biophysics - What happens to body chemistry at the speed of light?

Assume that I'm traveling at the speed of light in one direction. My brain is also traveling at the speed of light in that direction. Presumably there is at least one receptor site in my brain that is oriented in such a way that particles would need to travel faster than the speed of light to reach their destination receptor.

What would happen to those particles? Would my brain cease to function because these particles couldn't reach their destination?

Answer

You’re thinking of velocity addition the “usual” way: if you’re in a bus going 30 mph and you throw a ball forward at 10 mph then the ball will be going 40 mph according to someone outside the bus. But it turns out that this isn’t quite correct when you’re going at speeds ~10% or more the speed of light: the velocities have to add so that nothing goes faster than light. Instead of using the usual formula,

$$ v_\mathrm{total} = v_1 + v_2 , $$

we use the relativistic formula

$$ v_\mathrm{total} = \frac{v_1 + v_2}{1 + \frac{v_1 v_2}{c^2}} . $$

(To be clear, the relativistic formula is always correct; it’s just that when $v_1$ and $v_2$ are small—as they always are in everyday life—the denominator of this fraction will be basically 1, and so the formula reduces to the simpler one that we’re more used to.)

So the answer to your question is that it’s not a problem for a human to be going close to the speed of light. As sb1 pointed out, the electrons in your brain don’t know or care how fast your body is moving; as long as your entire body is moving at the same speed, all of your biological processes will continue exactly as before, because your body is at rest with respect to itself.

The other objection you raised was that the electrons in your brain—which are moving very quickly relative to your body—would be moving faster than $c$. As you can see from the second formula above, velocities always add so that their sum is less than $c$: even if your body is travelling at $0.99c$ (relative to someone at rest) and it contains an electron going at $0.99c$ (relative to your body, and in the same direction), that person at rest will measure the electron as moving at $0.99994c$.