Measured Against Reality

Monday, December 11, 2006

Nothing Can Move Faster Than Light

As a physicist-in-training, seeing physics misrepresented gets me angry. Some of the most common misrepresentations of physics involve the speed of light.

Occasionally I’ll see over-zealous headlines that proclaim “Scientists send [something] faster than light!” This is completely impossible. To explain why, we have to deal with Einstein’s theory of special relativity.

The speed of light (c) is hardwired into Maxwell’s equations, the equations governing electricity and magnetism. It is the speed at which light propagates in a vacuum, 2.99792 m/s. It’s a very fundamental constant.

There are three main reasons that no massive particle can move faster than (or at) the speed of light, the first has to do with velocity addition. In relativity, velocities don’t add simply, they follow the formula:



Close inspection of this formula reveals that nothing can accelerate to the speed of light by velocity addition. C is quite literally the speed limit.

Another reason has to do with energy. In relativity, the energy of a particle is equal to:



where the factor gamma is equal to:



As v approaches c, gamma approaches infinity, and so does the energy of the particle. That means any particle that has any mass needs infinite energy to move at the speed of light, which is impossible.

The last reason that nothing can move faster than c is that it would make gamma imaginary, which would render every equation of special relativity unintelligible.

You might have noticed that everything I said above only applies to massive particles, but the story is pretty much the same for massless particles, except they can only move at the speed of light.

What’s usually going on with those headlines is that the researchers have “slowed light down”, which is misleading as well, because light always moves at the speed of light. The only way it can be slowed down is by entering a medium with an index of refraction that’s greater than one (which is why I previously said “the speed of light in a vacuum”). Slowing light down in this way is possible, and it happens all the time. It’s why things appear to bend at the water-level (which has an index of refraction of about 1.3).

I’ve read articles that claim researchers got messages to arrive before they were sent by altering the speed of light, but it’s just not possible. These usually turn out to fit the mold of the aforementioned “index of refraction” changes. Besides, there’s no good reason to believe that causality can be broken, and no current theory allows it.

In short, nothing can move faster than light, get over it.

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7 Comments:

  • Wait a minute. Special relativity *posits* that c is constant and that the laws of physics (i.e. Maxwell's eqn's) are the same in all inertial reference frames. The equations of special relativity are *implied* by that postulate. If the equations of special relativity don't make sense for objects moving at superluminal velocities, then that *alone* doesn't show that nothing can move faster than c. I believe that the real reason that nothing can move faster than light is that we want the laws of physics to be the same in all frames of reference, if c were to change depending on how fast you were moving, then Maxwell's equations would then have to change as well.

    By Anonymous Anonymous, at 6:41 PM, December 11, 2006  

  • And that would be meaningful if there was any reason to think that relativity is incorrect, which there isn't. It has been verified to fantastic accuracy, which I forgot to mention in the main post.

    By Blogger Stupac2, at 6:44 PM, December 11, 2006  

  • You aren't very specific. Why does this refraction cause people to claim they have exceeded the speed of light?

    The explanations I recall involve front-loading the collapsing wave-form to make it appear that data appears to move faster than c, but I am a layman. Can you describe it more fully?

    By Anonymous Anonymous, at 6:53 PM, December 11, 2006  

  • I'm not saying that spec. relativity is incorrect. Certainly not. What I am saying is that the equations themselves have a deeper basis, the postulates of special relativity:
    http://en.wikipedia.org/wiki/Postulates_of_special_relativity
    (both of these I'm sure you know)

    Empirical results, by themselves, can never supply a *reason* for a theory being true or not. Verification is just that, verification, facts do not link themselves together to form theories.

    By Anonymous Anonymous, at 6:53 PM, December 11, 2006  

  • Hi StuPac - great blog, love most of your posts, but of course my first comment is a gripe:
    You dropped some digits when stating the speed of light, like a x10^8 or so ... and missed the main point of 'Faster than the speed of light' headlines, specifically FRAME OF REFERENCE.

    I do loves me some physics, and all people should have a hard science background!

    By Anonymous Anonymous, at 12:10 PM, December 12, 2006  

  • Interesting, I guess, but I think you're arguing against a straw man. I am not aware of anybody (outside of science fiction) claiming that something has surpassed the speed of light. And you didn't link to any such claims.

    By Blogger Ken Zirkel, at 1:10 PM, December 19, 2006  

  • I have also heard people claim this,just search the web for "Faster than light travel".

    By Anonymous Anonymous, at 7:59 PM, June 29, 2007  

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