Confirming Einstein's Theory: Measurement of Bending of Light

[thetexan]

I just watched a show on Einstein concerning this theory of general relativity. Around 1922 photographs of stars from an eclipse were used to measure the bending of light from those stars around the gravitational field of the sun. Those measurements were used to confirm Einstein's theory. All through the program it was stated that the predicted observed amount of bending proved his theory of space/time and the warping of space in the presense of a mass.

How so?

It seems that, at most, this proves that gravity has a predictable and measurable effect on light just like it has on an apple dropping from a tree. But how does this prove that the cause of the effect is a warping of space/time rather than the more classically accepted attracting force of Newtonian physics.

If the argument is that since photons have no mass they cannot be effected by an attracting force, therefore, the bending must be caused by something else...the bending of space/time, shouldn't it be pointed out that it has not been proven, at least to my knowledge, that photons indeed do not have mass. And, certainly, in 1922 it was not known whether photons had mass.

If photons are massless and are simply a unit of energy it should be remembered that fields of energy can be effected by other similar fields. For example, put two magnets, each with their own magnetic field, in close proximity to each other and the resulting field will be a warped, merged, combination of the two fields. Each field has some effect on the other.

If that is true, and photons are simply a small unit of an electromagnetic field, and that field can be influenced by another field, then isn't there at least one other possible explanation of the bending of starlight?

tex

 

[ghwellsjr]

The point is that prior to Einstein's prediction of the starlight being affected by the gravity of the sun, there was no other theory that would have come up with that prediction. Certainly, classical theory made no such prediction. Einstein didn't just decide out of the clear blue that the starlight would bend, he came to that conclusion after analyzing his new Theory of General Relativity and coming up with some tests that could disprove his theory. This was one and it did not.

That's how science works--come up with a new theory that explains more than what is now known, come up with a new experiment that can invalidate the theory and see if it holds up.

Of course, after we know the results of experiments and how various theories conform to these results, it is fairly easy to devise more trivially different explanations that also work, but until you can come up with a new theory that is enough different to make new predictions and experiments to distinguish that new theory from all the others, then it is not going to advance science.

 

[thetexan]

Yes,

But my point is that the bending of the starlight, in and of itself, doesn't prove the warping of space/time.

Einstein could have just as easily predicted the bending due to the gravitational attractive force of the sun rather than space/time warping.

What specifically about the bending of starlight and the experiment proves that the bending is due to the warping of space/time rather than simple gravitational force attraction?

tex

 

[Kevin_Axion]

It does, how would the classical equation: $$F_{grav}=\frac{Gm_1m_2}{r^2}$$ define the trajectory of a light ray or the force of gravity in the presence of a massive body if light has a mass of 0? This only occurs if there is a curvature in space-time and a light ray is forced to travel a geodesic along this "surface", which is defined by the structure of this object: $$g_{\mu\nu}$$.

 

[thetexan]

That's my point.

This is all based on the photon having zero mass. If that is true then I can see the results.

Is it true that photons have 0 mass? I thought this was still unproven.

tex

 

[Kevin_Axion]

It's true, any massive body can never travel at the speed of light and photons happen to which means they are massless. They still have energy though and can still interact with the stress-energy tensor. Like any other body in motion, they will follow the curvature of the space-time around them.

 

[PeterDonis]

Is it true that photons have 0 mass? I thought this was still unproven.

You can never *prove* that the photon mass is exactly zero, because there will always be some error bars around the experimental results. However, the error bars around the photon mass being zero are pretty small: the link below, which is the latest result I can find, gives an upper bound on the photon mass (meaning "size of error bar" around it being zero) of 10^-51 grams, or 7 x 10^-19 eV, or about 10^-24 times the electron mass.

Link:

http://www.aip.org/pnu/2003/split/625-2.html

 

[PeterDonis]

It does, how would the classical equation: $$F_{grav}=\frac{Gm_1m_2}{r^2}$$ define the trajectory of a light ray or the force of gravity in the presence of a massive body if light has a mass of 0? This only occurs if there is a curvature in space-time and a light ray is forced to travel a geodesic along this "surface", which is defined by the structure of this object: $$g_{\mu\nu}$$.

This argument doesn't completely rule out a "Newtonian" theory, because we can always redefine "mass" as it appears in that theory as "energy divided by c^2", which would give the photon a "mass" for purposes of reacting to gravity. Since the mass of the "reacting" body drops out of the Newtonian equations anyway (all objects "fall" with the same acceleration, even photons), this redefinition doesn't change any of the theory's predictions with respect to "massive" bodies (i.e., bodies that have nonzero rest mass, like planets or falling rocks), but does allow it to predict that light rays will "fall", i.e., bend, in a gravitational field.

The problem with this is that if we calculate the bending this way, using the Newtonian equations for a "particle" moving at the speed of light, we get an answer that is only half the experimentally observed value. If we use GR, on the other hand, we get the correct answer, the one that's experimentally observed. This shows that whatever it is that bends the light around a massive body, it can't be something that is completely explained by "Newtonian gravity".

 

[Kevin_Axion]

Won't you need a kinetic term for the energy though?

 

[Nabeshin]

You can hack together, within the Newtonian framework, a way to bend light with gravity. The best of such attempts gives a deflection HALF that predicted by GR. So the observation of the full prediction of GR is certainly strong support for the theory.

Also, stop using the word prove. One cannot prove ANYTHING in a physical science. All we do is PROVidE evidence for or against a certain theory. The case for GR was strengthened with Eddington's observation, and the case for it continues to be strengthened to this day. But we cannot prove it. Ever. But we, being reasonable individuals, put a certain amount of faith in a theory which has worked time and time again, since being the perpetual skeptic is scarcely productive.

Also to note, there are an amalgam of other theories which make similar predictions to GR in the regime we have tested it, but which differ in areas we have not. Most of these theories are promoted only by their inventor or perhaps a few other peers, but are generally not taken to be under the umbrella of well-established physics. Why? History, I suppose, since GR came first. You can read about some of these other theories, but be warned that at times you will walk the line between legitimate science and crackpottery.

 

[PeterDonis]

Won't you need a kinetic term for the energy though?

If I define "mass" for purposes of responding to Newtonian gravity as "energy divided by c^2", I mean total energy, including kinetic energy as well as "rest energy". After all, from this point of view, the photon's energy is *all* "kinetic energy" (since it has no rest energy).

Including kinetic energy for massive objects like planets and falling rocks doesn't make any real difference to the predictions because the kinetic energies of all such objects that we deal with under ordinary circumstances are so small compared to their rest energies. For example, the kinetic energy of the Earth in orbit about the Sun is about 100 million times smaller than its rest energy.

It's true that for some objects we can do experiments on, like subatomic particles in particle accelerators, kinetic energy is not much smaller than rest energy (in fact, it's often much larger). But those experiments happen so fast that the effects of gravity are negligible.

 

[pervect]

I just watched a show on Einstein concerning this theory of general relativity. Around 1922 photographs of stars from an eclipse were used to measure the bending of light from those stars around the gravitational field of the sun. Those measurements were used to confirm Einstein's theory. All through the program it was stated that the predicted observed amount of bending proved his theory of space/time and the warping of space in the presense of a mass.

How so?

If one restricts oneself to theories of gravity that can be modeled by the PPN formalism, then the doubling of the light deflection is a direct measurement of the PPN parameter gamma , in that none of the other PPN parameters affects the result of the light deflection experiment (at least according to the results in my text, which is "Gravitation" by Misner, Thorne, Wheeler, henceforth MTW. The discussion of light bending is on pgs 1100-1103.

The PPN formalism assumes that the path of light is predicted by some space-time metric, which is APPROXIMATELY of the form (MTW, p 1081)

$$ds^2 = -(1 - 2U + 2 \beta U^2+ 4\Psi) dt^2 + (1 + 2 \gamma U) [dr^2 +(r d\theta)^2 + (r \sin \theta d \phi)^2]$$

where U = 2M/r is the Newtonian potential. I HAVE OMITTED a few terms of the full PPN expansion of g_00 for my convenience in typing - they aren't important to the argument - see the wiki entry at http://en.wikipedia.org/w/index.php?title=Parameterized_post-Newtonian_formalism&oldid=397164800 or some other reference for the exact expression for g_00.

The PPN parameter gamma can be and is described as the amount of space curvature produced by a unit mass, as described in the wiki article. The fact that gamma curves space can be seen by considering the spatial metric induced by setting t = constant in the expression for ds, and noting that the circumference of a circle at r=R is not equal to 2*pi*diameter. The calculation of the radius and in particular the diameter is proving tricky enough that I won't get into it in more detail (the calculation for the diameter tends to 'blow up' unless care is taken to put in the finite radiius of the sun).

For those who like to use the Schwarzschild coordinate r, it should be noted that the PPN r is derived from isotropic coordinates, which use a different parameter r to describe the radius than the Schwarzschild coordinates do (MTW 1097). People who use a coordinate-indepenedent approach don't need to worry, those who do use coordinate dependent approacnes need to pay attention due to the limitations inherent in their approach.

I don't know if there is a simpler argument, or one which omits the assumption that gravity is describable by the PPN formalism. But the PPN formalism is a very general one that most modern theories of gravity satisfy (and Newtonian gravity can also be put into the PPN formalism with gamma=0). And in this formalism, gamma describes spatial curvature, and gamma is what is measured by the light-bending experiments.

 

[atyy]

The bending of starlight alone is not sufficient to distinguish GR from some other theories, such as Whitehead's. We believe GR to be the best theory at the moment because it has passed multiple tests http://mathnet.preprints.org/EMIS/journals/LRG/Articles/lrr-2006-3/ . Like any other theory, it is important to find out its limits, and scientists are still testing GR http://arxiv.org/abs/0903.0100 . At any rate, we know it is good enough to be used in practical applications like GPS http://relativity.livingreviews.org/Articles/lrr-2003-1/ .

Wrt this specific question, Newtonian physics does not predict in a consistent way the bending of light, although we can get such a prediction by an equivalence principle fudge.