# Give an interpretation of Einstein's theory of relativity?

Jul 18, 2015

The short version of this interpretation is that light, with an infinitely small mass, has a speed we consider infinite because if we approach it, we experience length contraction and time becomes relativistically infinite. Normally we find $0 \cdot \infty$ indeterminate... but light exists. The gist of it is that considering 4 dimensions (x, y, z, time) allows for the bigger picture to reveal itself. Not only can you move in space, but you move forward in time. Everything in everyday life is relativistic to a certain extent, but in all of this, light is exempt.

For the viewers, it starts on page 104 of this book:

Here's my interpretation of it.

First of all, a preface on the span of the magnitudes of values. There exists quantum values (on the order of electrons), everyday values, and relativistic values (on the order of near the speed of light). Light belongs to the relativistic areas.

The equation $E = m {c}^{2}$ relates energy with mass and speed. That alone is nothing special ($K = \frac{1}{2} m {v}^{2}$ is analogous... but not quite the same), but there's more to this.

Embedded within this is that the speed of light is essentially a speed that nothing can exceed. In some sense it is "infinite" (or unreachably large, to be technical about it). Intuitively, light has "no" mass, and yet, it clearly has a mass variable associated with it in this equation.

This is baffling, because how can something that has "no" mass have a speed? Furthermore, why then would Einstein state that the energy for light involves its mass?

In everyday physics, there is such a thing as relative velocity. You do talk about that in everyday physics. This is where we introduce non-inertial reference frames. Normally we can just say that an object's speed is "absolute" in an inertial reference frame, but when it starts approaching the speed of light, it gets to the point where in a non-inertial reference frame, its speed is actually "absolute", but not relative. Once it reaches the speed of light (assuming it does), it DOES have an absolute speed.

From the perspective of light, since light moves so quickly, everything else feels infinitely slow, and thus time is infinite (for light); if someone were to approach the speed of light, one would feel compressed. This is called length contraction. (If time is infinite, as part of a mass moves, another part of it moves behind it. But since time is infinite, nothing can move forward. If nothing can move forward or backward, its mass starts compressing.)

If you want to show yourself that time is infinite for light, consider the light clock:
https://en.wikipedia.org/wiki/Time_dilation#Simple_inference_of_time_dilation_due_to_relative_velocity

...and you will see that if you reach the speed of light, the square root is zero, and time becomes infinite.

But the interesting thing about light is that it exists in spacetime as something that actually has a constant speed in either an absolute or relativistic consideration. The book even says a "spacetime velocity vector [...] always has length c" (pg. 109).

That's where the book preview ends, unfortunately. But there you go, that's my interpretation.