Wednesday, January 16, 2008

Physics Factoid: E = m c squared

This is probably the most quoted formula.  Einstein's equation changed the world.  But what does it mean? 

I already defined c for you: it is the speed of light.

The only thing you need to know about c in this equation is that it is BIG (30 billion cm/s), and c squared [see Why c squared?], which is c times c, is VERY BIG (900 quintillion cm2/s2).  E stands for energy, and m for mass (the amount of matter).  So the equation is really

Energy = mass  x  BIG_NUMBER

Well, what the heck does that mean?   It means that matter and energy are really two sides of the same coin called mass-energy.  Matter can be converted into energy, and energy can be converted into matter.  Before Einstein, it was thought that they were completely separate things.  But they are not.  They are two different manifestations of the same thing.  They are like dollars and yen, except the units are grams and ergs.  But there is a VERY steep exchange rate.  For every gram of matter, you get 900 quintillion ergs.  If you could somehow convert a pound of matter (454 grams) completely into energy, you'd have enough to power the US electrical grid for about 4 days.  

Note, you can't actually convert 100% of matter into energy (since we don't have a ready supply of antimatter)—even thermonuclear fusion converts only about 1% of the matter involved into energy.
[confidence level: established, my qualifications: trained]


Michael said...

Why is the conversion factor c^2? I never understood this? Why isn't the formula something like E = m * 1567.8374 instead of E = m * c * c? I know it is not a coincidence that c * c is part of the equation, but I'm just trying to understand why the speed of light happens to also be involved in the conversion rate. Also, why c squared instead of just c? So many other constants in physics are just random numbers, so why not a random number here?

eyesopen said...

This is a good question. Here is a post to answer it.

Why c squared?

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