# Acceleration and Light

1. Mar 20, 2013

### big_bounce

Hello all ,

When a photon gets closer and closer to black hole , gravity affects photon and changes direction of photon's moving .
Is that mean photon gets acceleration near gravitational field ?

Thanks.

2. Mar 20, 2013

### HallsofIvy

Staff Emeritus
No. Gravity affects, directly, an object's energy. For "massive" objects, that means primarily its kinetic energy and so its speed. For light, which has no mass, the energy is plank's constant, h, times the speed of light, c, divided by the wave length of the light. h and c are constants so, if the energy increases, the wavelength decreases.

3. Mar 20, 2013

### DrDu

Yes, obviously light flying by a massive body changes direction and hence is accelerated, at least transversally. However the gravitational interaction with light is more complicated than with massive bodies. E.g. two light beam travelling parallel to each other won't attract each other but counter propagating rays do.

4. Mar 20, 2013

### Naty1

Light always travel at a constant speed 'c' locally in a vacuum....and it always follows a null geodesic [space-time path].

See 'gravitational lensing',

http://en.wikipedia.org/wiki/Gravitational_lensing

You can also read about the energy of light via 'gravitational redshift' or 'gravitational blueshift'......

5. Mar 20, 2013

### DrStupid

The acceleration is

$\vec a = \frac{2}{u} \cdot \vec v \cdot \left( {\vec v \cdot grad\;u} \right) - u \cdot grad\;u$

where u is the "local speed of light" according to the Shapiro delay.

6. Mar 21, 2013

### big_bounce

Any more idea ?
I didn't get clear answer .
Yes or no ?

I didn't talking about energy of photon .
I just want to know , does it get acceleration or not ?
If not , why ?
According to Newton's first law of motion we know objects in motion tend to stay in motion with the same speed and the same direction unless acted upon by an unbalanced force.
If we consider gravity a force, gravity must change direction of photon's moving .

Thank you

So you say when gravity affects photon , photon didn't changing it's direction and just follow space-time path ? and follow space-time path does not mean changing direction ?
Thank you

I searched internet but i couldn't find this equation
Can you give a link from University website ?
Thank you .

Last edited: Mar 21, 2013
7. Mar 21, 2013

### Naty1

Quote by Naty1
So you say when gravity affects photon , photon didn't changing it's direction and just follow space-time path ?

I'm not sure what you are saying here..it seems self contradictory.

Did you read the definition of a 'geodesic' or the link to 'gravitational lensing' ? They explain in more detail.

Gravity does cause a photon to follow a curved path when viewed from a distance.....

and follow space-time path does not mean changing direction?

It can do both.

8. Mar 21, 2013

### Naty1

yes, because the direction is changed, hence the velocity direction....but not the speed...

uniform circular motion, as an example, such as the rotation on the circumference of a rotating circle has constant acceleration and speed...but we say the velocity is constantly changing because the direction of motion is constantly changing.

9. Mar 21, 2013

### Ibix

The answer depends a bit on the question you are asking and the level at which you are asking it.

The speed of the light does not change in a gravitational field, if that is what you are asking. Instead, its wavelength and frequency change as HallsOfIvy said. However, light can change direction and you might call that an acceleration. Certainly it would be called an acceleration by Newton, but Newton's theory of gravity provides no mechanism for gravity to interact with light.

General Relativity does provide a mechanism, but it's a bit more complex. In GR, gravity is not a force. It is the geometry of spacetime. The basic concept is that everything moves along paths called "geodesics" unless there is a force acting. If there's no gravity, geodesics are straight lines, and objects move in straight lines. When there is gravity, geodesics are curved lines so objects follow curved paths (for example, the trajectory of a thrown ball is a geodesic). Whether or not following that curved path is an acceleration depends on your definition of acceleration - some people make a distinction between "proper acceleration" (when a force is acting) and "coordinate acceleration" (when spacetime is a funny shape) to avoid confusion.

Is that a straight enough answer? Or was it a curved geodesic?

10. Mar 21, 2013

### DrStupid

I derived it for gradient-index optics using the Huygens–Fresnel principle. Unfortunately I didn't kept the calculation. I just remember it was a little bit tricky.

11. Mar 21, 2013

### big_bounce

Good explanation .
Thanks for giving me your time and thanks all .