line. SInce light is electomagnetic in nature, then the limitations for the electric and magnetic fields must determine the limitation of the speed of light.

NOte: this description is ultimately flawed in its simplicity, but hey, if it could be explained in one paragraph, what's college for?

Last edited: Feb 15, 2004
8. Feb 15, 2004

### Integral

Staff Emeritus
It means that those values are experimental in the case of the permittivity and geometrical for the permeability. These 2 constants define how electromagnetic fields interact in free space.

In 1867 Maxwell cast his system of equations into the form of the wave equation. The constant I posted above was the theoretical speed of the waves predicted by this formulation.

It was this prediction that set the world of Physics on its ear for the next half century. Up to that point all velocities were believed to obey the Galilean transforms, that is, the velocity of a body always depended upon the velocity of the source. Here was the velocity of electro magnetic waves which appeared, according to Maxwell, to be independent of ANY motion, it was simply determined by the fundamental properties of space itself. This came to be known as Maxwell Conundrum, many waited for Maxwell to find his error. Others, famously, Michelson and Morley, set out to prove Maxwell wrong, experimentally. Instead of proving him wrong, they conducted the most famous "experiment that failed" and verified experimentally that the speed of light was independent of the earths velocity.

If you are concerned why c has the number 3 x 108 m/s, then look at Chroots answer. If you are concerned with why it is constant then you must start by understanding Maxwell's equations, and the Partial Differential Equation called the Wave equation. If that still does not satisfy you, and you still want to know why, we must answer that we do not know why. Physics does not address why, we can only model what is.

Last edited: Feb 15, 2004
9. Feb 15, 2004

### Vodka

i agree that the units are arbitrary [my favorate is the pascal ^_^], but that doesn't mean the speed of light is arbitrary. defining the speed would be arbitrary, but it doesn't travel any faster or slower [in the same medium] depending on the units used.

or, like the tshirt goes : ~3.00x10^8ms^-1 : its not just a good idea, its the law :)