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m74z00219
2010-Jan-20, 06:59 AM
Hi all, I either have a fascinating question or one with a big hole that I'm not seeing...we'll see.

Imagine that there are two objects in a hypothetical universe. A single photon and a dead planet (to serve as a gravitational source).

This photon is heading towards the planet such that its initial heading is not through the central axis of the planet. Now, it seems to me that this photon would be accelerated by the gravitational field of the planet (it's speed would not change, but it's velocity would). This was predicated by Einstein.

Because the photon is accelerating, wouldn't it theoretically emit gravitational radiation?

Is this further evidence that the disarray of my home isn't my fault?


Thanks,
M74

Tensor
2010-Jan-20, 07:33 PM
Hi all, I either have a fascinating question or one with a big hole that I'm not seeing...we'll see.

Imagine that there are two objects in a hypothetical universe. A single photon and a dead planet (to serve as a gravitational source).

This photon is heading towards the planet such that its initial heading is not through the central axis of the planet. Now, it seems to me that this photon would be accelerated by the gravitational field of the planet (it's speed would not change, but it's velocity would). This was predicated by Einstein.

Because the photon is accelerating, wouldn't it theoretically emit gravitational radiation?


The hole you're not seeing is that the photon isn't accelerating. It's following a null geodesic (http://en.wikipedia.org/wiki/Geodesic_(general_relativity)), which equates to free fall (ie, no acceleration).

m74z00219
2010-Jan-21, 01:49 PM
Thanks tensor, that was a great link. It had a decent explanation and so now I think I understand more than I did before.

Thanks,
M74

Tensor
2010-Jan-21, 03:45 PM
Thanks tensor, that was a great link. It had a decent explanation and so now I think I understand more than I did before.

Thanks,
M74

You're welcome. If you want to dig into a bit more, check out the two links at the bottom of that page. Geodesic and Geodesics as Hamilton Flows.

tommac
2010-Jan-21, 06:52 PM
A photon can not accelerate. What do you mean its velocity would change? Its velocity is c regardless .... all it would do is blue shift then red shift ( did I get this right? ). It would gain energy when it entered and lose the same amount of energy when it left the gravitational field.


Hi all, I either have a fascinating question or one with a big hole that I'm not seeing...we'll see.

Imagine that there are two objects in a hypothetical universe. A single photon and a dead planet (to serve as a gravitational source).

This photon is heading towards the planet such that its initial heading is not through the central axis of the planet. Now, it seems to me that this photon would be accelerated by the gravitational field of the planet (it's speed would not change, but it's velocity would). This was predicated by Einstein.

Because the photon is accelerating, wouldn't it theoretically emit gravitational radiation?

Is this further evidence that the disarray of my home isn't my fault?


Thanks,
M74

Tensor
2010-Jan-21, 08:07 PM
A photon can not accelerate. What do you mean its velocity would change? Its velocity is c regardless .... all it would do is blue shift then red shift ( did I get this right? ). It would gain energy when it entered and lose the same amount of energy when it left the gravitational field.

If you would have read his second post, you would realized that he misunderstood the concept of a massless particle and null geodesics. And actually, it's velocity isn't c, regardless. It's speed is c. Velocity is a vector and needs a speed and direction. You did get the red-blue shift analogy right though.

m74z00219
2010-Jan-23, 12:17 AM
You're welcome. If you want to dig into a bit more, check out the two links at the bottom of that page. Geodesic and Geodesics as Hamilton Flows.

I looked into it and it seems these null-geodesics relate directly to the principle of least action and the euler-lagrange equations. I studied this fascinating concept in a classical mechanics class.

So, would it be accurate to say that the path of a photon through a space of any curvature is the path of least action (ie: the null geodesic or shortest path)? For instance, I remember doing the math to find the shortest path from one point to another on a spherical surface. The answer turned out to be a circular path in which the circle intersects the center of the sphere (a great circle).

Anyway, I'm rambling now.

M74

Tensor
2010-Jan-23, 12:46 AM
I looked into it and it seems these null-geodesics relate directly to the principle of least action and the euler-lagrange equations. I studied this fascinating concept in a classical mechanics class.

Yep. You have the fascinating part right.


So, would it be accurate to say that the path of a photon through a space of any curvature is the path of least action (ie: the null geodesic or shortest path)?

Yes, but in the four dimensional manifold that models space-time, it's more correct to talk about the path having the longest proper time. Seem's counter-intuitive, I know.



For instance, I remember doing the math to find the shortest path from one point to another on a spherical surface. The answer turned out to be a circular path in which the circle intersects the center of the sphere (a great circle).

Anyway, I'm rambling now.

Not really rambling. You got it.