prove e=mc^2

shivaniits

if possible could you tag some good video lectures may be feymann or any other good source..thanks...!!

Whovian

Prove? This is like asking someone to prove Quantum Mechanics. Mathematically, there are a ridiculous number of consistent theories, so all we can do is fail to disprove it.

mathman

http://en.wikipedia.org/wiki/Special_relativity
http://en.wikipedia.org/wiki/Mass%E2...gy_equivalence

Try either of the above.

shivaniits

are there any good feymann lectures on special theory of relativity or quantum mechanics...???
thanks!!

shivaniits

@mathman thanks i will try them!!

haael

In special relativity, time is just another dimension, just like spatial distance. The numerical value of the speed of light is a proportionality factor between time and length units. This identification causes a series of other identifications.

Speed becomes an angle between the time directions between two moving reference frames. This also nicely explains Lorentz transformations and relativistic speed composition.

Mass, momentum and energy are also identified. The proportionality factors between the standard units of these parameters are: momentum is mass times c and energy is mass times c squared. That's all.

Electric and magnetic potentials also undergo an unification into electromagnetic potential.

This is the basic idea of the special relativity. We live in a 4D space. Our common 3D physical properties turn out to be spatial or time-like components of 4-dimensional properties. Time and space are the same, but our standard unit system (say SI system) has different units for them. When we want to convert from time to space, we need to multiply the numerical value of the property by some proportionality factor, which is always some power of c, depending on the dimesionality of our property.

shivaniits

so can we say this conversion of E=mc^2 doesn't happen at all
because it what we perceive from different reference frames due to account of special relativity
and we can't say that
actually a some lump let say of m mass is vanishing(or more precisely should i say converting to energy)... doesn't really happen whatever we measure is due to special relativity effect!!

mathman

Utter nonsense! Pair production converts photons to electron-positron pairs. Nuclear fission or nuclear fusion convert mass to energy.

bcrowell

The OP is asking whether we can prove it from more fundamental principles that have been established experimentally. The answer is yes, and that's exactly what Einstein did in his 1905 paper "Does the inertia of a body depend upon its energy content?," http://www.fourmilab.ch/etexts/einstein/E_mc2/www/

haael

You speak about converting rest mass to kinetic energy. This is indeed a physical process.

OP was refering to total mass and total energy as I understand. These quantities never change for an isolated system and are always proportional to each other with a factor c^2.

bcrowell

The OP just asked about [itex]E=mc^2[/itex] in general. If the two sides of the equation were always simply defined as synonyms, then the equation would be vacuous. That's not what the equation expresses.

It's also not true that total mass is separately conserved. Mass isn't even additive. E.g., in Einstein's 1905 paper, the body that emitted the two light rays in opposite direction lost an amount of mass L/c². Each light ray has zero mass. The sum of the masses has been reduced by L/c². However, if you put the whole system, in its final state, inside a box, its inertia is the same as that of the original system, and unequal to the sum of the three masses.

What's conserved isn't mass or energy separately but mass-energy.

genericusrnme

E=mc^2 is most easily proven through an action principle imo. Check out Landau and Lifshitz second book, classical field theory (only the first few chapters)

haael

It is, in all known theories. In QM for example, it comes from Noether theorem and the trivial fact that Hamiltonian commutes with itself.

It is.

No, they don't. They have zero rest mass, but nonzero total mass. It is a great mistake to confuse those two different quantities.

You don't need a box for the inertia to be the same. The inertia (total mass) of the system will be equal to the sum of the total masses of each particle.

Total mass is conserved. Total energy is conserved and equal to the total mass with a factor c^2. Rest mass is not conserved. Kinetic energy is not conserved. Potential energy is not conserved. Rest mass (times c^2), kinetic energy and potential energy summed up together give total energy.

There are different physical quantities calles "mass" and "energy" and they are not the same despite they have similar names.

DrGreg

haael, it seems you are not aware of the convention used by almost all physicists nowadays that the term "mass" on its own is taken to mean "rest mass". The version of mass you are talking about is nowadays called "energy" (divided by c²).

Neandethal00

No, nuclear fission does not convert mass into energy.
It releases binding energy of a nucleus.

To me so far, E=mc² is a conversion factor.
Conversion of Kg into Joules.

haael

I am aware, and that is why I always give the proper adjective here (rest, kinetic, potential, total).

This jargon is very misleading, by the way. Many non-specialists in the world have hard time understanding what all this actually means.

DrStupid

Classical inertial mass as defined by p=m·a is additive, the rest mass is not and both are conserved in isolated systems. Conversion of mass into energy or vice versa would violate this conservation as well as the conservation of energy.