How do u derive E=mc^2 ?

Question

if it involves experiments/observations pls explain

and how does it come from special relativity?

Answer 1

This site does a decent job.

http://www.karlscalculus.org/einstein.html

It's pretty easy once you realize you need the Lorentz invariance, gamma= 1/sqrt(1-v^2/c^2).
After you get that it's plug and chug. The Lorentz invariance isn't derived here but if you'd like to know where that came from let me know, it's simple and straight forward.

Answer 2

I once had a homework problem where I had to use the Lorentz Transformation equations to derive E = mc^2.

However, I don't think this came from his work with Special Relativity. I think this was a result of his work with the Photoelectric effect that started him down this road. The idea that the energy of a particle is tied to it's mass is long standing.

It was other people's experiments that measured the energy created or consumed when a particle became energy or vice versa. None of the stuff I read tells how he jumped to the conclusion that the coefficient of proportion that relates the mass and the energy just happens to be the square of the speed of light.

However, continued experiments bear out the accuracy of his supposition.

Answer 3

I'm quoting the very easy and best source here. You should get a primer on how E=Mc^2 gets its work around and if need more.
Contact me.
And Ha!! This Equation is just a starter to the "Special Theory of Relativity" while actually What Einstein and (all other over here on earth) wanted to arrive over the most "General Theory". This convolutes now to the most accepted "Super String Theory".

Answer 4

The Feynman Lectures on Physics are very good, and readable too.
NickiN's reference is good.
In the distant past, I read a monograph by Einstein on the meaning of special relativity.
One consequence of Special Relativity is that if you analyse the impact of "perfectly elastic bodies" travelling at relativistic velocities, in order for Conservation of Momentum AND Conservation of Energy to apply simultaneously, then each body must have an intrinsic energy equal to MoC^2.
The link to stored energy in fields (The A Bomb) and matter creation/annihilation was made later.

Answer 5

The formula was first derived by a famous french Physicist and mathermatian by the name of Henri Point Carre'in 1900.
Before relativity.
The formula is based on the definition of Energy which Lacarte and other Scientist alluded to. Basically Energy is the product of a mass and its velocity square.
Point Carre inserte the Velocity of light into this Energy equation.
Its not dificult to derive;
The relationship of the permeability of space and the permitivity of space is used.
This was first used by maxwell whos discovered it.

Permeability of space = mu sub o=The inverse of a magnetostatic force x inverse velocity squared.

Permitivity of space = epsilon sub o= a force density of electrostatic

Energy =value of structured mass x 1/ (epsilon sub o x mu sub o)
it folows
E =m x c^2

Answer 6

Einstein derived it after his first paper on Special relativity, which focused on looking at how electromagnetic fields transform between frames of reference at different speeds. After that paper, he wondered what would happen to bodies that emit electromagnetic waves and derived the result: "If a body gives off the energy L in the form of radiation, its mass diminishes by L/c²."

Answer 7

look at m first this is mass einstein was probably watching something and noticed that when c/velocity) reached 2nd power it created energy note einstein was foremost authority on formula composition note2 even if mass breaks up at c2nd it still becomes energy if it doesn't achieve c2nd mass won't achieve the described cummulative energy state note3 the potential of e will probably always be subject of study does e=mc/2 at all volumes of mass study/ if the properties of c =/2 then m=e always interesting to note that light is caused by contraction and light refers to catestrophe emissions from high density fusion /w possible magnetic frission created by trauma elemental fusion creates the state for catostrophic fission external. emission create waves interior internal emessions create heat creating fusion /catalysting the creation of more fission and mass velocity squared waves cyclical developement creates waves through density controlled emmission m*n*c/2 energy becoming emission low density emmission magnetic use transferred power to create fields described by other below wave only one type of energy field emmissions are transferred (E) from polarization i.e. axial motion source that is why atoms have internal frequencies ..radiation emmission from axial trauma(friction)sub energy fields are emission quotients that become inverted etc.

Answer 8

I entirely agree with Mr. Upright's answer. Einstein's derivation in the paper cited is easily understood.

Answer 9

No, you don't derive E = mc^2. Einstein already did that

Answer 10

it is a consequence of einstein's special theory of relativity

and i can't do the maths for you in this text only environment

but i will mention that the equation only applies to a body at rest, if it is moving then e = an infinite series