Measuring Deflection of Star Light During Eclipse: Separating Space-Time Effects

[Grossglockner]

TL;DR Summary

Does anybody know about experiments or observations that measure the effect of the energy of an electromagnetic wave on the deformation of space-time? Yes, it is a very small effect.

There is the famous experiment of measuring the "movement" of a star close to the sun during an eclipse. The stars position is determined before the disc of the sun moves just under it and than the position is again measured when the sun moves just "under" the star. The star will have appeared to have moved due to deflection of the light from the star by the gravity of the sun. The experiment has to be done during an eclipse to block most of the sunlight. There are actually two effects changing the curvature of space time in the vicinity of the sun..

By far the larger effect is the change in the space-time curvature due to the mass of the sun.
There is a much smaller effect of an additional change of the curvature of space time due to the the electromagnetic radiation of the sun. We observe the deflection of the light from the star due to both these effects. How does one separate the two effects?

Now I have two questions:

ONE: Does anybody know about experiments or observations that measure the effect of the energy of an electromagnetic wave on the deformation of space-time?

TWO: In the experiment of measuring the deflection of the light from a star during an eclipse of anybody separating the effect of the sun's mass on the deflection of the star and the effect of the energy of the electromagnetic radiated by the sun on the deflection of the star light?

In the third post (Post 3 of 3) i will explain why it is not absolute necessary for what I am doing, but I would like to have this information.

Philipp Kornreich

[Moderator's note: Off topic remarks removed.]

 

[PeterDonis]

There is a much smaller effect of an additional change of the curvature of space time due to the the electromagnetic radiation of the sun.

If you are referring to the EM radiation emitted by the Sun into space, practically all of it is further away from the Sun than the starlight whose trajectory is "bent" while passing close to the Sun, so it doesn't affect the bending.

Does anybody know about experiments or observations that measure the effect of the energy of an electromagnetic wave on the deformation of space-time?

I would not expect there to be any such experiments, since neither naturally occurring EM radiation in our current universe nor any EM radiation we can produce artificially has enough energy density to make its gravitational effects measurable with the current accuracy of our measuring instruments.

In the experiment of measuring the deflection of the light from a star during an eclipse of anybody separating the effect of the sun's mass on the deflection of the star and the effect of the energy of the electromagnetic radiated by the sun on the deflection of the star light?

No, for both of the reasons given above: the energy density of the EM radiation is way too small to have a measurable effect, and the EM radiation emitted by the Sun doesn't affect the bending anyway.

it is not absolute necessary for what I am doing

PF is not for discussing personal research. The question you ask about EM radiation is a legitimate question, but there is no need to explain anything about your personal research, and any such explanation is off topic.

 

[Grossglockner]

My Post:
"There is a much smaller effect of an additional change of the curvature of space time due to the the electromagnetic radiation of the sun".

PF Answer:

"If you are referring to the EM radiation emitted by the Sun into space, practically all of it is further away from the Sun than the starlight whose trajectory is "bent" while passing close to the Sun, so it doesn't affect the bending".

My answer to PF answer:

Thank you for your answer. But, I don't completely agree with your answer. The light radiated by the surface of the sun is actually not deflected by the change in the curvature of space-time due to the mass of the sun by symmetry. Thus, as you say, the radiation passes strait away from the surface of the sun to a good approximation. BUT the energy of the light radiating in a radial direction from the sun does effect the curvature of space-time around the surface of the sun. The curvature of the space-time is described by the second rank metric tensor. Thus the energy of the sun will effect a light beam passing, for example, parallel to the surface of the sun. There is momentum and energy transferred between the sun light radiating radially and a light beam passing approximately parallel to the surface of the sun. This effect is relatively very small.

In principle this effect can be calculated from the Einstein equation in the limit of slight space-time curvature. This still holds in the vicinity of the sun. The ratio of the sun's Schwarzschild radius to the radius of the sun is only 4.246127E-6. The off diagonal terms and the change from unity of the diagonal terms of the metric tensor are of the order of this ratio for slight curved space-time.

Alles Beste

Philipp Kornreich

 

[PeterDonis]

@Grossglockner if you want to reply to posts that others have made in your thread, do not start a new thread. Just reply in the same thread. I have moved your post into this thread since it is a reply to my post in this thread.

Also, please use the PF quote feature to quote portions of other people's posts that you want to reply to.

 

[PeterDonis]

the energy of the light radiating in a radial direction from the sun does effect the curvature of space-time around the surface of the sun.

Only a very, very small portion of it--the portion that lies between the Sun's surface and the light beam from a distant star that is passing close to the Sun's surface and being bent. This is an instance of the general theorem that in a spherically symmetric spacetime, only stress-energy closer to the center than a given event affects spacetime curvature at that event. Stress-energy farther out does not.

The off diagonal terms and the change from unity of the diagonal terms of the metric tensor are of the order of this ratio for slight curved space-time.

For the diagonal terms, what you say is correct, but it has nothing to do with your question. The deviations from unity in the diagonal terms are due to the total stress-energy that is closer to the center than the event in question (in this case, the ray of light from a distant star passing close to the Sun). Those terms do not give any information about how much of the total stress-energy is contained in EM radiation being emitted by the Sun.

For the off-diagonal terms, what you say is not correct; these are only present for light, and the stress-energy contained in the light being emitted by the Sun is many, many orders of magnitude smaller than the Sun's total stress-energy. So any off-diagonal terms in the metric just outside the Sun are similarly many, many orders of magnitude smaller than the deviation from unity of the diagonal terms.

 

[mfb]

Our uncertainty on the mass of the Sun is larger than the mass of Earth, and the only useful mass estimates comes from measuring the gravitational effect of the Sun.

Can we compare the gravitational effect with the rest energy of the Sun? No, we don't have a useful way to estimate the rest energy with non-gravitational effects.
Can we compare different gravitational effects? Yes. This is what gravitational lensing measurements do, they compare the observed lensing with the lensing expected based on the mass estimate from orbital mechanics. Gaia is expected to measure gravitational deflection of light from the Sun to one part in a million. That's about 14 orders of magnitude above the contribution of radiation to the mass of the Sun.