Anyone here look at Einsteins calculations?

[Goblin]

The most popular equation is E=mc2. I remember growing up the hype was only like 2 people in the world could understand the Theory of Relativity.

I have never looked at the actual calculations behind that simple equation. How it was derived.

I'm just curious if anyone here has looked at how it was derived. Is it as intense as the media leads one to think?

Comming up with the theory was genius but once the trick is reveaved does someone that is pretty strong in math have any chance of understanding it?
Maybe a dummies book on it :)

I was a physics major and pretty decent in math but I never took courses to the limits of mathmatics. I have read some books on General relativity but they kind of dummy it down, never showing how that equation was derived.

 

[quantumdude]

Comming up with the theory was genius but once the trick is reveaved does someone that is pretty strong in math have any chance of understanding it?

Sure, a bright high schooler could understand it. Undergraduate physics majors are required to learn it by their 3rd year. It's really not very complicated at all.

Here it is in AE's own words:

On the Electrodynamics of Moving Bodies

Go to page 22 (according to Adobe reader's count), towards the bottom. The result is stated there. W is the kinetic energy, 1/(1-v²/c²)^1/2mc² is the total energy, and mc² is the rest energy. In the equation E=mc², "E" refers to the energy of a particle at rest.

edit: fixed typo

 

[jamie]

I strongly recommend E=MC^2 by DAVID BODANIS isbn number 0-333-78033-7
This book tellls you all aout this equation (obviously) and its implications.
Hope you find it interesting

 

[pmb_phy]

The most popular equation is E=mc2. ... I'm just curious if anyone here has looked at how it was derived.

Yes.

Is it as intense as the media leads one to think?

Nah. Its a piece of cake.

Comming up with the theory was genius ...

Plenty of work in this area came before Einstein. Back in 1881 J.J. Thomson considered a charged sphere and found that the effect of charging the sphere was the same as is the mass of the sphere increased. He got the relation wrong though. In 1889 Poincare concluded that electromagnetic radiation behaved in some ways like a fluid with a mass density, rho, was related to its energy densit U, buy

\rho = E/c^2

In 1901 Kaufman (supposedly) found experimental evidence that the transverse mass of an electron increased with speed. In 1904 Lorentz found that the longitudinal mass was related to the speed and proper mass m₀ by

m_L = \frac{m_0}{ (1-v^2/c^2)^{3/2} }

Then came Einstein in 1905 and showed that when a body emits radiation of the amount E that its proper mass (aka "rest mass") decreased by

\Delta m = E/c^2[/sub]<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> ..but once the trick is reveaved does someone that is pretty strong in math have any chance of understanding it?<br /> Maybe a dummies book on it :) </div> </div> </blockquote>The math is very simple. See -<br /> <a href="http://www.geocities.com/physics_world/sr/mass_energy_equiv.htm" target="_blank" class="link link--external" rel="nofollow ugc noopener">http://www.geocities.com/physics_world/sr/mass_energy_equiv.htm</a><br /> <a href="http://www.geocities.com/physics_world/sr/einsteins_box.htm" target="_blank" class="link link--external" rel="nofollow ugc noopener">http://www.geocities.com/physics_world/sr/einsteins_box.htm</a><br /> <br /> This one is one that is new to the wonderful world of special relativity. Its in the flavor on Einstein&#039;s derivation but is momentum based rather than kinetic energy based. I found it to be easier to follow than Einstein&#039;s original derivation and is more logical<br /> <a href="http://xxx.lanl.gov/abs/physics/0308039" target="_blank" class="link link--external" rel="nofollow ugc noopener">http://xxx.lanl.gov/abs/physics/0308039</a><br /> <br /> <br /> If you have any questions or comments please post them. There are some typos in my website that I haven&#039;t corrected yet. Thanks.<br /> <br /> Pete

 

[pmb_phy]

Go to page 22 (according to Adobe reader's count), towards the bottom. The result is stated there. W is the kinetic energy, 1/(1-v²/c²)^1/2mc² is the total energy, and mc² is the rest energy. In the equation E=mc², "E" refers to the energy of a particle at rest.

edit: fixed typo

That is not Einstein's mass-energy derivation. That is a derivation of the kinetic energy of a particle. His derivation was in the paper Does the Inertia of a Body Depend on its Energy-Content?, Albert Einstein, Annalen der Physik, 17, (1905)



Pete

 

[quantumdude]

That is not Einstein's mass-energy derivation. That is a derivation of the kinetic energy of a particle.

Right. And on the other side of the = sign, we have the difference between the total energy and the rest energy. Let the KE go to zero, and we have E=mc².

 

[pmb_phy]

Right. And on the other side of the = sign, we have the difference between the total energy and the rest energy. Let the KE go to zero, and we have E=mc².

Yup. I understood that. I think I mispoke. I meant to say that that was not where Einstein introduced the relation of the energy of a body with its energy content. Einstein did not separate the terms as you did and make that interpretation of that equation as you did. I don't see how that can be done without first deriving the E = mc^2 relation but I'm not 100% positive on that. For example: You indicate that, when that expression is expanded, the first term is "total energy". What, in that paper, shows that this is true? What in that paper indicates that the second term in that expression is rest energy?

Pete

 

[quantumdude]

You indicate that, when that expression is expanded, the first term is "total energy". What, in that paper, shows that this is true? What in that paper indicates that the second term in that expression is rest energy?

It doesn't. Knowing the result, I read something into it that wasn't there.

 

[pmb_phy]

It doesn't. Knowing the result, I read something into it that wasn't there.

I hate it when I do that.

But that's the beauty of this forum and questions like this. We get to take a close look at how we think and then we can dig out all the hidden assumptions that we've made unconsciously. E.g. I didn't know why Einstein didn't interpret that as you said until I took a close look. And I only did that since I know that Einstein wrote an entirely separate paper on this. I didn't even know this paper existed until I started to really dig my feet into the concept of mass.

Pete

 

[homology]

and...

I just wanted to make a note for Goblin that while E=mc^2 is Einstein's most popular equation its not his most important. Its also not the pinnacle of either theory of relativity (special or general). Its important to keep that in mind so that when you see how easy the derivation is you don't throw up your hands and say "what, that's it, well heck I could have done that" there's a lot more to Einstein than E=mc^2

Kevin

 

[pmb_phy]

I have never looked at the actual calculations behind that simple equation. How it was derived.

Hi Goblin

I'm curious. You've seen derivations of this as a result of your question. Do you have any thoughts on the matter in retrospect?

Pete

 

[Nenad]

what do youmean by longitudinal.

 

[DW]

what do youmean by longitudinal.

In this case it is a reference to the case where the force is in the direction of the motion. Einstein's reference to transverse and longitudinal masses was not much more than a footnote in his paper noting that the relation between proper frame ordinary force and coordinate acceleration was not f ' = ma, but was
f &#039;_{L} = \gamma ^{3}ma_{L} and f &#039;_{T} = \gamma ^{2}m a_{T}. And no ,Einstein made no mistake in the exponents.

 

[Nenad]

thanx. That clears up things.