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

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 homogeneous 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. n Example of Quanta of geometry: Discreteness of area Organization n 1. General Relativity Discovery, Central Idea, Successes n 2. The Big Bang Curious history, Implications and Observations n 3. Quantum Gravity: Beyond Einstein Why, When, Challenges and Implications n 4. Loop Quantum Cosmology The big bounce, Implications and Observations Fate of the Big Bang of GR in LQG n What happens to the equations loop quantum gravity at the big-bang? They do not break down! Major departures from Einstein’s equations near the big-bang: Unforeseen, brand new Physics!! n The space-time continuum of general relativity tears but the quantum threads have a precise, well-defined behavior. Quantum physics does not stop! LQG equations tell us there was no big-bang: All Physical quantities remain finite!

Cover Story: New Scientist The other side of the Big-Bang

n Quantum geometry creates a new repulsive force which overwhelms usual gravitational attraction. n In the standard cosmological models, the universe bounces! The pre-Big-Bang branch joined to our post-big-bang branch by a quantum bridge. n Cosmic microwave background and inflation unaffected: They are not proofs that a big-bang occurred! Examples of New Quantum Forces

Neutron star White dwarf Binary

A novel quantum force associated with matter can combat gravity and halt gravitational collapse if the mass of the star is less than ~ 5 Mo Leads to new & fascinating types of stars! Completion of the Inflationary scenario

The Big Bang `singularity’ of GR is tamed in LQC and replaced by the big bounce where all physical quantities are finite.

Natural Questions:

• Is the desired inflationary phase after the bounce occur generically or do we need an extreme fine tuning?

• The inflationary paradigm presupposes a continuum a la General Relativity. Do the `quantum threads of geometry’ naturally freeze into a `smooth fabric’ providing this classical continuum at the onset of inflation?

Natural Questions:

• Is the desired inflationary phase after the bounce occur generically or do we need an extreme fine tuning? No fine tuning needed!

• Can one use general principles to choose a preferred class of initial conditions at the bounce which then evolve via Loop Quantum Cosmology equations to the assumed vacuum fluctuations at the onset of inflation? Yes, a natural infinite class exists. Summary : General Relativity (GR) n GR is a deep and marvelous theory; Conceptually compact, supremely beautiful, and accounts for many fascinating astrophysical phenomena. n Cosmology: Given the observed tiny inhomogeneities in the CMB of the young universe, GR successfully predicts the large scale structure we observe some 13.3 billion years later. n However GR is incomplete. Because it ignores quantum physics that is crucial in the early universe, its prediction that the Big-Bang is the Beginning cannot be trusted. Summary: Physics Beyond Einstein

n Impressive advances over the past two decades. By taking into account quantum physics on curved classical space-times inflation leads to a successful paradigm to account for the tiny fluctuations in the CMB that GR needs as input.

n But because space-time is classical, the Big Bang still persists. Physics just stops there. For conceptual coherence of fundamental laws, we need an even grander, deeper theory from which general relativity & known quantum physics emerge only as limiting cases: Quantum Gravity Loop Quantum Gravity (LQG) n In LQG, one has quantum matter as well as geometry from start. Einstein’s continuum is an approximation which breaks down near the Big Bang. But LQG does not break down! n There are no infinities. Big Bang is replaced by a Big Bounce. Brand new physics in the `Planck regime’. Provides a completion of the inflationary paradigm. Boundaries of our knowledge have been systematically extended very significantly: Scientific Progress is the discovery of a more and more comprehensive simplicity. ….. Lemaitre Epilogue

A really new field of experience will always lead to crystallization of a new system of scientific concepts and laws… When faced with essentially new intellectual challenges, we continually follow the example of Columbus who possessed the courage to leave the known world in an almost insane hope of finding land again beyond the sea.

W. Heisenberg, Recent Changes in the Foundation of Exact Science Non-Technical Articles/Clips/Videos See the Outreach Page of our Institute for Gravitation and the Cosmos gravity.psu.edu The physicists succeeded magnificently, but in doing so, revealed the limitation of intuition, unaided by mathematics; an understanding of Nature, they discovered, comes hard. The cost of scientific advance is the humbling recognition that reality is not constructed to be easily grasped by the human mind. Consilience, The unity of Knowledge Edward O. Wilson.