# Bending of light

1. Nov 26, 2013

### shounakbhatta

Hello All,

Kindly apologize if this question sounds rudimentary.

General relativity which shows the bending of light. Is it due to:

(a) Spacetime is curved due to massive objects and when light passes through that object, facing the obstruction it bends?

(b) There is as such no force which causes the photon to bend?

Am I right?

2. Nov 26, 2013

### Mentz114

I think you're nearly right. Perhaps

a) Spacetime is curved due to massive objects and when light passes near that object it is deflected.

is more accurate. There is no force.

Light bends in accelerated coordinates also, see http://www.newtonphysics.on.ca/einstein/chapter10.html

3. Nov 26, 2013

### shounakbhatta

Thank you.

One small question. When we are accelerating, we get a curve. Is it due to the curvature of spacetime or any specific property of acceleration?

4. Nov 26, 2013

### Mentz114

Acceleration is a vector so it has direction and magnitude and no other properties. The bending of light due to acceleration (say in the 'Einstein elevator' ) can happen in flat spacetime, so it cannot be attributed to spacetime curvature.

I've attached a paper by Ehlers and Rindler which may be helpful.

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• ###### Ehlers&Rindler-Light Bending.pdf
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5. Nov 26, 2013

### WannabeNewton

Don't confuse these two things. The deflection of light due to curved space-time geometry is an honest geometric effect and it doesn't disturb the fact that a null geodesic is describing this light ray; trajectories of observers and light rays being curved in different coordinate systems is a coordinate artifact. In the end light rays (within the geometrical optics approximation) always get described by null geodesics in the absence of non-gravitational interactions and that's what counts.

6. Nov 26, 2013

### shounakbhatta

So, can we say that when we are accelerating in even a flat spacetime, we get a curve?

Also, bending of light due to curved spacetime is a geometric phenomena and these two are different and should not be confused.

Mass causes the curvature and gravity is the geometric phenomena of curvature. Right?

7. Nov 26, 2013

### Mentz114

The equivalence principle states that the effect of acceleration cannot be distinguished from the effect of a gravitational field, with provisos about the extent of the experiment and the 'uniformity' of the field.

Mass and energy density cause curvature.

8. Nov 26, 2013

### WannabeNewton

Let me clarify something. If an observer is accelerating (flat space-time, curved space-time doesn't matter for what's to come) then this observer can measure this acceleration locally using an accelerometer. Geometrically, the worldline of the observer has a path curvature in space-time given by the 4-acceleration. This is an absolute measure of curvature of the worldline that has no dependence whatsoever on a choice of coordinate system (hence why it is a geometrically meaningful quantity). This goes back to the fact that the observer himself can measure the acceleration using an accelerometer.

On the other hand, we can choose a particular set of coordinates and write down the coordinate trajectory of the observer. This will give in general a curved trajectory for the observer in these coordinates and hence has no geometric meaning; it is simply the trajectory of the observer as represented in this specific choice of coordinates. I can just as easily go to a coordinate system that is comoving with the observer and in this set of coordinates the observer is always at a constant spatial coordinate and hence just has a straight line trajectory along the temporal axis.

Yep.

Last edited: Nov 26, 2013
9. Nov 26, 2013

### shounakbhatta

Thanks.

Ok, actually I was getting confused that acceleration causes a curve so it gives a hint that spacetime must be curved. Thank you for clearing the doubt.