Photons Affected by Pseudo Forces | Hyperspace by Michio Kaku

[deep838]

I was reading a book called "Hyperspace", by Michio Kaku, and there he gave a sort of introduction to general relativity. Well its not at all technical, just for reading and knowing...

There he claimed that space is curved because light rays will take a bent path inside an accelerating spaceship.

But he didn't explain why light rays would bend in the first place!

 

[WannabeNewton]

Light rays "bend" because space-time is curved not the other way around. More precisely, null geodesics in curved space-times will only locally be straight lines. Globally they will be non-trivial curves.

 

[deep838]

Okay, so why do we take space-time to be globally curved and not straight?

 

[WannabeNewton]

Do you mean not flat? In Einstein's theory it's because gravitation manifests itself as the curvature of space-time.

 

[PAllen]

Light rays bend in an accelerating spaceship for a very simple reason: the ship moves between emission on e.g. one wall, and the light hitting the other wall. Thus, within the ship, the light appears to follow a curved path.

The way to get from this to light bending in a gravitational field is the principle of equivalence. This says that locally, anything that happens in an accelerating rocket will happen indistinguishably in lab sitting on ground of large gravitating body (crudely, but good enough for our purpose). This principle has been verified to high precision and great generality. Thus light bends in the Earth lab. However, since the Earth lab is static, what accounts for light bending in this static scenario? Further, the direction of bending is toward the earth, everywhere around the earth. A reasonable way to account for this is curvature. By analogy, the straightest possible lines on a sphere curve, and two initially parallel geodesics (straightest possible lines) can converge or diverge.

This is all very much a hand wave, but it is possible to make this type of argument rigorously.

 

[deep838]

And why does gravitation require a curved space-time?

 

[WannabeNewton]

And why does gravitation require a curved space-time?

This is a consequence of the strong equivalence principle, at least from the way Einstein chose to use it.

 

[deep838]

Ok... thanks to both of you for making this a bit more understandable.

 

[pervect]

I should add to this that experimentally, we've observed the spatial part of space-time curvature. This is shown in particular by measurements of the PPN parameter gamma, by either light deflection and/or the Shapiro effect.

gamma = 0 is consistent with no spatial curvature, and is not consistent with measured results. gamma=1 is the amount of curvature predicted by GR, and is consistent with experimental results.

http://en.wikipedia.org/wiki/Parameterized_post-Newtonian_formalism in particular mentions that Cassini tracking puts |gamma-1| < .000023, where gamma is somewhat loosely described as "How much space curvature g_{ij} is produced by unit rest mass".