What Happens to Baseball When Light Speed is Just 88 MPH?

[DarkMetroid]

Okay, so the problem is that I'm supposed to analyze what the world would look like if the speed of light is 88 miles per hour (BTTF tribute), and so I naturally looked at the basics of baseball: the pitch. Yet something seemed wrong.

So, imagine playing baseball. For this problem, the pitcher and the batter are not moving with respect to each other. The batter prepares to bunt. Since the speed of light is 39.3 m/s, and the distance between the batter and the pitcher is 18.4 m, it will take (18.4m)/(39.3m/s) = 0.47 seconds before the batter even recognizes that the pitcher is throwing the ball. For that half second the event of pitching is in the elsewhere of the batter; he watches the wind-up as the pitcher marvels at his excellent pitch! Let’s say that, because of the increased effective mass of the ball at higher speeds, the pitcher can throw a fastball 30 m/s (67 mph) with respect to the players. This means it takes 0.61 seconds to reach the batter. Unfortunately, he had detected that it was pitched just 0.15 seconds before! That is not sufficient time to provide a useful reflex.

Yet doesn’t this seem to contradict relativity? It appears to the batter that the ball travels 18.4 meters in just 0.15 seconds, three times faster than the speed of light! What went wrong?

This would relate to the real world, because by the same math (that is somehow erroneous; I don't know), there would be a speed less than C in which the batter would observe the ball going faster than C.

 

[Chris Hillman]

This sounds like a homework problem (certainly I've seen instructors assign this as a problem). PF has a special section for these with some special rules.

 

[Count Iblis]

Note that the value of c isn't relevant in physics, it merely (partially) defines the system of units (or vice versa) and the whole point of units is that you can choose them as you please. So, in this problem you can just as well set c back to it's original value and then take the unit of length to be a redefined meter (let's call it meter') so that

c = 39.3 m'/s

Then express meter' in ordinary meters and you can solve the problem in ordinary units where c has the usual value of 299792458 m/s.

 

[cesiumfrog]

Yet doesn’t this seem to contradict relativity? It appears to the batter that the ball travels [..] faster than the speed of light![..]?

By the same logic, it "appears" that light travels instantly. And it "sounds" as though sound also travels with infinite velocity.

 

[Dale]

Yet doesn’t this seem to contradict relativity? It appears to the batter that the ball travels 18.4 meters in just 0.15 seconds, three times faster than the speed of light! What went wrong?

The batter (being a well-educated batter) knows the speed of light and (being a professional ball player) knows the distance to the mound. So he knows that when he sees the pitch it already happened .61 s earlier. So he knows that the total travel time of the ball is .76 s, not .15 s.

With all the importance of the speed of light it is a common misconception that relativity deals with the way things "look". Relativity is about what really happens, and propagation delays caused by the finite speed of light are always taken into account.