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So, I will begin by tracing relativity's roots to 1899, in fact, a hundred-years ago this week, and how that led to special relativity and tests of the foundations of general relativity. Then 20 years later, the famous measurements of the deflection of starlight led to one of the key tests of general relativity and later led to an important astronomical tool. 1939, strangely in what most people consider to be the wasteland for general relativity, the period between 1920 and 1960 or so, but in 1939 an important event occurred, or series of events, that led to the prediction of black holes. I will talk about the renaissance of experimental general relativity in 1959, which can be seen in a number of events that occurred during the academic year 1959-1960. 1979, twenty-years later, came the first evidence for the existence of gravitational waves that has spawned a potentially new field of astronomy. And then finally, today, I'll take a look to the future and talk about what is the outlook for further experiments for general relativity.
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You can see this even in the original Michelson/Morley experiment where you send a light beam, split it in two, and have the beam go down two arms and back and look at the interference of the fringes; the Michelson/Morley experiment that was a foundation for special relativity. But really what you're doing is comparing two clocks, one clock is a clock defined by the time it takes to go perpendicular to our motion through the putative ether. The other clock being defined by the motion of light down at the other arm. So you're comparing the frequencies of those two clocks. One can analyze this experiment from a number of different viewpoints but from the viewpoint of the ether's rest-frame -- I'm now thinking in 19th century terms -- this clock involves motion of a light ray across the river of the ether, so you have to move in a triangular kind of path, and you can calculate the time it takes for one transit in that clock. This clock is going upstream and then downstream along the ether river and so that transit takes a certain amount of time. And the two times are unequal unless you take into account the Lorentz contraction of this arm, that's parallel to the motion through the ether. Once you take that into account both clocks tick equally and you get no change in interference pattern and you get the null result of the Michelson/Morley experiment. That's the standard resolution of ordinary special relativity.
But now suppose you take the more general point of view that says the Speed of Light in this particular rest-frame is say c. But the characteristic speed that appears in the Lorentz transformations that you use for Lorentz contraction is a different speed, c0. Now, you could propose this as a simply ad-hoc proposal but it actually turns out that in a class of theories of gravity alternative to general relativity called Non-Metric Theories you can have cosmic fields, particularly tenser and vector fields, that modify Maxwell's equations in precisely a way as to produce this kind of effect. So this kind of thinking allows you to consider experiments like this as tests of the metrical character of gravity as well as just bare tests of special relativity.
Well, if you make that proposal that these two speeds could be different than you find that the fringe-shift depends on the speed through the rest-frame of the universe; the arm lengths; and this co- efficient which would be unity if both speeds were the same, i.e. if Lorentz invariance were valid.
Well, this idea, then, of comparing clocks whose basic orientation could differ relative to our motion through the universe as a test of the metrical character of gravity has become an important enterprise.
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But the best experiments to date are the so-called mass anisotropy experiments which measure whether or not two clocks, which are in fact the substates of an atom, whose orientation is determined say by the magnetic quantum numbers of the atom and maybe by a laboratory magnetic field, whether one atomic substate has the same ticking rate, or the same basic frequency, as another substate whose axis is oriented differently relative to our 300km/sec motion through the universe. So these kinds of anisotropies in local atomic energy levels can be tested by a variety of methods involving trapped atoms and such.
The first such experiment was the famous Hughes/Drever experiment, but in recent years, using laser cooled and trapped atoms, these kind of anisotropies have been limited with precisions that really are quite extraordinary. These are among the most precise null experiments performed in physics. And these again tell us that gravity should be locally Lorentz invariant, and so evidence that only a metric couples to ordinary matter.
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The first experiments of this sort were the Pound/Rebka experiments around 1959-1960. A hydrogen maser experiment is the best direct bound comparing clocks at different places in the gravitational field. This used hydrogen masers on a Scout rocket. But also, if there is any deviation from this basic formula, if alpha is not zero, then it turns out that alpha typically depends on the kind of clock you're using. So null gravitational red shift experiments are also important tests, experiments in which you compare two different clocks sitting side by side in a laboratory and you simply modulate the gravitational field in which they sit. So such clock comparisons can also provide bounds, and here's a null red shift experiment performed in Paris that yields about a 10-4 test. So clock comparisons play an important role in testing the foundations of the metrical idea of gravitation.
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But from that calculation you only get half the deflection of starlight, half the overall prediction. The other half comes from the fact that according to curved space/time theories of gravitation space is curved near a body like the sun. You can measure that curvature in at least a thought experiment by setting up a triangle near the sun, one of whose arms passes by the sun very close, and simply compare the sum of interior angles of that triangle to a similar triangle that is totally far from the sun where space/time is supposedly flatter. The difference in the sum of interior angles depends, is roughly half that same deflection, but it depends on a coefficient, gamma, which depends on the theory of gravity you are using to calculate the curvature. Gamma is one in general relativity, but could be different in different theories of gravity such as scalar-tensor gravity and so on; this parameterization of alternative theories of gravity is something I'll talk about a little bit later. But then, from this point of view, the total deflection is the sum of the two effects, a kind of ballistic effect and the curvature effect.
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Another effect on the propagation of light, that produces a delay in the propagation of light across the solar system from the earth to a planet or spacecraft as it passes by the sun, as the light passes the sun, the so-called Shapiro Time Delay, has also been measured using radar tracking techniques, and here the measurements agree with general relativity to about a part in a thousand. To a few parts in ten thousand, then, this coefficient supports general relativity.
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The observation on September 14, 1959 of the first radar echo from a planet. Although it was only discovered in the data afterwards, the echo was there in that particular day's observing run. And this would introduce the solar system as a laboratory for testing general relativity. March 1960. The submission to Physical Review of the Pound/Rebka measurement of the gravitational red shift. Kind of the first and beginning use of high precision tools for testing Einstein's predictions.
In June of 1960, the first of a new generation of theoretical papers that helped to elucidate general relativity's predictions so that one could really learn in a very simple way what general relativity predicted and what its observable consequences were. Later that year, Carl Brans worked on a new theory of gravity that came to be known as the Brans/Dicke theory that we'll see in a moment still is around to haunt us.
And then finally the observation of the first quasars that would foretell an important role for general relativity in astrophysics.
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General relativity predicts for all of these parameters (gamma - 1, beta - 1 and all the rest) predicts values exactly zero, and so the issue is what are the measured values of these parameters from different experiments. So, I've already pointed out that measurements of time delay and light deflection lead to values, let's say 3 x 10-4 relative to zero for gamma minus 1. Measurement of the perihelion shift and the Nordtvedt Effect (looking for a difference in the acceleration of the earth and the moon toward the sun) places strong bounds on beta at the few parts in 104 level. A number of parameters produce anomalous effects in gravity that could occur because our solar system is moving through the universe. These are kind of strange preferred frame effects. Many of these have been set, have been bounded very close to zero, one quite extraordinary bound using pulsars. All zero in agreement with general relativity. So, to an accuracy that is now better than a part in a thousand, at least in the weak field limit, general relativity appears to hold.
Now, if you wanted to think of the leading alternative theory of gravity, the so-called Scalar/Tensor Theory, originally the Brans/Dicke Theory. These observations, primarily the observation of gamma, place a lower bound on the coupling constant of scalar/tensor gravity of about 3,000. I'll say a little more about Scalar/Tensor theory shortly.
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Now it turns out that in general relativity, if you take general relativity as your model, these three relativistic effects all depend on the eccentricity, the orbital period, and the two unknown masses of the stars. So, if you assume general relativity, you have three constraints on two unknown variables and so a test of general relativity can be provided by asking whether those three constraints are mutually consistent.
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And here's the original overlap say plotting mass from 0 to 3 solar masses but I've blown-up this intersection region by a factor of about 300 to get this overlap and you see they overlap completely with each other; and this verifies general relativity at about the half a percent level.
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So this quantitative verification of the prediction of general relativity for gravitational waves gives one confidence that they really exist and motivates and gives a foundation for efforts to build gravitational wave detectors for gravitational radiation, about which we we'll hear from Kip Thorne a little later.
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But in recent years, like the hockey mask guy who could never be killed and appeared in movie after movie, the Brans/Dicke Theory is back and it ’s back in a more virulent mutant form in which the coupling constant is not a constant but itself is a function of the scalar field. Now this of course is not just an ad-hoc proposal; these kinds of generalized scalar/tenser theories are natural predictions of string inspired theories and so on, and they are also discussed extensively in certain kinds of inflation, and so on. So, these theories really do exist and they're well motivated but they have the property that physics could be very different in the early universe or say in the interiors of neutron stars where the scalar field could be very different than it is today while being very close to general relativity, say, in the solar system at present. So, one would like to improve the tests of these theories as a way to try to place bounds on the kinds of more fundamental theories that produce them.
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But it is strange that 100 years ago when Einstein was writing to his girlfriend talking about some vague ideas about electrodynamics and moving frames that today we would think about general relativity as a tool for astronomers, and possibly as a tool for everyday life. Thanks.
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Well, celebrating 100 years of physics as we are doing at this meeting in honor of the centenary of the APS is almost equivalent to celebrating a hundred years of relativity. What I would like to do in this talk is survey these hundred years of relativity by highlighting events that occurred, ironically and strangely at almost 20 year intervals in this hundred-year period. Each event illustrates a particular theme in the issue of putting Einstein's general Theory of Relativity to the test.
Well, in 1899, we had Einstein in love. In fact, 100 years ago this week, Einstein wrote a letter to his girlfriend, remember Einstein was just about 19-20 years old at this time, with a letter filled with lots of lovey-dovey stuff, that is quite quaint from today's perspective. But at the end of this letter, he says "my broodings about radiation are starting to get on somewhat firmer ground and I am curious myself whether something will come of them." Well, as we know, something did come of them ultimately by 1905 and later that year he wrote further letters about his beginning thinking about the problem electrodynamics and moving frames. This as we know led in 1905 to the Special Theory of Relativity.
From one point of view, special relativity is the foundation of all the physics but my point of view is to take special relativity as a foundation for general relativity; the idea that physics should be Lorentz invariant, or locally Lorentz invariant. This idea of testing special relativity as a foundation for general relativity has led to a number of extremely important high precision experiments and interestingly all of these experiments are based on comparing clocks.
This chart summarizes what has been done in this game. So here as a function of year on a highly non-linear scale, is this parameter delta which is just this coefficient, the difference between these two speeds and one. If delta is zero, then gravity is locally Lorentz invariant and you have some evidence that the only field in nature that couples to ordinary matter is the spacetime metric. You have no other cosmic tensor or vector kinds of fields that do such coupling. Now, the Michelson/Morley experiment then can be translated into a bound on this parameter at a level of about 10-2. An improvement of that Michelson/Morley experiment using lasers improves the precision by many orders of magnitude.
Well, these kind of clock comparisons also can be used to test another aspect of the foundations of general relativity, namely whether physics is locally position invariant, whether the rate of atomic clocks measured in local inertial frames is the same wherever that frame might be, and these are the standard gravitational red shift experiments. If you express the fractional frequency change in terms of the difference in gravitational potential divided by c2 then you measure a parameter, alpha, which is just the deviation from the normal prediction with unit coefficient.
Let me turn now to 1919, the second event in my little cavalcade of events for experimental relativity. That, of course, was the famous bending of starlight by the sun made by teams of British astronomers headed by Arthur Stanley Eddington . I remind you that the bending is 1.75 arc-seconds for a light ray that just grazes the surface of the sun. But it turns out that these experiments, while they were great triumphs of their day, were of rather low accuracy, and most modern observers feel they seriously underestimated systematic errors in those experiments. And so the question is what has happened since then?
One thing that has happened is a better understanding of what the light deflection really is. You can think of the light deflection from a more general viewpoint than simply general relativity, in which one half of the light deflection really goes back to our old friend Newton whose theory you can use to calculate the deflection of a body whose velocity is near the speed of light, a calculation actually first done by Cavendish, although never published by him. It was only discovered 100 years later, 150 years later on a scrap of paper in his collected papers that stated 'I have calculated the deflection of starlight and the answer is', and he gave the answer. Later done by von Soldner. Einstein, from a slightly different point of view, did this calculation using only the principle of equivalence.
Here then are the results for measuring this coefficient, one plus gamma over two, with one being the general relativistic prediction, and different experiments plotted. The red experiments are optical measurements of ordinary deflection of starlight, leading, in most recent days, to measurements using the Hipparcos astrometry satellite with results at about a few parts in a thousand in agreement with general relativity. Dramatic improvements, however, were made using radio astronomy to measure the deflection of starlight from quasars, leading in recent days using VLBI, Very Long Baseline Interferometric techniques; the most recent results published by Marshall Eubanks and collaborators, agrees with general relativity to about 3 parts in 10,000.
Now, the bending of light, of course, has now gone far beyond the question of simply testing Einstein's theory and is now a new tool for astronomers using the deflection of light by the galaxies and matter as a way to measure the mass in the neighborhood of galaxies and clusters to search for dark matter; to study the structure of mass distributions and so on. So, bending of light has now become a new tool. Einstein's gift to astronomy.
Now, as I said, from the early 1920's until about 1960 most people think of general relativity in that period as a kind of wasteland for general relativity. But in 1939, two events occurred that at least foretold some important future for the field. Those were the calculation by Oppenheimer, Volkoff and Snyder of the gravitational collapse of bodies and the structure of neutron cores. Here were the first papers that really elucidated the first details of black holes. Coupled with the first observations of cosmic radio waves it led, of course today, to an entire field of black hole astronomy about which many of us heard earlier from Roger Blandford. And here, although a lot of excitement has occurred recently, the future will bring even more excitement in terms of astrophysical observations and theory on black holes; numerical relativity to simulate the evolution of complicated systems involving black holes; and gravitational wave observations that will detect the waves from dynamical systems containing black holes. Ultimately, there may be important tests of strong field general relativity from observing those black holes.
1959, this next event in my cavalcade, in some sense was a year that foretold many future events and a renaissance for general relativity:
One of the important outcomes of this sort of ``year of portentous events'' was a systematic effort to test general relativity using measurements primarily in the solar system. One set of measurements, of course, were the measurements of the bending of starlight. And a whole class of experiments then was done that measured a number of other parameters that compare general relativity to alternative theories of gravity. This framework, called the Parameterized Post-Newtonian Framework, characterizes a broad class of geometric, or metric theories of gravity in terms of a set of parameters, 10 in all -- one parameter gamma, we have already talked about that controls the deflection of light, but there's another parameter, beta for example, that controls the perihelion shift that somehow relates to non-linearity in gravity, and other parameters that really tell you about a variety of generic effects that different theories can predict.
My next event is 1979, December 1979 to be precise, at the Texas Symposium on Relativistic Astrophysics in Munich, where the first announcement was made by Joe Taylor that he and his team had measured the damping of the orbit of the binary pulsar in an amount that agreed with the prediction of general relativity for damping produced by gravitational wave emission. So, that observation of the binary pulsar made use of the Arecibo radio telescope measured with now unbelievable precision, the parameters of the orbit that you might associate with a standard two-body Keplerian orbit: there's the pulse period with the errors here on the last digit. The orbital period in days, the eccentricity. But in addition to these, a number of post-Keplerian parameters, or relativistic-type parameters, such as the advance of the periastron at some four odd degrees per year; the effect of the gravitational red shift and the motion of the pulsar on the observed period of the pulsar clock that produces a modulating arrival time of pulses with an amplitude of 4 some odd milliseconds; and finally the rate of orbit decay of the period which one believes is due to gravitational wave damping.
So, for example, you can plot those three constraints on a graph of the pulsar vs. mass of the companion, and if the three curves, or really bands once you take the errors into account, if they overlap in a common region then that's a confirmation of general relativity.
Even more impressive than this is a plot of the orbital phase of the binary pulsar as a function of time. If the orbital period is decreasing than the orbital phase should decrease quadratically and this is a plot of the observed points, the observed phases of the binary pulsar from discovery in 1974. The curve that's superimposed there is not a fit to those points. The curve is the prediction of general relativity using the orbital eccentricity, the orbital period.
...and the two masses, which you can simply infer from these two curves: the perihelion shift and the red shift curve. You get those values of the masses that gives you a unique prediction for the rate of change of orbital period and a unique prediction for the phase change.
...and that is what that curve is, that's the prediction. And the great thing about this curve is that in 1992 when this data point was made Arecibo was shut down for two years for a major upgrade. As soon as Arecibo came back up, Taylor went down and measured the phase of the binary pulsar anew, and that was the new point measured; it fell right smack on the curve. And then when you do the detailed fitting you find this agrees with the prediction to better than half a percent.
Well, that brings me to the present, to 1999, and I would like to say a few words about the outlook for experimental tests of general relativity. This simply illustrates sort of a fact about the field of gravitational physics that sometimes isn't completely appreciated and that is the tremendous range in both distance scale and mass scales over which the entire subject takes an interest, ranging from the scale of the present universe down to the quantum gravity scale at the smallest imaginable scales. And, the kinds of scales of great interest, of course, lie along, or close to this line that corresponds to strong field gravity, relativistic gravity. On this side of course, you would be inside a black hole but near this line you would have strong gravitational effects. And so one would like to try to do experiments that test the strong field effects of gravity, or if you're confined to looking in weak field regions, to try and find evidence for gravitational effects that themselves occur at strong range. One would like to find in current day experiments performed here on human scales evidence that are kind of relics of the quantum gravity scale that might be predicted by theories for unification or quantum gravity.
So those kinds of ideas motivate a number of future experiments. One kind of experiment that people are talking about improving is the test of the weak equivalence principle, the equality of free-fall of bodies of different composition. Ordinarily, we think of this principle as being a justification for the idea of curved space/time. It is a foundation for general relativity. And current experiments are accurate to about a part in 1012;
say from the Eot-Wash experiment performed by Eric Adelberger and his group at the University of Washington, also from lunar laser ranging measurements; all confirm that bodies fall with the same acceleration to levels at or better than a part in 1012.
But many models of quantum gravity or unification such as String Theory generically predict there should, at some level, be violations of the equivalence principle caused by interactions of matter with new fields, such as dilaton or moduli fields or new particles. Although there are not very robust predictions of where these levels of violations should occur, this idea has motivated the search for improved experiments that would make a dramatic change, or a dramatic improvement over current levels. And so one idea is to do a space experiment, a space test of the equivalence principle, that would verify the principle to a level of 10-18 and so could look for, or probe for such new kinds of physics.
Another issue that will be of some interest in the coming years in experimental gravity has to do with the Brans/Dicke Theory. As I've already pointed out, the kind of evidence that supports general relativity to better than a part in a thousand places a strong bound on the original version of the Brans/Dicke Theory, which I remind you is a theory that is essentially general relativity but with the modification of an added scalar field that only couples to gravitation. And roughly speaking in the Brans/Dicke Theory, the theory merges smoothly to general relativity, as this coupling parameter omega becomes large. Currently, the bound on omega, as I've said, is that omega should be larger than 3,000 and largely for this reason the original Jordan/Brans/Dicke Theory was thought to be dead.
So one experiment that can measure this coupling constant to high accuracy and can perform another very important test is Gravity Probe B. An experiment to launch into space around the earth an array of gyroscopes, four gyroscopes in all, that will measure two effects: geodetic precession, which is the precession of gyroscopes caused by the fact that they are moving in the curved space/time around the earth, and the smaller frame dragging precession caused by the dragging of space/time around the earth because of the earth's rotation. The goal is to measure these effects to about .4 milliarc-seconds per year, with a launch date set for October of 2000. So it could measure this geodetic procession with very high precision, possibly as high as a part in 105 which would test the Brans/Dicke omega. The test of frame dragging will be of 1% precision but will test this very important Machian-type effect that really tells us something about how inertial frames are defined in the universe.
Another thing one can think about looking for in the next 10-20 years are tests of general relativity by direct detection of gravitational waves. Once waves are directly detected, as opposed to looking for the damping in an orbit like the binary pulsar, you could measure such things as the polarization states of the waves; the relative speed of gravitational waves compared to light and so on, as well as the properties of the relativistic sources that produced the waves. One could possibly study the detailed structure of black holes' space/time with looking at gravitational waves.
The final thing I want to mention at this point, 100 years after the love-struck Einstein's musings about fundamental theory that might solve problems in physics, is the extent to which general relativity has had practical applications. The one that I like to quote the best has to do with the Global Positioning System, which is the navigation system about which some of us heard in the next room just a short time ago, which uses atomic clocks on spacecraft to provide precise navigation for military and commercial uses. Well, it turns out that the gravitational red shift and the time dilation of special relativity cause the clocks on the satellites to tick at different rates than clocks on the ground and this effect has to be taken into account for the system to work. The system requires, say, 50 nanosecond accuracy in all clocks to function, but this rate offset is actually enormous. It's 39,000 nanoseconds/day, most of which is the general relativistic gravitational red shift effect. So if this effect were not taken into account in GPS the system would fail to function in less than an hour. The effect, in fact, is taken into account electronically in the clocks before they're even launched because it's roughly a constant offset.
(Question & Answer Session)