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

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In summary, the equation E=mc^2 only applies for a theoretical particle at rest (p=0) and is only approximately satisfied in nature where everything is in motion. However, if "m" is relativistic mass, then "E" is the total energy of that particle and the equation E = m c^2 is exact. The speed of light is an exact value determined by two constants in Maxwell's equations, representing the dielectric constant and magnetic susceptability of empty space. This speed is independent of the speed of the source of the electromagnetic wave, providing the basis for Einstein's theory of relativity.
  • #1
ChemGuy
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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?
 
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  • #2
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.
 
  • #3
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.
 
  • #4
Jheriko said:
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. [itex] E = m c^2 [/itex] applies and is exact in that sense.
 
  • #5
rbj said:
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, [tex]m=m_0[/tex], as far as I know it is usually the context that the equation is used in.
 
  • #6
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"
 
  • #7
Darryl said:
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.
 
  • #8
selfAdjoint said:
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.

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

1. What is E in the equation E=mc^2?

E stands for energy in the equation E=mc^2. It represents the amount of energy that an object possesses due to its mass.

2. Does E always equal mc^2?

No, E only equals mc^2 in the special case when an object is at rest. In other situations, such as when an object is moving, the full equation is E^2=(mc^2)^2+(pc)^2, where p represents momentum.

3. What is the significance of the speed of light in the equation E=mc^2?

The speed of light, represented by c, is a fundamental constant in the universe. It is the maximum speed at which anything can travel and plays a crucial role in the relationship between mass and energy in the equation E=mc^2.

4. Is E=mc^2 the same as the law of conservation of energy?

No, while E=mc^2 does demonstrate the conversion of mass into energy, it is a specific equation derived from Einstein's theory of special relativity. The law of conservation of energy is a broader principle that states energy cannot be created or destroyed, only transformed from one form to another.

5. Can E=mc^2 be used to calculate the energy of anything?

Yes, E=mc^2 can be used to calculate the energy of any object or system, as long as the mass is known. This equation has been used in a wide range of fields, from nuclear energy to astrophysics, to calculate the energy released or required for certain processes.

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