Question

I'm just reading a book about gravity. An example it gives is a spaceship accelerating. A beam of light travelling at right angles to the direction of movement of the spaceship enters it via a small pinhole. The book states that the beam of light would appear to bend to an observer within the spaceship. Intuitively this makes sense - if the ship were travelling at 0.5c, for example, and was 10m across (from the pinhole to the opposing wall) then I'd expect the light to hit the wall 5m further back down (assuming the ship is accelerating "up") from the pinhole - the wall would have moved 5m further in the time it takes the light beam to cross the interior to the opposing wall

I think I'm fundamentally misunderstanding though. The book states this is down to the acceleration of the ship and goes on to talk about how using equivalence the same bending would be a result of gravity. In my description above though, it's the velocity that causes the apparent bending, and the same would be visible if the ship was maintaining a constant 0.5c. I suspect that if this were the case (constant 0.5c) there would be no bending at all, but I'm not understanding why

Can anyone enlighten me?

Answer 1

It's not the velocity that causes the bending, it's the acceleration! If the spaceship were moving by any but constant velocity in the absence of a gravitational field, the path of the photons would be straight, wouldn't it? The motion of any uniformly moving object (or photon) always looks straight in any other inertial (uniformly moving) frame. The path gets curved, "parabolic", just because the velocity isn't constant.

The equivalence principle equates the situations of an accelerated spaceship with a static spaceship sitting in the gravitational field, with the correspondence a?g. So if the path of the photon is curved in the accelerated spaceship, it should be curved in the gravitational field (but with no extra motion), too, although I am not quite sure whether this simple argument produces the right factor of two that a naive Newtonian "attraction acting on light" misses relatively to the correct general relativistic calculation.