Physics
Special Relativity: Time Dilation and Length Contraction
‘Special Relativity’
A phrase thrown around by many, yet understood by a few, but always hearing about how it’s one of the most revolutionary ideas thought up by Einstein. In fact, his paper on special relativity was his third and most famous article, written during his ‘Annus Miribalis’ (miracle year in Ancient Italian), leading to his rapid rise in worldwide fame as a genius. Considering its importance, it’s only right and responsible for us physicists to understand what it is, and how we can observe and prove Einstein’s once ludicrous claims.
Fundamentally, special relativity concerns the idea that speed changes space, time and mass. Not our perception of it, but the actual ‘fabric’ of spacetime itself.
Instead of throwing a bunch of outlandish claims and equations at you, let’s have a look at real-world examples to understand them better.
Time Dilation
Muons are subatomic particles travelling near the speed of light and are created 60km above the surface of the Earth, where cosmic rays collide with the atmosphere. This would mean that it takes approximately 200μs to travel from the atmosphere to the surface, where they’re detected.
Muons also have a half-life of 2μs, meaning after 2µs, half of the original muons are expected to still be alive. This implies that over the 200µs trip from the atmosphere to the earth, only 1 in 2¹⁰⁰ is expected to not have decayed.
However, in reality, one in eight muons are detected on the surface of the Earth. Mathematically, what does this imply?
Well, whilst the journey from the atmosphere to the surface lasted 200μs from our frame of reference, must have only lasted 6μs for them.
So this is the first dogma of Special Relativity that makes it special.
Each second lasts longer (compared to someone standing still) the faster you travel. Time slows down / contracts the faster you travel.
As a consequence of time dilation, either the distance or velocity of the muons (from their frame of reference) must change to make s = vt hold true. We know that velocity can’t have changed, otherwise it would be greater than the speed of light, which is impossible. Thus assuming that velocity is constant, the distance travelled by the muons from their frame of reference is only 1800m, whilst from one of a stationary observer, it is 60km.
And that leads us to the second dogma of Special Relativity.
Length contracts as a consequence of high velocities. The faster you travel, the shorter the distance becomes (to your frame of reference).
Considering those undertaking physics degrees have the highest average IQ (not flexing it’s a statistic), it’s counterintuitive how most physics pretty much defies logic, common sense and intuition. Special Relativity is just another one of those important topics which sound crazy because there is no way we can experience anything like it in real life. And despite the number of thought experiments and paradoxes that have been come up with to try to disprove SR, there’s also been an overwhelming number of evidence proving its validity, from the muons I used above, to atomic clocks that were synchronised on Earth and now are out of sync. But I think it’s this weirdness of physics that makes it really interesting. You’re forced to ask questions that nobody dares to ask, and answer them by breaking out of social bounds and thinking out of the box, even if it leads to absurd answers which defy how we perceive reality.
The third and fourth consequences of special relativity will be in another article, as they are heavily conceptual.
