# Why does light travel so fast

Gold Member
Thanks!

Amen

Rap
Well, I've been thinking about this. There are a bunch of dimensionless constants of the universe, like, for example, the fine structure constant &alpha; which has to do with the electromagnetic force, and involves the charge and mass of an electron. Another one is the gravitational coupling constant &alpha;<sub>G</sub> which has to do with the gravitational force, and involves the mass of an electron and the gravitational constant. I guess there are others, having to do with the other forces, weak, strong, etc. I always thought that if you had another universe where all the dimensionless constants were the same, you would not be able to detect that you were in a "different" universe. In other words, all the lengths, times, masses, etc. might be "different", but if you used the same procedures to define units of length, time, mass, etc., the numerical value of the fundamental constants (speed of light, Planck constant, mass of electron, electron charge, vacuum permittivity, gravitational constant, etc.) would all be the same. If they were not, you would be detecting that you were in a "different" universe.

But I can't get it to work. If you take three fundamental constants, electron mass (m), Planck constant (h) and speed of light (c), you can form a fundamental mass (m), a fundamental length (L=h/mc) which is the Compton wavelength, and a fundamental time (T=h/mc^2) which is 1 over the Compton frequency. If you go to a new universe, where the speed of light is c' (as measured by our present universe meter sticks and clocks) but all the dimensionless constants remain the same, then some or all of the fundamental constants will have to change their values in order to keep the dimensionless constants the same. That means that the Compton wavelength may change by some unknown factor due to the change in the speed of light, and the possible corresponding changes in the Planck constant and the mass of the electron required to keep the dimensionless constants the same. Suppose the values of h and m in the new universe are h' and m' as measured by our clocks and meter sticks. Then the new Compton wavelength will be L'=h'/m'c' and the new Compton time will be T'=h'/m'c'^2. The new speed of light will be measured as L'/T'=c', not c!. For example, if, in the new universe, the speed of light were cut in half, and h and m remained the same, and the dimensionless constants were kept constant by changing the vacuum permittivity and the gravitational constants, then all lengths would double in the new universe, but all times would quadruple. A meter stick would be twice as long, but a clock would click 4 times more slowly, and the numerical value of c would be half of what it is in our universe. It appears that the speed of light is something that must have its particular value in order for the universe to be what it is, and it is a valid question to ask why it has the value it does. Either that or I missed something...

PhanthomJay
Homework Helper
Gold Member
It appears that the speed of light is something that must have its particular value in order for the universe to be what it is, and it is a valid question to ask why it has the value it does. Either that or I missed something...
Thanks for the response! The most popular responses to the question regarding why the speed of light is what it is are:
1.) "It just is", and
2.) "Its the way we define the meter and second"

Neither one of these satisfies me.....I think it's got something to do with Feynman's sum of histories...but what do I know about the quantum world....and If I read Hawking correctly, he's on his knees worshipping Gravity................:surprised

Thanks again.

Rap
Number 1 is not very satisfying and 2 is wrong. My wrong (I think) idea was that if the speed of light changed, but every dimensionless constant stayed the same, you would not be able to tell that anything had changed, because other things would have to change to keep the dimensionless constants the same, and the dimensionless constants are what determines the physics of the universe. The meter stick would change, the second would change, and the numerical value of the speed of light in meters/sec would come out the same.

Rap
I think I figured out where my argument went wrong: c' is the speed of light in the other universe as measured by us, not by them. So cancel that whole argument. I go back to my original argument. It makes no sense to ask how fast is light any more than it makes sense to ask how long is a meter, or how long is a second. The minute you answer that question, you have made reference to some other velocity, length, or time. So what you are really asking is why is that ratio what it is.