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Einstein and Beyond Big Bang and the Quantum: Einstein and Beyond An Ode to the eternal themes of the `Beginning’ and the `Origin’ Abhay Ashtekar Institute for Gravitation and the Cosmos The Pennsylvania State University Florida Atlantic University, Boca Raton Frontier of Science Public Lecture, April 6th 2012 Organization n 1. General Relativity Discovery, Central Idea, Successes n 2. The Big Bang Curious history, Implications, Observations n 3. Quantum Gravity: Beyond Einstein Why, When, Challenges, Implications n 4. Loop Quantum Cosmology The Big Bounce, Implications, Observations Intellectual Tension: Einstein (1908) n Newton’s theory of gravity based on Newton’s model of space & time. Incompatible with special relativity n New theory of gravity? n 1913: Planck visits Einstein in Zurich. “As an older friend, I must advise you against it, for, in the first place you will not succeed, and even if you succeed, no one will believe you.” Planck to Einstein n Solution: 1915 General Relativity A new model of space-time Discovery of General Relativity “During the last month, I experienced one of the most exciting and most exacting times of my life, true enough also one of the most successful. …. Now the marvelous thing which I experienced was the fact that not only did Newton’s theory result as first approximation but also the perehelion of mercury (43” per century) as second approximation. ….” Einstein to Sommerfeld November 28, 1915 “of general theory of relativity, you will be convinced, once you have studied it. Therefore, I am not going to defend it with a single word.” Einstein to Sommerfeld February 8, 1916 Gravity is Geometry ! n Space-time no longer an inert background or stage. n Gravitational field is encoded in the very geometry of space-time: Possible because, like geometry, gravity is omnipresent and non-discriminating. n Matter tells space-time how to curve. Space-time tells matter how to move. Geometry intertwined with matter via Einstein’s equations. THE NEW YORK TIMES, MONDAY, NOVEMBER 10, 1919 LIGHTS ALL ASKEW IN THE HEAVENS ____________________ Men of Science More or Less Aa agog Over Results of Eclipse Observations. __________ EINSTEIN THEORY TRIUMPHS _________ Stars Not Where They Seemed or Were Calculated to be but Nobody Need Worry. __________ A BOOK FOR 12 WISE MEN __________ No More in All the World Could Comprehend it, Said Einstein When His Daring Publishers Accepted it. General Relativity n Einstein’s theory of general relativity is widely regarded as an intellectual triumph of twentieth century Science. Conceptually, it displays Francis Bacon’s “strangeness in proportion” that characterizes the most sublime of human creations. Mathematically, it is beautiful and, observationally, it has withstood the most stringent tests ever performed. n There is no excellent beauty that hath not some strangeness in proportion. … Francis Bacon On General Relativity It is as if a wall which separated us from the truth has collapsed. Wider expanses and greater depths are now exposed to the searching eye of knowledge, regions of which we had not even a pre-sentiment. …Hermann Weyl When Henry Moore visited the University of Chicago some years ago, I had the occasion to ask him how one should see sculptures: from afar or from nearby. Moore’s response was that the greatest sculptures can be viewed --indeed should be viewed-- from all distances since new aspects of beauty will be revealed in every scale. Moore cited sculptures of Michelangelo as examples. In the same way, the general theory of relativity reveals strangeness in the proportion at any level in which one may explore its consequences. …Subramanyan Chandrasekhar Einstein’s Triumph General Relativity accounts for a very large array of fascinating astrophysical Phenomena. Organization n 1. General Relativity Discovery, Central Idea, Successes n 2. The Big Bang Curious history, Implications, Observations n 3. Quantum Gravity: Beyond Einstein Why, When, Challenges, Implications n 4. Loop Quantum Cosmology The Big Bounce, Implications and Observations Cosmology Change is Eternal n Evolution of Geometry: Einstein’s Equations (Space-time Curvature) = 8πG (Matter stress-energy) n Observations: Homogeneity and Isotropy on large scale (the grandest realization of the Copernicus Principle) n Geometry must be Dynamical, Ever-Changing n Universe began with a Primordial Explosion 13.7 ± 1Billion years ago Big Bang: The Issue of the Beginning n Fascinating history: Friedmann (1921-24), LeMaitre (1926-65) Philosophical Preferences & Ideology: Gamow, Pope Pius XII & Lemaitre (1951) Soviet program: Lifshitz, Khalatnikov (late 50s …) Steady State: Hoyle, Bondi, Gold, Sciama, (till 70s) Cyclic Universe: Dicke, Sakharov, Weinberg, Wheeler, … n Remained outside mainstream physics until Nucleosynthesis was understood (1948-65) Cosmic Micro-wave Background (CMB) (1965 on) OUR UNIVERSE... Cosmic Microwave Background The CMB: COBE, WMAP, etc Snapshot of the Dark energy universe when it was domination era 380,000 years young! t Spectacular success Mater domination Extremely Homogeneous: era x 1.over the last two decades:T¯ =2Powerful.73K interplay between theory and high Formation of the CMB 2. Tiny anisotropies Universe becomes transparent precision observations especially∆T through5 Radiation domination era ¯ 10− (opaque Universe) space missions,T ≈ COBE & WMAP 2 27 Cosmic Microwave Background When it was 380,000 years old, the Universe was extremely homoge- neous as Lemaitre had envisaged. An almost uniform temperature of 2.725K (perfect black body!) But tiny inhomogeneities of 1 part in 100,000. Cosmic Microwave Background …Into the complex … large scale structure of the universe seen now, 13.3billion years later. î⏎⏎ TINY inhomogeneities seen in CMB when the universe was 380,000 years young grow obeying general relativity… Triumph of General Relativity! In human terms: from the snapshot of a baby 1 hour after birth, providing an accurate profile at age 40! Organization n 1. General Relativity Discovery, Central Idea, Successes n 2. The Big Bang Curious history, Implications, Observations n 3. Quantum Gravity: Beyond Einstein Why, When, Challenges, Implications n 4. Loop Quantum Cosmology The Big Bounce, Implications, Observations Beyond General Relativity: Why? n So far, we applied General Relativity to cosmology but ignored quantum physics. Justified because we focused only on the large scale structure and ignored what happened in the early era before the universe was 380,000 years young. n But this does not provide any real understanding of the origin of the tiny inhomogeneities in the CMB! Had to just accept that these seeds existed and used observations to tell us their properties, needed in subsequent calculations. n The issue of the Beginning and the Origin pushed back but only the the CMB era. Need quantum physics for a deeper, more complete understanding. Origin of Inhomogeneities in the CMB? • Inflation: Soon after the Big Bang the universe underwent a phase of rapid expansion. At the onset of this phase universe was completely homogeneous EXCEPT for the ever present vacuum fluctuations which cannot be gotten rid of even in principle! • The vacuum fluctuations are shown to grow in time to produce exactly the inhomogenities Formation of the CMB seen in the CMB! Universe becomes transparent Generation of cosmic inhomogeneities The origin of the observed large scale structure: Quantum13 27 Nothingness! Beyond Inflation: Why? n The idea that CMB inhomogeneities arose just from inevitable, fundamental Heisenberg uncertainties is awe inspiring. But some fundamental problems still remain. n Inflation continues to assume that the space-time geometry is still given by General Relativity and then incorporates small quantum corrections. There is still a Big Bang with infinite matter density and curvature. Space- time ends and Inflationary physics throws up its hands & comes to a halt! We need a more complete union: Quantum Gravity! Einstein on the necessity of Quantum Gravity “Nevertheless, due to the inner-atomic movement of electrons, atoms would have to radiate not only electro-magnetic but also gravitational energy, if only in tiny amounts. As this is hardly true in Nature, it appears that quantum theory would have to modify not only Maxwellian electrodynamics, but also the new theory of gravitation.” (1916) “One may not assume the validity of field equations at very high density of field and matter and one may not conclude that `the beginning of the expansion' should be a singularity in the mathematical sense.” (1945) Why is the problem, so difficult? n In general relativity, gravity is coded in space- time geometry. n Quantum gravity Quantum geometry!! n What are atoms of geometry? How do they fit together to give us a continuum under normal circumstances? Can quantum gravity provide us with equations that still hold at & beyond the Big Bang where the continuum tears and classical physics stops? n Geometry itself must become quantum mechanical. How do you do physics without a space-time continuum in the background? A Theory Meeting These Challenges When does Quantum Geometry become important? n Fundamental constants: G, C, h Sets the scale at which Einstein’s continuum completely breaks down! n Planck length Extremely small even for the sub-atomic world $1020: US budget for a 100 million years at the 2011 rate! n Extremely tiny scale. But comes to forefront at extremely high space-time curvature, precisely when General Relativity fails. n To go beyond general, relativity, we have to use LQG equations governing quantum threads rather than Einstein’s equations governing the continuum fabric of space-time. Quantum Geometry in Loop Quantum Gravity n Hallmark of LQG : Retains Einstein’s fusion of geometry and gravity but uses `quantum geometry.’ n Not only Matter but Space and Time are also Quantum from Birth! Brand new mathematical and conceptual tools to do physics without space-time continuum. n Key Consequences: n The Fabric of space woven by 1-dimensional quantum thread. Quantum geometry, polymer-like. Einstein’s continuum only in an approximation.
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