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• E=mc^2 may be the most famous equation in the worldbut what you might not know is

• that it isn't the whole story. It just describes objects that have mass and that aren't moving.

• The full equation is E, squared, equals m c squared, squared, plus p times c, squared,

• where p represents the momentum of the object in question. This might all seem a bit confusing,

• but in fact you can draw it as a right triangle with sides E, m c squared, and p times c - and

• just use the pythagorean theorem (a squared plus b squared equals c squared) to give you

• the equation.

• Also, from here it's clear to see that for an object that isn't moving and thus doesn't

• have any momentum and thus p is zero, we get back our good ole' friend E=mc2. On the other

• hand, if the particle in question is massless (like light), then mass is zero and we get

• E equals p times c. This tells us that the energy of a massless particle (like a photon

• of light) is the same as its momentum (up to a factor of the speed of light).

• In fact, the closer the energy of something is to p times c, the closer that something

• is to behaving like light (I mean, look here, this tiny little bit of mass is hardly mass

• at all).

• Anyway, as an example, an object's velocity is equal to the speed of light times the ratio

• of the object's momentum to energy - or pc over E. If your momentum increases, p times

• c gets closer and closer to equaling your energy, so their ratio gets closer and closer

• to being one, and your speed gets closer and closer to light speed. But because of that

• tiny little bit of mass, the momentum side of the triangle will always be a little bit

• smaller than the energy side. No matter how hard you try to increase your momentum, it

• never quite gets to the point where p times c equals your energy, and thus your velocity

• can never quite reach the speed of light, all because the hypotenuse of a right triangle

• is longer than its legs.

E=mc^2 may be the most famous equation in the worldbut what you might not know is

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# E=mc² is Incomplete

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Why Why posted on 2013/03/28
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