Did Einstein get it right?

Professor John Barrow

As the title implies today, I want to tell you something about the extent to which Einstein’s predictions about some aspects of the universe have been tested by astronomical observations, and I am going to pick on the General Theory of Relativity, rather than the Special Theory of Relativity, for testing.

2005 was the centenary of Einstein’s creation of the Special Theory of Relativity, and a number of other things as well, in 1905.  But 10 years after that, in 1915, Einstein developed what became known as the General Theory of Relativity.  It is a new theory of gravitation, and it makes a number of very remarkable and very precise predictions.  I want to show you something about what those predictions are and how well they have turned out.

While I was preparing this talk, I made an interesting – I hate to call it a discovery, but an uncovery, about Einstein.  While looking at a Swiss city website for something else, I came across a copy of a rather remarkable newspaper advertisement placed by Einstein in 1902.  He had just finished as a student, and had begun work at the Patent Office, and he did not have very much money, and so he placed an advertisement offering tuition in mathematics and physics to students and school children.  I looked a little further to see what happened as a result of this advertisement.  It seems that there was only one person who replied!  He was a fellow student called Maurice Solovine.  He and Einstein met, no tutorials were ever given, no money ever changed hands; they decided they liked one another so much, they would just meet and have drinks and coffee and discussion about science and philosophy together.  Eventually, they formed a little society that they called the Olympic Academy, which had a few further friends added to it, and they would just meet to talk about what was going on in science and the philosophy of science.

Interestingly, one person who joined that group was someone called Marcel Grossman, another lifelong friend of Einstein, who he met first through this club.  Grossman was a mathematician, a far better mathematician than Einstein, and when Einstein needed to learn some fairly high level mathematics to express his Theory of General Relativity, it was to Grossman that he turned, and Grossman taught him the mathematics that he needed in order to express the General Theory of Relativity. 

So all that grew out of a little advertisement.  What a lost opportunity for many students!  They would have learnt about the Theory of Relativity long before anyone else in the course of those tutorials.

Well, what was the situation at the end of the 19th Century with our understanding of gravity?  Gravity had not really been invented by Newton, but at least a way of describing it had been invented by Newton almost 300 years ago.  Newton’s Law of Gravity, which we learn at school, is a rather simple formula.  It tells us that if we have 2 masses, big M and little m, and their centres are separated by a distance R, at different points in space, not overlapping, then the force between them is an attractive force, a negative force, and it is given by a formula, where the distance apart is R, the masses are the Ms, and there is some new constant of gravitation that we usually call Newton’s Constant, although Newton never wrote it down – he just wrote the proportionality.  This Law of Gravity worked rather nicely for a very long time.  It described everything that was known about the motion of the Earth, explained why it was flatter at the poles than at the equator, explained the motions of the Moon, and many other things as well. 

Certainly in Britain, there was little imperative, little motivation, to try to supersede Newton, and in many other areas of mathematics in fact, Newton’s achievement really rather held up the development of science and mathematics in Britain, because it was a hallowed canon of results, so that if you attempted to improve upon them, you were somehow undermining them and letting in the Continentals and the French!

Some of the things that went with this simple formula; you will remember Newton’s Laws of Motion.  The first one you learn at school: bodies acted upon by no forces either remain in a state of constant velocity, motion, or they remain at rest.  So, in particular, bodies acted upon by no forces do not accelerate.  Another thing that were missing from Newton’s theory was a way of looking at the effects, if any, of gravity on light.  Does gravity act on light?  Do light rays get bent by gravity?  And the other problem at the end of the 19th Century was a peculiar and rather technical one.  It was about the motion of the planet Mercury.  It did not agree with the predictions of Einstein’s theory.  

We will unpick some of these things in a moment, but let me remind you what was the basic structure of Einstein’s Theory and how he really solved that first problem about bodies being acted upon by no forces not accelerating.  As we will see in a moment, unfortunately there are lots of bodies that are acted upon by no forces that seem to accelerate.

The Newtonian picture of space/time was really rather simple. Space was a bit like this stage I am walking about on.  At any moment, there was a great stage of space, absolutely fixed throughout the universe, nothing you could do could alter it, distort it, destroy it, bring it into being, or whatever.  Time was a straightforward line running from the past into the future, so it was a linear continuation of events.  F=MA, Force is equal to Mass times Acceleration, all these other Newtonian laws that you learn at school, are all acted out on this stage of space.

Well, these simple laws of motion that we know and love, unfortunately, are problematic when you think about them a little more carefully, and Newton appreciated this fully and formulated them very carefully.  So let’s take the one that bodies acted upon by no forces do not accelerate…

Suppose that you are sitting inside a rocket that is going into space, and you set the rocket spinning, and you look out of the window, if they have windows on spaceships – I think they do!  So if you look out of the window, what would you see?  Well, if the rocket is rotating in that sense, you would see the stars rotating past you in the opposite sense, as the rocket span around.  Things that rotate are accelerating, so you would be seeing objects acted upon by no forces accelerating.

Newton’s formulation of the Laws of Motion is very, very careful to exclude this situation.  What Newton said is that if you are an observer who moves in such a way that you do not accelerate, so you do not rotate, you do not move with accelerating speed, then you will observe that Force is equal to Mass times Acceleration, and bodies acted upon by no forces move at constant velocity or remain at rest.  Only those special non-accelerated observers will see those simple laws of motion to hold.  Our rotating astronaut is not one of those special observers.  Newton called them inertial observers.  This is very worrying. It means that there is a special class of observers in the universe who, by virtue of their simple motion, find the laws of nature to be simpler than those found by other people.  This is a situation at the very least I call undemocratic.  Einstein thought this is not the way the laws of nature should be, that anybody, no matter how they moved, whether they were rotating, accelerating or sitting at rest, they should find the laws of nature to be the same.  Einstein’s formulation of a new theory of gravitation cured this problem.  All observers, no matter what their motion, find the laws of nature to be the same.

In order to achieve that, in brief, what Einstein gave up was the notion that space was a fixed stage which could never be changed by anything that happened in the universe.  So for Einstein, space was not a fixed tabletop on which motions were performed, but it was more like a rubber sheet in which the motions of masses deformed the geometry of space and, as objects move, they change the geometry, and the shape of the geometry then dictated how things would move. 

You see what is the advantage of this; if we put a mass down in space, if it is a large mass, like the Sun, it produces a big deformation of the geometry of space in its vicinity.  Far away from the mass, things become increasingly flat and undistorted, and all that happens in this distorted geometry is that things move in a very simple way.  They move so that in going from A to B, they take the path of shortest time.  So if you want to go from A to B, because the geometry is curved, your path will not be a straight line like it would be on a flat surface but the path is slightly distorted, it approaches the mass a little bit, and then it goes away.  This shortest time path, which we call a geodesic, is curved, but it is nonetheless the shortest path that there can be on a curved surface.  If you fly from London to New York, the aircraft is moving, as it were, over the curved surface of the Earth; the shortest path that the flight could take is the curved path, a great circle on the Earth’s surface joining London to New York.

So the larger the mass, the more distorted the geometry will be, and this distortion has all sorts of unusual small and detailed effects, that if a planet is in orbit around a star like the Sun in this curved geometry, the presence of the curvature creates a number of small corrections to the path that it takes, compared with a picture where space is completely flat and things just move in Newtonian orbits.

To show that this is not just another way of looking at things, suppose a star were to pulsate in some complicated way, then it would be like putting your hand on the trampoline and bouncing it up and down.  There would be ripples and waves, which would spread out, getting smaller and smaller as they got further away from where you were hitting the surface.  These would be like waves of curvature in the geometry, and they are what we call gravitational waves.  So you can expect to be able to go out and look for gravitational waves, a new sort of radiation in Einstein’s theory.

The other thing that is unusual in his theory is if there is anything that is rotating.  In Newton’s theory, where space is just like a tabletop, if I have a ball and I spin it on the surface, it does not alter the geometry of the space in any way far away.  The object just spins like a top on the tabletop.  But if space is a great rubber sheet and we spin something, it is like twisting the rubber sheet, and that twist will be felt further away, we will convey some of the twisting at distances far away from the spinning object, and so if that object spins and you are near it, you will be dragged around in the same direction.

What Einstein did that was very hard, and where he needed Dr Grossman’s help, was that he was able to find the complicated system of equations which told you what was the shape of the geometry that is created by a particular sort of object, having a particular sort of motion when it’s present in the space.  These equations automatically had the property that they had the same form for every observer who used them, no matter how they are moving.  So that is why the theory is called relativity, and why it is called the General Theory of Relativity, because it achieves this for any observers, whether they are accelerating, rotating or whatever.  The earlier theory of relativity, the Special Theory, was special because it was just for observers who were moving with constant speed relative to one another.

So Einstein supplies the recipe for discovering the distortion and the shape of space and the passage of time that any particular combination of stars and galaxies and objects produces – in principle.  I say in principle because the equations are extraordinarily difficult to solve.  There are 10 of them, they depend on 4 different quantities, they are highly non-linear, and very, very difficult to handle, even on a computer.  However, fortunately, the simplest, and in some ways the most interesting, solutions of the equations were found almost immediately.

What happens if you just put a spherical star down in space – what is the gravitational field of the Sun?  If you know that, you can then work out how do the planets move, what happens to light, and so on.  So that is the starting point, and the next step is to look at one of those awkward problems that I mentioned about the motion of the planet Mercury.  Here, the French do enter the story right at the beginning…

Urbain Leverrier was a great French astronomer of the 19th Century, and one of the things that he did was to predict the existence of Neptune.  He was someone who studied the motion of planets in the solar system in great detail.  The planet he was most interesting in was the planet Mercury, and the reason for that is that the motion of the planet Mercury in practice has a very particular property.

In an ideal world, where the Sun is perfectly spherical and there is a planet that goes around in an elliptical or a circular orbit, that comes exactly back to where it started, the orbits of the planet are closed.  But in the real world, where the planets may be going around the Sun that is not perfectly spherical, where there may be other planets nudging it gravitationally, things hitting it, the actual orbit that a planet like Mercury follows is not closed.  It is rather like a rosette.  In its first orbit, it goes round in an ellipse, it does not quite come back to the same place, and so the next time it goes round it is a slightly displaced ellipse, and the next time round, it will be displaced a bit more.  If you followed it over a huge period of time, it would trace out a rosette, but would not in general close.  This phenomenon is called procession.  Procession is the advance of the maximum point from one orbital revolution to the next, or you could measure it from the point of closest approach, the perihelia. 

Leverrier focused particularly on the fact that planetary orbits are not closed.  In the solar system, you can measure, over a long period of time, the extent to which Mercury’s orbit is not closed.  Mercury is the best orbit to look at.  It is closest to the Sun, it is feeling the strongest gravity from the Sun, so these effects are more pronounced for Mercury than they would be for the Earth, or for Mars, or for Venus.  What Leverrier pointed out is that if you measure the extent to which that orbit shifts, it does not shift by very much, and because it does not shift by very much, it is conventional to talk about what the shift would be over a period of 100 years.

Mercury I think has a period of about 88 days or something like that, so this is the cumulative shift over many, many orbital revolutions - and the total amount, over a century - is about 5,600 seconds of arc.  One degree is 60 minutes of arc, one minute is 60 seconds of arc, so this is one three-thousand-six-hundredth of a degree, is a second of arc, so it is a bit more than a degree or so, over this huge period of time. 

Lots of this shift is entirely understandable but, first of all, you have to take into account that when the Earth rotates, it wobbles a little bit, so the North Pole is pointing to a slightly different direction in the sky.  Every 25,000 years or so, it sweeps out a circle in the sky.  So you think of the Earth being like one of those little tops on their stand, as it spins round, it processes in a circle.  At the moment, the North Pole, north direction, happens to be pointing towards a convenient star that we call the Pole Star, but at the time of Julius Caesar, it would not have been pointing towards a convenient star.  So when Shakespeare says that Caesar is ‘constant as the Northern Star’, it is a complete anachronism.  There was no Northern Star when Caesar was around.   And in the future, there may again be a different Northern Star, or none at all.   First of all, when you look at the procession, a good deal of it, most of it, is just being caused by our own procession.  So we take that out – it is not interesting.

The next effect is that Mercury is feeling the small perturbations of the other planets, so it is not only feeling the gravitational field of the mass of the Sun, but of Venus and Mars and Earth and Jupiter and so on, and those other little nudges, of the other planets as they move, also try to shift Mercury’s orbit.  When you take those away, there are another 530 seconds of arc, and there could be a contribution from the Sun itself if it was not quite spherical, but that was known to be, thought to be, really rather small.

After Leverrier had done all these subtractions, there was still a mysterious amount of procession, 43 seconds of arc every hundred years, that could not be explained.  At the end of the 19th Century, there was this curious anomaly that Newton’s Theory of Gravity could not explain the motion of the planet Mercury.

People came up of course with all sorts of possible answers to this problem.  One was the idea that there was a hidden planet in the solar system, and this became known as Vulcan, the idea being that the planetary contributions to the procession had been underestimated, so if you hide another object away, it has to be quite near the Sun, and eventually there was evidence for a planet of the size and sort and position that was needed to explain the missing procession.  Well, maybe there was a planet but it broke up into pieces, and so it would be a ring of debris, rather like the rings of Saturn.  That was another idea that was investigated.  Another more serious suggestion was that the Sun was actually non-spherical, that the polar diameter significantly different to the equatorial diameter.  Very difficult to test, because you have got to look at the Sun – the best time to do it is during an eclipse – and the Sun is active, and at different times, there are flares and activity on the surface.  Quite difficult to define what you mean by the diameter, at the end of the 19th Century, as well as to measure it.

Another idea that was taken seriously was that Newton’s Theory of Gravity was not quite right; that if you changed the theory very, very slightly, you could get some extra procession.  The change is really rather peculiar.  You have got to add, instead of a one over R squared force law, you have one over R to the power 2.00001.  This is completely arbitrary, it is just introduced to explain this strange observation – there is no other motivation for it, and there is no other consequence.  This was not really a very attractive way of solving the problem so, for that reason, I say they all really failed.

When Einstein first developed his theory, he very quickly set about checking whether it had anything to say about this problem, and in fact it did, because when he puts down the Sun in the geometry and produces the distortion of space, then when planets move, they pick up an extra procession effect because they are moving in this distorted geometry.  Einstein predicts that there is an additional source of procession, created by the curvature of space, and he can calculate it fairly easily and very precisely.  It depends on Newton’s gravitational constant, 6 pi, the sum of the mass of the Sun and the mass of the planet Mercury, and the distance that the planet Mercury is away from the Sun, so the size of its orbit, speed of light  squared, and this is a measure of the shape of the orbit.  So E is the eccentricity of the orbit, and as the eccentricity gets bigger and bigger, as E gets closer and closer to one, then the effect gets bigger and bigger and bigger.  The eccentricity of the orbit of Mercury is not terribly big, but when you put in the 2 masses, you put in the radius, and the eccentricity, all of these you can measure, pretty accurately, what Einstein got was a prediction of 42.98 seconds of arc per century.  The missing 43 seconds of arc was precisely, almost precisely, within the experimental error, explained by this new theory with its curved space.  This is a remarkable prediction, with no free fudging parameters as it were.  At one stroke, it was able to explain this great problem of Leverrier.  Einstein knew immediately that there was something deeply right about this theory.

Jumping forward in time, really to the 1970s, because it is the same effect, I want to tell you next about something very dramatic that was discovered in 1974, because it is something that shows you the same type of effect.  The effect with procession, 43 seconds of arc per century, is really very, very small.  In 1974, an American graduate student, Russell Hulse was sent on an observing project by his supervisor, Joe Taylor from Harvard, to the Arecibo Radio Telescope on Puerto Rico.  This is the telescope that is set into the Earth’s surface, so it is the biggest radio telescope in the world.  It is not steerable, but you just let the Earth’s rotation do that for you.  You will have seen this telescope in one of the James Bond films, where there is a great chase and fracas in the dish - so the astronomers were not able to play cricket in the dish on that day!

What Hulse was sent to do as a graduate student was to make some observations of pulsars.  Pulsars are neutron stars.  They are things about the mass of the Sun, but about the size of London, so they have a density of a single nucleus.  They are made of neutrons crammed together, side by side, fantastically dense, and if they formed from the collapse of a star, just like the ice skater as she spins and brings her arms in, she spins up, so the neutron stars spin faster and faster and faster as they collapse from being stars to being neutron stars.  Activity on the surface, emitting radiation, will then, to an external observer, look rather like a lighthouse.  So if you see this spinning neutron star, say spinning round 400 times a second, far away, when the lighthouse beam faces you, you will see a flash of radiation.  Pulsars were discovered rather earlier by Jocelyn Bell, they were seen on their own, with all sorts of different periods and spin rates, so they were understood in some sense as being very rapidly rotating compact neutron stars.

The pulsing periods are fantastically accurately maintained, so the pulsing period might remain the same to one part in 10 followed by 10 zeros, so you could use them as a clock that was potentially more accurate than any clock that we have on Earth, more stable.

Hulse was very mystified because, when he set about observing these pulsars for his supervisor, he came across one where there were very rapid changes in the frequency of the pulsing; so over a period of few years, there were huge changes in the pulsing rates.  This was completely inexplicable.  The neutron star could not be changing its density or condensing on that sort of timescale – fantastic forces would have been required for that.  Hulse was very quickly on the ’phone to his supervisor back in Harvard, Joe Taylor, telling him about these strange observations, about this varying pulsar.  Taylor was very quickly on the aeroplane down to Puerto Rico to try and understand what was going on – this was in 1974.

In the weeks that followed, between them, they gradually figured out what must be going on, that they were not just seeing a single, isolated pulsar, but they were seeing a pulsar which was in a binary star system.  So there are 2 objects orbiting around their common centre of gravity – the pulsar and something else.  They did not know what it was, for the moment.  As the pulsar went around its orbit, the Doppler effect produced a change in the frequency of its emitted signals, so that when it is coming towards you, you see a higher frequency, and when it is going away, you see a lower frequency.  So it is like the guy on the motorcycle zooming past your house [neee-awww] when he is coming towards you, the frequency goes up, and as he goes away [neee-aw], it goes down…the same effect…  It works with light as well as with sound. 

By a meticulous programme of observations over the coming months, Taylor and Hulse managed to deduce everything that you would want to know about this orbiting system.  This was a fantastic discovery.  These objects are moving at one per cent of the speed of light.  There is a procession effect, like with Mercury, but instead of 43 seconds of arc per century, here we have got about 4 degrees per year, so all these relativistic effects that Einstein uncovered are massively amplified.  The eccentricity of the orbit is very large, about 0.6.  It is very clean.  Nothing else is going on.  There are no hidden objects.  There are no star quakes on the pulsar surface.  Observation revealed that the other object is very likely to be another neutron star, with a very similar mass.  It could be a black hole, in principle, but there do not seem to be any x-rays being emitted from it as it captures material, so most likely it is another neutron star. 

The situation that Taylor and Hulse uncovered is summarised here.  The period of the pulsing of a pulsar is, on average, about 59 milliseconds.  Every 7¾ hours, it completes a complete orbit around the system, and the procession you can measure with this extraordinary precision, to 6 decimal places.  The other thing that you can measure, by using the pulsing as a clock, you can even measure the rate at which the period of the orbit is changing, and you can do that to an accuracy of two-parts in a trillion per year.  This is one of the most accurate measurements that you can make anywhere in science.

This system is like a magic box in the sky.  If you wanted to design a theoretical laboratory to test the Theory of Gravitation with fabulous precision, you would be hard pressed to create something as exquisitely useful as this.

One day, in the far future, the procession and the motion of this system will shift it around so it points in another direction in the universe, and it will not be available for people living on planet Earth to test the Theory of Gravitation.  It will point towards perhaps other civilisations in the universe that will be able to use it in the same way. 

It is no longer unique.  Other binary pulsar systems have been found, at different distances, with different descriptions.  They are not as fine-tuned and as useful as this one, but who knows?  One day we may find another one.

What you can do with this system is to test the same sorts of ideas that we mentioned for the planet Mercury.  It s much more complicated now because the motion of the objects, there are 2 of them, the distortions of the geometry are much more complicated – this is a non-trivial exercise.  Taylor and Hulse did this in wonderful detail and were awarded the Nobel Prize for their trouble many years later.  Hulse never even stayed on in astronomy, so when he finished his PhD, he changed field completely and became a plasma physicist and remained as a plasma physics professor at Princeton, where Taylor is.

In this system, the gravitational fields are so strong that gravitational waves are being produced.  You remember I said if you wobbled space time in one place, ripples will carry off energy from those motions off towards infinity?  In this system, the wobbling is really quite severe, and gravitational waves are predicted to be emitted and they remove energy from the system.  When you do that, you remove energy, things move a little more slowly, so they get a little closer together, and the period changes.  So the period of the orbit will get shorter as it gets smaller, and you can predict this in very great detail.  The beautiful thing is that if gravitational waves really are produced, at exactly the same rate that Einstein’s theory predicts, then the orbit should be seen to decay at precisely the rate that the period is observed to decay, to an accuracy of 12 decimal places.  So this system allows you to indirectly deduce the existence of gravitational radiation, even though you cannot yet directly detect it.

At the moment, there are many experiments seeking to detect gravitational radiation in other places.  The prime candidates are really other things like the binary pulsar that a hundred billion million years further down the line of their history, because eventually the radiation will cause so much energy to be lost that the 2 objects will spiral together and coalesce and in effect explode in a huge burst of gravitational wave energy.  That is what astronomers look for.  These events should really be rather common.  In the final throes of the explosive merger, there will be a big burst of gravitational waves that can be predicted, their frequency, their characteristics, in some detail.  So the whole search for gravitational radiation that was launched about a year ago – detectors are now running, albeit in a fairly engineering mode – the first candidate they ever expect to see producing gravitational waves will be counterparts of the binary pulsar elsewhere in the universe that are about to hit one another at the end of their lives.

So that is where the perihelion procession led, to this extraordinary high precision system.  The second interesting prediction of Einstein’s theory was about the bending of light.  I remember when I was a student going to hear a talk about light bending, and after the speaker had talked for about 3 minutes, someone in the audience put their hand up and said, ‘Will you be talking about spoon bending as well?’!

Light bending can be described in Newton’s theory, although technically the theory would break down if you tried to deal with objects like photons of light that move at such high speeds, but nonetheless, you could just slavishly regard photons as little particles with a certain mass that moved at that very high speed.  This was something that was done long ago by Henry Cavendish, after whom the Cavendish Laboratory at Cambridge is named.  He was the person who also first measured that constant of gravitation of Newton’s with very high precisions, so he was a great 18th Century experimental physicist.  Another German astronomer called Soldner did the same calculation a few years later.  Cavendish never published his version I think

What they were able to do was to work out, if you had an object like the Sun and you had light coming in from a long way away, that just grazed past the surface of the Sun, then as it got close to the Sun, you might think of the gravitational pull of the Sun deviating the path of the light.  How much is the deviation expected to be?  When they are calculated, the answer is rather simple.  It depends again on the mass of the Sun, the radius of the Sun, where the light is just grazing past, and the square of the speed of light: Newton’s constant.  It is very small.  The Newtonian prediction is that the light from a distant star, it will be deflected by just 0.87 seconds of arc, as it went past the Sun.

Einstein did the same calculation.  At first, he did not get it right.  Before he had the theory, he really duplicated what these people had done and then tried to find a way of making this prediction even before he had his equations of general relativity.  When he had the equations, he was able to do the same problem properly, and the answer is very interesting, because it is twice as big as the Newtonian answer.  It is not just a little bit different.  The factor of 2 comes because of this distortion of space.  The curvature of space around the Sun reduces this quite significant increase in the bending of the trajectory of an incoming ray of starlight.  So you are looking at about 1¾ seconds of arc deviation from a perfect straight line.  Well, you now have the problem of how you would go about measuring that.

Here is the situation.  If you look at the Sun, for example, you can appreciate that you are not going to get very far trying to detect where a beam of starlight is coming from.  You have to somehow blot out the Sun stopping you seeing anything.  So what you need to do is look at the Sun during a complete eclipse of the Sun, when the disc of the Sun is obscured, and then you can see the positions of stars in the background that are very, very close to the disc of the Sun.

So if you looked at the Sun when an eclipse was taking place.  If there was no bending of light, then when you look through your telescope, you would look out there, and that would indeed be the place that the light was coming from.  But if light is being bent by the gravitational field of the Sun, then when you look out in that direction, you see an image on the sky, but the light has really come from an object that is positioned over there. 

Well, you need an eclipse; they come along every so often.  You need a star; we have got one.  You need more stars in the background; there evidently are some.  So you are in business to try and do this.  The problem was the First World War.  During the First World War, scientists did not do very much astronomy, but they were aware that in 1919, there was going to be a complete eclipse of the Sun, which would be visible from several places on the Earth’s surface, that were ideal for observing and testing these predictions.  The story of doing that testing is a long and humanly rather interesting one. 

I will only say a few things about it, and it revolves around the great Arthur Stanley Eddington.  Eddington, who was the greatest British astrophysicist of the 20th Century, was also a Quaker, and a very committed pacifist.   So during the First World War, there was something of a problem as to how the Admiralty and others would deal with Eddington.  He was an employee of the Royal Greenwich Observatory, a great astronomer.  He was he going to be imprisoned.  If he was asked to serve and refused, they would have to do that.  Somehow, the Astronomer Royal intervened, and created a position, a prospect, whereby Eddington, in return for not being called up, would plan and lead an expedition to test the General Theory of Relativity in 1919: as it turned out, one year after the end of the First World War.  Remarkably, during the First World War, British and German astronomers maintained quite close contact with one another, particularly via the Dutch, and there was a lot of mutual interest in the expedition to test this theory.  This is a delicate matter, you can imagine, politically: British astronomers going out to test a Theory of Gravity proposed by Einstein, who was perceived as being German, in order to overthrow Newton’s Theory.

In 1919, 2 expeditions were set up, as an insurance, because this is a very difficult set of observations to make, and you have only got to have cloud cover, a storm in one place, and there will not be any observations at all.  So 2 missions were created, one led by Eddington to Principe and one to Sobral by Crommelin. Principe is on the coast, it is an island on the coast of Guinea; Sobral is in Northern Brazil.  There was to be a complete eclipse of the Sun on the 29th of May in 1919, and the idea was to have made 2 sets of observations of a particular distant star field, once at a time when things were in the same position and the Sun was on the other side of the sky, and then during the complete eclipse, and this would enable you to figure out how much the images had shifted when the Sun was in front of them compared with when the Sun was on the other side of the sky, because when the Sun is in front of them, its gravitation field is deviating the incoming starlight.

Well, the weather was rather threatening, and Crommelin’s data probably really was not very satisfactory, but Eddington’s was.  Eddington’s mathematical expertise really helped here, in that he was able to use statistical techniques and optimisation techniques to make sure he extracted the best possible information from the photographic situations. 

So what you are doing, as it were, is that you have your comparison picture of the star field when the Sun is somewhere else, and then you take a photograph when the complete eclipse occurs, and you are interested then in comparing the 2 pictures to see how much the star positions have shifted because of the Sun’s presence, and you are looking to see if that shift is 1¾ seconds of arc, as Einstein predicts.

Eddington’s analysis of Einstein’s predictions, of course, was a great triumph.  It was spot-on within the experimental errors: 1¾ seconds of arc was the shift that Eddington’s group so, and Eddington reported this at a meeting of the Royal Astronomical Society in London in November 1919.  This was the beginning of Einstein’s great scientific celebrity.  As a result of the correctness of this prediction, Einstein became a great public figure, and a byword for scientific genius.

There was a story in The Times – which sounds just like The Sun – ‘Men of science more or less agog over results of eclipse prediction’.  ‘Stars were not where they seemed or were calculated to be, but nobody need worry,’ and then something about a book for 12 wise men.  I don’t know what that was – I do not think there was ever any book that Einstein intended to write about this.  This may just be his paper, and I do not know where the 12 wise men came from, because Eddington at the time was asked by the press, ‘Is it true that there are only 3 people in the world who can understand this new theory of gravity?’ and Eddington was rather quiet, as he was generally anyway, and then the journalist asked him, ‘What causes you to pause?’ and he said, ‘I was just wondering who the third person was’!

There is a photograph of Einstein and Eddington, sitting together on the bench in the garden of the observatories in Cambridge, where Eddington was the premium professor.  This was taken many years later.  Perhaps they are swapping stories about committees and grant funding and whatever!

This prediction of the light bending was the second great triumph of Einstein’s theory, that distinguished it quite dramatically from Newton’s theory.  You could regard those observations as showing you, in some sense, Newton’s theory was incorrect, or at least it could not deal with the motion of light and the effect of gravity on light.

There was one further test of general relativity, which was not one which Einstein himself predicted, and it was only found in 1964.  It is sometimes known as the time delay effect or echo delay, and it was noticed by an American scientist called Irwin Shapiro.  Irwin is a rather tantalising scientist who you do not often see or hear speak because he will not fly on aeroplanes - and I think he is a bit nervous on trains as well!

What Irwin Shapiro noticed was that there was another but different effect of light moving through this distorted curve space created by the Sun or any other object, and it was that if you sent a signal out to something and there was a mirror or a receiver on the something, and it then sent the signal back, if you could measure the round time travel trip, you would find that it was different to what you would expect in a Newtonian world of flat space.  So the curved space produces a little effect on the overall travel time around the circuit.  At first, you could imagine that you might do this.  Suppose you had some way of sending a light signal back from the Sun, what are timescales involved?  Well, you are looking at a delay, so a general relativity prediction, there should be a little delay of about 2 microseconds.  This is easy to measure, but it is not so easy to figure out what it is you are measuring, where the light is really coming from.

One of the first ideas of Shapiro was to bounce radio signals off planets like Venus or Mercury, so one of those early space probes that landed on Venus had a little transponder which was able to receive and send signals back to Earth so we could measure this time delay effect.  You are using radio signals here, this light bending that Eddington first mentioned by looking at starlight moving round the Sun.  It soon became apparent, in the 1970s, that there were much, much better ways to do this, that you do not look at starlight, but you look at radio waves from quasars on the other side of the universe, and look at the extent to which the radio waves are bent as they go past the Sun.  You can locate the positions of the quasars with very, very great accuracy by looking when they get occulted by the Moon.  So the light bending culture, as it were, of experiment moved away from looking at starlight during eclipses to looking at radio waves from distant quasars, and similarly you are looking at radio waves.  A better way to do it, once you have got transponders on spacecraft, is not to be limited to be looking at Venus, for example, but to have a spacecraft that is moving at some trajectory around the solar system, maybe in orbit, and you can therefore produce quite elaborate time delay experiments by looking at the travel time back and forth in different positions along the spacecraft’s orbit.  So you can test the predictions of this theory not just at one moment, but over a long period of time as the spacecraft moves different distances away.

The last bit of this story is that just a couple of years ago this has been done in even greater exquisite detail by the Cassini space probe.  This space probe was able to test these predictions to an accuracy of one part in 100,000, so it is a quite extraordinary feat of instrumentation.

Back in 1919, the light bending tests of Eddington and then Campbell and others centred around the general relativity prediction, but there were uncertainties – they were about 3%, something like that.  As you move forward in time, you start using quasars, so you start to use radio waves, and the uncertainties come down, and they become so small that you cannot really represent them.  So the accuracy with which Einstein’s theory of light bending by the Sun is tested is good to a couple of parts in 10,000.

The situation overall of light bending is really quite extraordinarily accurate.  It is a sobering thought when people talk about how can you know these sorts of things that are going on the other side of the universe.  We do not know anything in subjects like economics, human behaviour, biology, with anywhere approaching the accuracy and statistical significance that we understand Einstein’s Theory of General Relativity.

So did Einstein get it right?  I think you would say yes!

© Professor John Barrow, Gresham College, 26 October 2006