Energy-mass equivalence question

[Charlie G]

The book I'm reading on special relativity is a ficitonal conversation between Newton and Einstein. Einstein is explaining relativity to Newton. Its a very good book in my unprofessional opinion, but one thing I'm having problems with is energy-mass equivalence.

I'm not having trouble with the concept, but the equation. In the chapter, Newton has just learned of relativistic mass increase, so he is trying to modify his old energy equation E=1/2mv squared (sorry I don't know how to make the squared sign lol, could anyone tell me how to do that as well) to work for objects moving at relativistic speeds. In the next chapter Newton comes into talk about his work he had done during the night, he says that he believes the equation for the energy of an object moving at relativistic speeds is E=Mc squared, where M is the moving mass and the objects speed is so close to c at relativistic speeds he calls the objects speed c.

Now the problem I'm having is the book doesn't really explain the math (it was meant for the layman like myself, though I really wanted alittle more detail). It did go on to E=myc squared, and ultimatly E=mc squared for an object at rest. But why, in the equation, was 1/2 the mass dropped for the entire mass? Speed squared was kept but the mass portion of the equation changed. I was hoping someone could tell me why this was done.

 

[bernhard.rothenstein]

The book I'm reading on special relativity is a ficitonal conversation between Newton and Einstein. Einstein is explaining relativity to Newton. Its a very good book in my unprofessional opinion, but one thing I'm having problems with is energy-mass equivalence.

I'm not having trouble with the concept, but the equation. In the chapter, Newton has just learned of relativistic mass increase, so he is trying to modify his old energy equation E=1/2mv squared (sorry I don't know how to make the squared sign lol, could anyone tell me how to do that as well) to work for objects moving at relativistic speeds. In the next chapter Newton comes into talk about his work he had done during the night, he says that he believes the equation for the energy of an object moving at relativistic speeds is E=Mc squared, where M is the moving mass and the objects speed is so close to c at relativistic speeds he calls the objects speed c.

Now the problem I'm having is the book doesn't really explain the math (it was meant for the layman like myself, though I really wanted alittle more detail). It did go on to E=myc squared, and ultimatly E=mc squared for an object at rest. But why, in the equation, was 1/2 the mass dropped for the entire mass? Speed squared was kept but the mass portion of the equation changed. I was hoping someone could tell me why this was done.

Many textbooks propose the following approach to the link you are looking for.
Start with m=m(0)/sqr(1-bb) ; b=v/c. For small v/c we can expand m as a series of powers of b
m=m(0)(1+bb/2+...) (1)
Multiply (1) by cc in order to obtain
mcc=m(0)cc+m(0)vv/2 (2)
in which Newton recognizes his kinetic energy m(0)v^2/2...

 

[Dale]

Hi Charlie,

The mass energy equivalence formula can be derived from the fact that photons have momentum which is proportional to their frequency. Basically, if an object emits two photons of equal and opposite momentum in its rest frame then it remains at rest. Transforming that to a frame where the object is moving then one photon is redshifted and the other is blueshifted. The one that is blueshifted carries more momentum than the one that is redshifted and so, to conserve momentum, the mass of the object must have gone down. When you work out how much mass was lost you get m=E/c²

 

[Naty1]

You can also read Einstein's own discussion for the general public at

http://www.bartleby.com/173/ chapter 15 of RELATIVITY, The Special and General Theory.

 

[Charlie G]

Thx for all the replies, the bartelby website was really helpful:)