what-if.xkcd.com/1/

So as you may or may not know there is an excellent web comic out there that I am convinced that my friend Trip writes, although I know in reality he doesn’t, Randal Munroe does, called xkcd. It is a comic about a lot of things and since becoming popular the writer/artist has branched out into a lot of things that are also neat and interesting. One of the things he’s started doing recently is a series answering fan-supplied questions about ridiculous or interesting or ridiculously interesting topics. They have been very good so far and in my realm of expertise they all seem to be spot on. All that is except the first one he did. In this one he successfully did something that only a few other people have done in the history of the world and that is that he touched on my particular area of expertise, which is the combined area of aerospace and nuclear science/engineering. I’m more of a space guy as per the aerospace side of things, which is important for the proceeding argument because I am not disputing his interpretation of events as they would play out in the aerodynamic sense.

So here is the question: What would happen if you tried to hit a baseball thrown at roughly 90% the speed of light?

Randal’s answer is very good, from a purely Newtonian physics combined with Quantum Mechanics, which takes care of the small stuff, point of view, but I think it falls short in two distinct areas. The first is in his treatment of material solid structures and the composition of the ball as it hurtles through the air going 90% c (c is the typical letter used as shorthand to denote the speed of light. 0.9c is shorthand for 90% the speed of light). I’m not a structures guy for the most part, but I have a feeling that the ball’s solid structure wouldn’t last past the first few impacts with the air molecules. Either the ball would rip itself asunder due to wave propagation through the lattice of the leather and rubber or the chunks of the ball would explode out of the back of the ball as individual pieces of the ball were de-accelerated by the molecules they interact with and ripped from their lattice, taking anything behind them with them. Either way, the ball would never reach the batter as a ball, but it might reach him has a de-accelerated mass of plasma, which is basically what Randal suggests will happen…which means that this is basically a nitpicky kind of thing.

The second shortfall I think has more wide-ranging consequences and that is the explanation of the effects inside of Newtonian Mechanics. Unfortunately at 0.9c the ball, and anything in relation to the ball (a.k.a. the pitcher, batter, audience, the earth, and the guy overlooking the game from a hill a block away) have to be considered in the realm of General Relativity. Without getting too into it, because honestly I’m more of a Special Relativity kind of guy, an object traveling at 0.9c which has mass can have a tremendous impact on the local curvature of spacetime (a.k.a. gravity), hence distorting both how everything is related to each other in space and how events will transpire in time. Since general relativity depends on matter that has momentum and energy our baseball scenario needs to be considered in terms of how the baseball will affect local gravity. Usually we only concern ourselves with matter that has lots of energy and how they affect gravity, stuff like stars and planets. But here we have something that has matter and an extra-ordinary amount of momentum (which is just mass times velocity). Theoretically these objects would have an effect on gravity similar to high energy matter.  Now I don’t have any evidence to give you as to what effects it will have since we don’t typically see things with the mass of your average baseball coming anywhere near 0.9c in speed. Our Galaxy for instance is only flying through space at roughly 600 km/s, roughly .002c. The sun is going something near 220 km/s around the center of the milky way. The earth is going around the sun at roughly 107,300 km/h, and is rotating at 1674.4 k/h if you are standing at the equator. Now let’s say that everything is aligned such that all those velocity vectors add together, which it would every once in a while (give or take a few millennium), you’re still only moving at 850 km/s, which is still only 0.0028c. Sure you could also be on a rocket moving as fast as we can move things, but you’re not going to get much faster than 0.0028c. So we just don’t have any real hard data about what happens to large solids at speeds of 0.9c, or what they do to space-time in their general area.

But this is what I think would happen, given what we do know about general relativity. As the baseball is moving from the pitcher’s mound to the plate, disintegrating into a fast moving ball of plasma, it will also curve spacetime around it created a local gravitational pull. This will in turn cause everything close to the ball to pull toward the ball. The pitcher would literally be dragged behind the ball after he let it go. The batter, umpire, other players, people in the stadium, the ground, and everything else nearby gets pulled toward the ball as well, while the ball is moving. It would be like the ball was a really strong electro-magnet and everything around it was metal. As the ball moved through space everything would move toward it…and because it’s plasma, everything would be slowly disintegrated and then fused…which would in effect release more energy to fuse more things. As the ball progresses through space the only hope that the fusion reaction does not become self sustaining is that it sucks in enough iron, and similarly high binding energy elements, that the plasma ball burns more energy breaking apart matter (breaking molecular bonds and fissioning atoms) than it makes putting it back together (fusion). In the event that it drowns itself (Not literally, water is actually a terrible idea in this circumstance…although it might work given the hydrogen bonds…hmmmmm) then you will indeed get the explosion as Randal states, although I imagine it would be larger…likely taking out a larger chunk of the surrounding city. Luckily due to the structure of most matter laying around a baseball field it is highly likely that the fusion reaction will not become self-sustaining. In the event that it did become self-sustaining, congratulations someone just “pitched a star”.

There is another element to consider here as well and that is the effect on time. Anything close to the plasma ball will feel the effects of gravitational time dilation. This means that anything close to the ball will experience time at a different rate. So for the pitcher, batter, and everyone in the stadium everything happens before they know what happened. But for the observer on a hill, everything that happens near the plasma ball is in a kind of weird slow motion, not really that slow mind you, but slow enough to see the ball of pure light streak from the pitcher to the batter, while starting to implode, and then of course the resulting explosion.    

 

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