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heavybody
03-10-2003, 07:28 PM
I would guess most of you guys know what this equation is,my question is why is "squaring the speed of light"significant.Why does multiplying this number times itself matter ? Why isn't multiplying mass times the speed of light enough? After all light moves pretty fast all by itself. I do not understand the "squaring" part.

thank you
heavybody

MarkD
03-10-2003, 10:09 PM
Energy is measured in Joules (SI system).

Mass is meassured in Kilograms (SI system).

Speed is measured in meters per second (SI system).

Energy = force x distance = mass x acceleration x distance = mass x speed / time x distance

Therefore joules = kg * m/s * m / s = mass * velocity ^2

Josh W
03-13-2003, 07:27 AM
MarkD replied as to why it works out in terms of units, but that doesn't explain "where it comes from".

And you can't blame him. I mean, only one guy ever has derived that equation from nothing.

But the question is, why is it c^2? Why not (1/16)(c^2)? Why isn't there some other factor.

There are all kinds of physical energy out there....energy in magnetic fields, kinetic energy (the energy in moving objects), potential energy (an object that is up high has more potential energy than an energy that is low), potential differences (voltage), and "Mass Equivalent Energy".

This last energy (mass equivalent energy) is equal to the mass in question times the speed of light squared. And, this is difficult energy to comprehend, because we almost never ever ever see it.

If you were in Hiroshima or Nagasaki in 1945, you saw it. See, in a nuclear reaction, mass is converted directly into energy...all different forms of energy...some of it is light (that which we see), some of it is heat, some of it is soundwaves, and some of it is kinetic...that which creates incredible flying objects, like city blocks.

See, if you do the math, 1 gram (there are 28.5 grams in an ounce, for those not-so-metricly inclined) of mass as enough "mass equivalent energy" to light a 100 watt lightbulb for over 30,000 years...if the mass is converted straight into energy. Yeah, that's one gram. That's why nuclear energy is so highly sought after.

But I've cutely sidestepped your question.

See, in order to derive your equation, you need to deal with special relativity (or, even worse, general relativity). I won't go into too much more detail here, becuase it's very complicated, and writing equations in this text box is nearly impossible (it requires a lot of exponents in fractions inside of square-roots).

But let me give you an example of where this occurs. There are many subatomic particles (K mesons, for example) that are radioactive, and decay into two pi-mesons. If we look in the frame of the K-meson, it's still. But when it decays, these two pi-mesons shoot off in opposite directions...and they're really moving....they are moving at relativistically high speeds. However, it can be shown using special relativity that THE TOTAL MASS OF THE SYSTEM HAS DECREASED. Wow. It just disappeared.

But while that has decreased, the kinetic energy of the system has increased. That is, before the K-meson was stationary, and now we have two very fast particles. That energy came from the mass that was lost.

Kinetic energy is expressed as: KE = (0.5)(m)(v^2) where m is the mass and v is the velocity of the mass.

Now, the "mass equivalent energy" is the amount of energy created from the decrease in mass. This is equal to the total kinetic energy of the system.

Mass Equivalent Energy = 2 x (0.5)(m)(v^2 of the pi-mesons).
= 1 x m x v^2

So, like MarkD was saying, we need this Mass Equivalent Energy to have the same units as (mv^2). This is satisfied if we have the mass equivalent energy proportional to the speed of light squared.

I know that skirts your question still, and it would be easier if I could whip out some formulas for realitivistic mass and momentum, but that ain't easy.

As an interesting aside....because mass has an energy equivalence, energy likewise has a mass equivalency.

For example, the energy of light is known to be E = hv, where h is Planck's constant (a known constant) and v is the wavelength (related to the color) of the light. However, E = mc2 = hv, so m = hv/c2. Remember, v is the wavelength here, not the velocity (in physics, they use the greek letter nu, which looks like a slanted v). We know h, v, and c, so we can determine the 'mass equivalency' of a photon.

Now, this mass is very very small, getting photons shined on us feels nothing like getting rocks thrown at us, because of this. But one can do experiments where you set up a piece of foil in a vacuum (to reduce air resistance). If you shine light on this (say the foil is suspended from thread), you can make the foil move. That's converting energy into mass (sorta...it actually converts it into momentum, momentum into force, and it 'forces' the foil to move). Converting mass into energy is like blowing up cities.

I gotta get over this insomnia.

Josh