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Time in the Physical Universe:
From antiquity to Einstein and beyond
Abhay Ashtekar
Center for Gravitational Physics and Geometry
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
Space and Time
Space: that which is between and around objects.
Time: whose flow manifests itself through change.
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 nonliving elements (ajīva)… and four material
substances (dravyas): space (Ākāśa), time
(kăla), motion (dharma-dravya) and rest
(Jaina Arts, Calico Museum, Ahmedabad)
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 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…
Two Main Models of Time
Rebirth Death
Chinese Cultures
Hellenic Cultures
Linear Time
Cyclic Time
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.
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.
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
Philosophy of Mathematics and Natural Sciences
by Herman Weyl
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
The Value of Science
by Henri Poincaré
Table of Contents
Part First
The Mathematical Sciences
Chapter I.
Chapter II.
Chapter III.
Chapter IV.
Intuition and Logic in Mathematics
The Measure of Time
The Notion of Space
Space and Its Three Dimensions
Autore I.S. Newton, Trin. Coll. Cantab. Soc. Mathefeos
Profeffore Lucafiano, & Societatis Regalis Sodali.
S. P E P Y S, Reg. Soc. P R Ǣ S E S.
Julii 5. 1686.
Jullu Societatis Regie ac Typis Jolephi Streater. Profat apud
Plures Bibliopolas. Anno MDCLXXXVII.
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
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?
Key Features of Newton’s Model
of Space and Time
Space is represented by an infinite 3-dimensional
Time is represented by an infinite 1-dimensional
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
Space-time diagrams
3 events
(y,z suppressed)
“Experiment” : Phone call
Car-phone hung up
Car-phone picked up
Distance = 1 mile
Phone call: Space-time description
x = 1 mile
x' = 0
t' = t
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
Speed of light c = 675 million mph for both
Confirmed by the Michelson Morley Experiment (1887)
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
Resolution: Einstein 1905
Special 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!
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.
Lifetime of an elementary particle
Now v = 0.999c, so
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
Einstein 1908-1915
Never 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
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
New Model of Space-Time:
Space-time no longer an inert background or
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
Men of Science More or Less
Agog Over Results of Eclipse Observations.
Stars Not Where They Seemed
or Were Calculated to be
but Nobody Need Worry.
No More in All the World Could
Comprehend it, Said Einstein When
His Daring Publishers Accepted it.
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
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
…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
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
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.
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
Is Time Cyclic or Linear?
No longer Metaphysics or Philosophical Aesthetics
Question is reduced to observable properties
d0: critical density
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
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?
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
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!!
Quantum Cosmology
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
Exciting possibilities open up: Being investigated
Emphasis: Observable consequences on our side of the Big Bang
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!
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