# Einstein’s equation

*E*=*mc*². Everybody knows this formula, but not everyone knows *what it is*, what it means. How can three letters and an exponent mean so much?

Let’s start by defining those letters:

*E* is the *energy*;

*m* is the mass;

*c* is a constant, i.e. the speed of light in a vacuum, which corresponds to 299792458 m/s, or approximately 3 · 10^8 m/s;

This means that *E* is the energy of an object of mass *m* traveling at the speed of light *c*. This is the definition of *kinetic energy*:

The kinetic energy of an object is the energy that it possesses due to its motion.

Source: Wikipedia

But where does this formula come from? Since the object travels at the speed of light, we are talking of uniform linear motion, expressed by the equation

where:

*s* is the *space*;

*v* is the *velocity*;

*t-t0* is the time the object moves for (t is the current time and t0 the *initial* *time*; example: an objects that starts moving after 3 seconds and stops at *t* = 8 *s*;);

*s0* is the initial space (for example an object that starts moving at 5 m away from the point of reference);

This is the graph space-time:

As you can see it is a straight line, indicating it is uniform motion, i.e. the velocity is constant.

In our case, since we are talking about speed of light, the equation becomes:

Assuming light doesnt’ have an initial time and an initial space, we can write it as

We know that energy is measured in J (joules), or, equivalently N · m (Newtons per second), therefore

where *F* is the force and *s* the space.

We also know that F=ma and that a=c/t, hence

*s*/*t* is equal to *v*, *c* in this case:

Obviously, *c* · *c* is simply *c*², therefore

This is how we find the famous equation.

This wonderful formula allows us to show that light has energy; light is made of photons which have a mass and, of course, travel at the speed of light. If something has got a mass and moves at a certain speed, it must also have an energy.

The mass of a photon is 3.68 · 10^-51 kg, hence an energy of

As you can see, it has an incredibly small energy, this is why we can’t move object with light. The only ways to increase *E* would be to increase m and/or c, but they are constant, so it’s not possible. We can introduce another equation for the energy of a photon though, known as the *Planck’s equation*:

where E is still the energy, *h* is Planck’s constant, approximately equal to 6.626 · 10^-34 m² · kg/s, and *v* is the Greek letter *ni*, which is the frequency.

Since both equations express *E*, we can compare them:

This shows that the energy also depends on the frequency, so if we could create a laser with an extremely high frequency we could move objects. This is just my theory though!

Anyway, I really hope that you found this post interesting and if you liked it give it a like, I would really appreciate it!

The proof is not so easy..The generalised proof is complicated