# Urgent Help : Einsteins derivation of e=mc^2

1. Jan 4, 2005

### uraknai

hi,

This has probably been asked and answered a million times before so sorry but here goes. I urgently need help with a Maths University project about the A-Bomb which will include a chapter on Special Relativity and e=mc^2. I have read loads of books but they treat special relativity from a modern view point whereas I need to know how Einstein "figured out" e=mc^2 as it's a projcent on the impact and development of maths. Can anyone explaine how Einstein derived e=mc^2 or recommend and books/websites. Also, does anyone have any useful mathematical info on the development of the A-Bomb that might help?

Thanks

2. Jan 4, 2005

3. Jan 5, 2005

### Mk

Where did E^2=m^2c^4+p^2^2 come from?

And why can't users view their own "warnings?"

4. Jan 5, 2005

### Tide

Actually, it's

$$E^2 = m_0^2 c^4 + p^2 c^2$$

and it is the same as $$E = mc^2$$ which uses the "relativisitc mass" whereas the previous expression uses the "proper mass."

5. Jan 8, 2005

### Mk

Ummm, which one is rest mass and which one is not? Rest mass is proper mass? Right?

6. Jan 8, 2005

### Staff: Mentor

...and you can derive it by starting with the relativistic equations for energy and momentum:

$$E=\frac {m_0 c^2} { \sqrt {1 - \frac {v^2} {c^2}}}$$

$$p=\frac {m_0 v} { \sqrt {1 - \frac {v^2} {c^2}}}$$

and combining them so as to eliminate v.

Right. It's also known as "invariant mass".

Last edited: Jan 8, 2005
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