Why can't we surpass the speed of light? Einstein tells you
Why can’t we travel faster than the speed of light? Einstein explained this pheonmenon through his famous equation
which is the last of his four celebrated works in 1905 (Albert Einstein’s Year of Miracles) titled Does the inertia of a body depend on its energy content?. This paper entails arguably the most famous formula so far: Mass-Energy Equivalence
From
For the rest of the post, we use high school physics to proof these famous results!
1. Review from high school physics materials
- Momentum Conservation Principle (动量守恒定律): For a system (with two objectives) has 0 momentum, it always holds:
multiply both sides by time t, we further have - Electromagnetic waves:
- Theorem of Momentum:
2. Proof of
Einstein’s Thought Experiment. Imagine there is a box with length
By
then by
Then by the definition of momentum
On the other hand, for photon
Let the mass of photon be
Which gives
This can be generalize to not only photon but all particles!
Quite easy! Right?
Proof of
Recall
Now by
Take integral, we obtian
When
In particular, for photon, by
Finally, use
Again, use
That’s it! Now you know why