Posted by: maroonmaurader | March 9, 2010

On the impossibility of superluminal travel

So I just thought up a straightforward proof by contradiction for why relativity must forbid faster-than-light travel (I believe it’s original, but someone else might have made it before). It requires no math, and I hope is reasonably approachable.

To begin with, an experimental fact. All observers see light traveling at c. If you have an incredibly accurate stopwatch, yardstick, and flashlight, you can go out and measure this for yourself. It doesn’t matter whether you’re in a car approaching the flashlight at 100 mph, sitting by the road watching the flashlight, or standing there holding the flashlight watching the light move away; you will see it travel at the exact same speed. It’s a counter-intuitive fact, but true nonetheless. If you are willing to accept this, then I can demonstrate that it leads to clear paradox to simply contemplate superluminal (faster-than-light) travel.*

Suppose you have a superluminal spaceship with a flashlight on the front. Suppose you start flying towards me (at some speed greater than light) and at the same instant turn the flashlight on, aimed at me. When you reach me, you drop a curtain so any light behind you doesn’t get through. Then the only light I see is light that reaches me before you do. The question is, do I see the light from the flashlight or not? Let’s look at it from two perspectives – yours and mine.

From your perspective: the flashlight is on the front of the spaceship. All observers see light traveling at c. So the light is in front of the ship, and it must reach me before you do. Dropping the curtain as you pass doesn’t prevent me from seeing the light, as it has already reached me.

From my perspective: you are approaching faster than c. The light is approaching at c. Both start at the same time and place, so you will reach me first. Therefore, when you drop the curtain it will prevent me from seeing the light.

I both saw and did not see the light; this contradiction makes it clear that superluminal travel is impossible.

*Edit: captainfalcon pointed out that I neglected to specify the other major principle of special relativity (and the one from which the name derives); it is also necessary for this argument to be truly complete. Loosely speaking: there is no such thing as “absolute” velocity, only velocity relative to something else. Thus, while I described the spaceship as flying at superluminal velocity, this was actually shorthand for the following: “I observe the spaceship approaching me at a speed greater than that of light”. Someone on the spaceship won’t see the spaceship moving at all (that’s what it means to be on the spaceship). From their perspective, the spaceship is stationary, and I am approaching them at a superluminal velocity.

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Responses

  1. Its a pretty good way of putting things. I am pretty sure I came across something similar in a physics book in high school, but without the curtain, just the two observers and a flashlight. Not surprising, considering the subject, but I think yours is a better way of constructing the proof. Also, why must you all shit on the hopes of people who dream of exploring the galaxy?

  2. Why is it that those in the spaceship can’t say that because they are traveling faster than the light emerging from the flashlight, that light drops behind them?

    • You’re absolutely right, as it stands the argument is incomplete; I’d forgotten to explicitly lay out the other major principle needed for this argument. Post updated to reflect.


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