Can a baseball travel through the Sun? A baseball moving sufficiently close to the speed of light could theoretically spend less than a nanosecond inside of the Sun in the balls frame. If a baseball were traveling close enough to the speed of light, could it pass through the Sun?
Edit: Imagine a single proton traveling with 1 TeV of relativistic kinetic energy. It can and does pass right through a human body without fusing, stoping or destroying the person and so on. Now imagine a baseball with enough energy that a single layer of the Sun only one atom in thickness can be easily penetrated without taking away all of the relativistic momentum of the particles constituting the baseball. Then imagine the scenario again with two atom thickness and the required energy to penetrate that layer. Then continue this exercise until a baseball passes through the Sun. If you think that it would "burn up" how would its 4 momentum be conserved? I think it's just a matter of what velocity is required to make it to the other side.
 A: No, it could not. The issue of how much time it spends inside the sun is not relevant, even though it at first might seem so. A baseball at rest inside the sun for a sufficiently short time would only experience a very short exposure to the "normal" (at rest with respect to the sun) thermal and radiative effects that exposure, and so would be OK. If the baseball were traveling at relativistic velocities, though, the particles constituting the sun would, relative to the baseball, be slamming into it at the speed of light. This would cause lots of awful things for the baseball. For one, some of the particles hitting the approaching surface of the baseball would undergo nuclear fusion with it. For another, there would be significant spallation chewing away at the approaching surface of the ball. It would basically be the same as Randall Munroe describes in his first XKCD What-If. So even though the baseball would only be exposed to the sun for a very short time, the processes destroying the baseball due to its relativistic collision would also proceed very quickly, so the baseball will still not have a good time.
