I know E=mc^{2} essentially means energy = mass. One might think why not just say E = m? But I also know that: Every object travels through space and time at the speed of light. So now one might think why not just E=mc? That's essentially where I'm stuck at now. I'm not sure why it's necessary to ^{2} the c. I know that light waves only travel at right angles, but I don't know if that has any relevance to the formula.
That's nowhere close to true. For example, the planets in the solar system are moving much slower than that. Right angles to what? You might be thinking about the magnetic and electric fields.
Common misconception: Everything does not necessarily travel at the speed of light. Everything's proper velocity's magnitude is c (under only the influence of gravity? I think). E=mc^2 wasn't a guess. It was derived by a thought experiment of Einstein's and described in his paper "Does the Inertia of a Body Depend upon its Energy Content." There he found that with a discrepancy between the measurements of mass between multiple inertial reference frames is that the measured difference is E/c^2. In other words m=E/c^2 or E=mc^2.
Another thought I had that might help me understand this, what does Einstein mean by "energy"? Energy is defined different based on type (kinetic, potential, mechanical, electric, etcetera). I read his paper but he refers to it mostly in general. I see, so would it be more accurate to say: Every object travels through space and time with the velocity's magnitude of light?
Because one form of energy can be transformed into another and the total amount of energy is conserved, the specific form of energy doesn't make much difference. Indeed, it's often best to think of rest mass as just another form of energy - this thread may be helpful: www.physicsforums.com/showthread.php?t=720053 It is true that the magnitude of the four-velocity four-vector is always ##c##, but unless you are very clear on the underlying math, it's easy to be misled if you think of this as "traveling".
Particles do not travel in space-time. All we're doing is normalizing the 4-velocity of time-like particles by using proper time as the worldline parameter.
I suspect that the thread starter knows nothing about physical units. Which means that any attempt to teach him some special relativity will be waste of time.
Sorry for taking so long getting back to this thread. I wanted to do a lot more research and come back with more confidence. I'll discuss my current thoughts now. I think the reason mass is multiplied by the speed of light (as opposed to the speed of sound or some other variable) is because light in a vacuum is constant and so can give you precise reliable numbers to work with. I think the reason the speed of light is squared has to do with the nature of momentum: To move a given object twice as fast for example, wouldn't take twice the energy/work but rather 4 times, thrice as fast 9 times, etcetera.
You seem to be on the right track when you note that energy is quadratic in velocity and not linear. But there's another very useful way of approaching this problem that you seem to be missing. See, for instance dimensional analysis http://en.wikipedia.org/wiki/Dimensional_analysis. Then try visiting Google calculator, and typing in the expression kg * (meter per second)^2 =