In fact, **E = mc**^{2} is one solution of the more general formula, which is:

**E**^{2} = m^{2}c^{4} + p^{2}c^{2}

Where**E** is energy, **m** is mass, **p** is momentum and **c** the speed of light. At rest, i.e. zero momentum, this reduces to:

** ****E**^{2} = m^{2}c^{4}

By taking the square root of either side, there are more solutions: for example, ** **

** E = mc**^{2}, as well as: **E = ****-****mc**^{2} Note the "minus" sign.

Einstein saw no relevance in the other solutions, so you see them rarely. In fact, the mass equivalent of the energy in a gravitational field is negative.

Where

Einstein saw no relevance in the other solutions, so you see them rarely. In fact, the mass equivalent of the energy in a gravitational field is negative.

Special Relativity states that all uniform motion is relative, and that there is no absolute state of rest. What does that really mean? Though you may be sitting at your computer reading this, you are moving as the Earth rotates on its axis, and moves around the Sun which itself is moving through the Galaxy. Let us say you have a ruler, and a piece of wood, and you measure the length of the piece of wood. You then get on a train that is moving at a constant speed and measure the piece of wood again. You get the same result. Now, you are on the platform and measure the length of the piece of wood as it travels past you at a constant speed relative to you. You get a different length! Length contraction based on motion, which was first proposed by Fitzgerald and Lorentz in 1904, was shown to derive directly from Special Relativity. Special Relativity is “special” in that it applies only to uniform motion; that is, no acceleration is involved. General Relativity applies to accelerated motion, including the affect of gravity.

It is linked to Time Dilation, also predicted by Special Relativity. In 1971, using a pair of incredibly accurate atomic clocks, one stationary on Earth, the other flown around the world many times in an airoplane, it was shown that time slowed down for the clock in motion. Another proof involves a sub atomic particle called a µ-meson. Mesons produced under laboratory conditions decay, on average, after a little more than 2 microseconds. µ-mesons produced by cosmic rays travel very close to the speed of light, and are observed to live around five times longer, in line with the predictions of relativity. At the speed of light, time ceases to pass at all. Thus, zero mass particles like a photon that always move at the speed of light, experience no passing of time. To us, a photon takes about 8 minutes to get from the Sun to the Earth, and gamma rays from the exploding star GRB 090423 have taken 13.1 billion years to reach us. To the photons, however, both journeys are instantaneous!

It is linked to Time Dilation, also predicted by Special Relativity. In 1971, using a pair of incredibly accurate atomic clocks, one stationary on Earth, the other flown around the world many times in an airoplane, it was shown that time slowed down for the clock in motion. Another proof involves a sub atomic particle called a µ-meson. Mesons produced under laboratory conditions decay, on average, after a little more than 2 microseconds. µ-mesons produced by cosmic rays travel very close to the speed of light, and are observed to live around five times longer, in line with the predictions of relativity. At the speed of light, time ceases to pass at all. Thus, zero mass particles like a photon that always move at the speed of light, experience no passing of time. To us, a photon takes about 8 minutes to get from the Sun to the Earth, and gamma rays from the exploding star GRB 090423 have taken 13.1 billion years to reach us. To the photons, however, both journeys are instantaneous!

Special Relativity is “special” in that it applies only to uniform motion; that is, no acceleration is involved. General Relativity applies to accelerated motion, including the affect of gravity.

Special Relativity is based on two fundamental principles:

* that the speed of light is the same for everyone whatever their relative motion, *and

* that matter and energy are related by the formula **E = mc*^{2}* ** *(see **note **below)

The University of Illinois has a good description of Special Relativity.