Light bending due to gravity...

[MDJH]

So I was thinking about the idea that light is pulled by gravity... if my understanding (the analogy of light in an accelerating elevator being treated as equivalent to light accelerating due to a force acting on it) is close enough to accurate my logic here should work.

 

Ok, so basically energy is proportional to the product of mass and the square of the speed of light; this resembles the formula for centripetal force, which is proportional to the product of mass and the square of the speed of light, except also divided by the radius of the circle.

 

So according to this logic, the centripetal force that pulls on a photon of light would be proportional to the ratio dividing the energy of the photon by the radius of a hypothetical circle it would be spinning in.

 

This in turn suggests that said radius would be proportional to frequency of the photon, and inversely proportional to the gravitational force. Therefore, how sharp the bending of the light is depends not only on the gravity, but also on how low-frequency the light is.

 

Would I be correct in assuming, therefore, that given approximately equal gravitational forces on each, a longer-wavelength photon would be more easily pulled in by gravity than a shorter-wavelength photon would? Is this why morning/evening sunlight is safer than early-afternoon sunlight?

[swansont]

No, your comparison with the centripetal force doesn't work. The similarity of equations, such as they are, does not carry the implications you propose.

 

The "safety" of sunlight has to do with the amount of atmospheric attenuation and the geometry of exposed surface area.

[lemur]

it makes sense that gravity would compress EM waves. The question is how those EM waves would remain intact and get compressed without the source velocity toward the target increasing. I would expect a high gravity target, such as a black hole, to blue-shift EM waves some but for those waves to fragment into multiple strands of compressed wavelengths. Is this presumptive?

[swansont]

it makes sense that gravity would compress EM waves. The question is how those EM waves would remain intact and get compressed without the source velocity toward the target increasing. I would expect a high gravity target, such as a black hole, to blue-shift EM waves some but for those waves to fragment into multiple strands of compressed wavelengths. Is this presumptive?

 

Absent any other interaction, why would there be multiple paths for the photons?

[lemur]

Absent any other interaction, why would there be multiple paths for the photons?

 

I didn't say anything about multiple paths. What I said was that if EM waves get blueshifted/compressed, but the flow of energy from the source doesn't increase, then the beam should fragment into multiple compressed pulses with breaks of some kind in between. This seems logical if you think of a certain segment of light as containing a certain number of waves within a given distance (say 1 million per meter to make it simple). Then if you blueshift that light to a shorter wavelength, the million waves cannot fill up the whole meter so I would think gaps would have to form at various points in that meter of light. Doesn't that make sense?

[swansont]

I didn't say anything about multiple paths. What I said was that if EM waves get blueshifted/compressed, but the flow of energy from the source doesn't increase, then the beam should fragment into multiple compressed pulses with breaks of some kind in between. This seems logical if you think of a certain segment of light as containing a certain number of waves within a given distance (say 1 million per meter to make it simple). Then if you blueshift that light to a shorter wavelength, the million waves cannot fill up the whole meter so I would think gaps would have to form at various points in that meter of light. Doesn't that make sense?

 

We already have that — EM radiation is in the form of photons. It's not one continuous wave.

[lemur]

We already have that — EM radiation is in the form of photons. It's not one continuous wave.

How does that change what I am talking about? If a million photons are in a meter of light and the light blueshifts so that the same number of photons must occupy 0.9 meters, the there is 0.1 meter whose photon density cannot be as high as the other 0.9 meter, right? If the blueshift is caused by the source moving toward the target, that would be a different story because the light is being compressed from the source. The same would be true if the target is moving toward the source. But what about when the gravity of the target is pulling the radiation toward it? Wouldn't you then have light-compression without additional emissions from the source, resulting in fragmentation of the beam into relatively discreet groups of photons/waves?

[swansont]

AFAIK length contraction occurs gravitationally, too. If the wavelength shrinks, so does the distance, and by the same amount.

[granpa]

time runs slower in the gravity well so the light becomes compressed. There is no need for breaks.

 

This can be seen easily with special relativity.

I dont see any easy way to solve for length contraction in a gravity well.

[swansont]

 

I dont see any easy way to solve for length contraction in a gravity well.

 

http://www.mth.uct.ac.za/omei/gr/chap8/node8.html

[granpa]

that implies that space stretches in a gravity well. (only in the direction of the gravitational fied lines)

Edited September 9, 2010 by granpa