As we celebrate 100 years of General Relativity I shall discuss Einstein’s enduring legacy. The Einsteinian revolution changed forever the way we think about spacetime and the universe and still shapes current research at the frontiers of fundamental physics and cosmology. I shall review the current status of Einstein’s theory and the ongoing attempts to construct a quantum theory of gravity and to unify all the forces of nature.

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Thank you and good morning everyone. It’s a pleasure to be here once again. I thought it would be appropriate this year, when we celebrate 100 years of general relativity, to talk about the enduring legacy of one of our greatest colleagues: fellow Nobel Laureate Albert Einstein. Albert Einstein, of course, is known to us all and around the world. He is after over 100 years still the most famous physicist - with the possible exception of Steven Hawking. And we all know this picture of Einstein, the wise old man, the kind, passionate exponent of peace and harmony. This is Einstein actually 100 years ago when he formulated his laws of gravity and of dynamical space-time. And this is Einstein as a younger man at his office, the patent office, when he shook up the world in 1905 with his works on special relativity and quantum mechanics. Einstein is known for many things - these pictures are iconic. But what you’re perhaps less aware of is how incredibly eloquent he was. His prose was exquisite. His papers in physics are a joy to read. And to all the young students, by the way, I urge you, go back and read the original papers in all parts of physics. They are usually so much better than the text books. And Einstein is known for his quotes - he is one of the most quotable people in the world. He wrote 4 of my favourite quotes. This is quite appropriate after the British (doesn't say "voted for the exit from the EU" – laughter, applause). And then,"Insanity: doing the same thing over and over again and expecting different results." And then physics, "God is subtle but he is not malicious." God for Einstein meant nature - who is indeed subtle but not malicious, we hope. And then the quote which I took as a guidance for making this talk: Now, Einstein burst onto the world scene of physics in 1905 with his theory of special relativity. He actually hated that name. He knew it would give ammunition to the post modernists. He preferred a theory of invariance. Because what he really did in reconciling Maxwell’s theory of electromagnetism – which he regarded as the paradigm of classical physics - and Newton’s laws of motion. Which together were simply inconsistent and had to be reconciled according to him. And he did that by taking as THE principle that there is no privileged observer, no privileged reference frame. All observers have an equally valid description, the same description, of physical reality. And in order to achieve that there must be underlying symmetries of nature that allow one to transform the point of view of one observer to that of another. It’s interesting that this principle, that there’s no privileged observer, Einstein applied to all of life and to politics: There is no privileged nation, there is no privileged religion, there’s no privileged race. What he took as fundamental, was the principle of symmetry. And he wanted to call this theory the theory of invariance. He revolutionised the way we view symmetry in nature. His great advance was to put symmetry first. Not to take the symmetry as a consequence of dynamical laws, as his contemporaries Lawrence and Parker Ray were want to do. But rather to make the symmetry principle as the primary feature of nature that constrains, restricts, inspires the allowable dynamical laws. A profound change of attitude which lead, by and large, to the realisation that symmetries come first and we should search for new symmetries. And use them in our description of nature which has largely guided the development of our understanding of the fundamental laws of nature throughout the 20th century. And that continues today - a profound change of attitude. He also changed the way we think about space and time – as you know, he unified space and time. The symmetry transformations that were the basis of special relativity transformed space and time together. And, consequently, there was no absolute notion of simultaneity. This was perhaps his most radical modification of our preconceptions that 2 events, well, one happens before the other or vice versa. But in reality there can be events which are, we say 'space-like separated', no signal could be transmitted between them, with a velocity less or equal to the speed of light. And therefore no way of telling which came first. And that depends on the observer, it’s relative. In fact, much of the history of elementary particle physics and the development of the standard model and attempts to go beyond it, are looking for new hidden symmetries of nature. They must be hidden because otherwise we would have seen them already. That might explain and enlarge the scope of our theory. One of the most exciting ideas that still has not been ruled out by experiment, is the idea of super-symmetry. Transformations of an enlarged notion of space-time. A space-time which contains extra quantum dimensions. Dimensions measured with numbers that anti-commute. And the symmetry being rotations in superspace. This symmetry is beautiful mathematically and has the potential of answering many of the problems that we face beyond the standard model. And it unifies the kinds of particles we have in nature, bosons on the one hand and fermions on the other. And we can look for it - and we are. My colleagues are looking for it desperately at Cern - the large hadron collider - and they might very well find it. There’s a little bump at 750 Gv - it might be a sign of supersymmetry, it might be nothing, who knows. We will find out. But if it turns out to be supersymmetry, we will have to accept the fact that we live not just in space-time but in superspace-time. After 1905 there were 2 outstanding issues from Einstein’s point of view. The first was that Newton’s theory of gravity was inconsistent with relativity. This was a contradiction, this was impossible. Everyone who accepted Einstein’s special relativity knew that. And many people tried to reconcile the 2 in obvious ways. But Einstein followed his own path based on his other thing that bothered him after special relativity. Namely, he wanted to extend the principle that there’s no privileged observer to accelerated observers as well. What is special about inertial observers, moving with a constant velocity? He wanted there to be no privileged observer in any sense. Many others knew, that one was going to have change Newton’s theory. But Einstein also wanted not only to do that but to extend the principle of relativity. And this led him, after much thought, to a programme which he enunciated in 1907. In which he imagined that it would be conceivable to extend the principle of relativity to systems that are accelerated with respect to each other. And in this famous paper he based his strategy and his goal on Galileo’s discovery that all bodies fall with the same acceleration. Or, we would say that the gravitational mass, that is the source of the force of gravity, is equal to the inertial mass that you must divide the force by to get the acceleration. This principle was enunciated by Galileo who was, of course, known to Newton who did experiments. Newton established that the equivalence principle to 1 part in a 1000. This was improved over the years by Bessel, by Eotvos famously, by my colleague in Princeton, Bob Dicke, and is now being extended. We now know that the equivalence principle is correct to 1 part in a trillion, a million million - it is amazing. This is what we all love about physics. This is the only place in science where we measure quantities to a precision of 1 part in a trillion. And some colleagues will spend their lives heroically trying to extend that by an order of magnitude or 2 – most likely failing, but what a heroic journey. And then, suddenly, in 1907, sitting at his desk in Bern in the patent office, he had an idea based on the equivalence principle. He thought, what would happen if a man falling off a roof did experiments. He would drop something which would fall and accelerate with him with the same acceleration. He would conclude there is no gravity. This latter is now called the 'elevator thought experiment'. Because when questioned by reporters, after Einstein became famous, they would all ask him: Well, what happened to the man who fell off the roof? So Einstein considered 2 systems. Let’s use the elevator: A rocket going upwards with a constant acceleration g and then an elevator at rest in a uniform gravitational field -g. And he said, consider these 2 systems S1 being accelerated with an acceleration g. And S2 at rest in a gravitational field with an acceleration -g. The physicists in each frame of reference, the moving elevator, the stationary elevator, in a gravitational field, do all the experiments they can do. They get exactly the same results. There is a symmetry, a principle of invariance. This was the principle that he based his search for the relativistic laws of gravity on, the equivalence principle. based on the fact that all bodies are accelerated equally in the gravitational field." And then: "At our present state of experience – notice as a good physicist, he qualifies it, who knows there might be a deviation at the trillionth percent point. But "at our present state of experience we have no reason to assume that these systems differ from each other in any respect. And therefore we shall assume a complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system." If this were true it would achieve its goal of extending the principle of relativity to accelerated observables. And, conversely, it would give a way of understanding the origin of gravity. Which you could always transform to a reference frame in which you didn’t feel the force of gravity. And then, going back, you could deduce what gravity looked like. This was what he pursued with stubbornness for the next 8 years. Others tried to construct theories of relativistic gravity but ignoring this principle which he held on to like a bulldog. He knew now which direction to go. And it wasn’t easy, it was very difficult. Equivalence principle was enunciated in 1907. It wasn’t really until 1912 that he realised that the field that transmitted the mediated gravity, the dynamics of space-time, that enabled one to have this equivalence of accelerated observables, was the metric tensor that determines the distance between points in a curved manifold. He had to learn differential geometry with the help of his mathematical friends. And then it was difficult: mistake after mistake, misconception. But finally, in 1915, and in the article published just a little over 100 years ago, he announced Einstein’s equations. Which relate the curvature of space-time, how space-time is a curve manifold, much like the surface of the earth, a sphere is curved, to the source of gravity which is mass - mass is the same as energy of a body at rest. Energy and momentum - the energy momentum tensor, given by the Einstein tensor, which describes the curvature of gravity. This was announced November 25th 1915, in one of 4 talks he gave at the Prussian academy of science that year. Interesting, the 3 other talks are all on experiments. All the time he was finally getting to the final form of his equations, he knew that he had to compare the predictions of this with experiment. He had done so before. In a previous version of his theory, which was incorrect, he had calculated the deflection of light by the sun. The sun would pull on the light, deflect its curve; you could measure that during a solar eclipse. He predicted what you could have derived from Newton’s theory, 0.87 degrees. And that was wrong. There was an expedition set out to measure that deflection of light in 1914, which, lucky for Einstein on the one hand, the war broke out, the expedition was cancelled. Unlucky for him because he was a pacifist living in Berlin and notoriously opposed to the war. In 1915, in his correct theory, he realised that the deflection would be twice that value. And indeed, after the war an English expedition, led by Eddington, confirmed that and made Einstein a worldwide famous figure. The other experimental verification of his theory was a postdiction of a phenomenon that had been observed already in the 19th century, the advance of the perihelion of mercury. A discrepancy with Newtonian gravity, an outstanding puzzle that many scientists had tried to understand. And he knew that his modification of Newton’s theory would change that calculation. And in his previous version he’d calculated the advance of the perihelion and gotten the wrong result. But when he had his final equations, he sat down and rapidly did the calculation again. And got exactly on the nose the deviation. He must have been in 7th heaven. He predicted the red shift of light in the gravitational field, which was only confirmed later by 1959 and is, of course, an essential part of GPS. Makes all these things work. I want to discuss the legacy of Einstein that persists till today. It still shapes the way we work in fundamental physics. Dynamical space-time: the fact that after Einstein’s theory we’ve had to confront the fact that space-time is not just out there, rigid frame. It's dynamical, it moves, it fluctuates. The ability, for the first time ever in physics, to construct a quantitative theory of the universe, of a cosmos. And the goal which he spent the rest of his life trying to achieve, but still guides us: the search for a unified theory. So Einstein’s theory of gravity is based on the fact that space-time is dynamical, the metric of space-time. And its curvature gives rise to what we call gravity. It obviously, at large distance, reduces to Newtonian gravity, as it must because Newton’s theory is still very good. That’s how we plan and send rockets to the moon. So a guiding principle for any advance in theoretical physics is always that it agree with great precision, in some limit, with the previous theory. And Einstein’s theory is like that. But it has something new. It has a field, the metric tensor of space-time. And the field like any other field can fluctuate, can oscillate. Those oscillations are gravitational waves. That’s what makes his theory of gravity consistent with special relativity. Because when you shake the sun it takes some time for the earth to respond: the waves of gravity spread out from the sun with the speed of light. And miraculously this, 1916 is also the year in which we, finally, observed those waves. At least 2 times. Now with the incredible experiment done by LIGO, the Laser Interferometer Gravitation Wave Observatory. This is one of the facilities in - I think this is in Hanford, in Washington - where we have an interferometer, a few miles long. And the gravitational wave, passing by through the earth, changes the lengths of the arms. And you can measure the minute shift in distance and compare with theory, with Einstein’s theory and the theory of black holes, merging to form a bigger black hole. And these are the signals that are observed in the 2 observatories, one in Louisiana and one in Washington. They are right on top of each other. They’re much, much bigger than the ambient noise. And they agree precisely with the predictions of general relativity of Einstein, 100 years before in a sense, so accurately that they can be used to measure the masses of the black holes that merged and the amount of energy that was radiated - which is immense. And this now will give science, Astrophysics, a tool for exploring the universe with new telescopes. These interferometers which can see gravitational waves and measure and observe the properties of compact objects, like black holes, neutron stars and so on. Black holes were discovered 100 years ago, theoretically, by Schwarzschild. They seemed rather strange. Einstein never believed in them, they had strange properties. But now they’ve turned out, as in this example but many others, to be real astrophysical objects. And they continue to be, in addition, subjects of thought experiments, that "kein Gedanke" experiments that Einstein loved to carry out. Especially after Hawkins' realisation that in quantum theory black holes aren’t black. A black hole is a region of space where there’s so much energy density that light can’t escape, so they’re invisible. But quantum mechanically you can tunnel through and light does escape. Black holes radiate and disappear. And the conundrum - I’ll come to the conundrum. These theoretical objects, which were disbelieved by Einstein, many theorists and all observers until recently, are now believed to be abundant throughout the universe at the centre of every galaxy – this is the black hole and the Keplerian orbits around it - that tell us what its mass is: the centre of the Milky Way. They presumably are the fuel of gamma ray bursts. And they raise theoretical conundrums because if you throw information into them, if you throw stuff into them that contains information, like half of a correlated quantum pair, you seem to be forced into a mixed state. You lose information. And this has provided one of the strongest clues or problems, paradoxes, to those of us who have been trying to understand the reconciliation of dynamical space-time and quantum mechanics. Extrapolating Einstein’s theory to very short distances or very high energies provides another, many other paradoxes and problems. Which are often the guiding principles for people in the kind of game that I am involved in of looking for fundamental laws. Since the extrapolation of Einstein’s theory at very short distances gives fluctuations of space-time, quantum fluctuations that are uncontrollable, 'space-time foam' as it’s sometimes called. We are sure that we will have to go beyond Einstein’s theory, as he expected and as he himself tried to do. And we are faced with one of our major challenges today, my opinion, is to understand the true nature of space and time. Einstein taught us that space-time is dynamical. And at very short distances it fluctuates in an uncontrollable way. Many of us believe that it probably will be, in a beyond Einstein theory, best described as an emergent concept. Good at large distances – 'large' compared with 10^-33 centimetres or something like that – but still not a fundamental concept in physics. We’re asking, in a sense, what space-time is made of. Now I briefly want to describe the other legacies. Physical cosmology is perhaps the most important. Before Einstein cosmology was addressed by religion, by philosophy. We have a lot of beautiful stories. But it wasn’t science. But as soon as Einstein wrote down his equations, he realised, and others immediately, that the structure and the history of the universe is the subject of physics. In fact, Einstein feverishly began to work on a mathematical model of the universe, after 1915. And he constructed a model of the universe which he thought should be static - it’s a bad model. But he wrote to the de Sitter in 1917, "From the standpoint of astronomy, of course, I have erected but a lofty castle in the air. For me, however, it was a burning question, whether the relativity concept can be followed through to the finish or whether it leads to contradictions." You see, he had his equations which govern space-time - and the universe is space-time. He had to apply them. And he was worried that he would get nonsense. Nobody had ever in the history of physics tried to construct a mathematical theory of space-time of the universe. So he was worried. And although his models had problems and were soon discarded, he was satisfied that, Now I’m no longer plagued with the problem which previously gave me no peace." But he knew that he perpetuated something in gravitation theory which What he really didn’t like was introducing a parameter in his theory, the cosmological constant, which really was there - his fundamental principles allowed for it - and he used it to construct a static universe. Some people have called that his "biggest blunder". I don’t believe that. His biggest blunder was not predicting the expansion of universe. He was convinced that the universe was static, unchanging. You go out at night there are stars that look today like they looked yesterday. He was convinced that the universe was static. It isn’t. He could have predicted the expansion of the universe - that was his biggest blunder. He also, by the way, developed the tools that allow us – he never believed that one would ever figure out really what the universe was. And now we have, and partly with his aid. He showed how you can use the deflection of light around massive objects to map out the structure of matter to the universe. And this so-called bullet cluster where 2 clusters of galaxy are colliding. This stuff here is dark matter, the blue stuff which is measured, observed by astrophysicists who measure the deflection of light from these quasars behind the dark matter through it. And that’s how you map out, observe, dark matter in the universe. And today - Einstein would never have believed this -, after only 100 years, we have a complete, extremely detailed, quantitatively successful history of the universe. From the very beginning through a period of rapid accelerated expansion, just the normal expansion structure formation of galaxies, of planets and, we now believe, accelerated expansion dictated by his cosmological constant. We still, however, don’t know how it began, the Big Bang. And Einstein taught us that the universe is the history of space-time. And if you’re going to solve this problem, if you have a solution to the theory that explains the dynamics of space-time, it had better give a consistent description of the beginning. Or what happens at the boundary if there is a boundary and/or at the end. And that is an issue that, again, science has never had to address and, until now, was the realm of religion and philosophy. But we can no longer avoid that question. And in discussing the structure of the cosmic microwave background and the theory of inflation, we must address what happened at the beginning. What is the initial condition for the universe? What are the rules? Never asked this question. We don’t even know what the rules are. I will end briefly with the search for a unified theory which was Einstein’s obsession over the years. He always regarded his specific theory as provisional, to be replaced by a more comprehensive unified theory of space-time and matter. He always, looking at his equations, his famous equations, thought the left hand side was beautiful, the consequence of this profound symmetry of space and time. And the right hand side ugly and arbitrary and singular, the structure of matter. And he laboured for decades unsuccessfully to move the left hand side to the right hand side and explain matter from geometry. Didn’t succeed. Today we have an incredibly successful comprehensive theory of the forces and of the elementary constituents of matter, which describes the constituents of matter as made up of quarks and leptons and the forces inside the atom and the nucleus as electromagnetism. My favourite: the strong nuclear force and the weak nuclear force. Together with the Higgs sector, this completes the standard model which is incredibly successful, the most precise quantitative successful fundamental theory we’ve ever had. It could, in principle, work from the Planck length, where things tend to break down, to the edge of the universe. Extrapolating this theory, we have hints that the forces unify at that energy scale, together with gravity. And we pursue ideas of unification, like string theory. But it is very difficult to go from the large to the small, from the standard model to the grand unified theory, from now to the beginning. It’s much easier to go from the small to the large, from unified to broken, from the beginning to now. But Einstein gave us encouragement, and warning. He said, "The successful attempt to derive delicate laws of nature along a purely mental path, by following a belief in the formal unity of the structure of reality, encourages continuation in this speculative direction. The dangers of which everyone vividly must keep in sight who dares to follow it." So we continue in that direction. We ask about space-time, whose properties seem to be disappearing in this investigation to be replaced by something else, whose rules we don’t really know yet. So Einstein’s legacy - dynamical space-time, physical cosmology, unified theory - continue to shape our exploration of the fundamental laws of physics. Dynamical space-time: we now ask, what is space-time made out of? Physical cosmology: we’re faced with a question, what is the initial, and perhaps final, state? And in our attempts to construct a unified theory, we continue to explore how the forces unify. And I will skip to Einstein’s - so at the end of the 20th century, Time Magazine had to choose a person of the century. And, as theoretical physicists, I’m sure we are especially, but all physicists, all scientists, we’re very proud that the person they chose as person of the century was this theoretical physicist. Who not only was a great scientist but a great humanitarian and who used his fame and celebrity for the good of mankind. Thank you. (Applause)

# David Gross (2016)

## One Hundred Years of General Relativity - The Enduring Legacy of Albert Einstein

# David Gross (2016)

## One Hundred Years of General Relativity - The Enduring Legacy of Albert Einstein

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