Time in the Physical Universe: From antiquity to Einstein and beyond

1. Time in the Physical Universe:From antiquity to Einstein and beyond Abhay Ashtekar Center for Gravitational Physics and Geometry

2. Evolution of the Notion of Time • Ancient Traditions • Newton’s Masterpiece: Principia • Einstein’s Insight: Special Relativity • Einstein’s Triumph: General Relativity • Glimpses into the third Millennium

3. Space and Time • Space: that which is between and around objects. • Time: whose flow manifests itself through change.

4. Jainism is an ancient non-vedic religion of India… It asserts that the universe is uncreated and eternal, consisting of innumerable life principles (jīva) and non-living elements (ajīva)… and four material substances (dravyas): space (Ākāśa), time (kăla), motion (dharma-dravya) and rest (adharma-dravya)…. (Jaina Arts, Calico Museum, Ahmedabad) Jainism

5. Aristotle on the Reality of Time At Phys. IV. 217b32ff. Aristotle asks whether time isamong the things that are or among the things that are not. (217b31).1 He presents three exoteric arguments which suggest that time either is not at all or scarcely and dimly (217 b32-3): …. But whereas time consists of parts, some of them have been and some are to come, but none of them is. The now is not a part. For a part measures [the whole] and the whole must consist of parts. But time seems not to consist of the nows. (218a3-8) ] It is not easy to see whether the now, which seems to bound the past and the future, always remains one and the same or is successively different. Suppose (i) that the now is always different. Then, .... the nows too will not be simultaneous with each other, and the previous now must always have perished. (a) The now cannot have perished in itself, since that is when it is; and (b) it cannot have perished in any other now, for…

6. Two Main Models of Time Rebirth Death Death Birth Judeo-Christian Chinese Cultures Linear Time Hindu-Buddhist Hellenic Cultures Cyclic Time

7. Cyclic Time • Eastern Thought: Dawning with recreation, ending with dissolution and reabsorption of the world spheres with all creatures into the absolute. ( Jataka Stories: Buddha reincarnations.) • Hellenic Thought: Aristotle and Plato speculated that every art and science had fully developed many times and then perished so time returned to its beginning and all things restored to their original state. Pythagoras taught that there is an eternal reoccurrence of successive ages.

8. Traditions Hindu-Hellenic Traditions: • Space predominates over time. Time is cyclic; the temporal-repetitive world is less real or attractive than timeless forms. Fascination with absoluteness of Euclidean geometry of space concentrates on present. Judeo-Christian Traditions: • Time predominates over space. The movement of time is directed and meaningful. The future is new; it cannot be frustrated by cycles of time.

9. It is not, I believe, too much to say that all vital problems of philosophy depend, for their solution, on the solution of the problem of what space and time are, and, more particularly, how they are related to each other. -S. Alexander Gifford Lectures Glasgow, 1916-18

10. Philosophy of Mathematics and Natural Sciencesby Herman Weyl Contents PREFACE BIBLIOGRAPHICAL NOTE PART II. NATURAL SCIENCE Chapter I. Space and Time, the Transcendental External World 16. The Structure of Space and Time in Their Physical Effectiveness 17. Subject and Object (The Scientific Implications of Epistemology) 18. The Problem of Space

11. The Value of Scienceby Henri Poincaré Table of Contents TRANSLATOR’S INTRODUCTION PREFATORY ESSAY INTRODUCTION Part First The Mathematical Sciences Chapter I. Intuition and Logic in Mathematics Chapter II. The Measure of Time Chapter III. The Notion of Space Chapter IV. Space and Its Three Dimensions

12. PHILOSOPHIǢ naturalis PRINCIPIA mathematica Autore I.S. Newton, Trin. Coll. Cantab. Soc. Mathefeos Profeffore Lucafiano, & Societatis Regalis Sodali. IMPRIMATUR. S. P E P Y S, Reg. Soc. P R Ǣ S E S. Julii 5. 1686. LONDINI Jullu Societatis Regie ac Typis Jolephi Streater. Profat apud Plures Bibliopolas. Anno MDCLXXXVII.

13. Revolution Newton was hardly an unknown man in philosophic circles before 1687. Nevertheless, nothing had prepared the world of natural philosophy for the Principia … A turning point for Newton, who, after twenty years of abandoned investigations, had finally followed an undertaking to completion, the Principia also became a turning point for natural philosophy. Richard S. Westfall Nature and Nature’s laws lay hid in night; God said, Let Newton be ! & all was light. Alexander Pope (1688-1744)

14. Reaction to the Principia Newton’s book took Britain by storm. Almost at once became the reigning orthodoxy among natural philosophers. On the Continent, its triumph was more protracted. Nevertheless, it was refused to be ignored…According to his own account, Leibniz saw the review in the Acta before he received the book itself. Ever mindful of his intellectual capital, he saw Newton forstalling him on several problems on which he had thought in the past. His initial response to the Principia, then, was the hasty composition of three papers which he rushed to the Acta to defend his own priority: a paper on refraction, a paper on motion through resisting media, and a paper on orbital dynamics set in the framework of a vortical theory. What word of praise could have surpassed his action?

15. Key Features of Newton’s Model of Space and Time • Space is represented by an infinite 3-dimensional continuum • Time is represented by an infinite 1-dimensional continuum • Time intervals between any two events are absolute, observer independent • No absolute rest frame; All velocities relative (spatial distance between events is observer dependent in general)

16. Space-time diagrams 3 events t x t x (y,z suppressed)

17. “Experiment” : Phone call 60mph Car-phone hung up Car-phone picked up Distance = 1 mile

18. Phone call: Space-time description t (earth) t' (Car) x x = 1 mile t' = t x' = 0

19. The Jolt (~1865) • Maxwell’s Synthesis of knowledge about electricity and magnetism • Prediction of Maxwell’s equations: speed of light in empty space is a universal constant, independent of the observer 60mph Speed of light c = 675 million mph for both Confirmed by the Michelson Morley Experiment (1887)

20. Now, my own suspicion is that the universe is not only stranger than we imagine, but it is stranger than we canimagine. J.B.S. Haldane

21. Resolution: Einstein 1905Special Relativity: New Model of Space & Time • Space and time fuse together to form a 4-dimensional continuum • Absolute simultaneity lost time intervals between events ----like spatial separations---- are observer dependent. Duration of the phone call ~ (1 minute) (1 – 10-14) ↓ A hundred thousandth of a Billionth of a minute! Effect miniscule because c = 675 million mph!

22. Fermi Accelerator Lab Aerial view of the Fermi Lab Tevatron which is four miles in circumference. It uses a series of accelerators to keep adding energy to subatomic particles, until they are racing around at 99.9999 percent of the speed of light in a vacuum.

23. Lifetime of an elementary particle (lab) t t' (particle) x' (particle) x lab Now v = 0.999c, so

24. Einstein ~1908: New Problem • Newton’s theory of gravity based on Newton’s model of space & time. Incompatible with special relativity • New theory of gravity? • 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 • Solution: 1915 General Relativity A new model of space-time

25. Einstein 1908-1915Never at Rest A Vulgar Mechanick can practice what he has been taught or seen done, but if he is in an error he knows not how to find it out and correct it, and if you put him out of his road, he is at a stand; Whereas he that is able to reason nimbly and judiciously about figure, force and motion, is never at rest till he gets over everyrub. Isaac Newton to Nathaniel Hawes 25 May 1694

26. 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

27. New Model of Space-Time: • Space-time no longer an inert background or stage. • Gravitational field is encoded in the very geometry of space-time. • Matter tells space-time how to curve. Space-time tells matter how to move. • Geometry intertwined with matter via Einstein’s equations.

28. THE NEW YORK TIMES, MONDAY, NOVEMBER 10, 1919 LIGHTS ALL ASKEW IN THE HEAVENS ____________________ Men of Science More or Less 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.

29. General Relativity • 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. • There is no excellent beauty that hath not some strangeness in proportion. Francis Bacon

30. 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 structures 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

31. Stretching of Space-Time Continuum by Heavy Bodies: Physical Effects • You call from a mountain top to your friend in a hotel in the valley. How long did the call last? • Effect dramatic in strong gravitational fields. Black Hole of 1 solar mass: Radium 3 km If your friend is 6 kms from the black hole and calls you

32. What use is it ? Does it matter? • Why care? Conditions have to be so extreme!! • Not really. Both special and general relativity effects on Δt critical for GPS! What seems like fantasy today is essential for tomorrow technology. • Fundamental laws of Nature always matter.

33. Change is Eternal • Evolution of Geometry: Einstein’s Equations (Space-time Curvature) = 8πG (Matter stress-energy) • Observations: Homogeneity and Isotropy on large scale (the grandest realization of the Copernicus Principle) • Geometry must be Dynamical, Ever-Changing • Universe began with a Primordial Explosion • Two Greatest Mistakes of Einstein’s Life • The fascinating story of the Cosmological Constant

34. Is Time Cyclic or Linear? • No longer Metaphysics or Philosophical Aesthetics • Question is reduced toobservable properties d<d0 a(t) d=d0 d>d0 t d0: critical density

35. Big-Bang • Current Observations + General Relativity: --On a large scale, space is flat; No Recycling --Universe is 13.7 ± 1Billion years old • But at the big-bang, curvature is infinite energy density infinite. • General Relativity fails; Einsteinian Physics Stops. General Relativity applied beyond its domain of validity! Fails by its own criteria. • Near the big-bang, the very large meets the very small • Atomic and subatomic world ruled by Quantum Physics completely ignored by General Relativity • Need a deeper paradigm: Quantum General Relativity

36. Challenge for the Third Millennium • Fundamental constants: G, C, h Scale at which the continuum completely breaks down! What replaces it ?? What is the new arena for all `happenings?’’ • Planck length Extremely small even for the sub-atomic world 1020: US budget for a 100 million years at the 2005 rate! • But Einstein’s ideas still pave the way: Geometry ~ Matter • We know: Matter is made of atoms. What are atoms of geometry?

37. Frontiers: Quantum Theory of Geometry • Quantum theory of Geometry developed primarily at the Center for Gravitational Physics and Geometry at PSU. Now used by research groups world-wide. • Fabric of space literally built from 1-dimensional quantum threads. ‘Polymer Geometry’. Continuum only an approximation. • Quanta of Geometry. Example: Discreteness of Area Smallest area quantum

38. Checks: Black Hole Puzzles • Detailed theory of Black Hole Entropy. • Delicate check of consistency of the three pillars of theoretical physics: General Relativity, Quantum Mechanics and Thermodynamics. • New physical processes. Beginning of last century quantum physics taught us Radiation and Matter two facets of the same reality • General Relativity: Geometry ~ Matter • Can Quanta of Geometry be converted in to quanta of matter and vice versa? Hint: Hawking's famous discovery (1974): Black holes radiate quanta (quantum tunneling) Geometry changes, area decreases but is a continuous variable. • Quantum Geometry completes the story! Einstein's vision elevated to quantum physics. Einsteinian Alchemy!!

39. QuantumCosmology • Classical physics fails in extreme conditions near Big Bang • New Paradigm: Quantum Geometry • Quantum physics does not stop at the Big Bang Well-defined Physics –dictated by Quantum Einstein Equations. • Space-time fabric torn apart violently; Quantum threads fluctuate wildly But quantum state of the universe has well-defined evolution across the big-bang! • Exciting possibilities open up: Being investigated Emphasis: Observable consequences on our side of the Big Bang

40. Summary: A Brief History of Time • Notions of Change and Time, The Beginning and The End fascinate us all. Civilizations have reflected pondered over these issues for over 2000 years. • In the beginning of the 20th century Einstein fathomed the deepest secrets of Nature, of which the humankind did not even have mildest inkling! Deep ramifications not only on Science and Technology but also Philosophy. Paradigms shape the very questions we can ask meaningfully. • Enormous progress could occur because: We could stand on the shoulders of giants; and We have the powerful Scientific Method • The New Millennium surely has even bigger surprises for us. We already have fascinating glimpses through Quantum Geometry. Breakdown of the continuum is radical paradigm shift because all physical theories presupposed it! In particular, it reshapes the question we can meaningfully ask about The Beginning and The End!