Redshift and Gravitational lensing

[Devil Particle]

There was a famous experiment I read about a while back where an astronomer went to Australia, I believe, during a solar eclipse and measured the location of a star whose position in the sky was close to the position of the sun. The result was that the star's position appeared to shift and the explanation was that spacetime around the sun was bent due to the gravity of the sun. My question is does anyone know if a similar experiment has been done that also measures the spectra of the background star? Would the background star's spectra appear to be red-shifted? I've been curious about this for a while and would appreciate any insight.
Thanks.

[Beta]

Would the background star's spectra appear to be red-shifted?

In theory, no. If you sent a light source down into the gravity well, like mounting a laser on Mercury, then it would appear to be slightly red-shifted when viewed from Earth. Likewise a laser mounted on Earth would appear slightly blue-shifted to an observer on Mercury. But the star you mention is still far away, and the color of its light doesn't depend on the path it takes to get here.

To put it another way, suppose the star looks red when viewed from interstellar space. On Earth it will look white, and on Mercury it will look blue. It is blue-shifted on the way down to Mercury and then red-shifted on the way back up to us. (Note that I am exaggerating; none of these shifts are visible to the human eye.)

[Chris Peterson]

There was a famous experiment I read about a while back where an astronomer went to Australia, I believe, during a solar eclipse and measured the location of a star whose position in the sky was close to the position of the sun. The result was that the star's position appeared to shift and the explanation was that spacetime around the sun was bent due to the gravity of the sun. My question is does anyone know if a similar experiment has been done that also measures the spectra of the background star? Would the background star's spectra appear to be red-shifted? I've been curious about this for a while and would appreciate any insight.

Gravitational redshift depends on the difference in gravitational potential between the source and the receiver. Nothing that happens in the middle has any effect. The photon will be slightly blueshifted as it falls into the Sun's gravitational well, but will then be redshifted back as it climbs out of that well. So we would see no difference from here.

[Devil Particle]

Thanks for the replies. I was thinking the same thing. A follow-up question: Does the light travel the same distance in both senarios?

[Beta]

A follow-up question: Does the light travel the same distance in both scenarios?

No, but the exact answer depends on what you mean by "both scenarios".

If you mean during an eclipse vs. six months later, the Earth will move to the side of the sun closer to the star in question. It will be two Astronomical Units (about 3x10⁸ km, or 1000 light-seconds) closer to the star, so the path will be that much shorter. Then there's six months' worth of the relative motion of Sol and the star in question, but I don't know what star it was or its relative velocity so that could make the path longer or shorter.

If you mean General Relativity being true vs. not, according to GR gravity changes the shape of spacetime. The presence of the Sun will change the shortest path between Earth and the star, and light always takes the shortest path. I'd have to do some tough math to be certain, but I'm pretty sure that the presence of the sun (i.e. during the eclipse) makes the shortest path longer according to GR .

[alter-ego]

The presence of the Sun will change the shortest path between Earth and the star, and light always takes the shortest path. I'd have to do some tough math to be certain, but I'm pretty sure that the presence of the sun (i.e. during the eclipse) makes the shortest path longer according to GR .

You are right on both accounts, and the good news is the math has already been done. An effective index of refraction can be defined for traveling through a weak gravitational potential, and is >1 (for vacuum and zero gravity, index = 1). As you might know, masses of standard stellar densities like our sun, (excluding black holes and neutron stars) are all examples of weak gravitational fields. Some theoretical highlights are found here. Since the velocity of light is constant, an index >1 means it takes a longer time for light to travel through a gravitational field, and consequently, this means a longer distance. This time delay has been known for decades and is referred to as the Shapiro time delay. The Wiki time delay discussion also presents "simple" analytical solutions for both delay and increased path length.

[Devil Particle]

Gravitational redshift depends on the difference in gravitational potential between the source and the receiver. Nothing that happens in the middle has any effect. The photon will be slightly blueshifted as it falls into the Sun's gravitational well, but will then be redshifted back as it climbs out of that well. So we would see no difference from here.

I think Chris' statement is correct for a uniform linear gravity well. What happens in this case is the light from the distant background star is following a longer, curved path when observed during an eclipse. So in addition to the light being blueshifted as it falls into the Sun's gravity well and being redshifted by an equal amount as it climbs out would there be an affect on the spectrum due to the increased length of the path and/or the Shapiro time delay?

For instance, if the distance between an observer and a distant object increases, the distant object would appear to be moving away from the observer, hence redshifted. Wouldn't it?

[Beta]

What happens in this case is the light from the distant background star is following a longer, curved path when observed during an eclipse.

Yes, but in this context the word "curved" might not mean exactly what you think it does.

So in addition to the light being blueshifted as it falls into the Sun's gravity well and being redshifted by an equal amount as it climbs out would there be an affect on the spectrum due to the increased length of the path and/or the Shapiro time delay?

For instance, if the distance between an observer and a distant object increases, the distant object would appear to be moving away from the observer, hence redshifted. Wouldn't it?

No. Light is not frequency-shifted by the distance it travels. If the distance is increasing, the light it is red-shifted while the distance is increasing, but during the eclipse the rate at which the sun is changing the path length is negligible.

[Ann]

I think I have read about a distant quasar whose light has passed through a massive cluster of galaxies (or something) in four different ways, so that we on the Earth see four dfferent quasars close together, when in reality these four points of light emanate form the same source. Interestingly, when the light from this quasar flickers, it seems to flicker at different times in the four different images that we see of the quasar. Obviously the four paths that light takes from the quasar to us are not of the same length.

Ann

[Chris Peterson]

I think I have read about a distant quasar whose light has passed through a massive cluster of galaxies (or something) in four different ways, so that we on the Earth see four dfferent quasars close together, when in reality these four points of light emanate form the same source. Interestingly, when the light from this quasar flickers, it seems to flicker at different times in the four different images that we see of the quasar. Obviously the four paths that light takes from to quasar to us are not of the same length.

Yes, the paths are different lengths. But they all show exactly the same redshift- mostly cosmological redshift, and also a barely detectable gravitational redshift. The fact that the light took different paths because of gravitational lensing didn't result in different redshifts.

[Beta]

I guess I should amend my statement that light always takes the shortest path. Light always takes the extremal path, which in practice means that it won't take a path if there's a slightly different path that's shorter. So for example if a candle is next to a mirror, you'll see light coming to you along two paths, one direct and one visiting the mirror. Obviously the direct path is shorter, but the light takes both because each of those two paths has the property that any slight variation (such as being slightly curved or crooked, or reflecting off a slightly different spot of the mirror) will make it longer. The same applies to gravitational lenses; there can be more than one path that is shorter than all of its immediate neighbors.

To be more precise, "longer" means more wavelengths, so if you consider things like propagation through matter (air, water, glass) which changes the wavelength, this actually explains (or at least predicts) the way lenses and mirages work.