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SpaceTiger
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#13
Dec1-05, 03:09 PM
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Quote Quote by michael879
I thought the classical way of finding the bending of light was by finding the mass of light with whatever debroglies thing is (I forget but I know frequency is in there), and then using that mass to find the gravitational attraction with F = GMm/r^2.
Calculating an effective mass for light doesn't really do anything for you because the deflection angle doesn't depend on the mass of the object being deflected. One way you can roughly derive the classical deflection angle is with the impulse approximation. Imagine you have a massive object with momentum, [itex]p=mv[/itex], coming towards a more massive object in a way such that the distance of closest approach is [itex]r[/itex]. We'll assume that the total deflection angle is small, so we can simply calculate the total impulse provided to the moving body along a straight line path. We could use calculus to get it precisely, but it's easier to say that:

[tex]\Delta p=F\Delta t\simeq\frac{GMm}{r^2}\times\frac{2r}{v}=\frac{2GMm}{rv}[/tex]

The deflection angle is just the added momentum (above) divided by its original momentum. This is because the impulse was perpendicular to the direction of motion. Anyway, this gives:

[tex]\alpha=\frac{\Delta p}{p}\simeq\frac{2GM}{rv^2}[/tex]

Since the result is independent of mass, it's not unreasonable to expect that light would experience a similar deviation, so naively, we can just substitude [itex]c[/itex] for [itex]v[/itex] and get the result I gave above:

[tex]\alpha=\frac{2GM}{rc^2}[/tex]

Keep in mind that this is not the correct result. The correct one is relativistic and gives a factor of two larger, this is just an explanation of how a classical physicist might have approached the problem.


and is it rly off by exactly a factor of 2? that seems like a huge coincidence....
It's not a coincidence, really. It's common for results obtained by classical analysis to be similar to their relativistic equivalents. After all, relativity approaches classical physics in certain limits.