Einsteins thoughts behind c2 in E=mc2

[Incyder]

I've seen a previous threads where it was a mathematical consistency based on four-dimensions, and a host of other reasons. I'm currently trying to reconcile my belief that it has to do with time dilation and the observer effect.

 

[jedishrfu]

Perhaps this derivation will help your understanding

http://www.emc2-explained.info/Emc2/Deriving.htm#.VMRN2oFOKrU

 

[td21]

The square (^2) comes from the definition of Energy. (momentum is proportional to velocity => Force = dp/dt => Energy = Integral of force w.r.t distance=> Energy is proportion to velocity squared). This also can trace back to the definition given by Leibniz and Chatelet. But this does not lead to the c term.
The c comes from the conservation of momentum and the postulates of special relativity proposed by einstein (which leads a different addition of velocities compared to that in Newtonian mechanics).

 

[Incyder]

Perhaps this derivation will help your understanding

http://www.emc2-explained.info/Emc2/Deriving.htm#.VMRN2oFOKrU

I've read that. I am completely a layman in this rodeo. That math seems to be the only refuge for some. I was hoping that knowledgeable people here could possibly tell me if the observer effect had any bearing on two observable quantities, both being the speed of light.

 

[Ibix]

The maths simply shows you that E=mc² is implied by the statements "The laws of physics are the same in all frames of reference" and "The speed of light in the same in all inertial frames of reference". That's pretty much all there is in the way of thinking underlying it.

Nuclear reactors and nuclear weapons are a fairly powerful demonstration that the thinking is justified.

The observer effect doesn't really come into it. E=mc² is just the end of a chain of reasoning from the principles I stated.

By the way, the tone I read into your posts suggests to me that you might want to take another glance at the personal theories parts of the guidelines for posting before continuing the conversation. Apologies if I am castlng aspersions.

 

[bcrowell]

The title of the thread suggests that you're just asking about the factor of c². Is that correct? It has to be there because of units. In the relativistic system of units normally used in relativity, c=1, so the equation is simply E=m. To convert it back to SI units, you put in the c².

If you want to know more generally about how Einstein arrived at E=mc², you could just read his original paper: http://www.fourmilab.ch/etexts/einstein/E_mc2/www/

 

[Dale]

I agree with bcrowell, it is just a unit conversion factor. It comes about because the SI system uses incompatible units for energy, momentum, and mass, just like the traditional nautical system uses incompatible units for distance (nautical miles) and depth (fathoms).