Mass energy equivalence

[Urmi Roy]

I obtained an analytical description of time dilation and length contraction which describes why these occur at high speeds. However there was no such analysis of Einstein's famous equation E=m(c squared).
Instead, a derivation that I found in http://www.karlscalculus.org/einstein.html starts off with

m =

m0
√1 - v2/c2

Then they derive the formula using calculus.

Is an analytical treatment for E=m(c squared) possible? Is there any thought experiment which helps us to realise the applicability of the mass-energy equivalence?

[diazona]

Um... the web page you linked to does give an analytical derivation of E=mc^2 (although technically the equation is E^2 = m^2c^4 + p^2c^2). I'm not sure what else you're looking for...

[DaleSpam]

I think the mass energy equivalence stems from the conservation of momentum and the fact that photons have momentum.

[Urmi Roy]

I think DaleSpam provided me with what I wanted to know,though it would be better if it was elaborated a bit,(meaning how we can derive the formula from the very basic theory of conservation of momentum (applied to photons)).

[DaleSpam]

OK, it has been a while so I am a little sketchy on the details, but it is something like this:

Suppose an object at rest of mass M emits a pair of photons each of energy E/2 and one to the left and the other to the right. Those photons carry equal and opposite momentum so the object remains at rest. Now, consider the same situation in a frame moving to the right, the right photon is blueshifted and the left photon is redshifted, so the photons carry some net momentum to the right, and we know the object's velocity, so by conservation of momentum the object's mass must have changed. When you work out the amount of the change you find that it changed by an amount m=E/c².

I am sure that is missing some important details, but it is something to that effect.

[Urmi Roy]

Okay,so I guess that through this very revolutionary experiment,which is based upon the doppler effect of electromagnetic waves and the law of conservation of momentum gave Einstein the whole idea.
At the same time there seems to be no derivation as such for the formula which originates from the law of conservation of momentum --it was something that Einstein found to fit in perfectly with the other rules of nature,that's why we can arrive at it fom other sources like the one I found on that webpage I mentioned earlier,right?

[Urmi Roy]

I've been googling on this topic after getting a hint from DaleSpam's last post and I think I've finally found what I've been looking for.

If you are interested, please check this page out-- http://galileo.phys.virginia.edu/classes/252/mass_and_energy.html

[Naty1]

I obtained an analytical description of time dilation and length contraction which describes why these occur at high speeds.

If true, this would be BIG news!. BIG<BIG news and pulitizer, emmy and Nobel worthy.

Not to nitpick, but nobody knows why these occur, why space and time are dynamic; nobody even knows what space and time are. But we do have the Lorentz relationships.

Interesting derivation at the Virgina website, Thanks!!!