4 The Experimental Basis of Einstein's Theory

It is unfortunate to note that the situation with respect to the experimental checks of general relativity theory is not much better than it was a few years after the theory was discovered - say in 1920. This is in striking contrast to the situation with respect to quantum theory, where we have literally thousands of experimental checks. Relativity seems almost to be a purely mathematical formalism, bearing little relation to phenomena observed in the laboratory. It is a great challenge to the experimental physicist to try to improve this situation; to try to devise new experiments and refine old ones to give new checks on the theory. We have been accustomed to thinking that gravity can play no role in laboratory-scale experiments; that the gradients are too small, and that all gravitational effects are equivalent to a change of frame of reference. Recently I have been changing my views about this. The assumption of the experimentalist that he can isolate his apparatus from the rest of the universe is not necessarily so; and he must remember also that the “private” world which he carries around within himself is not necessarily identical with the “external” world he believes in. Particularly in the case of relativity theory, where one thinks one knows the results of certain experiments, it is all the more important to perform these crucial experiments, the null experiments. For example, the Eötvös experiment has not been repeated, in spite of the tremendous improvement in experimental techniques now available. An improvement by a factor of 1,000 in the accuracy of this experiment should be possible, and it is a disgrace to experimental physics that this has not yet been done. It is a measure of our strong belief in the foundations of relativity - the principle of equivalence - that this has not been done; but an excellent example that our beliefs are not always correct was provided for us by the events of last week, when it was discovered that parity is not conserved in beta decay! This experiment could have been done much sooner, if people had thought it was worth doing.

Professor Wheeler has already discussed the three famous checks of general relativity; this is really very flimsy evidence on which to hang a theory. To go a little further back: the Eötvös experiment is in some ways very powerful; it is really remarkable that such wide ranging conclusions should be drawn from a single experiment. It measures the ratio of mass to weight for an object, and sees whether this varies with the atomic weight of the element involved, the binding energy of the atoms, and things of this kind. One finds that, to about one part in ; the ratio is independent of the constitution of the matter. It does not prove exact equality of mass and weight, contrary to the assertion in one well-known text on relativity; it proves it to one part in , which is quite a different thing! To considerable accuracy, it also shows that electromagnetic energy has the same mass-weight ratio as the “intrinsic” mass of nucleons, since in heavy nuclei the electromagnetic contribution is an appreciable fraction of the total binding energy. On the other hand, gravitational binding energy is generally negligible and one cannot infer its constancy from the Eötvös experiment.

I would like now to refer to the table below, which may indicate where some of the troubles lie.

These are the famous dimensionless numbers - and of course everyone will say, “He’s fallen into that trap!” I’ve written in dimensionless form the important atomic and astrophysical constants, and arranged them according to order of magnitudes; we see that they group themselves in the remarkable way indicated. The masses of elementary particles, the fine structure constant, and other “strong” coupling constants are all of order unity (using the term “order of magnitude” rather loosely!). Then the “weak” coupling constants have reciprocals squared all of order . At we have the gravitational coupling constant; everything so far has been an “atomic constant.” But also at we have the constants associated with the universe as a whole; the age and the Hubble radius; while at we have the number of particles out to the Hubble radius.

What is queer about these? The atomic numbers are queer because if we think nature is orderly and not capricious, then we would expect some day to have a theory from which these numbers would come out, but to expect a number of the order of to turn up as the root of our equation is not reasonable. The other thing we notice is the pattern: being squared, and being squared; and finally the strange equality of the “universal” constants - age of the universe, Hubble radius - to the gravitational coupling constant, which is “atomic” in nature.

What explanations exist for these regularities? First, and what ninety percent of physicists probably believe, is that it is all accidental; approximations have been made anyway, irregularities smoothed out, and there is really nothing to explain; nature is capricious. Second, we have Eddington’s view, which I may describe by saying that if we make the mathematics complicated enough, we can expect to make things fit. Third, there is the view of Dirac and others, that this pattern indicates some connections not understood as yet. On this view, there is really only one “accidental” number, namely, the age of the universe; all the others derive from it.

The last of these appeals to me; but we see immediately that this explanation gets into trouble with relativity theory, because it would imply that the gravitational coupling constant varies with time. Hence it might also well vary with position; hence gravitational energy might contribute to weight in a different way from other energy, and the principle of equivalence might be violated, or at least be only approximately true. However, it is just at this point that the Eötvös experiment is not accurate enough to say anything; it says the “strong interactions” are all right (as regards the principle of equivalence), but it is the “weak interactions” we are questioning. I would like therefore to run through the indirect evidence we have. There would be many implications of a variation with time of the gravitational constant, and we must see what the evidence is regarding them.

Assuming that the gravitational binding energy of a body contributes anomalously to its weight (e.g., does not contribute or contributes too much), a large body would have a gravitational acceleration different from that of a small one. A first possible effect is the slight difference between the effective weight of an object when it is on the side of the earth toward the sun and when it is on the side away from the sun. This would arise from the slightly different acceleration toward the sun of a large object (the earth) and the small object. If we estimate his effect, it turns out to be of the order of one part in on , which I think there is no hope of detecting, since tidal effects are of the order of two parts in . The mechanism of the distortion of the earth by tidal forces would have to be completely understood in order to get at such a small effect.

Another way of getting at this same effect would be to look at the period and orbit radius of Jupiter, and compare with the earth, to see if there is any anomaly. Here the effect would be of the order of one part in , which is on the verge of being measurable. Possibly by taking averages over a long period of time one can get at it; I haven’t talked with astronomers and am not sure.

Another interesting question is this: are there effects associated with motion of the earth relative to the rest of the matter of the universe? All the classical “ether drift” experiments were electromagnetic; what about gravitational interactions? Could their strength depend on our velocity relative to the co-moving coordinate system? We can say something about this, assuming the effect to be of the order of , where is the ratio of earth velocity to light velocity. We know the velocity of the sun relative to the local galactic group; but we know nothing of the velocity of the galactic group relative to the rest of the universe, except that it is not likely to be much greater than 100 km/sec. Supposing it unlikely that the motion of the local group would be such as to just cancel the motion of the sun relative to it, we can say that the velocity of the sun relative to the rest of the universe is perhaps of the order of 100 km/sec. Then the annual variation in , owing to the fact that the earth’s velocity at one time of the year adds to and at another time subtracts from the sun’s velocity, amounts to about one part in . This could conceivably give rise to an annual variation in “g” which could be detected, for example, by a pendulum clock. Now the best pendulum clocks are not quite up to this; but an improvement of a factor of ten would make this effect detectable, if it exists.

There is, however, an indirect way of getting at this effect: any annual variation of the gravitational interaction would give rise to an annual variation of the earth’s radius, and hence of the earth’s rotation rate. Now such an annual change is in fact observed. The earth runs slightly slow in the spring. The effect is, within a factor two, roughly what you might expect from assuming 100 km/sec. and putting in the known compressibility of the earth. However, it is possible to explain it also purely on the basis of effects connected with the earth itself, such as variations of air currents with seasons. Also the irregular character of the variation indicates at least some contribution from such factors.

GOLD: It varies from one year to the next a bit, so it is certainly not to be attributed to relativity.

DICKE: It’s not too clear. Certainly part of it varies, but what the variation amounts to is not too obvious because its measurement depends on crystal clocks and they haven’t been too good until recently so we can’t go back far in time.

Now there is some other evidence on the question of a long period change in the gravitational interaction as we go back into the past. If gravity was stronger in the past, the sun would have been hotter, and we ask whether we can then account for the formation of rocks and creation of life. The accompanying figure (4.2) shows what we can say about the temperature of the earth.

This figure gives the temperature of the earth as a function of time as we go into the past, “0” on the scale representing the present. I have assumed that as the temperature rises, the amount of water vapor present in the atmosphere increases, and the sky becomes completely overcast. Then if we use the known albedo of clouds (.8), and the black body radiation in the infra-red, we get the curve shown for the temperature, assuming the age of the universe to be 6.5 billion years. The temperature rises slowly to about C one billion years ago. Evidence for life as we know it exists back to about 1.0 billion years. Life could have been present back 1.7 billion years, when the temperature would have been about C. According to biologists, algae from hot springs are known capable of living at such temperatures, so life could have existed then. There is evidence for a fairly sharp cut-off on the existence of sedimentary rocks at about 2.7 billion years, even though the solar system is about 4 billion years old. This agrees with our curve, since at the temperature corresponding to that age, about half the water would be in the atmosphere, and the pressure would be so high that its boiling point would be about C. There would still be enough liquid water to form sedimentary deposits. However, at slightly higher temperatures, the critical temperature of water would be exceeded, only vapor would exist, and sedimentary rocks would not have been formed.

I would say that the evidence does not rule out the possibility of the sun’s having been hotter in the past.

There is some additional indirect evidence arising from the problem of the formation of the moon. The moon has a density so low that there are only two possible explanations: first, different composition from the earth; second, a phase change in the earth that leads to a very dense core. The second is, however, hard to believe, because if the core is assumed to be liquid iron, the total amount of iron in the earth is in agreement with what we believe to be the abundance of iron in the solar system as a whole. If we say the composition is different, we notice that it seems to be about the same as that of the earth’s mantle. This in turn suggests Darwin’s old explanation, that the moon flew out of the earth. The earth was formed first and was rotating with a period of about four hours, when as a result of tidal interaction with the sun, a large tidal wave was set up which split the earth into two parts; then as a result of tidal interaction between moon and earth, the moon gradually moved out to its present position. The latter part of this account is probably right, as we know from the evidence on slowing down of the rotation rate as deduced from comparison of Babylonian eclipse records with modern ones. However, if the earth was rigid then as it is now, the natural frequency of oscillation would have been too high for the first part of the account to be correct. With a liquid earth, the period is more nearly right, but Jeffreys’ objection, that turbulent dampening would prevent the buildup of a wave to the point of producing fission, arises. However, Professor Wheeler has pointed out recently that this objection may be met by including the effect of the magnetic field of the earth in damping the turbulence. Now the only difficulty is keeping the earth liquid, since the rate of radiation from a liquid earth is so great that it would freeze up in a hundred years - nowhere near a long enough time to set up the oscillation required. One thing which could keep it liquid would be a hotter sun!

There is another bit of evidence on this: the moon is distorted in such a way that it has been called a “frozen tide”; it corresponds somewhat to the shape it would have had if it had frozen when at about a quarter of its present distance from the earth.

GOLD: This is not correct; the present shape is not at all what it would have been at any closer distance.

DICKE: This is true, but there is the possibility that the moon was somewhat plastic at the time of freezing so that the biggest distortions would have subsided somewhat to give you dimensions compatible with what is now seen.

GOLD: If the moon were formed by a lot of lumps falling together, it would have an effect on how strong the moon is, and what disturbance it could bear; then it could have three unequal axes, as it does.

DICKE: Yes; this is the other explanation for the moon’s shape, that big meteorites piled into it and made it lopsided.

Another piece of indirect evidence on this is connected with the problem of heat flow out of the earth. There is evidence for the earth’s core being in convective equilibrium; and heat flowing out of the earth’s core seems to be the only reasonable mechanism at present for a convective core. The question is how that heat gets out. It may be that there is radioactive material at the center which is the source of the heat flowing out; but potassium would be expected to be the biggest source of heat, and it is so active chemically that we expect to find it in the mantle only. If, however, gravity gets weaker with time, there would be a shift along the melting point curve of the mantle which would lead to a slow lowering of the temperature of the core, and heat flowing at such a rate as to keep the mantle near the melting point. If we put in a reasonable melting point curve for the mantle, we find this contribution to the heat flowing out of the earth is of the order of one-third of the total heat. So the evidence is not incompatible with the idea that gravity could be weaker with time, even though radioactive materials are of sufficient importance so that one would not attempt to account for the heat flow out of the earth solely on this basis.

There is some small bit of evidence that there may be something wrong with beta decay: the beta coupling constant may be varying with time. This comes from the evidence on Rubidium dating of rocks. The geologists on the basis of their dating of rocks assign a half life for Rb 87 decay of about years. There has been quite a series of laboratory measurements giving values of about years; on the other hand one particular group has consistently got a value lower than five. So this is up in the air; but I think that before long we will have a definitive laboratory value for the half-life.

Finally, l may just mention last week’s discovery that parity is not conserved in beta decay. What the explanation for this is no one knows, but it could conceivably indicate some interaction with the universe as a whole.

DE WITT called for discussion.

BERGMANN: What is the status of the experiments which it is rumored are being done at Princeton?

DICKE: There are two experiments being started now. One is an improved measurement of “g” to detect possible annual variations. This is coming nicely, and I think we can improve earlier work by a factor of ten. This is done by using a very short pendulum, without knife edges, just suspended by a quartz fiber, oscillating at a high rate of around 30 cycles/sec. instead of the long slow pendulum. The other experiment is a repetition of the Eötvös experiment. We put the whole system in a vacuum to get rid of Brownian motion disturbances; we use better geometry than Eötvös used; and instead of looking for deflections, the apparatus would be in an automatic feed-back loop such that the position is held fixed by feeding in external torque to balance the gravitational torque. This leads to rapid damping, and allows you to divide time up so that you don’t need to average over long time intervals, but can look at each separate interval of time. This is being instrumented; we are worrying about such questions as temperature control of the room right now, because we’d like stability of the temperature to a thousandth of a degree, which is a bit difficult for the whole room.

BARGMANN: About three years ago Clemence discussed the comparison between atomic and gravitational time.

DICKE: We have been working on an atomic clock, with which we will be able to measure variations in the moon’s rotation rate. Astronomical observations are accurate enough so that, with a good atomic clock, it should be possible in three years’ time to detect variations in “g” of the size of the effects we have been considering. We are working on a rubidium clock, which we hope may be good to one part in .

BONDI: One mildly disturbing fact is this: the direction to the center of the galaxy also lies in the plane of the ecliptic. Why should this be so? I see no relation to the effects you have been discussing, but this might be included in the list of slightly curious and unexplained facts about the universe.

ANDERSON: There has been some discussion of the possibility that elementary particles have no gravitational field - or that there exist both “active” and “passive” gravitational mass.

GOLD: I would strongly advise the Eötvös experiment with a lump of anti-matter!

DICKE: One should also try seeing whether positronium falls in a gravitational field - but how can one do it?

GOLD: I think a more relevant experiment is to do it with anti-protons or anti-neutrons rather than positronium. Wilson at Cornell thinks it could be done - for a few million dollars.

DICKE: Is there some reason why it is better to do it with anti-protons rather than positrons?

GOLD: A scheme is possible according to which - not that I believe it - anti-gravity would be possessed only by particles of a specific gravitational charge; then it would not be possible to have more than one type of such charge, and you would have to assign it to the nucleon.

WITTEN: We are starting at our laboratory some experiments to measure precisely the time dilation effect predicted by the special theory of relativity. Two sets of observations exist regarding this prediction. One is the famous experiment of Ives and Stilwell who observed the effect by measuring the shifts of spectral lines omitted by moving atoms; the other is the various measurements on the lifetime of the -meson in different frames of reference. Neither method has so far been carried to its highest attainable accuracy.

We are going to do the experiment using basically the techniques of Ives and Stilwell with improvements. We shall observe lines emitted or absorbed by hydrogen, helium, or lithium atoms or ions. The expected accuracy at velocities comparable to those used by Ives and Stilwell should be a factor of about 100 greater than theirs. By going to higher velocities the relative accuracy should be greater. We hope to measure the angular dependence of the effect; it has been measured so far only in one direction. lves and Stilwell¹ have observed in their experiment a tendency towards disagreement with theory at high velocities and have suggested a possible source of experimental error that leads to this tendency. This point should be investigated. We shall eventually extend the measurements to large enough to detect effects of the fourth order . We hope to develop techniques sufficiently well to do a precise measurement of the effect at highly relativistic velocities. Another goal is to make the time dilation measurement for ions moving in a magnetic field and being accelerated. The purpose here is to see if there is any shift in the spectral line of a kinematic origin due solely to the acceleration of the clock with respect to the observer.

Footnotes