Odd insights from the Special Theory of Relativity

3-4 minute read

I have been studying the theoretical aspects of the Special Theory of Relativity. Although I lack a firm mathematical understanding of all the principles, I have a few questions lingering on my mind. It is challenging to fathom the ideas that lead to this whole facade. This write-up is about some mind-boggling afterthoughts.

Maxwell’s Equations

Maxwell’s Equations give out the value for the constant speed at which electromagnetic waves propagate in the vacuum.1 This mathematical constant is popularly known as the speed of light, \(c\). Long after its discovery, scientists measured the speed of light which came out to be the same as predicted by Maxwell’s Equations.

Entanglement with the Special Theory of Relativity

Maxwell’s Equations predicted the speed of light but didn’t define its inertial frame of reference. When we talk about speed, it’s always relative to something, but Maxwell’s Equations mentioned no such thing. The only viable explanation that scientists could come up with at the time was that an invisible, unobservable substance, called Aether, constitutes the vacuum of space. It is the medium through which gravitational forces and electromagnetic waves propagate.

Later in 1905, Einstein contradicted the presence of Aether in his Special Theory of Relativity. It stated that light or any other electromagnetic waves don’t propagate through Aether, or rather, the speed of light is a universal constant.2 All observers will measure it precisely the same in their reference frames, irrespective of the motion of its source.

Let us consider yourself as a stationary observer and that I am travelling towards you with a flashlight at \(10\%\) the speed of light. Now if you were to measure the speed of light emitted from the flashlight, you will still find it to be \(c\) rather than \(1.1 \times c\).3

To put it other words, if the speed of light remains constant for both observers, it must imply that at least one or both quantities constituting the speed — i.e., distance (or length) and time — must vary in different inertial frames. In the previous example, when the source was moving towards the observer, we concluded that the speed of light remains the same. It must mean that the stationary observer was observing the time for the moving source to be passing by faster.

Food for thoughts

Does light itself experience time?

The following equations represent how time dilates for a source in motion. Here, \(v\) is the speed of the source as observed by a stationary observer, \(\gamma\) is the Lorentz Factor, \(t\) is the time as measured by the source, and \(t'\) is the dilated time as observed by the observer. Lorentz Factor arises in the derivation of the Lorentz transformation used to transform measurements across inertial reference frames in Special Relativity.4

\[\beta = \frac{v}{c}\] \[\gamma = \frac{1}{\sqrt{1 - \beta^2}}\] \[t' = \gamma \times t\]

Now let us consider a quantum of light, a photon moving towards an observer. From the photon’s frame of reference, it is stationary while the observer is moving towards it at the speed of light. The Lorentz Factor, \(\gamma\) here tends towards infinity. Does it mean that the photon doesn’t experience time? A simple answer can be a no, but this question is the hardest to answer because answering it implies discovering the theory of everything. A hypothesis that unites the physics that deals with subatomic particles, with the physics that deals with large objects.

So does it mean that time travel is possible?

To the future? Yes! To the past? It’s hard to tell! To time travel to the future, all you have to do is travel very fast for some time and then return home. If you also read the General Theory of Relativity before leaving, you may find it worthwhile to orbit around an object considerably more massive than Earth.