November 2015 was the centennial of a landmark event in the history of science. In this month in 1915, Albert Einstein presented his General Theory of Relativity (GR for short) to the Prussian Academy of Sciences. In a series of four papers Einstein presented a new vision that completely transformed our understanding of the universe. Arguably an event of such a significance had not occurred since the publication of Newton's "Philosophiae Naturalis Principia Mathematica". GR was the culmination of a decade long meditation by Einstein on the relationship between space, time and gravitation. Einstein's theory was a substantial generalization of Newton's theory of gravitation. Already in 1905, Einstein had abolished the Newtonian concepts of absolute space and absolute time and had replaced them with a unified notion of "spacetime" (the geometrical formulation of this was due to Minkowski). In the Special Theory of Relativity (SR for short), Einstein made two fundamental postulates - that the laws of physics are the same in all inertial frames of reference; and that the speed of light is the same constant in all inertial frames of reference. As a consequence, he had demonstrated that the spacetime has some unique properties, one of which is that no signal could travel faster than the speed of light. In addition, the lengths of moving bodies, the passage of time and the mass of an object are no longer absolute quantities, but are affected by the relative motion of the observer's frame of reference. Thus in SR spacetime had an effect on moving bodies. However, the spacetime of SR was itself unaffected by the presence of matter. In GR, Einstein replaced the static and "flat" spacetime of SR with a new dynamic spacetime that is curved by the presence of matter. The gravitational field was shown to be simply a manifestation of the curvature of spacetime. Einstein postulated in GR, that the laws of physics are the same in all frames of reference including accelerated frames (this is known as the Principle of Covariance). In the language of modern mathematics this can be stated as "the equations of physics should be invariant under all diffeomorphisms of the spacetime manifold". The Principle of Equivalence is the empirically observed fact that all frames of reference in a uniform gravitational field behave in the same way as a uniformly accelerated frame of reference. Einstein had the insight that this implied a deep connection between spacetime geometry and gravitation (in fact the Principle of Covariance is a stronger form of the Principle of Equivalence). Using this principle and the effects of SR on lengths and time intervals, Einstein argued that the geometry of spacetime in a gravitational field had to be non-Euclidean. This led him to conclude that the metric properties of spacetime represent the gravitational field near a massive object. Using the mathematics of Riemannian Geometry developed by Bernhard Riemann, Tullio Levi Civita, and others, Einstein developed a geometrical theory of space, time and gravitation culminating in his famous Field Equations of Gravitation (shown in the picture above). The equations relate a geometrical quantity (the Einstein tensor) to the matter "density" (the Energy-Momentum tensor). Einstein also noticed that objects tend to move in optimal paths known as geodesics in a uniform gravitational field and postulated that the same was true in all gravitational fields. The dynamics of moving bodies in a gravitational field could be predicted based on equations of geodesics. In summary, "spacetime tells matter how to move; matter tells spacetime how to curve" (a quote by John Wheeler). The bending of starlight in the presence of a massive object (like a star or a galaxy) was one of the remarkable predictions of this theory. This prediction was famously verified by Arthur Eddington in 1919, which made Einstein an overnight sensation and a household name.
To celebrate this occasion, many conferences were held around the world. I had the privilege to attend the Einstein Conference in Berlin between November 30 and December 5. The conference was actually a combination of two conferences jointly organized by the Max Planck Institute for Gravitational Physics (also known as the Albert Einstein Institute) and the Max Planck Institute for the History of Science. It was held in the Harnack Haus, a place where Einstein used to lecture regularly when he was a professor in Berlin.
There were two parts to the conference: a technical part and a historical part. The first half (Nov 30 - Dec 2) was devoted to the latest technical developments in the fields related to GR. The second half (Dec 2 - Dec 5) was devoted to various historical aspects of the development of GR in the last century. The conference was a gathering of a variety of individuals interested in the field including theorists, mathematicians, experimentalists, astrophysicists, cosmologists and historians of science. There were a few luminaries present - including the famous physicist and author Roger Penrose, the Nobel Laureate (and String Theorist) David Gross and the veteran cosmologist Jim Peebles. The range of topics were broad and the talks were mostly accessible to a semi-technical audience. There were talks on the attempts to detect Gravitational Waves, on the astrophysics of Black Holes, on the latest developments in Cosmology, experimental tests of Gravity, the mathematical theory of Black Holes, the Black Hole Information Paradox, String Theory and Quantum Gravity. The historical talks focused on the early decline of GR during the post-war period and the revival (renaissance?) of GR as an active area of research in the 60s and 70s. There were also talks on some of the controversies surrounding the Black Hole Information Paradox and String Theory. There were panel discussions and some debates on some of the recent attempts to quantize gravity. Given the august nature of the conference (celebration of Einstein's work) the debates were of a civil nature. During the coffee breaks there was a booth hosted by Springer Verlag and IOPscience (publisher of the journal "Classical and Quantum Gravity"). The latter was giving away volumes of latest issues of CQG, which are also available online. Springer had some of their latest books on GR on display. Needless to say I came back with quite a stash of books and journals from this conference.
One of the best parts of the conference was an exhibit at the basement of the Harnack Haus entitled "Einstein's Road to General Relativity". The exhibition contained original manuscripts of Einstein, including a notebook containing his notes on tensor analysis, his letters on his formulation of the so called "Entwurf Theory" (Outline theory) of GR, some of the mistakes he committed in his calculations, which were corrected by his friend Michele Besso and a magnificent manuscript containing his full exposition of GR.
The manuscripts are owned by the Hebrew University of Jerusalem and were on loan to the Max Planck Institute for the conference. A facsimile of the manuscripts were launched on a Space X Dragon spacecraft to the International Space Station in 2013 and were signed by the Italian astronaut Luca Parmitano before being returned to earth.
I have compiled here a list of lectures (organized by broad subject areas) along with a summary of some of the talks with some pictures from my photo album of this visit.
Gravitational Waves
09:00 - 10:00 Rai Weiss (Massachusetts Institute of Technology, Cambridge):
"Gravitational waves: Theoretical insight to measurement"
10:00 - 10:30 Daniel Kennefick (University of Arkansas):
"Waves without Energy - Einstein and the enigma of gravitational waves: Do they actually transport energy?"
11:30 - 12:30 Abhay Ashtekar (Penn State University, University Park):
"Even a tiny cosmological constant casts a long shadow"
Rai Weiss is a leading figure in physical cosmology (especially Cosmic Microwave Background radiation) and gravitational wave detection. He has been involved with the LIGO (Laser Interferometer Gravitational Observatory) experiments from their very inception. Rai gave an excellent talk on the history of gravitational waves, starting with Einstein's paper in 1918 in which he calculated the effects of gravitational waves resulting in the famous "quadruple formula". The formula computed the change in the metric as a function of changes in the quadruple moment of the mass. Einstein arrived at this in analogy with electrodynamics where accelerating charges produce electromagnetic waves and are a function of the dipole moment of the charges. However, Einstein found that energy of the waves was of the order of (v/c)^5, which is an incredibly small number. The weakness of the gravitational waves led Einstein to assume that they would never be detected. In fact Einstein and Rosen even came to the conclusion in 1936, that gravitational waves simply do not exist. Einstein and Rosen's paper was rejected by the Physical Review and they published the paper in another journal. There followed a period of considerable confusion after this. It was only much later that the work of Felix Pirani, Hermann Bondi and other firmly established the possibility that gravity waves do in fact exist. On the experimental side there was the pioneering work of Joe Weber, which was unfortunately discredited due to false claims of having detected gravitational waves. The gold standard in this field according Rai Weiss was the discovery in 1975 of the binary pulsar "PSR 1913 + 16" by Hulse and Taylor, who showed remarkably that the period of revolution of the pulsar decreased due to energy loss in gravitational waves precisely as predicted by the quadruple formula. This was a sensational discovery and provided the impetus for attempts to directly observe gravitational waves. Rai Weiss gave an overview of the LIGO experiments, the amazing degrees of sensitivity achieved by Advanced LIGO and the remarkable LISA Pathfinder mission to detect gravitational waves using interferometers in space. Daniel Kennefick's talk added additional color to the history of the theory of gravitational waves.
Abhay Ashtekar is a leading relativist from U Penn and is most famous for his "Loop Quantum Gravity" approach to quantizing GR. He did not spend any time on quantum gravity a controversial topic needless to say), but instead focused on the problem of calculating the effect of the cosmological constant on the energy of the gravitational waves. There are numerous conceptual issues that crop up and the problem is non-trivial.
Relativistic Astrophysics
11:30 - 12:30 Andrea Ghez (University of California, Los Angeles):
"Our Galactic Center: A Laboratory for Exploring the Physics & Astrophysics of Black Holes"
15:00 - 16:00 Reinhard Genzel (Max-Planck-Institut für extraterrestrische Physik, Garching):
"Testing the Massive Black Hole Paradigm in the Center of the Milky Way"16:00 - 16:30 Luisa Bonolis (Max Planck Institute for the History of Science, Berlin):
"From “Dark Stars” to Gravitational Collapse within Einstein’s Theory: The Emergence of Relativistic Astrophysics"
One of my favorite talks of the conference was the one by the UCLA astronomer Andrea Ghez. Andrea is a famous for her TED talks (and other presentations on BBC, Discovery and Nova) on the hunt for a supermassive black hole at the center of our galaxy. She uses advanced advanced imaging techniques known as Adaptive Optics at the Keck Telescopes (in Hawaii) to study the center of our galaxy known as Saggitarius A*. In particular, she studies the motion of stars near the dark center of the galaxy to estimate the density of mass at the center, which turns out to be 10 million times that of the Sun. This is the strongest evidence we have to date of the existence of a supermassive black hole. Andrea's results confirmed and extended the work done by Reinhard Genzel's group at the Max Planck Institute in Garching. Genzel also gave a talk on how these independent groups are reinforcing each other's work. A fascinating aspect of Andrea's talk were some of the puzzles emerging from the observation of the center of our galaxy. In particular, a puzzle is the proliferation of young stars and the paucity of old red giants in the vicinity of the black hole. Another is the behavior of the gas cloud G2, which is showing accretion phenomena, but also survived periapse (closest approach) to the black hole. The theory is that the gas cloud is actually a binary star merger that is driven by the black hole!
Mathematics of Black Holes
14:00 - 15:00 Sergiu Klainerman (Princeton University, Princeton):
"Are black holes real? - A Mathematics perspective"14:30- 15:00 Yvonne Choquet-Bruhat (Université Pierre et Marie Curie/Sorbonne):
"Some memories from meeting Einstein, 1951-1952"
Mathematical general relativity started with the work of Yvonne Choquet-Bruhat, who was a young French mathematician studying under Jean Leray at the Institute for Advanced Study at Princeton at the time that Einstein was at the Institute (1951-52). Leray suggested to Yvonne that she study the so-called "Cauchy Problem" for Einstein field equations. A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain. Einstein's equations are non-linear hyperbolic equations. Yvonne showed the local existence and uniqueness of solutions to the vacuum Einstein equations. Yvonne is 92 years of age today, but nevertheless is mentally sharp. She talked about her meetings with Einstein and the experiences that she had. She described Einstein as a kind old man who was disengaged from the prevailing scientific community, but took an interest in the work of the young mathematician. Yvonne showed her results to Einstein, who was very patient, kind and gracious towards her and gave her encouragement to continue her research in the field. Yvonne painted a picture of a man who had withdrawn himself from the community of physicists. He never attended any physics lectures or seminars. He had a fixed routine and stuck to that routine. His whiteboard was always covered with equations that were attempts at unifying gravity with electromagnetism. He did not actively follow the latest developments in nuclear and particle physics. He tried gently to get Yvonne engaged in his attempts at unification, but as a young graduate Yvonne did not want to get into an area that had limited potential for success. Eventually Yvonne left IAS to join the teaching faculty at the University of Marseilles. Einstein wished her all the best in her teaching career and Yvonne was a little disappointed that he did not wish her the best in her research. Overall, Yvonne remembers Einstein as a kindly, old and somewhat lonely individual who was willing to make time for a young student like her. It was a very moving talk.
Mathematical GR is now a very active area of research, especially in the differential geometry and PDE community. Famous mathematicians such as Shing Tung-Yau and Rick Schoen have made substantial contributions to the field including the proof of the "Positive Mass Theorem" (also known as the "Positive Energy Theorem"), which states that the "energy" of an asymptotically flat spacetime is non-negative and is zero only for flat Minkowski spacetime. Sergiu Klainerman is an expert in the theory of non-linear hyperbolic PDEs and mathematical GR. He described some of the hard mathematical problems in the mathematical theory of black holes. Specifically, he talked about the problems of rigidity and stability of Kerr black hole solutions of Einstein equations (solutions for a spherically symmetric rotating mass). Essentially these problems deal with whether the known solutions exhaust all possible vacuum blackholes and whether the solutions are stable under arbitrarily small perturbations of the metric. The difficulty of such problems is indicated by the fact that in a landmark paper Klainerman and the Greek mathematician Christodoulou proved the stability of flat Minkowski space in 1993. Klainerman also talked about the mathematical problem of Collapse, whether certain initial conditions can indeed result in the creation of a stable black hole. It was some pretty heavy stuff, but fascinating nevertheless.
Pictures: Klainerman
Experimental Tests of GR
10:00 - 11:00 Eric Adelberger (University of Washington, Seattle):
"Tests of Einstein's equivalence principle and Newton's inverse-square law"Progress in science is impossible without precise experiments and measurements. Henry Cavendish famously demonstrated the absence of any force due to gravity inside a hollow shell of matter. This was an indirect evidence for Newton's inverse square law of gravitation. However, the Hungarian experimentalist Loránd Eötvös was the first to use a torsion balance to make direct measurements of Newton's inverse square law of gravitation in the early 1900s. Inspired by Eötvös, a unique group of experimentalists at the University of Washington that call themselves Eöt-Wash are pushing the boundaries of precision measurements of the inverse square law, Newton's gravitational constant G and the principle of equivalence. The motivation behind these experiments is to attempt to detect quantum gravity effects or other types of forces in hitherto unexplored length scales. So far no such effects have been discovered at length scales of the order of 10^-15 cms and the equivalence principle (and therefore GR) has withstood any attempts to detect violations. Given the enormous focus on string theory, quantum gravity, LHC and other high energy experiments it is refreshing to see a group that is using simple mechanical approaches to make high precision measurements of gravity. The LIGO experiments (attempting to detect gravity waves) and the Eöt-Wash experiments are part of a fascinating trend in experimental physics attempting to make measurements at a mind-boggling level of precision (length scales of a fraction of the diameter of a proton!). The technology used to cancel out the noise due to seismic and human activity and even accounting for quantum noise at such length scales will surely have applications far beyond gravity experiments.
Black Hole Information Paradox
14:00 - 15:00 Ted Jacobson (University of Maryland, College Park):
"Einstein's equation from maximal entropy of vacuum entanglement"
12:15 - 13:00 Jeroen van Dongen (University of Amsterdam and Utrecht University):
"Can we understand the Black Hole Information Paradox by studying its history?"
"Can we understand the Black Hole Information Paradox by studying its history?"
One of the most exciting areas of modern theoretical physics concerns the physics of black holes. Black holes arise out of solutions to Einstein's field equations and were considered by most physicists (including Einstein) to be a mathematical curiosity that had no physical meaning. Through the remarkable developments in both theoretical and experimental astrophysics in the latter half of the 20th century their reality became widely accepted. Hawking and Penrose are two of the leading lights in the theory of black holes. Their extensive work on singularities established that black holes are an essential aspect of general relativity. What is interesting is that a black hole is at the same time one of the simplest objects in the universe and also one of the most complex objects. The former became evident when Hawking and others showed that a black hole can be completely characterized by its mass, angular momentum and charge ("the no hair conjecture"). The latter was the subject of the talk. It starts with the discovery by Jakob Bekenstein and later Hawking that black holes must carry an entropy that is proportional to the area of the event horizon of the black hole. This was an amazing application of the 2nd law of thermodynamics to the subject of black holes. However, this then begs the question as to source of the enormously large entropy of black hole, which on the face of it seems to be an exceedingly simple object. There must some kind of ensemble that leads to the entropy. Recent work of Strominger and Vafa have provided some tantalizing clues, indicating that the so called "branes" of string theory account for the entropy. In any case, an even more remarkable development in the theory of black holes occurred when Hawking declared that black holes radiate and all information that went into the creation of the black hole is lost in the thermal radiation. This caused a stir in the physics community and has been the subject of numerous articles and books including a popular one by Leonard Susskind. The subject is an active area of research and seems to be still unresolved (notwithstanding recent announcements by Hawking and others). These were fascinating talks on an esoteric topic, which has captured the popular imagination. My favorite part of Ted Jacobsen's talk was when he talked about the recent experiments on "analog black holes". These are black hole like objects created in fluids (such as Bose-Einstein condensates). The second talk focused on some of the recent controversies involving string theory and the black hole information paradox.
Einstein's Legacy
11:30 - 12:30 David Gross (Kavli Institute for Theoretical Physics, Santa Barbara):
"The Enduring Legacy of Albert Einstein"
16:30 - 17:30 Joseph Polchinski (Kavli Institute for Theoretical Physics, Santa Barbara):
"Quantum Gravity and Strings"David Gross is a Nobel Laureate in Physics and one of the leaders in the field of String Theory. Edward Witten, who is considered one of the greatest physicists today was a student of Gross. Joe Polchinski is also one of the leading practitioners of string theory, author of an authoritative textbook on string theory and a central figure in the subject of black hole information paradox. Both are strong and influential proponents and defenders of string theory and have been at the center of some of the controversy surrounding string theory. They both were coming off of another conference in Germany on the question of whether string theory is real science. David's lecture on Einstein's legacy was quite masterful and well presented although he did make a plug for string theory at the end. Polchinski gave an overview of string theory, the successes and the challenges ahead. Not everyone in the audience bought into the vision. In particular, there were some who were actively pursuing alternative models of quantum gravity such as "Loop Quantum Gravity". During lunch, one of the old relativists told me sadly that "the particle physicists have taken over relativity". String theory has had some amazing recent successes, but many challenges remain. It remains to be seen how the subject evolves. The most important takeaway from Gross lecture was Einstein's role in changing how physicists thought about symmetry. Symmetry has played a central role in particle physics and in theories like the Standard Model.
Pictures: David Gross
Penrose Diagrams and Conformal Geometry
9:30 - 10:15 Roger Penrose (Oxford University):
"Conformal Geometry"
10:15 - 11:00 Aaron Wright (Harvard University):
"New Ways of Seeing in the Renaissance of General Relativity: Penrose Diagrams as Paper Tools"
Roger Penrose is a legendary physicist, fellow graduate student and collaborator of Hawking and a prolific author of books such as "The Road To Reality" and "The Emperor's New Mind". It was great to see him speak although I understood very little of his lecture on Conformal Geometry. He has been thinking a lot about thermodynamics and cosmology and has a specific model on cosmic evolution that attempts to resolve some of the questions related to very low entropy at the beginning of the universe. His model seems to propose a cosmic cycle involving the big bang and big crunch. My favorite part of both of these talks was the discussion of Penrose diagrams. These diagrams allows one to represent the infinite space around a black hole on a piece of paper! It is essentially a pictorial "compactification" of infinite spacetime that makes it easy to reason about behavior of particles near a black hole. The second talk suggested that Penrose's discovery and presentation of these diagrams played a central role in the revival of general relativity as an active area if research in the latter half of the 20th century.
Effective Field Theories, Matter from space, etc.
9:00 - 10:00 Thibault Damour, (Institut des Hautes Études Scientifique)
The Problem of Motion in General Relativity: A Centenary Assessment
12:15 – 13:00 Dennis Lehmkuhl (California Institute of Technology)
On Different Approaches to the Problem of Motion in General Relativity
14:00 – 14:45 Domenico Giulini (University of Hannover)
Matter from Space
The main gist of these talks were early attempts to understand the role of matter in general relativity. As one speaker put it Einstein's field equation involves the "beautiful and clean" left hand side (the Einstein tensor expressing the geometry of spacetime) and "messy and ugly" right hand side (the energy momentum tensor) representing the density of matter-energy, the flux of matter-energy and the pressure due to matter-energy. The right hand side is where quantum properties of matter start becoming relevant. I walked into one of the talks after visiting the Einstein exhibition, where the speaker was talking about Feynman's attempts to derive a quantum theory of gravity. His approach was to create a quantum field theory involving spin 2 particles (gravitons) and in Minkowski spacetime and derive general covariance based on certain constraints that were imposed by this approach. His approach which he captured in a series of lectures suppressed the geometrical aspects of the theory. Later Steven Weinberg apparently gave a similar but more effective treatment of this approach. These approaches treat gravity as just another field that has a quantum field theory like any other force. All this left me in a state of shock, since Einstein's approach started with general covariance and naturally led to a geometrical theory of spacetime. It was somewhat disconcerting to see that being swept aside by a standard quantum mechanical treatment of gravity (known as "gravity as an effective field theory") based on spin 2 gravitons. In any case I understood very little of it and resolved to read more on the subject when I had the time.
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