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Jul
13
comment Why did we need relativity to derive $E=mc^2$?
@JerrySchirmer think of two masses on the ends of the compressed spring and the change in kinetic energy of the system when the spring is released - is this change in kinetic energy, and therefore change in potential energy in the the compressed spring, invariant? I would say yes, but if you say no then maybe I need to have a closer look :)
Jul
12
comment Why did we need relativity to derive $E=mc^2$?
@jerry potential energy, such as that stored in a compressed spring, is invariant though, right?
Jul
12
comment Why did we need relativity to derive $E=mc^2$?
Since his first derivation is what's causing the confusion then really you should be commenting on on that, don't you think?
Jul
8
comment Why did we need relativity to derive $E=mc^2$?
Do you think you could stick with the original derivation of Einstein since that's what the OP is referring to?
Jul
8
comment Why did we need relativity to derive $E=mc^2$?
@ron kinetic energy is zero when v is zero. The constant c is to do with the arbitrariness of the measurement of potential energy to within a constant and this is the internal energy of the mass.
Jul
7
comment Why did we need relativity to derive $E=mc^2$?
Stachel is just saying that the internal state is like the mass, in being defined in the rest frame and all other observers agreeing upon this value. On page 217 they also remark that Einstein was not correct in stating that the change in kinetic energy is independent of the qualities of the body - its internal state $S_0$ before, and $S_1$ after.
Jul
6
comment Why did we need relativity to derive $E=mc^2$?
@RonMaimon have a look at the paper and please tell me if you think it's reasonable to keep C the same in both equations, because to me it looks as if he's assuming the internal energy remains constant: fourmilab.ch/etexts/einstein/E_mc2/www
Jul
6
comment Why did we need relativity to derive $E=mc^2$?
My point was why shouldn't the internal energy contribute to the radiation, rather than the mass? Isn't this a physical assumption? And since energy is frame dependent, I'd expect potential energy to be also.
Jul
5
comment Why did we need relativity to derive $E=mc^2$?
@RonMaimon if you look at the derivation, the constant C doesn't change during emission of radiation and so the internal energy is constant - why should this be so?
Jul
5
comment Why did we need relativity to derive $E=mc^2$?
In your link you say "Because the H-E terms measure the change in energy of the box due to the relative motion of the two frames only, the additive constant C representing any other energy left over (such as the internal molecular energies of the box etc) is constant" why shouldn't the internal energy of the body and therefore C change?
Jul
4
comment Why did we need relativity to derive $E=mc^2$?
The main problem with the derivation is it assumes mass is converted to radiation, whereas the conversion of internal energy to radiation is an established explanation anyway. E.g heating an object causes it to radiate where internal kinetic energy is converted to radiation.
Jul
4
comment Why did we need relativity to derive $E=mc^2$?
There isn't one way of deriving $E=mc^2$, although by the sounds of it, you're referencing Einstein's controversial first derivation which lead to others upto the 1940s.
Jul
1
awarded  Citizen Patrol
Jun
25
comment Why don't most physics programs study the primary sources?
@RonMaimon goddamnit you're right on Newton.
Jun
25
comment Why don't most physics programs study the primary sources?
yeah, his second law as in "A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed" which isn't expressed as proportional to the rate of change of momentum. And Lagranges Analytical Mechanics is very long winded when it comes to explaining virtual work, whereas Feynman does it in a paragraph - why? because we've moved on from 250 years ago as teachers and researchers refine and improve the interpretation and techniques. Please remove the -1
Jun
24
comment study quantum mechanics without physics background
+1 for the Griffiths recommendation. The reviews on Amazon.com are very favourable and his electrodynamics books is great.
Jun
22
comment Why don't most physics programs study the primary sources?
I think even Maxwell isn't worth reading today because he predates special relativity. Far better to read the works of talented teachers who teach as a profession and get feedback such as Griffiths with his Classical Electrodynamics book. Prof Lewin is another fantastic teacher who hasn't written a book, but has lectured on the web and maybe this is his medium. Maybe you're starting to fall asleep in the past and not keeping upto date with modern books.
Jun
22
answered Why don't most physics programs study the primary sources?
Jun
22
comment Does a static electric field and the conservation of momentum give rise to a relationship between $E$, $t$, and some path $s$?
Jackson and Griffiths don't say anything about this stuff so can you recommend a good book that goes into this?
Jun
3
comment How did L.H. Thomas derive his 1927 expressions for an electron with an axis?
I know that Goldstein and Jackson do it in the spirit of Thomas via the Lorentz matrix.