- #1

- 437

- 13

How is this formula derived? And why is the speed of light squared? Is there a reason for that?

Thanks.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter FeDeX_LaTeX
- Start date

In summary, Einstein found that mass and energy are equivalent, and that by emitting light, an object reduces its mass by a certain amount.f

- #1

- 437

- 13

How is this formula derived? And why is the speed of light squared? Is there a reason for that?

Thanks.

- #2

- 120

- 0

http://www.btinternet.com/~j.doyle/SR/Emc2/Derive.htm

Google is your friend :).

Google is your friend :).

Last edited by a moderator:

- #3

Staff Emeritus

Science Advisor

Homework Helper

- 16,054

- 5,111

https://www.physicsforums.com/showthread.php?t=386435

You can probably find others if you search a bit.

- #4

- 6,724

- 427

Einstein found this result in a 1905 paper, titled "Does the inertia of a body depend upon its energy content?" This paper is very short and readable, and is available online. A summary of the argument is as follows. Define a frame of reference A, and let an object O, initially at rest in this frame, emit two flashes of light in opposite directions. Now define another frame of reference B, in motion relative to A along the same axis as the one along which the light was emitted. Then in order to preserve conservation of energy in both frames, we are forced to attribute a different inertial mass to O before and after it emits the light. The interpretation is that mass and energy are equivalent. By giving up a quantity of energy E, the object has reduced its mass by an amount E/c2.

Although Einstein's original derivation happens to involve the speed of light, E=mc2 can be derived without talking about light at all. One can derive the Lorentz transformations using a set of postulates that don't say anything about light (see, e.g., Rindler 1979). The constant c is then interpreted simply as the maximum speed of causality, not necessarily the speed of light. Constructing the mass-energy four-vector of a particle, we find that its norm E2-p2c2 is frame-invariant, and can be interpreted as m2c4, where m is the particle's rest mass. In the case where the particle is at rest, p=0, and we recover E=mc2.

A. Einstein, Annalen der Physik. 18 (1905) 639, available online at http://www.fourmilab.ch/etexts/einstein/E_mc2/www/

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51

- #5

Homework Helper

Gold Member

- 3,272

- 2,302

go to

www.shadycrypt.com

and click on the "E=mc

Share:

- Replies
- 10

- Views
- 504

- Replies
- 6

- Views
- 1K

- Replies
- 74

- Views
- 2K

- Replies
- 9

- Views
- 1K

- Replies
- 78

- Views
- 3K

- Replies
- 25

- Views
- 1K

- Replies
- 45

- Views
- 2K

- Replies
- 45

- Views
- 2K

- Replies
- 25

- Views
- 2K

- Replies
- 18

- Views
- 865