Light Bending: Comparison of Theories

[worlov]

In the essay „Über die Ablenkung des Lichtes I am Schwere*feld der Sonne“ ( http://adsabs.harvard.edu/full/1931ZA...3..171F ) the authors - Freundlich,
Klüber and Brunn - presented 1931 graphically the results of three expeditions, which took place 1919, 1922 and 1929. They put together all the measurements,
so that it gave a comprehensive presentation of 99 test points (illustration).

For the authors the theory of relativity is clearly failed: „It looks quite evident that the theoretical (lower) hyperbole is not represented by the values.“ Therefore,
they still draw the upper hyperbola for the light deflection at the solar limb by 2.24". The high quality of the image allows precise to determine the coordinates of
the measuring points. This data can for example be entered into the Excel spreadsheet and processed. In particular we are interested for the sum of squared
deviations between theoretical curves and real measurement values​​. The smaller it is, the better the compensation. The next charts are sorted by rise
of the sum, i.e. first get the best results.

And this as the table again:

Placement / Author / Equation / Type / Sum of squared deviations
-----------------------------------------------------------------------------------------
1. Freundlich / 2.24"/r / empirically / 2.57
2. Schmeidler 1.75"/r + 0.3"/r² / empirically / 3.19
3. A straight line / -0.07r + 0.9 / empirically / 3.31
4. Gerber / 2.62"/r / theoretically / 3.45
5. Courvoier / 1.546"/r + 0.221" / empirically / 3.47
6. Einstein / 1.75"/r / theoretically / 3.48
7. Soldner / 0.87"/r / theoretically / 10.92

 

[bcrowell]

I don't speak German, so I had to run a few things through google translate to understand what this was about:
"Über die Ablenkung des LIchtes I am Schwerefeld der Sonne"="On the deflection of light in the gravitational field of the Sun"
"ablenkung in bogensekunden"="deflection in arcsec"
"sonnenradien" = "solar radii"
"die gestrichelte kurve stellt den hyperbolischen abfall zufolge der relativitatstheorie dar, die strichpunktierte den aus den potsdamer messungen gefundenen abfall unter voraussetzung des hyperbolischen gesetzes"="the dashed curve is the hyperbolic slope, according to the relativity is that the dot-dash potsdamer measurements found in the waste under the condition of the hyperbolic law" [obviously a poor translation, but I guess this means that the dot-dash one is just an arbitrary fit to a hyperbola?]

It's always interesting to see real historical science and contrast it with the idealized fairytale version that you see presented in textbooks. However, the deflection of light by gravity has been measured to much higher precision in modern times, and it's in excellent agreement with GR: http://relativity.livingreviews.org/open?pubNo=lrr-2006-3&page=articlesu7.html (See figure 5.) There are indeed other theories of gravity that have been seriously studied in modern times: http://relativity.livingreviews.org/Articles/lrr-2006-3/ Some of them are still compatible with experiment, e.g., Brans-Dicke gravity with a large value of the $\omega$ constant.

 

[worlov]

However, the deflection of light by gravity has been measured to much higher precision in modern times, and it's in excellent agreement with GR: http://relativity.livingreviews.org/open?pubNo=lrr-2006-3&page=articlesu7.html (See figure 5.)

These measurements were made ​​for very large distances from the sun. For example, observation angle of Hipparcos varied between 47° and 133°. But the solar radius is 16' = 0.27°. The observation angle of 47° correspond to roughly 47° / 0.27° = 176 solar radii. 1985 Schmeidler systematized the results of several observations and suggested its empirical formula for the deflection of light near the sun: 1.75"/r + 0.3"/r^2 ( http://adsabs.harvard.edu/full/1985AN...306...77S ). He set the limit of 5 solar radii. Lower this limit the general relativity is clearly violated and 176 >> 5. Modern results are so good because the researchers look away

 

[Dale]

„It looks quite evident that the theoretical (lower) hyperbole is not represented by the values.“

It looks like a good fit to me, particularly considering that there are no free parameters. How many free parameters do the other theories have? While having free parameters does allow a theory to fit data better the uncertainty in the parameters makes it worse at predicting data.

But I definitely reject the absurd premise that the Freundlich figure represents the sum total of all valid data on the subject and that the modern tests are not valid.

 

[bcrowell]

Worlov, this thread was deleted, and your account permanently banned, for crackpottery. I argued for reversing those decisions on the ground that you had presented data from peer-reviewed papers, and it was agreed that it was OK to reverse them, on the condition that I do the work of dealing with the resulting situation. I agreed to do that, but please be aware that you are treading on thin ice. There are several problems with what you've done so far:

(1) The rules https://www.physicsforums.com/showthread.php?t=414380 , which you agreed to when you joined, state that "(i) All posts must be in English--posts in other languages will be deleted." It is not conducive to discussion that so much of your OP was in German, and you should not expect folks here to go to the amount of trouble that I went to in running it through google translate.

(2) It is one of the hallmarks of crackpots to try to poke holes in extremely old, low-precision experiments, while ignoring more recent evidence. You were aware of the more recent evidence, as shown in your #3, so it was disingenuous not to reveal that.

(3) Your statement in #3 that all the modern, high-precision measurements are at large r values was misleading. Please refer again to the link I gave in #2, which states that the Cassini data were for r=1.6 solar radii. Although the Cassini result was a measurement of the Shapiro time delay rather than an angular deflection, both types of measurements constrain the same PPN gamma parameter.

(4) You talk about comparison of "theories," but you have not named any competing theories. Fitting data to an arbitrary function is not a theory.

-Ben