I'm trying to understand the meaning of each of the basic tests of General Relativity, and I thought this forum might be a good place to pose my questions.
1. Deflection of light by the sun
2. Gravitational red shift
3. Precession of Mercury's orbit
I understand #1. GR says that gravity bends light, so this is a direct test of it.
Is #2 based on the same exact principle? That is, since gravity affects light, therefore we get kind of a Doppler effect? Or is it more complicated then that?
Is #3 based entirely on the premise that gravity travels at the speed of light? Newton's laws predict a certain precession based on the instant effect of gravity from other planets. Does GR get a different (and more accurate) calculation solely due to the finite speed (and delayed effect) of gravity? Or is there some other aspect of GR that feeds into the calculations?
The point of my questions is, do these tests simply prove that A) gravity travels at the speed of light and B) light is bent by gravity? If so, then would any other theory that fit these two requirements find the same support in these tests?
Thanks.
The reason for gravitational redshift is time dilation. You can also think of it as light gaining or losing energy as it travels between different gravitational potentials.
The precession of Mercury's orbit occurs because when Mercury is closer to the Sun, it experiences more time dilation than when it is farther away. This causes a slight additional force on Mercury, causing its orbit to precess.
These observations do prove that gravity travels at the speed of light and that light is bent by gravity. My theory predicts the same effects, and yes, it also does find the same support in these observations.
The precession of Mercury's orbit occurs because when Mercury is closer to the Sun, it experiences more time dilation than when it is farther away. This causes a slight additional force on Mercury, causing its orbit to precess.
These observations do prove that gravity travels at the speed of light and that light is bent by gravity. My theory predicts the same effects, and yes, it also does find the same support in these observations.
All three tests are predictions of GR. Specifically, they test GR in the Weak Field Limit. There are other theories of gravity which reduce to the predictions of GR in the Weak Field Limit, so none of these tests proof that GR is the one, true theory, but they show that GR is more correct than Newton's theory.
1. Deflection of light by the sun is experimentally tricky. Other proofs along this path inclusing deflections of starlight by Jupiter and the obvious galactic-sized gravitational lens. Some Newtonian theories predict deflection of starlight, but in the opposite direction and by a different amount.
2. Redshift, is predicted by any thoery of gravity which has a principle of local position invariance (LPI). This says no "direction'' in spacetime is mathematically distinguished from any other.
2. Redshift, is predicted by any thoery of gravity which has a principle of local position invariance (LPI). This says no "direction'' in spacetime is mathematically distinguished from any other.
gravitational red shift: according to gtr, static clocks held close to an isolated massive object run more slowly than static clocks which are further away, in the sense that radio signals and other EM radiation "climbing away" from a massive object are red-shifted, as recieved by a distant static observer, by an amount first computed by Einstein as early as 1913. Today, this effect would be considered a test of principle of local position invariance, and thus a test of a large class of "metric gravitation theories", not just a test of gtr. The effect has been verified by progressively more accurate experiments since the classic experiment of Pound and Rebka in 1961, and the best current experimental results confirm the effect to within about 0.02% of the value predicted by assuming LPI.
In addition, careful observations of a very rapidly rotating pulsar (neutron star) have confirmed to within a few percent. that this effect also works as advertised elsewhere in the universe. Futhermore, the ASCA X-ray satellite has observed very strongly gravitationally redshifted light emitted from the inner edge of the accretion disk a supermassive black hole in the galaxy MCG-6-30-15. This light appears to come from r = 10m to r = 3m; note that the inner edge of the accretion disk is located at r = 6m, so these observations appear to confirm that very hot material is leaving the disk and plunging into the event horizon, effectively disappearing at about r= 3m, just as gtr predicts!
Last but not least, the clocks aboard the Global Positioning System satellites in effect test every day both the gravitational red shift effect and the kinematical red shift predicted by str to within 50 nanoseconds per day (the str effects and gtr effects account for a comparable amount of the rate by which the satellite clocks differ from the rate of comparable clocks on the Earth's surface), and if either of those predictions were not correct, the clocks would drift by 40 microseconds per day, which would immediately render the GPS system completely useless!
Recall from the above that gravitational redshift is actually a measure of the post-PPN parameter alpha; here again is the graph from the paper by Will summarizing various measurements of alpha.
3. Mercury's orbit is a prediction that Einsteinian orbits are not purely Keplerian. Not only is the speed of gravity finite, but there is gravitomagnetism which makes gravity a non-central force. The two effect almost cancel out and so Newton's theory is approximately correct.
There are many more tests of GR, and a history of theories which have been rejected experimentally. There are some theories which appear to be mathematically indistiguishable from GR, so these are lumped in with GR. There are some other theories which only approximate GR in the weak field limit, and to test these experimentally we plug them into a Parameterized Post-Newton (PPN) model of gravity and see how close their predictions come to reality. GR is the first theory to make the cut.
More to read about this here: (Follow the links to find some really nice sites.)
http://math.ucr.edu/home/baez/RelWWW/tests.html
http://forum.physorg.com/index.php?showtop...indpost&p=99550
1. Deflection of light by the sun is experimentally tricky. Other proofs along this path inclusing deflections of starlight by Jupiter and the obvious galactic-sized gravitational lens. Some Newtonian theories predict deflection of starlight, but in the opposite direction and by a different amount.
QUOTE
light bending: according to gtr, the images of stars near a foreground isolated massive object such as the Sun should be displaced outwards from their usual positions by an amount first computed by Einstein in 1915. This effect could be consider the simplest kind of gravitational lensing effect. As is well known, a team of astronomers, including Arthur Stanley Eddington, confirmed Einstein's prediction that a stellar image which according to Newtonian gravitation would just graze the limb of the Sun would be displaced outwards by 1.75 seconds of arc during the solar eclipse of 1919. Many further observations of other exclipses have since been made, but these observations were too uncertain to provide very accurate tests. However, the effect should be the same for any frequency of EM radiation, including radio waves, and in recent years the Very Long Baseline Array Interferometer (VBLI) array has been used to confirm the prediction of gtr to within 0.1%, Most recently, the Hipparchos star mapping mission confirmed the effect for occultations by the major planets such as Jupiter, as well as our Sun.
2. Redshift, is predicted by any thoery of gravity which has a principle of local position invariance (LPI). This says no "direction'' in spacetime is mathematically distinguished from any other.
QUOTE (->
| QUOTE |
| light bending: according to gtr, the images of stars near a foreground isolated massive object such as the Sun should be displaced outwards from their usual positions by an amount first computed by Einstein in 1915. This effect could be consider the simplest kind of gravitational lensing effect. As is well known, a team of astronomers, including Arthur Stanley Eddington, confirmed Einstein's prediction that a stellar image which according to Newtonian gravitation would just graze the limb of the Sun would be displaced outwards by 1.75 seconds of arc during the solar eclipse of 1919. Many further observations of other exclipses have since been made, but these observations were too uncertain to provide very accurate tests. However, the effect should be the same for any frequency of EM radiation, including radio waves, and in recent years the Very Long Baseline Array Interferometer (VBLI) array has been used to confirm the prediction of gtr to within 0.1%, Most recently, the Hipparchos star mapping mission confirmed the effect for occultations by the major planets such as Jupiter, as well as our Sun. |
2. Redshift, is predicted by any thoery of gravity which has a principle of local position invariance (LPI). This says no "direction'' in spacetime is mathematically distinguished from any other.
gravitational red shift: according to gtr, static clocks held close to an isolated massive object run more slowly than static clocks which are further away, in the sense that radio signals and other EM radiation "climbing away" from a massive object are red-shifted, as recieved by a distant static observer, by an amount first computed by Einstein as early as 1913. Today, this effect would be considered a test of principle of local position invariance, and thus a test of a large class of "metric gravitation theories", not just a test of gtr. The effect has been verified by progressively more accurate experiments since the classic experiment of Pound and Rebka in 1961, and the best current experimental results confirm the effect to within about 0.02% of the value predicted by assuming LPI.
In addition, careful observations of a very rapidly rotating pulsar (neutron star) have confirmed to within a few percent. that this effect also works as advertised elsewhere in the universe. Futhermore, the ASCA X-ray satellite has observed very strongly gravitationally redshifted light emitted from the inner edge of the accretion disk a supermassive black hole in the galaxy MCG-6-30-15. This light appears to come from r = 10m to r = 3m; note that the inner edge of the accretion disk is located at r = 6m, so these observations appear to confirm that very hot material is leaving the disk and plunging into the event horizon, effectively disappearing at about r= 3m, just as gtr predicts!
Last but not least, the clocks aboard the Global Positioning System satellites in effect test every day both the gravitational red shift effect and the kinematical red shift predicted by str to within 50 nanoseconds per day (the str effects and gtr effects account for a comparable amount of the rate by which the satellite clocks differ from the rate of comparable clocks on the Earth's surface), and if either of those predictions were not correct, the clocks would drift by 40 microseconds per day, which would immediately render the GPS system completely useless!
Recall from the above that gravitational redshift is actually a measure of the post-PPN parameter alpha; here again is the graph from the paper by Will summarizing various measurements of alpha.
3. Mercury's orbit is a prediction that Einsteinian orbits are not purely Keplerian. Not only is the speed of gravity finite, but there is gravitomagnetism which makes gravity a non-central force. The two effect almost cancel out and so Newton's theory is approximately correct.
QUOTE
precession of periastrion of objects such as a planet orbiting a more massive object such as a star: according to gtr, non-circular orbits of planets around a star (or of satellites around the Earth) are not exact Keplerian ellipses, but are more like ellipses which slowly "rotate" so that their point of closest approach (periastrion) slowly "precesses" in the direction of motion of the orbiting object. The precession predicted by gtr was first computed by Einstein in 1915, who found that it precisely accounted for an unexplained "extra-Newtonian" precession of the planet Mercury in its orbit around the sun, in the amount of about 43 seconds of arc per century. (The total precession is much larger, about 5600 seconds per century, but almost all of this is explained by perturbations of the orbit of Mercury due to Jupiter and other Newtonian astrodynamical effects. Because in the limit of weak fields and slow motion (the motion of Mercury around the Sun falls into this category), gtr behaves pretty much like Newtonian gravitation, the previously known explanations for all but the ``extra-Newtonian'' 43 seconds also apply in gtr, but gtr's first great success was that it also explained the "extra" precession which could not be explained by Newtonian astrodynamics. Since 1915, progressively more accurate observations have tested the effect using the orbits of all the inner planets (specifically: the ``extra-Newtonian'' precession of Venus is observed to be 8 seconds of arc per century, and the ``extra-Newtonian'' precession of Earth is observed to be 5 seconds of arc per century, both also in perfect agreement with the prediction of gtr), the orbits of various asteroids, and the orbits of various spacecraft.
The PPN parameter which controls this precession is betabar; the above mentioned observations show that betabar agrees to 0.1% with the gtr value. The main source of uncertainty in these measurements is the value of the quadrupole moment of the Sun; helioseismology suggests that this moment is less than 10^(-7), but if it were larger, the estimated value of betabar might be affected.
The PPN parameter which controls this precession is betabar; the above mentioned observations show that betabar agrees to 0.1% with the gtr value. The main source of uncertainty in these measurements is the value of the quadrupole moment of the Sun; helioseismology suggests that this moment is less than 10^(-7), but if it were larger, the estimated value of betabar might be affected.
There are many more tests of GR, and a history of theories which have been rejected experimentally. There are some theories which appear to be mathematically indistiguishable from GR, so these are lumped in with GR. There are some other theories which only approximate GR in the weak field limit, and to test these experimentally we plug them into a Parameterized Post-Newton (PPN) model of gravity and see how close their predictions come to reality. GR is the first theory to make the cut.
More to read about this here: (Follow the links to find some really nice sites.)
http://math.ucr.edu/home/baez/RelWWW/tests.html
http://forum.physorg.com/index.php?showtop...indpost&p=99550
Thanks for the great replies. I have lots to read...
I like this site on light deflection because it has pictures and numbers.
http://www.astro.ucla.edu/~wright/deflection-delay.html
http://www.astro.ucla.edu/~wright/deflection-delay.html
QUOTE (cefarix+Jun 19 2006, 09:05 PM)
The reason for gravitational redshift is time dilation. You can also think of it as light gaining or losing energy as it travels between different gravitational potentials.
cef?
Light's energy is conserved in General Relativity. So if it has more or less energy it started off that way.
cef?
Light's energy is conserved in General Relativity. So if it has more or less energy it started off that way.
QUOTE (rpenner+Jun 21 2006, 06:48 AM)
I like this site on light deflection because it has pictures and numbers.
Well, such animation illustrates clearly, the light speed isn't invariant from outer observer perspective....
Well, such animation illustrates clearly, the light speed isn't invariant from outer observer perspective....
I agree.
It's a known prediction of Newtonian dynamics that light should move FASTER near the sun, but Einstein predicts that there will be a delay (Shapiro Delay), which you can say (as Einstein and Pentcho Valev have) that light is moving slower, or you can say (as modern textbooks say) that gravitation slows time.
Locally, we expect light to be measured at the same speed because our clocks will be slowed by the same amount.
It's a known prediction of Newtonian dynamics that light should move FASTER near the sun, but Einstein predicts that there will be a delay (Shapiro Delay), which you can say (as Einstein and Pentcho Valev have) that light is moving slower, or you can say (as modern textbooks say) that gravitation slows time.
Locally, we expect light to be measured at the same speed because our clocks will be slowed by the same amount.
Just an observation... Does anyone take into consideration how light is actually measured by the eye? When we measure the speed of something should'nt we take into acount the ability of the measuring device? It seems to me that light does'nt move at all. How can something without mass.... move? What I've understood light to be is simply an empty space. A space that gets filled by matter, however small that matter is.
The Eye determines everything it see's by the speed that the objects are moving. If you doubt that, then you should watch a rotating black and white alternately painted disk when it's spinning. It will turn different colors even though the only two colors on the disk are black and white. The reason? the speed of change between what your eye perceives directly in front of it, causes the mind to return a color to the brain. The color itself is fictional. I does'nt actually exist. Your eye simply measures the difference between the speed of one moving particle and the other. all color is perceived this way. the maximum speed difference that your eye can see is white, the slowest speed difference your eye can see, is black. What your eye actually does when you see light, is to compare the slowest moving thing "Nothing", with the fastest moving thing "Gravity" The difference (depending on the content percentage) returns the color white to your brain. Light actually has no color - If you look between the moon and the sun you will see black. but yet when you look at the moon it is a bright whitish color. If the light itself were actually white, it would be white between the moon and the sun since the sun provides the light. Now, you see black between the moon and the sun because the speed of gravity that flows through your eye and the speed of gravity flowing through space is almost the same speed. therefor the speed difference is small and the resulting color sent to the brain is black because your viewing far more gravity than you are anything else. In essense light only does one thing, it's what allows you to see everything else. It actually does'nt exist. It is the space between. You can measure the speed of things you can't see by using light, but the smallest thing you can't see, will be the fastest thing that moves.... and that can only be determined by the size of the particle itself. Since your eye can only measure speed differences by comparing particles, that speed will be determined by the size of the particle that the eye can measure. Likewise the speed of light can only be measured by the size of the smallest particle in the device that is measuring it or by the speed that light appears to travel inside of the smallest particle. Since that particle is not able to be measured, because any device that could measure it would have to be made of smaller particles than the smallest particle (not possible) it must be calculated by other means. Using the interaction between light and gravity we can get an idea of how fast the gravity is moving, and thus get a grip on the size of the smallest particle being thrust from the center of the earth, but because we don't have access to the surface of the sun we really can't tell how fast light is traveling up there but we can make some assumptions if you consider the gravity of the sun and other such issues.
Omnivisone
The Eye determines everything it see's by the speed that the objects are moving. If you doubt that, then you should watch a rotating black and white alternately painted disk when it's spinning. It will turn different colors even though the only two colors on the disk are black and white. The reason? the speed of change between what your eye perceives directly in front of it, causes the mind to return a color to the brain. The color itself is fictional. I does'nt actually exist. Your eye simply measures the difference between the speed of one moving particle and the other. all color is perceived this way. the maximum speed difference that your eye can see is white, the slowest speed difference your eye can see, is black. What your eye actually does when you see light, is to compare the slowest moving thing "Nothing", with the fastest moving thing "Gravity" The difference (depending on the content percentage) returns the color white to your brain. Light actually has no color - If you look between the moon and the sun you will see black. but yet when you look at the moon it is a bright whitish color. If the light itself were actually white, it would be white between the moon and the sun since the sun provides the light. Now, you see black between the moon and the sun because the speed of gravity that flows through your eye and the speed of gravity flowing through space is almost the same speed. therefor the speed difference is small and the resulting color sent to the brain is black because your viewing far more gravity than you are anything else. In essense light only does one thing, it's what allows you to see everything else. It actually does'nt exist. It is the space between. You can measure the speed of things you can't see by using light, but the smallest thing you can't see, will be the fastest thing that moves.... and that can only be determined by the size of the particle itself. Since your eye can only measure speed differences by comparing particles, that speed will be determined by the size of the particle that the eye can measure. Likewise the speed of light can only be measured by the size of the smallest particle in the device that is measuring it or by the speed that light appears to travel inside of the smallest particle. Since that particle is not able to be measured, because any device that could measure it would have to be made of smaller particles than the smallest particle (not possible) it must be calculated by other means. Using the interaction between light and gravity we can get an idea of how fast the gravity is moving, and thus get a grip on the size of the smallest particle being thrust from the center of the earth, but because we don't have access to the surface of the sun we really can't tell how fast light is traveling up there but we can make some assumptions if you consider the gravity of the sun and other such issues.
Omnivisone
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