Special Relativity without a doubt is a very counter-intuitive area in physics, where time no flows at different rate for different observers and objects can never reach the speed of light no matter how much energy you provide it.
With these counter-intuitive findings, comes paradoxes. Famous ones include the twin paradox and ladder in barn paradox.
These paradoxes of special relativity at first seems like a contradiction, but upon further scrutiny remains consistent within the principles of special relativity, and exposes us to our error in reasoning, allowing us to gain a deeper understanding of the weirdness of Special Relativity.
For this article I'll discuss a paradox that arises in simple time dilation.
Consider the classic example of time-dilation, involving one travelling in a train at a speed v, and another stationary. I'll just call the moving observer A, and the stationary observer B.
According to special relativity, time dilation will occur. Suppose they are carrying stop-watches with them; the time reading of A is lower than B's. Meaning that compared to B, A's time is moving slower according to the equation:
Where γ is the Lorentz factor with a value more than 1. This leads us to conclude that for a moving observer, time will slow down.
However consider the other postulate of Special Relativity: The laws of physics is the same for all observers regardless of their speed as long they don't accelerate.
This leads to a paradox. From A's perspective, B is moving too but in the opposite direction so B's time should be slower than A, leading B to conclude that:
Which contradicts the earlier finding that A's time is slower than B. So whose time is slower? Is it possible for both of their time to be faster and slower at the same time?
This is definitely a mind-screw paradox in time dilation that took me a very long time to finally resolve it.
I'll save the resolution of this paradox to another article, so stay tuned!