# Is the Light REALLY bent?

I've learned that always, the light go straight. The as Einstein's gravitation therory, the light can be bent in bented space-I mean, curved space. Actullay, I think that if we in the space which interrupted by gravity, we can SEE a straight light. (The direction can be choosed by observer) So, what is right??

• When space(time) is bent (curved), what does straight mean? – Alfred Centauri Oct 11 '17 at 2:24
• I mean, when it(space) curved, maybe the observer (in the same acceleration coordination system with light) can see the light direction as a straight line. But I'm not sure about this. – Alfred Kim Oct 11 '17 at 3:40
• Possible duplicates: physics.stackexchange.com/q/107930/2451 and links therein. – Qmechanic Oct 11 '17 at 7:16

## 2 Answers

Well this matter is probably mostly quibbling about fine definitions, but light follows so-called lightlike geodesics in spacetime, so as a matter of principle I would say that it follows "straight lines". A geodesic is simply the notion of a straight line generalized to the case where the geometry in question does not fulfill Euclid's parallel postulate. You can't do any better that this to generalize the notion of a straight line in Euclidean geometry.

Now, this generalization does not have all the properties of a Euclidean straight line - we've lost the parallel postulate, after all. In particular, the geometric distortion means that it can "look" bent from the point of view of a distant observer (in the sense that its projection onto a distant, inertial astronomer's field of view is a curved line). And it is no good defining "straight" to be something that projects onto a straight line on this astronomer's field of view, because that definition would be observer dependent. You can't conserve any more of the notion of straightness in non-Euclidean geometry than what is encapsulated in the definition of the notion of geodesic.

A minor pedantic point: the principle that light travels in straight lines only holds if the wavelength / frequency is much smaller than the length scale over which spacetime deviates significantly from flatness. Otherwise, diffraction effects become significant.

Newtonian Theory

I've just noticed that you've tagged your question "Newtonian Gravity". In Newtonian gravity, which takes place in flat spacetime, light is indeed bent. It's a little bit problematic defining exactly what one means by gravitational action on light in this model, but any small mass travelling at $c$ follows the same, Newtonian, bent path uniquely defined by any tangent to the path. This assertion in this theory depends on what light's composition is: if we solve Maxwell's equations in flat spacetime, we get Euclidean straight lines for the Eikonal approximation (ray theory) regardless of what gravitating mass is present, so there is no bending. Newton thought of light as a particle, therefore it is clear he would have predicted the bent, Newtonian path would he have known the speed of light $c$. All we can say in Newtonian theory is that if we assume there is some small coupling constant between light and the gravitational field that isn't present in the flat spacetime Maxwell's equations, then light follows well defined bent paths uniquely defined by any tangent to those paths, and that the paths are independent of the coupling constant, as long as it is nonzero (it can be arbitrarily small) and not so large that the light itself disturbs the Newtonian gravitational field.

The deflexion predicted from these small mass paths is what people are talking about when it is said that Newtonian theory predicts half the deflexion of GTR.

If you are really interested in the Newtonian theory of deflexion of light, then I certainly can't claim to be knowledgeable about all the theory. There was a great deal of thought put into this question in the late nineteenth century before 1915: it's quite a large topic in itself.

• Newton/GR deflection is flipped. Newtonian theory predicts HALF the deflection of GR. en.wikipedia.org/wiki/Gravitational_lens – Gary Godfrey Oct 11 '17 at 4:56
• @GaryGodfrey Thanks: i had the order of things in my sentence the other way around to what I was thinking. Fixed now. – WetSavannaAnimal Oct 11 '17 at 7:04
• Brilliant answer as always dear Rod. I hope you don't mind if I use this chance to also bring another post to your attention, hopefully if time allows, your input would be most valuable. In any case, thanks for all your wonderful contributions to this website, I always thoroughly enjoy reading your answers. Best wishes – user929304 Oct 11 '17 at 13:24
• So... I understanded like this; In the space area, not anymore space doesn't follow Euclid's parallel postulate. So there is no valuable to define the straight line. Whether the distace between astronomer and light is long or short, the Light can be viewed curved. – Alfred Kim Oct 13 '17 at 3:03

Something is clearly bent. You can imagine two not quite parallel beams of light passing by opposite sides of a massive object, arranged so that they cross each other in two places, once before the object and once after the object.

Straight lines in a flat Euclidean space don't do that.

General Relativity is flexible enough for you to describe this as bending the beams of light, or as bending space-time, or whatever. But whichever way, something is bent.

• Gravitational lensing (where you see two images of a source of light behind a massive object) is basically observing the double-intersection: the source of the light is one crossing-point of the light-rays, the telescope looking out from earth is the second. – user1998586 Oct 11 '17 at 7:58