If astronomers could measure the wavelength of light coming from the sun and compare it to the wavelength it should have without gravity, it should confirm general theory of relativity. Answer as to how will that happen. Assume I have no mathematical background and am just a layman.
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Well, you measure the spectrum from outside the earth's atmosphere using a satellite, you send a satellite near the sun and measure the spectrum there. Then you compare. You can also directly measure it (in principle even on earth), by using spectral lines: The sun spectrum has a few frequencies missing where elements absorb light (Fraunhofer lines). You can test where those lines should lie in the lab and then measure the shift from the sun. However, it'll be quite tiny, so I'm not sure precision is enough for the sun. – Martin Sep 03 '16 at 09:46
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1In any case, there is a lot of information in http://en.wikipedia.org/wiki/Tests_of_general_relativity and https://en.wikipedia.org/wiki/Gravitational_redshift – Martin Sep 03 '16 at 09:47
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More on experimental tests of GR. Related: http://physics.stackexchange.com/q/9474/2451 – Qmechanic Sep 03 '16 at 10:15
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@Qmechanic -- Unfortunately, the only answer to that old question was written by someone who ascribes to nonconventional physics of his own making. There's a word that describes such people ... – David Hammen Sep 03 '16 at 10:42
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This explanation requires, as Martin says above, a lot of exaggeration to show the effect.
Above: Spectrum measured at surface of Sun, that is without gravity.
Above: Spectrum of Sun measured from Earth, after the light has been affected by the gravity of the Sun
Please bear in mind that the movement of the black lines towards the right (red shifting) is greatly exaggerated, as the Sun's gravity is so weak, also that this is not the spectrum of the Sun, just a sample star.
The black lines represent elements which are present in distinctive patterns on stars such as the sun.
Most importantly, we have no way of measuring the solar spectrum at the surface of the Sun, for obvious reasons we are looking at the light after the gravitional effect has occured.
The movement of the lines indicates a slight increase in wavelength as the photon moves a distance away from the sun. If the Sun were 10 times more massive, it's gravity would enhance the effect.
Another way of view the effect is the picture below, with blue (higher energy/shorter wavelengths) at the bottom and red at the top. The spring shape is irrelevant to the idea. Again, this effect is greatly exaggerated for clarity.
Original image by User:Vlad2i, slightly modified.
In astrophysics, gravitational redshift or Einstein shift is the process by which electromagnetic radiation originating from a source that is in a gravitational field is reduced in frequency, or redshifted, when observed in a region at a higher gravitational potential. This is a direct result of gravitational time dilation - if one is outside of an isolated gravitational source, the rate at which time passes increases as one moves away from that source. As frequency is inverse of time (specifically, time required for completing one wave oscillation), frequency of the electromagnetic radiation is reduced in an area of higher gravitational potential. There is a corresponding reduction in energy when electromagnetic radiation is red-shifted, as given by Planck's relation, due to the electromagnetic radiation propagating in opposition to the gravitational gradient. There also exists a corresponding blueshift when electromagnetic radiation propagates from an area of higher gravitational potential to an area of lower gravitational potential.
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In order for the gravitational redshift to be "a direct result of gravitational time dilation", absurd fudge factors should be introduced. In particular, the speed of light falling towards the source of gravity must DECREASE (acceleration of falling photons in the gravitational field of the Earth must be NEGATIVE, -2g). See John Rennie's comment here: http://physics.stackexchange.com/questions/77227/speed-of-light-in-a-gravitational-field The alternative hypothesis - redshift is due to variation of the speed of light - needs no fudge factors and is compatible with the Pound-Rebka experiment. – Pentcho Valev Sep 03 '16 at 12:55
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The alternative hypothesis: There is no gravitational time dilation. The gravitational redshift is due to the variation of the speed of light predicted by Newton's emission theory - light falls with the acceleration of ordinary falling bodies (g in the gravitational field of the Earth). – Pentcho Valev Sep 03 '16 at 13:04