# 100m sprint at light speed.

1. Aug 4, 2010

### idiotphysics

Help me out please. I need a definitive comment for a book I'm writing. Hypothetically - if Usain Bolt were to approach (c) in a 100m sprint - his mass would become infinite right? basic E=Mc2.

At inifinite mass - space-time would warp (correct?). And light would bend (right?)

Can I say that time will appear to slow down to an observer (spectator) watching Usain in motion?

Note: I am an economist not a physicist. So please dont shoot me down if I have it wrong. Correct me. But I really need a good answer. Many thanks!

2. Aug 4, 2010

### fatra2

Hi there,

Not an expert in this field either, but
True, but not with this equation. This tells us only that energy and mass are closely related. His mass would follow something like this:

$$\frac{m}{\sqrt{1-\frac{v^2}{c^2}}}$$

Not from what I understand of it. The space-time dimension would change for Usain, but not for you that is watching him. For the bendin light, and again from your point of view, it would be hard for light to bend around him, since he would be moving at the same speed.

Once again, not from my understanding of the sîtuation. Nothing happened to you, therefore, why would time/space or any other dimension change just because he is running. But these parameters would change for him.

Now, as I said, I am not an expert in relativity. So if I made mistakes, I am also here to learn something new.

Cheers

3. Aug 4, 2010

### bcrowell

Staff Emeritus
This depends on what you mean by "warp." To me, that word could refer to two different things: (1) The difference in the perception of flat spacetime between two observers in different states of motion. (2) Curvature of spacetime.

If you mean 1, then the answer is yes. If you mean 2, then it depends on the observer. In Bolt's own frame, spacetime is flat. In the frame of an observer watching him run at close to c, Bolt's high mass-energy causes intense gravitational fields, which GR describes in terms of curvature of spacetime.

This depends on whether "bend" refers to (1) aberration, or (2) bending of light by gravitational fields.

To the spectator, it's the runner's time that appears to slow down, not his own time. To the runner, the spectator's time appears to slow down.

4. Aug 4, 2010

### bcrowell

Staff Emeritus
There's nothing wrong with the OP's use of $E=mc^2$ to express this relationship. Depending on conventions about what is meant by the symbol m (rest mass or relativistic mass), your equation and his can give the same result. (As a minor technical point, it isn't really correct to try to use either one of these relationships to find gravitational fields, because in GR the source of the field is the stress-energy tensor, not the scalar mass.)

He can't move at c. He can only move at a speed close to c.

5. Aug 4, 2010

### idiotphysics

1. So is it fair to say that to a spectator (stationary) it would appear as if Bolt was running through an invisible sticky syrup or slow motion?

2. I read somewhere that for the runner (in this case Bolt) it would seem as if he was standing still (at reast) and if he looked at the crowd - they would be zipping by.

What are the facts please? And my gratitude for your time & interest.

6. Aug 4, 2010

### yossell

Well...this is a bit confused. Of course, from the spectator's view, he's going at incredible speed - close to the speed of light, so not slow motion in this sense. His run would be over in a flash. But it's also true that, from the spectator's point of view, Bolt's wrist-watch, his heart-rate, all the process would be slowed down.

However, one exciting fact that always gets the readers going is the fact that Bolt would look incredibly thin. Moving objects shrink in the direction of motion (in the stationary observer's frame), so Bolt would appear to be incredibly compressed and flattened, probably not even a hair's breadth between his back and front.

meh - this is just the relativity of motion - the idea that you can treat an object moving with constant velocity as at rest, and other things moving wrt to him. In a sense, this is an everyday experience - just go on a train or a plane and it seems as though the world is zipping by. In practice, there are frictional forces acting on runners which slow them down, and that's why running requires effort. This isn't really particularly relativistic.

What's shocking is that, from Bolt's point of view, it's the audiences clocks that are running slow, and the track that seems to have been length contracted to a hair's breadth. Now, that is relativistic.