Why is the speed of light what it is?

Question from Son: Why isn't the speed of light different from what it is? Why isn't it faster or slower?

Hmm... Good question.

First, let's get something straight. The "speed of light" almost invariably refers to the speed of light in a vacuum. The speed of light through glass is different from that through a vacuum, and it's different through water (et cetera, et cetera, et cetera). The speed of light is dependent on the medium through which it passes. In general, a vacuum is the medium we're speaking of when we talk about "the speed of light."

Then let's first talk about the speed of light in a vacuum. That speed is approximately 300,000,000 meters per second. Here's the NIST definition (by way of the definition of the meter):

The metre is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.

Okay. That's close enough to 300,000,000 m/s for right now.

But, WHY?

Some of the brightest minds in physics have been asking this question for as long as the speed of light has been known.

Paul Dirac had a theory called "Large numbers hypothesis", which noticed that some very large numbers in physics were similar in magnitude. There's no reasoning behind his theory besides arguing that because they're both very large and have a similar scale, they must be related. In particular, he argued that the strength of gravity decreases as the age of the universe increases. There's no observational evidence for this, and most physicists consider the LNH to be numerology rather than physics.

There has been some speculation that the mass of a photon (the particle that makes up light) is not zero. A massive photon could allow variability in the speed of light; the speed of light would vary depending on its wavelength (color). Some studies have reported that the rest mass of a real photon is less than 10^-63 kg. That's pretty close to massless.

Again, this doesn't seem to answer the questions: Is the speed of light constant and why does the speed of light have the value it has.

First, a rest mass of zero does limit the speed of light to being constant, in our current paradigm. In the well-tested theory of Relativity, the speed of light is required to be constant.0

Second, a massless photon does not tell us WHY the value of c is 300,000,000 m/s, just that the speed doesn't vary.

So, WHY is it 300,000,000 m/s? Well, for one, because that's how a meter is defined. ;)

That's a lame answer, but it might help to understand that maybe we should move to a more fundamental unit. (here's a hint: Unfortunately, at some point in this discussion, we may just throw up our hands and say, "because that's the way it is and we don't know why, yet.")

According to quantum physics, there's a smallest size anything can be. This size is called the planck length and is about 1.6x10^-35 meters or about 10^20 times as small as the diameter of a proton. Quantum physics claims that there is nothing that is smaller.

There is another fundamental unit called the planck time, which is the time it takes for a photon traveling at the speed of light to travel the distance of the planck length. This is about 10^-43 seconds. There is no smaller unit of time. Now, if you pay attention to the units here (time and length), you'll notice that the speed of light (length/time) is fundamental to the definition of space-time (length and time). That is, the maximum rate at which information can travel (speed of light) through a medium is fundamentally dependent on the minimum size of the medium through which it is traveling (space-time).

So, why 299,792,458 m/s ?

Well, because our every-day units are in no way directly related to the quantum size of the universe. They need to be something we can understand in our day-to-day lives.