Two questions about Special Relativity

[49ers2013Champ]

1) Why is the velocity of light called "c"? Okay, before you answer this, I am fully aware that the scientific community doesn't like questions that start with "why", but I just do not understand why it's not "v" or "q" or any other random letter. I've learned how precise scientists are with everything so there must be a reason why the velocity of light is represented by the letter "c" and not some other letter.

2) Why--again, I know Donis or Wannabe or Spam won't like this word, but I honestly can't think of the right word to use--is it that, mathematically speaking, the velocity of light must be squared and then mulitplied by the mass to derive the energy content of something? I mean, if the equation read E=MC, that would completely throw it all off, right? But what is about the squaring that makes things so much different?

If all this has been explained in another thread, please post a link. Otherwise, I look forward to your answers.

 

[jtbell]

For question 1, see http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/c.html

This is the first hit in a Google search on "why is the speed of light called c"

 

[49ers2013Champ]

Thanks, JT.

I thought about googling it, but I trust the people here more than I do google. That link is a little confusing. The "constant" word makes sense--light is the same speed in all frames--but celeritas (Latin for speed, according to the article) didn't make as much sense. What do most US scientists consider the letter c to represent, constant or celeritas?

 

[king vitamin]

2) Why--again, I know Donis or Wannabe or Spam won't like this word, but I honestly can't think of the right word to use--is it that, mathematically speaking, the velocity of light must be squared and then mulitplied by the mass to derive the energy content of something? I mean, if the equation read E=MC, that would completely throw it all off, right? But what is about the squaring that makes things so much different?

If all this has been explained in another thread, please post a link. Otherwise, I look forward to your answers.

Well the units in E = mc don't make any sense. In any case, the real content to E = mc^2 is the fact that relativity implies a massive body at rest contains energy proportional to mass. Since E/m has units of velocity squared, really the only dimensionfull proportionality constant one could have for an object at zero velocity in relativity theory is c^2.

The real question is, why is it E = mc^2 rather than E = (1/2)mc^2 or some other constant in front? You really need to work out the math to find that the constant is exactly 1.

(note: I assume everywhere that m is defined as the rest mass)

 

[PeterDonis]

Why...is it that, mathematically speaking, the velocity of light must be squared and then mulitplied by the mass to derive the energy content of something?

Because all $E = mc^2$ is really telling you is how to convert from mass units to energy units. It's not really telling you anything about physics, just about the units we use. We normally use different units for mass and energy because of historical accident: we assigned units to mass and energy long before we realized that they were really just different forms of the same thing.