Thread: Gravitational deflection of light - measurements

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Gravitational deflection of light - measurements

I have a little problem with the measurements carried out by Eddington and others.

Namely: with respect to what they measured the deflection of light at the edge of the sun = 1.7''?

After all any measurements were performed in the presence of the sun, so how do they know what are the trajectories of light rays from the stars, in the absence of the sun?

I suspect that they photographed at night the same area of the sky.
But then the sun was still present, so the deflection is not going to zero, but only smaller!

Position of the stars in the night picture: a_n, while in the day (during the eclipse): a_d, so they calculated the difference:
r_d - r_n = 1.7''

They could not determine the actual deflection of light at the edge of the Sun, but only the difference.
Is that right?

2. Originally Posted by Hetman
I have a little problem with the measurements carried out by Eddington and others.

Namely: with respect to what they measured the deflection of light at the edge of the sun = 1.7''?

After all any measurements were performed in the presence of the sun, so how do they know what are the trajectories of light rays from the stars, in the absence of the sun?

I suspect that they photographed at night the same area of the sky.
But then the sun was still present, so the deflection is not going to zero, but only smaller!

Position of the stars in the night picture: a_n, while in the day (during the eclipse): a_d, so they calculated the difference:
r_d - r_n = 1.7''

They could not determine the actual deflection of light at the edge of the Sun, but only the difference.
Is that right?
Yes, there is gravitational distortion from the Sun all over the sky, not just at the grazing position, but it is so slight at locations far from the Sun that it was unobservable in Eddington's time. The uncertainties in measuring his photographs swamped it. For the Hipparcos spacecraft it was significant in measuring star positions and had to be taken into account, and it will be even more so with Gaia. At 90 degrees from the Sun, the deflection is about 4 milliarcseconds, and the change in the spacing of two stars a degree apart will be a small fraction of that.

See this Wiki article on this topic:
http://en.wikipedia.org/wiki/Tests_o...tional_lensing

3. The astronomers who measured the deflection of light near the Sun back in 1919 (see Dyson et al., 1920, http://adsabs.harvard.edu/abs/1920RSPTA.220..291D), and on several occasions since then, made two sets of measurements:

a) the positions of a group of stars surrounding the Sun during a solar eclipse (during the day)
b) the positions of the same group of stars many months later (at night)

For example, Dyson et al. compared measurements made on May 29, 1919, during the eclipse, to measurements made in July, 1919, when the Sun was far from this region of the sky.

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OK. But what is the deflection at night - in the opposite direction: 180 degrees?

We can not assume in advance that it is zero. Science does not work that way.

a_0 - a_180 = 1.7''

then full deflection is equal: a_0 + a_180 = ?

5. Originally Posted by Hetman
I suspect that they photographed at night the same area of the sky.
But then the sun was still present, so the deflection is not going to zero, but only smaller!
I think the reason you can do it is because the sun moves with regard to the stars. So if you take a picture of a star one day earlier, and then you notice that the position of the star is moving vis-a-vis other stars as the sun approaches, then you have a good idea that the light has been bent (either that or the star has jumped!).

6. Originally Posted by Hetman
OK. But what is the deflection at night - in the opposite direction: 180 degrees?

We can not assume in advance that it is zero. Science does not work that way.

a_0 - a_180 = 1.7''

then full deflection is equal: a_0 + a_180 = ?
IIRC, what they did was compare the relative positions of stars at night, and then during the eclipse. They measured the differences on the plate itself--stars even a couple degrees away from the sun are not as affected.

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^ What grapes said ^

Originally Posted by Hetman
OK. But what is the deflection at night - in the opposite direction: 180 degrees?

We can not assume in advance that it is zero. Science does not work that way.

a_0 - a_180 = 1.7''

then full deflection is equal: a_0 + a_180 = ?
Yes, but ...

Until quite a bit later - the 1960s IIRC - the deflection in parts of the sky, due to the Sun, much further than few degrees from the Sun was too small to measure.

And the relative positions of stars (i.e. one compared with others) was known to be stable over periods of days to months (over longer periods something called "proper motion" had been observed, going back many decades), except for the parallax of some nearby stars, etc*. The general problem of establishing a robust coordinate system 'on the sky' had certainly received much attention, well before 1919 (and the effort to establish such a system is ongoing, see, for example, this website on the International Celestial Reference Frame).

The upcoming GAIA mission aims to measure the apparent positions of stars so accurately and precisely that the gravitational deflection due to the Sun will be a large signal, all over the sky.

* with relatively cheap equipment, an amateur astronomer today can easily detect, and accurately measure, the parallax and proper motion of Barnard's star, over periods as short as a few months!

8. Originally Posted by Hetman
OK. But what is the deflection at night - in the opposite direction: 180 degrees?

We can not assume in advance that it is zero. Science does not work that way.

a_0 - a_180 = 1.7''

then full deflection is equal: a_0 + a_180 = ?
The theory predicts that the deflection of a star directly opposite the Sun will be zero. Surrounding stars will be deflected toward it ever so slightly, so a given star field centered on that position will appear slightly compressed. Gaia should be able to detect it.

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Imagine the following situation:
we are in a huge spherical lens, such as gas bubble whose density increases toward the center.

What we observe on the outside - how the image will deform?
A. We are located in the center of the bubble
B. at a certain distance from the center

10. Originally Posted by Hetman
Imagine the following situation:
we are in a huge spherical lens, such as gas bubble whose density increases toward the center.

What we observe on the outside - how the image will deform?
A. We are located in the center of the bubble
B. at a certain distance from the center
From the center, I would expect no distortion. From a point away from the center, I would expect distortion similar to what we see around actual massive bodies such as the Sun.

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Originally Posted by Hetman
Imagine the following situation:
we are in a huge spherical lens, such as gas bubble whose density increases toward the center.

What we observe on the outside - how the image will deform?
A. We are located in the center of the bubble
B. at a certain distance from the center
We are in a gas bubble that increases in density toward the center. We call is the atmosphere.

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Originally Posted by Hetman
Imagine the following situation:
we are in a huge spherical lens, such as gas bubble whose density increases toward the center.

What we observe on the outside - how the image will deform?
A. We are located in the center of the bubble
B. at a certain distance from the center
I'm not sure if you're asking about gravitational lensing - according to General Relativity - or the more familiar 'optics' lensing.

First, then, a word about ordinary lensing: it is chromatic, meaning that angle through which a dispersive medium bends, or deflects, a ray of light depends on the wavelength (or frequency) of the light ('light' here means electromagnetic radiation). In contract, gravitational lensing is achromatic: all wavelengths are bent the same (the angle a ray of light is deflected, by a massive body, is the same, no matter what its wavelength).

A "gas bubble whose density increases toward the center" is actually a pretty good description of a galaxy or a galaxy cluster, except that 'cold dark matter' replaces 'gas'!

As Hornblower has already said, in situation A there is likely to be no image deformation. However, there will be an observable effect, one that could closely resemble the 'dark energy' we observe. As a result, some cosmologists have studied models based on this idea; they go by the collective name 'void cosmology' (because they assume the opposite, namely that we are at, or near, the centre of a giant void).

There will certainly be distortions (deformations) of images of distant objects in situation B; the distortion will vary across the sky, and will depend on things like the radial density profile, our actual position, and the total mass of the spherical lens.

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Originally Posted by Nereid
The upcoming GAIA mission aims to measure the apparent positions of stars so accurately and precisely that the gravitational deflection due to the Sun will be a large signal, all over the sky.
It can already be seen clearly in the HIPPARCOS data:
Determination of the PPN Parameter gamma with the HIPPARCOS Data
(the analysis covered distances between 47 and 133 degrees from the Sun)

Bye,
Thomas

14. Originally Posted by Nereid
As Hornblower has already said, in situation A there is likely to be no image deformation. However, there will be an observable effect, one that could closely resemble the 'dark energy' we observe. As a result, some cosmologists have studied models based on this idea; they go by the collective name 'void cosmology' (because they assume the opposite, namely that we are at, or near, the centre of a giant void).
Whilst Nereid is not making any statements about void models in the above, (and not wanting to divert the lensing discussions), I'm curious ...

Perhaps I'm 'jumping the gun' a little (??), but my current impression is that most void Cosmological models, (from an acceleration mechanism perspective), have considerable observational evidence against them, almost to the point of being considered excluded from serious consideration (??).

Is my impression shared on this front ?
(Advice on this, would be most welcome .. )

Regards

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Originally Posted by Selfsim
Whilst Nereid is not making any statements about void models in the above, (and not wanting to divert the lensing discussions), I'm curious ...

Perhaps I'm 'jumping the gun' a little (??), but my current impression is that most void Cosmological models, (from an acceleration mechanism perspective), have considerable observational evidence against them, almost to the point of being considered excluded from serious consideration (??).

Is my impression shared on this front ?
(Advice on this, would be most welcome .. )

Regards
Yes, they do ... now.

At the time they were developed, IIRC, it was quite unknown just how well they'd be able to match the observational data of the day; if not for any other reason than because no one had actually developed any such models.

But that's how astrophysics is supposed to work (and actually works), right?

16. Originally Posted by Nereid
But that's how astrophysics is supposed to work (and actually works), right?
Yep .. sure does !

Cool.

Thanks, Nereid .. (just revalidating understanding ! )

I think most were ruled out following the COBE CMB analyses, as they were pretty well overwhelmingly at odds with several of those measurements ..

Regards

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I still do not see a solution of the problem.

a_0 - a_180 = 1.7''

It is the relative deflection only, which for an observer at the center of the lens will be zero, although the full deflection can be arbitrarily large!

a_90 - a_180 = 0.004'', it does not help, because the deflection a_180 must be almost the same, due to the almost identical ray paths from these directions by a sphere to the observer.

18. Originally Posted by Hetman

It is the relative deflection only, which for an observer at the center of the lens will be zero, although the full deflection can be arbitrarily large!
Your statement makes no sense. "An observer at the center of the lens" makes no sense. I suspect that you have in mind something quite different than everyone else. Could you perhaps draw a diagram to help us understand what you are trying to say?

19. Originally Posted by Selfsim
...my current impression is that most void Cosmological models, (from an acceleration mechanism perspective), have considerable observational evidence against them, almost to the point of being considered excluded from serious consideration (??).
I'm not sure how you're defining void cosmological models, but isn't anti-deSitter space a void cosmological model? Apparently you don't want to toss that one aside since it plays the co-star in...

"the AdS/CFT correspondence (anti de Sitter/conformal field theory correspondence), sometimes called the Maldacena duality... the conjectured equivalence between a string theory and gravity defined on one space, and a quantum field theory without gravity defined on the conformal boundary of this space, whose dimension is lower by one or more."

...as wiki describes it. Certainly it was once a "conjecture," but isn't that what Maldacena proved...?

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Originally Posted by Cougar
I'm not sure how you're defining void cosmological models, but isn't anti-deSitter space a void cosmological model? Apparently you don't want to toss that one aside since it plays the co-star in...

"the AdS/CFT correspondence (anti de Sitter/conformal field theory correspondence), sometimes called the Maldacena duality... the conjectured equivalence between a string theory and gravity defined on one space, and a quantum field theory without gravity defined on the conformal boundary of this space, whose dimension is lower by one or more."

...as wiki describes it. Certainly it was once a "conjecture," but isn't that what Maldacena proved...?
There's a difference between a solution to the vacuum field equations and "void cosmological models". The former are specific spacetime geometries that have no mass in them (ie solutions to the vacuum field equations, examples are minkowski, de Sitter, anti-de Sitter, schwarzschild, kerr-newman,...). A void cosmological model is a model that tries to explain our observations of dark energy by saying we happen to live in the center of a huge void in the universe, which would give about the same observational signature as dark energy.

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Ok, let's try again.

Before the eclipse, the relative positions of nearby stars and the star of interest are carefully determined. Whether the group is 90 degrees away from the sun (3 and/or 9 months), 180 degrees (6 months), it doesn't matter, the error is negligible. Then, during the eclipse, when the star of interest appears very close to the edge of the sun, and is only visible due to the eclipse, its position with respect to the nearby stars is compared to that measured previously. Voila, the star appears displaced by the amount predicted by Ol' Al. The trick is that the light from the star of interest passes very, very close to the Sun, while the reference stars are much farther away and are very little affected.
Last edited by John Mendenhall; 2012-Mar-22 at 01:58 AM. Reason: clarity (see followin post); typo

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One Year for the Stars to Move Around the Sun

Also, after re-reading your OP, you do understand that although the stars appear to move around the Earth every day, the position of the Sun with respect to the stars takes a year to complete a circuit? That's what all that astrology nonsense is about, as the Sun moves slowly from constellation to constellation around the zodiac. The measurements of the relative positions of the stars nearby the star of interest had to be made months earlier. The night of the day of the eclipse, they are still close by the Sun.

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Originally Posted by StupendousMan
Your statement makes no sense. "An observer at the center of the lens" makes no sense. I suspect that you have in mind something quite different than everyone else. Could you perhaps draw a diagram to help us understand what you are trying to say?
Looking from the center of a spherical lens did not observe any deformation (differences) - right?

Now we move from the center of the sphere a small distance, say 10 meters - what will change?

Probably not much.

Currently we are 150 million km from the center of the lens.

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Originally Posted by Hetman
Imagine the following situation:
we are in a huge spherical lens, such as gas bubble whose density increases toward the center.

What we observe on the outside - how the image will deform?
OK, Hetman; I get it; you simply want to model the gravitational bending of light as refraction in an optical medium. Yes, that can be done, and it has already been done by your friend Eddington. Its probably not commonly known that he was first to realize that refraction in an optical medium can precise express the same results as Gen Relativity concerning the deflection of starlight.

The idea was originally suggested by Einstein, and was exploited first by Eddington....After doing the solar deflection measurements you referred to, and writing a book endorsing Einstein's General Theory , Eddington also showed that, "We can thus imitate the gravitational effect on light precisely, if we imagine the space around the sun filled with a refractive medium which gives the appropriate velocity of light...."...(Sir Arthur Eddington (1920), Space, Time & Gravitation, Cambridge Univ. Press (reprinted 1987)) ....see the entire book here: http://www.archive.org/details/space...vita00eddirich Click on "PDF" on left side to download ...(give it some time - much patience...and go to page 109).

This perspective was later shown to be true more explicitly by others ..
for example...
http://resources.metapress.com/pdf-p...5&size=largest

This was not intended to replace Gen Rel. Theory, but merely to provide a more intuitive and simplier heuristic approach to understanding gravitational deflection.

G^2

-" Man who eats family photo will soon be spitting image of his father".-
Last edited by Gsquare; 2012-Mar-22 at 05:54 AM.

25. Originally Posted by Cougar
I'm not sure how you're defining void cosmological models, but isn't anti-deSitter space a void cosmological model?
Hi Cougar;
.. What caveman said .. ... AdS spacetime is weird, too ... good topic, perhaps, for another thread sometime ...
Cheers

26. Originally Posted by Hetman
I still do not see a solution of the problem.

a_0 - a_180 = 1.7''

It is the relative deflection only, which for an observer at the center of the lens will be zero, although the full deflection can be arbitrarily large!

a_90 - a_180 = 0.004'', it does not help, because the deflection a_180 must be almost the same, due to the almost identical ray paths from these directions by a sphere to the observer.
You are somehow creating a problem in your mind where there is none. Light coming in from directly opposite the Sun will be slightly blueshifted from going deeper into the Sun's gravitational field as it approaches, but there is no deflection for the simple reason that the field is radially symmetrical around the light ray. We could say figuratively that the gravity is "pulling" in line with the motion.

For a light ray coming in at 90 degrees, there is a weak crossways action, too weak for Eddington to measure in his time but detected by Hipparcos. For a ray grazing the Sun (a_1/4, not a_0, to use your notation) there is a much stronger crossways action, there for everyone to see at the familiar 1.7 arcsecond. If we replace the Sun with a hypothetical transparent body of the same mass, then a ray from directly behind its center will not be deflected at all, because the field is radially symmetrical at all points along the trajectory. Rays approaching from directions between the center and the limb will be deflected by varying amounts that depend on how the mass is radially distributed.

27. Originally Posted by caveman1917
A void cosmological model is a model that tries to explain our observations of dark energy by saying we happen to live in the center of a huge void in the universe...
Oh, that void.

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Originally Posted by Hornblower
You are somehow creating a problem in your mind where there is none.
This is a common problem known in the systems of linear equations:
http://en.wikipedia.org/wiki/Underdetermined_system

a - b = 1.7''
a + b = x

solve the system, we need x - full deflection.

Originally Posted by Hornblower
Light coming in from directly opposite the Sun will be slightly blueshifted from going deeper into the Sun's gravitational field as it approaches, but there is no deflection for the simple reason that the field is radially symmetrical around the light ray. We could say figuratively that the gravity is "pulling" in line with the motion.
We did not measure the coordinates of one star, but the angular distances between stars.

Originally Posted by Hornblower
For a light ray coming in at 90 degrees, there is a weak crossways action, too weak for Eddington to measure in his time but detected by Hipparcos. For a ray grazing the Sun (a_1/4, not a_0, to use your notation) there is a much stronger crossways action, there for everyone to see at the familiar 1.7 arcsecond. If we replace the Sun with a hypothetical transparent body of the same mass, then a ray from directly behind its center will not be deflected at all, because the field is radially symmetrical at all points along the trajectory. Rays approaching from directions between the center and the limb will be deflected by varying amounts that depend on how the mass is radially distributed.
I think, some of 'rays' coming from the outside and running into the center of a spherical lens must bent!
They overlap, and hence the observed increase in energy - shift towards blue.

29. Whatever it is in your line of thought that continues to bother you appears to defy your attempts at articulating it qualitatively with words, not to mention quantitatively with mathematics.

Originally Posted by Hetman
This is a common problem known in the systems of linear equations:
http://en.wikipedia.org/wiki/Underdetermined_system

a - b = 1.7''
a + b = x

solve the system, we need x - full deflection.
What attribute of the system is indicated by x? Your words are no help to me. Perhaps it is time to start posting some pictures. They don't need to be pretty. Scans of pencil-and-paper sketches will do.
We did not measure the coordinates of one star, but the angular distances between stars.
I never said otherwise. Hipparcos measured the angular separations of numerous pairs of stars, kept track of changes as the Sun migrated among them over the course of a year, and used elaborate mathematical reductions to home in on the individual deflections that were the combined effects of gravitational refraction and annual parallax. That math is far beyond the scope of the Wiki article you linked.

I think, some of 'rays' coming from the outside and running into the center of a spherical lens must bent!
They overlap, and hence the observed increase in energy - shift towards blue.
If I am not mistaken, a ray headed directly toward the center of a transparent, spherically symmetrical massive body will be blueshifted on the way in and redshifted on the way out the other side. That shifting has nothing to do with the deflection of adjacent off-center rays. The central ray will not be deflected one iota, for reasons I covered in the previous post.

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Originally Posted by Hornblower
What attribute of the system is indicated by x? Your words are no help to me. Perhaps it is time to start posting some pictures. They don't need to be pretty. Scans of pencil-and-paper sketches will do.I never said otherwise. Hipparcos measured the angular separations of numerous pairs of stars, kept track of changes as the Sun migrated among them over the course of a year, and used elaborate mathematical reductions to home in on the individual deflections that were the combined effects of gravitational refraction and annual parallax. That math is far beyond the scope of the Wiki article you linked.

If I am not mistaken, a ray headed directly toward the center of a transparent, spherically symmetrical massive body will be blueshifted on the way in and redshifted on the way out the other side. That shifting has nothing to do with the deflection of adjacent off-center rays. The central ray will not be deflected one iota, for reasons I covered in the previous post.
Have you heard about the problem of a frog in the water well?

Straight rays that target center of the sphere (or even any point), is just a subset of all the rays, that hit the center, but after the deflection.

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