Title: Time in the Physical Universe: From antiquity to Einstein and beyond
1 Time in the Physical UniverseFrom antiquity
to Einstein and beyond
 Abhay Ashtekar
 Center for Gravitational Physics and Geometry
2 Evolution of the Notion of Time
 Ancient Traditions
 Newtons Masterpiece Principia
 Einsteins Insight Special Relativity
 Einsteins Triumph General Relativity
 Glimpses into the third Millennium
3Space and Time
 Space that which is between and around objects.
 Time whose flow manifests itself through change.
4Jainism
 Jainism is an ancient nonvedic religion of
India It asserts that the universe is uncreated
and eternal, consisting of innumerable life
principles (jiva) and nonliving elements
(ajiva) and four material substances (dravyas)
space (Akasa), time (kala), motion
(dharmadravya) and rest (adharmadravya).  (Jaina Arts, Calico
Museum, Ahmedabad)
5 Aristotle on the Reality of Time
 At Phys. IV. 217b32 ff.
 Aristotle asks whether time is among 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 b323) 
 . 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. (218a38)  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
6Two Main Models of Time
JudeoChristian Chinese Cultures Linear Time
HinduBuddhist Hellenic Cultures Cyclic Time
7Cyclic 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. 
8Traditions
 HinduHellenic Traditions
 Space predominates over time. Time is cyclic
the temporalrepetitive world is less real or
attractive than timeless forms. Fascination with
absoluteness of Euclidean geometry of space
concentrates on present.  JudeoChristian 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,
191618
10Philosophy 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
11The Value of Scienceby Henri Poincaré
 Table of Contents
 TRANSLATORS 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
12PHILOSOPHI? 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 ? S E S. Julii 5. 1686.
LONDINI Jullu Societatis Regie ac Typis
Jolephi Streater. Profat apud Plures Bibliopolas.
Anno MDCLXXXVII.
13Revolution
 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 Natures laws lay
hid in night God said,  Let Newton be !
all was light. 
Alexander Pope 
(16881744)
14 Reaction to the Principia
 Newtons 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 ignoredAccording 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?
15Key Features of Newtons Model of Space and Time
 Space is represented by an infinite 3dimensional
continuum  Time is represented by an infinite 1dimensional
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 Spacetime diagrams
3 events
t
?x
?t
x
(y,z suppressed)
17Experiment Phone call
60mph
Carphone hung up
Carphone picked up
Distance 1 mile
18Phone call Spacetime description
t
t'
(Car)
(earth)
x
?x 1 mile
?t' ?t
?x' 0
19The Jolt (1865)
 Maxwells Synthesis of knowledge about
electricity and magnetism  Prediction of Maxwells 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 can imagine.
 J.B.S. Haldane
21Resolution Einstein 1905Special Relativity New
Model of Space Time
 Space and time fuse together to form a
4dimensional continuum  Absolute simultaneity lost time intervals between
events like spatial separations are
observer dependent.  Duration of the phone
call  (1 minute) (1 1014)
 ?
 A hundred thousandth of a
Billionth  of a minute!

Effect miniscule because c 675 million mph!
22Fermi 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.
23Lifetime of an elementary particle
(lab)
t
t'
(particle)
x'
(particle)
x
lab
Now v 0.999c, so
24Einstein 1908 New Problem
 Newtons theory of gravity based on Newtons
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
spacetime
25Einstein 19081915Never 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 every rub. 
Isaac Newton to Nathaniel Hawes  25
May 1694
26Discovery 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 Newtons 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
27New Model of SpaceTime
 Spacetime no longer an inert background or
stage.  Gravitational field is encoded in the very
geometry of spacetime.  Matter tells spacetime how to curve.
 Spacetime tells matter how to move.
 Geometry intertwined with matter via Einsteins
equations.
28THE 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
29 General Relativity
 Einsteins theory of general relativity is widely
regarded as an intellectual triumph of twentieth
century Science. Conceptually, it displays
Francis Bacons 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  presentiment.

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. Moores response was that the
greatest sculptures can be viewed indeed should
be viewedfrom 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
31Stretching of SpaceTime 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 ?t critical for GPS! 
 What seems like fantasy today is
essential for tomorrow technology.  Fundamental laws of Nature always matter.
33Change is Eternal
 Evolution of Geometry Einsteins Equations
 (Spacetime Curvature) 8pG (Matter
stressenergy)  Observations Homogeneity and Isotropy on large
scale  (the grandest realization of the Copernicus
Principle) 
 Geometry must be Dynamical, EverChanging
 Universe began with a Primordial Explosion
 Two Greatest Mistakes of Einsteins Life
 The fascinating story of the Cosmological
Constant
34Is Time Cyclic or Linear?
 No longer Metaphysics or Philosophical Aesthetics
 Question is reduced to observable properties
d
a(t)
dd0
dd0
t
d0 critical density
35BigBang
 Current Observations General Relativity
 On a
large scale, space is flat No Recycling  Universe
is 13.7 1Billion years old  But at the bigbang, 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 bigbang, 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
36Challenge 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
subatomic world 
 1020 US budget for a 100 million years
at the 2005 rate!  But Einsteins ideas still pave the way Geometry
Matter  We know Matter is made of atoms.
 What are atoms of geometry?
37Frontiers 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 worldwide.
 Fabric of space literally built from
1dimensional 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 Quantum Cosmology
 Classical physics fails in extreme conditions
near Big Bang  New Paradigm Quantum Geometry
 Quantum physics does not stop at the Big Bang
 Welldefined Physics dictated by Quantum
Einstein Equations.  Spacetime fabric torn apart violently Quantum
threads fluctuate wildly  But quantum state of the universe has
welldefined evolution across the bigbang!  Exciting possibilities open up Being
investigated  Emphasis Observable consequences on our
side of the Big Bang
40Summary 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! 