Einstein’s special theory of relativity is arguably the most amazing physical theory ever conceived. It utterly transformed our view of the universe, completely eradicating the view that space and time are independent quantities and giving us a new unified fabric of space-time. It led us to the revelation that energy and mass can be converted into one another, and resulted in the world’s most famous physical equation,
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which tells us that a mass m, times the speed of light c squared, is equivalent to (and can be converted into) an amount of energy E. This observation forms the basis of nuclear energy, and it paved the way to all of modern particle physics such as the experiments being done at the Large Hadron Collider.
Perhaps the most fascinating thing about Einstein’s special relativity is that it leads to a collection of “paradoxes” that seem to violate our common-sense nature of the world. Resolution of these false “paradoxes” demonstrate that the theory is wonderfully and incredibly consistent — and the best part is that many can be resolved using at most high-school algebra.
There are a variety of seeming contradictions in special relativity that turn out to be quite the opposite: the most famous of these is the “twin paradox“, in which one twin brother does a round trip to a distant star at high speed and returns to Earth, and there is a discrepancy in the ages of the twins when they return.
I’ve talked about the “twin paradox” in the context of another post; I thought for this one I’d discuss another unusual aspect of special relativity. If you know anything about relativity, you probably know that it implies that nothing can go faster than the speed of light, which happens to be
.
In fact, the only thing that we know that can even match the speed of light is light itself! As far as we know at this stage, no massive particle can achieve c, though it can come arbitrarily close to that speed.
With that in mind, if you were to jump into a rocketship and blast off to Alpha Centauri, which is 4.37 light years away from Earth, what is the fastest possible time that it could take you to get there with the fastest spaceship possible?

Image of Alpha Centauri (left) and Beta Centauri (right), via Wikipedia.
A natural first guess would be to say it would take approximately 4.37 years, since I can go no faster than the speed of light. In fact, however, it turns out that with a fast enough spaceship, you could get to Alpha Centauri in as little time as you like — even 10 minutes or less!
How is this possible? In explaining it, we will have to probe to the heart of two fundamental and surprising results from Einstein’s theory: time dilation and length contraction. An important piece of the puzzle is noting that I asked how long it takes you to get to Alpha Centauri, not how long someone on Earth says it takes for you to get there…
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