Photon wavelength shift from gravitational lensing?

[toliynyk]

The basic question is: will a photon traveling through a vacuum lose some of its energy due to interactions with gravity from a massive body?
Gravitational lensing implies that the photon will change its initial direction but is its energy conserved (i.e. differences in blueshift/redshift before and after the point of closest approach to the gravitational origin)? Classical theory implies that both objects contribute to the gravitational interaction and since the photon is assumed to be massless, then the delta in kinetic energy should come from its wavelength... any suggestions?

 

[Bill_K]

The energy of the photon will be the same before and after the interaction. That is true, at least, for the kind of gravitational lensing that we observe, where the deflection is extremely small.

If you imagine an extreme situation in which the photon has a very close approach to a black hole and consequently undergoes a large deflection, then the statement needs to be qualified: in the rest frame of the black hole. In a rest frame in which the black hole is moving, the photon (or any other projectile) will experience a "slingshot effect" similar to the one that has been used to add speed to a planetary spacecraft as it undergoes a close approach to Jupiter.

 

[toliynyk]

The energy of the photon will be the same before and after the interaction. That is true, at least, for the kind of gravitational lensing that we observe, where the deflection is extremely small.

So what I understand is that if there hypotheticaly IS some sort of energy shift going on, it lies well within the current observational error? If so, can't this effect stack up in, say, x->infinity lensing events? i.e. a photon slowly snaking through billions of light years of variable gravitatioanl fields... even if the effect is miniscule it'll to get "tired". I know I would :)
Which leads to an other question - has anyone done the calculations on the probability and posible magnitude of such an event? I keep getting the standard redshift equation when I try to calculate this so I'm rather confused...

 

[Drakkith]

I would say that the average photon experiences equal amounts of gravitational pull in all directions over a long period of time, probably having little overall effect on it's observed frequency once it reaches us.

 

[Vanadium 50]

So what I understand is that if there hypotheticaly IS some sort of energy shift going on

There is not. The photon enters the gravity well and gains an energy E1. It then leaves the gravity well and loses an energy E2. E1 = E2.

 

[Bill_K]

On a very large scale there is something called the Integrated Sachs-Wolfe Effect. When passing through a gravitational potential well a photon will lose part of its energy, because the expansion of the universe causes the well to be shallower on the way out than it was on the way in. This effect can be seen in the small variations from uniformity of the cosmic microwave background.