Is E=mc^2 an Exact Equation or an Approximation?

[ChemGuy]

I thought I read something that said is was only a close approximation. If you did the full treatment you had to make a couple of assumptions to get it to that form. Does anyone know if that is correct?

 

[Los Bobos]

You don't have to make any assumptions to get the relativistic equation
E^2 + (pc)^2 = (mc^2)^2, which comes straightforwardly from the length of the momentum four-vector, but if you want to get the classical limit (low speed), you naturally end up with a Taylor expansion and by cutting it from second order you end up with E = mc^2 + 1/2mv^2.

 

[Jheriko]

The equation E=mc^2 only applies for a theoretical particle at rest (p=0) so although the relation is precise for a theoretical object, it is only approximately satisfied in nature where everything is in motion.

 

[rbj]

The equation E=mc^2 only applies for a theoretical particle at rest (p=0) so although the relation is precise for a theoretical object, it is only approximately satisfied in nature where everything is in motion.

that is not entirely correct. it depends on what you mean by "m". if "m" is relativistic mass, or the mass of a particle as observed in any inertial reference frame, then "E" is the total energy of that particle (interpreted as the sum of rest energy or "invariant energy" which would be zero for so-called "massless particles" and kinetic energy) as observed in the same inertial frame or reference. $E = m c^2$ applies and is exact in that sense.

 

[Jheriko]

or the mass of a particle as observed in any inertial reference frame, then "E" is the total energy of that particle

Aren't inertial reference frames only approximate constructs too? i.e. doesn't GR say something like "inertial frames only exist in the limit of the very small"?

I did make a bit of a mistake assuming that, $$m=m_0$$, as far as I know it is usually the context that the equation is used in.

 

[Darryl]

i have some questions about those values, e, m, c. hopefully they are not too silly. (but you never know with me !).

the speed of light, whwhy is it the value it is, i guess it has to be some value, but why the value that it is ??

i have read in these forums, (somewehre) that within maxwels equations there are 2 constants that allow you to calculate the speed of light..

q. do any of these two constants required prior knowledge of the speed of light to derive ?

or does maxwell equations independently derive the speed of light ?

either way, does the measured speed of light exactly equal the calculated speed of light from maxwell ??

if a photon traveling at the speed of light (otherwise its not a photon!), experiences ZERO TIME, and ZERO DISTANCE. its existence is "emitted" "no time or space passes" this is absorbed.

to me if a photon experiences NO TIME or SPACE, until it interacts with an electron.
i also read when a photon hits an orbiting electron is sent the electron into a higher energy state.

Is it true, that while the electron is in the higher energy state, and atom has more MASS ?

does this increase in mass agree with E = MC2 ??

so can you derive the speed of light, and does it agree with what we measure (what error, and why). ?

can a photon be looked at as a particle with a 0 (zero time) half life, so the instant it experiences time, or space, its decays into electron mass ?
(by e=mc2)

if the photon experiences "NO TIME" how is it possible for IT to travel at a fixed speed, a photon does not know about motion, so what is driving photons to move, (or exist).

could it be that a vast number of photones are created, but its ONLY the ones traveling at 300,000 k/s that exist, all the rest (below the speed of light decay immediately). ??

mabey its not "all photons travel at 300,000 ks" but "all photons that are detectable or that don't decay in an instant are traveling at 300,000ks"

 

[selfAdjoint]

have read in these forums, (somewehre) that within maxwels equations there are 2 constants that allow you to calculate the speed of light..

q. do any of these two constants required prior knowledge of the speed of light to derive ?

or does maxwell equations independently derive the speed of light ?

Yes, Maxwell's equations can be transformed to give the wave equation for an electromagnetic distrubance. In that equation, a constant represents the speed that the disturbance travels at. And this constant is just the quotient of two numbers from the original equations, representing the dielectric constant of empty space and the magnetic susceptability of empty space. So these two numbers, which have no obvious connection to speed, determine the speed of electromagnetic waves though space. And of course light is such a wave, in Maxwell's. When you measure these two constants and divide one value by the other, whatt do you get? Ta DA! you get c! ~300,00 km/sec.

Note that these numbers do not ever depend on the speed of the SOURCE of that electromagnetic wave; this gave Einstein his first clue: Maxwell's theory says the speed of light is independent of the speed of its source. Put that together with Galilean relativity, and you have the basis of Einstein's 1905 paper on the Electrodynamics of moving bodies.

 

[tehno]

So these two numbers, which have no obvious connection to speed, determine the speed of electromagnetic waves though space. And of course light is such a wave, in Maxwell's. When you measure these two constants and divide one value by the other, whatt do you get? Ta DA! you get c! ~300,00 km/sec.

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You can take permability of vacuum is:$$\mu_0=4\pi 10^{-7} N/A^2$$ is an exact value (set per definition).