# Light deflection at high speed

1. Sep 21, 2006

### Ich

Hi,

someone asked me how light would be deflected when the sun were moving at high speed along the light ray.
The simple answer is: transform in the sun´s rest frame, calculate the deflection and transform back to the observer´s frame. The result is that the deflection would be greater when viewed from a different frame.

I have now two questions:
1. Is this correct?
2. Is there a way to explain the result natively in the observer´s frame, something like a strengthening of the sun´s gravitational field in transverse direction, increase of the relativistic mass of the sun, or gravitomagnetics?
I hope someone can help.

2. Sep 21, 2006

### RandallB

Hard to tell what your talking about; but assuming you mean a beam of light coming toward the Sun & Earth such that you will see the deflection on earth.

Then you change the motion of the Sun & Earth in their common FrameOfRef to a speed of say 0.8c away from the source of the light you are watching.

The deflection will remain the same, the only difference will be in the color of the light you are observing as it red shifts. No change in math, mass, gravity or gravitomagnetics? As the light will still be traveling at “c” as observed by Sun and Earth. Just a different color.

Last edited: Sep 21, 2006
3. Sep 21, 2006

### pervect

Staff Emeritus
Yes, the approach is correct.

As far as I know there are no correct shortcuts, i.e. the above is the simplest approach. It's certainly the most straightforwards approach.

4. Sep 21, 2006

### RandallB

????
Are you saying you agree that;
"The result is that the deflection would be greater when viewed from a different frame."
Which would mean light with a lower Hz (red) should deflect more than others light (blue). I don't think that is the case.

5. Sep 21, 2006

### pervect

Staff Emeritus
The amount of deflection will not depend on the frequency of the light.

The way I understand the problem is this:

At infinity, light will travel in essentially a straight line path. One pretends that space-time is flat everywhere, and then extends the straight-line course that light takes at infinity so that the two lines (the two lines being "before" and "after" the light encounters the mass) meet at a point. One then measures the angle between the two straight lines. This angle, measured entirely in flat space and flat space-time, is called the 'angle of deflection'. This is a coordinate dependent quantity. I'm not exactly clear on how pernicious the coordinate dependencies are in this problem, offhand.

6. Sep 21, 2006

### RandallB

I agree.
But the OP as I see it, is asking how would the deflection change with that some light if you were to change the Sun & its reference by moving it at a high speed in the same direction as the light. You seem to agree with the OP in your earlier post that the deflection would change (larger deflection) due to the movement of the Sun. I disagree, it should see the same thing as it already sees with other light coming by with more red shift and deflecting the same as the blue light. Because that is all that will happen to the original light, become more red, if the sun is moved as the OP asks.

7. Sep 22, 2006

### pervect

Staff Emeritus
Pretend everything is in flat space-time. Distances in the direction of motion will contract, while transverse distances will not. This will cause the angle to change.

8. Sep 22, 2006

### Ich

Thanks for the answers.
Maybe I didn´t express myself very clearly, but pervect obviously understood what I meant: the deflection as measured in a frame moving relative to the sun.
Could you imagine a more complicated approach which treats the problem in the moving frame, avoiding the LT-shortcut? The one who asked me likes "explanations", not only the result. Is there a way to describe it in Post-Newtonian terms?

9. Sep 22, 2006

### exponent137

Is this true.
When I am standstill I measure angle 1.75"" of starligh deflected by the sun. When I very fast move closer to the sun (equivalently as sun move very fast) the distance to the star and sun become gamma times smaller. So the angle become larger?

10. Sep 22, 2006

### RandallB

OK you did not mean the “when the sun were moving at high speed along the light ray” from the OP.
Rather the question was just for an observer travel by the sun in the same direction as the photons being deflected.

Then the ‘explanation’ is a simple SR problem observing the triangle that forms the angle of deflection. The observer sees no change in the perpendicular side length but observes the length of the side parallel to the direction of relative travel as shorter. The changes in observed angles, as pervect pointed out, are then obvious.