Non-Cosmological Interpretation of Redshift

[Garth]

Doesn’t general relativity predict different travel paths (and therefore times) for different frequencies in case of gravitational lensing? Orbits of massless particles in a Schwarzschild spacetime are dependent of the particles’ energies (if I recall correctly).

Not pure GR - the null-geodesic is the same from the emission event A to the reception event B, although there may well be more than one null-geodesic from A to B if everything is symmetric around the lensing mass, if not the other geodesics arrive at the observer at a different time, events B', B'' etc. The question is: Do photons travel on null-geodesics? Generally the answer is they do unless you want to rewrite GR!

Garth

 

[Nereid]

[...] the frequency-dependent travel-time effect (due to friction with the vacuum field) is a very small effect that is more sensitive to column depth and density than to small variations in field density over thin domains. Optical lensing in polarized vacuum fields will result in frequency-dependent effects like chromatic aberration, but I don't think we will be able to detect arrival time smearing from such interactions. The arrival times of various frequencies will be essentially simultaneous (within our ability to detect them) but the light of shorter wavelengths will be deflected more readily than the longer wavelengths, like in classical optics.

(my emphasis) ... do you have an equation or two? How about some OOMs to quantify 'very small'? From what we already have - say, the redshift of a high-z QSO is the same (to 1%? 0.1%?) from UV (say, 200nm) to NIR (say, 2 micron) (a quick of the literature should be able to nail these OOMs more closely) - what OOM constraints can you put on 'very small' (i.e. negative results show it must be smaller than xxx)?

 

[SpaceTiger]

Not pure GR - the null-geodesic is the same from the emission event A to the reception event B, although there may well be more than one null-geodesic from A to B if everything is symmetric around the lensing mass

There can be multiple ones even if everything isn't symmetric, but yeah, I agree with the rest.

 

[hellfire]

Not pure GR - the null-geodesic is the same from the emission event A to the reception event B, although there may well be more than one null-geodesic from A to B if everything is symmetric around the lensing mass, if not the other geodesics arrive at the observer at a different time, events B', B'' etc. The question is: Do photons travel on null-geodesics? Generally the answer is they do unless you want to rewrite GR!

OK, thank you for your answer, it seams I was wrong. I have taken a short look into Schutz. The energy of a photon does actually enter the equation for a photon's orbit, but not alone: it is always the relation between angular momentum and energy (Schutz calls this impact parameter). I have to study this more seriously.

 

[Garth]

There can be multiple ones even if everything isn't symmetric

But not between the two events A & B, if non-symmetric the various null-geodesics that pass between positions A' & B' will take different times to complete their non-similar journeys. .

Garth

 

[SpaceTiger]

But not between the two events A & B, if non-symmetric the various null-geodesics that pass between positions A' & B' will take different times to complete their non-similar journeys.

Well, I see that the paths of the rays would have to be symmetric (i.e. same travel time) in that case, but it's not clear to me that you couldn't achieve a pair of symmetric null geodesics with an asymmetric mass distribution. Is there some sort of uniqueness theorem for strong lensing that would enforce this?

 

[Chronos]

My first reaction is ... get a grip. Gravitational lensing is a misnomer. Gravitational mirage is more like it. The effect is mostly a displacement of the apparent position of the lensed object.