How does Superman fly?

I've seen in several places where so-called physicists have declared that the scene in the first Superman movie, in which he flies around the Earth and reverses the flow time, is impossible. This is because they have not thought through his mode of propulsion and the results that derive from that.

First, how does Superman fly? Well, the last time I checked, he didn't fuel up on bean burritos before going on a trans-atlantic flight. This means that he is not likely expelling and kind of propellantto get his thrust. But, if he doesn't have anything coming out his back end, then he must not be able to get forward thrust, hence he can't fly. QED. Not so fast, says the geeky general relativist. He can get an effect that looks like thrust from an outside observer. It's obvious that he must have some way of manipulating the gravitaional field locally around his body. Whether he has some exotic matter in his cells, or whatever, the details of the mechanism are left out for now. Once you accept the fact that he can manipulate the gravitational field, all of his powers become logical conclusions from this fact. He can fly because he isn't thrusting himself up, but altering his local gravitational field so that he falls upwards. He can anchor himself to the ground and stop a steaming locomotive because he alters his ADM mass to appear much heavier to an outside observer. He can catch a falling Lois Lane without liquefying her insides by altering her acceleration downwards, once she gets close enough to him to fall into his general relativistic effects.

And, he can make time on the Earth go backwards. By flying around the Earth, he sets up a rotating ring of severely warped spacetime. This sets up closed causal loops that allows him to slip backwards to a point in the Earth's past. Simple really :-)

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