Columbia University Institute for Strings, Cosmology, and Astroparticle Physics (ISCAP), the Perimeter Institute, and UNC Chapel Hill

# Origins of Time's Arrow

Posted November 16, 2007

Presented By

### Overview

Many features of dynamics as described by physical laws have time reversal invariance, meaning that symmetry should exist over the duration of an event when comparing what happens when time runs forwards with what happens when time runs backwards. But this contradicts much of what physicists and cosmologists observe.

As Columbia University's Brian Greene asked in his introductory remarks to an October 15–16, 2007, conference held at the Academy, "How is it that time reversal invariant dynamics give rise to a universe that certainly doesn't appear at all to reflect that time reversal invariance?" Finding an answer to this question has become an important challenge for theoretical physics, and will need to be addressed in any theory that will successfully bridge the divide between quantum mechanics and general relativity, and unify it with cosmological observation.

This gathering brought together many of the world's leading experts on this problem.

### Web Sites

Time's Arrow on WikipediaA generalist's introduction to some of the concepts discussed in this conference. See also T-symmetry.

The Einstein Equations and the Rigidity of Quantum MechanicsA Web seminar by Gary Gibbons on topics germane to his talk.

Institute for Strings, Cosmology, and Astroparticle Physics (ISCAP)Columbia University institute that brings together theoretical physicists, astrophysicists, and observational astronomers to address key problems in particle physics and cosmology.

Perimeter Institute for Theoretical PhysicsBased in Waterloo, Ontario, the Perimeter Institute specializes in cross-discliplinary work in cosmology, particle physics, quantum foundations, quantum gravity, quantum information theory, and string theory.

University of North Carolina, Chapel Hill Department of PhysicsAmong other fields, UNC offers programs in astrophysics, high-energy physics, and string theory.

### Books and Articles

Albert DZ. 2003. Time and Chance. Harvard University Press, Cambridge, MA.

Albert DZ. 1994. Quantum Mechanics and Experience. Harvard University Press, Cambridge, MA.

Albrecht A, Inglesias A. 2007. The clock ambiguity and the emergence of physical laws. arXiv:0708.2743v1.

Albrecht A. 2004. Cosmic inflation and the arrow of time. In Barrow JD, Davies PCW, Harper CL, eds. *Science and Ultimate Reality: Quantum Theory, Cosmology and Complexity*. Cambridge University Press, Cambridge, UK.

Albrecht A. 1994. The theory of everything vs the theory of anything. Occhionero F, ed. Proceedings of "The Birth of the Universe and Fundamental Forces." Rome, May 1994. arXiv:gr-qc/9408023v2.

Banks T. 2007. Entropy and initial conditions in cosmology. arXiv:hep-th/0701146v1.

Brown MG, Freese K, Kinney WH. 2004 [submitted]. The phantom bounce: a new oscillating cosmology. arXiv:astro-ph/0405353v2.

Dvali G, Redi M. 2007. Black hole bound on the number of species and quantum gravity at LHC. arXiv:0710.4344v1.

Gambini R, Porto RA, Pullin J. 2004. Realistic clocks, universal decoherence and the black hole information paradox. *Phys. Rev. Lett.* 93: 240401.

Gambini R, Porto RA, Pullin J. 2003. Consistent discrete gravity solution of the problem of time: a model. In Kokkotas KD & Stergioulas N, eds. *Recent Developments in Gravity*. World Scientific Publishing, Hackensack, NJ.

Gambini R, Pullin J. 2007. Relational physics with real rods and clocks and the measurement problem of quantum mechanics. *Found. Phys.* 37: 1074-1092.

Gibbons GW. 1998. Wrapping branes in space and time. arXiv:hep-th/9803206v1.

Gibbons GW. 1972. The time symmetric initial value problem for black holes. *Comm. Math. Phys.* 27: 87–102.

Gibbons GW, Pohle H-J. 1993. Complex numbers, quantum mechanics, and the beginning of time. *Nucl. Phys. B* 410: 117-142. (PDF, 207 KB)

Gibbons GW, Pope CN. 2007. Time-dependent multi-centre solutions from new metrics with holonomy SIM(n-2). arXiv:0709.2440v1.

Hertog T, Horowitz GT. 2005. Holographic description of AdS cosmologies. *JHEP* 0504: 005. arXiv:hep-th/0503071v2. (PDF, 252 KB)

Holman R, Mersini-Houghton L. 2005. Why the universe started from a low entropy state. arXiv:hep-th/0511102v3.

Holman R, Mersini-Houghton L, Takahashi T. 2006. Cosmological avatars of the landscape II: CMB and LSS sgnatures. arXiv:hep-th/0612142v1.

Kobakhidze A, Mersini-Houghton L. 2004. Birth of the universe from the landscape of string theory. *Eur. Phys. J.* C49: 869-873.

Mersini-Houghton L. 2006. The arrow of time forbids a positive cosmological constant lambda. arXiv:gr-qc/0609006v2.

Mersini-Houghton L. 2005. Can we predict lambda for the non-SUSY sector of the landscape? *Class. Quant. Grav.* 22: 3481-3490.

Price H. 1997. Time's Arrow and Archimedes' Point. Oxford University Press, New York.

Smolin L. 2006. The Trouble with Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next. Houghton Mifflin, Boston.

Wald RM. 2005. The arrow of time and the initial conditions of the universe. Write-up of talk given at Workshop on the Arrows of Time 2004, Seven Pines, Minnesota. Dec 17–20, 2004. arXiv:gr-qc/0507094v1.

### Speakers

##### Gary Gibbons, FRS, PhD

University of Cambridge

e-mail | web site | publications

**The Emergent Nature of Time and the Complex Numbers in Quantum Cosmology**

The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in cosmology when the notion of positive frequency ceases to be well defined. One also has to face this problem in quantum cosmology. I use this to argue that this suggests that at a fundamental level quantum mechanics may be really real with not one but a multitude of complex structures. I relate these ideas to other suggestions that in quantum gravity time evolution may not be unitary, possibly implemented by a super-scattering matrix, and the status of CPT.

##### David Albert, PhD

Columbia University

e-mail | web site | publications

**Physics and Chance**

The point at which chances enter into the fundamental physical laws of the world is discussed in the context of several different strategies for solving the quantum-mechanical measurement problem, and it is pointed out that one of those strategies may provide a new and unprecedentedly simple foundation for statistical mechanics, and that it may enhance our understanding of the origins of the direction of time.

##### Laura Mersini-Houghton, PhD

University of North Carolina-Chapel Hill

e-mail | web site | publications

**Why Did the Universe Start in Such an Extraordinarily Ordered State?**

The problem of the selection of the initial conditions and its conditioning by the arrow of time remains one of the most fundamental mysteries in our understanding of nature. I will describe a proposal where the selection is determined by the competing dynamics of matter and gravitational degrees of freedom on the ensemble of the initial 3-geometries. The backreaction of matter modes that induces decoherence on the 3-geometries also cleanses out the phase space of initial conditions from the low energy patches (terminal universes) since they can't survive the gravitational instabilities, thereby superselecting only high energy/low entropy patches (survivor universes) on the multiverse. Here I advocate the view that any theory of quantum gravity must contain a multiverse or, equivalently, a phase space landscape, in order for questions such as the selection of the initial conditions of the universe to be meaningfully addressed. By unitarity, traces of the nonlocal entanglement of our initial patch with others survive today and may be imprinted on CMB and LSS. These imprints provide a window to the quantum gravity era, and specifically for testing this proposal. It is intriguing that one of the predictions made by this proposal in 2006 for the existence of a void at z<1 and size ~200Mpc was recently directly observed by the Minnesota group (2007) at those parameters, as a cold spot in the sky.

##### Andreas Albrecht, PhD

University of California, Davis

e-mail | web site | publications

The Clock Ambiguity and the Emergence of Physical Laws

At least since the times of Boltzmann people have wondered about the relationship between the arrow of time and the state of the universe. This question gets even more interesting when one combines these ideas with the theory of cosmic inflation. I will discuss number of interesting topics in this area, including the relationship between cosmic inflation and the “Boltzmann’s Brain” problem.

##### Max Tegmark, PhD

Massachusetts Institute of Technology

e-mail | web site | publications

**The Origin of Time and Complexity: Why Was the Entropy So Low, and Why Wasn't It Even Lower?**

A key discussion topic at this meeting is why our observable universe traces back to an unusually simple and seemingly unlikely state, and how this may provide a key clue about fundamental physics. After speculating about what this clue may be telling us, I emphasize and analyze a second possible clue that has received less attention: that the complexity of this early state was still vastly larger than it could have been, and vastly larger than the complexity required to describe many candidate "theories of everything" that purport to provide a complete description of physical reality. Intriguingly, both of these clues can independently be argued to indicate the existence of parallel universes.

##### Lee Smolin, PhD

Perimeter Institute

e-mail | web site | publications

**Time as a Fundamental, Non-emergent, Aspect of Reality**

According to a widely held belief, time is not fundamental in quantum cosmology but must emerge only at low energies. I argue that the arguments from quantum cosmology to the elimination of time are likely incorrect and propose instead that time is fundamental and non-emergent. This issue is relevant for the question of how to get falsifiable theories from a landscape of theories, as a non-emergent, real, time makes possible mechanisms of selection in which the statistical distribution of parameters can be evolving in time and far from equilibrium as in the thesis of cosmological natural selection. I argue that this is necessary as approaches to the landscape in which there is a static, timeless statistical or quantum state on the landscape are unlikely to yield falsifiable predictions. This talk is based partly of work in progress with Roberto Unger.

##### Tom Banks, PhD

Rutgers University

University of California, Santa Cruz

e-mail | web site | publications

**Holographic Cosmology and the Arrow of Time**

I briefly outline the holographic approach to space-time and its connection with supersymmetry. The holographic cosmology based on this approach shows that generic initial conditions for the universe lead to a dense black hole fluid in which all causally connected degrees of freedom are, at all times, in complete thermal equilibrium. This model has a built-in arrow of time, but no thermodynamic arrow of time. I argue that the thermodynamic arrow of time, and the necessity for a very low entropy initial condition for the universe, MAY be derivable from the requirement that the initial conditions of our universe are the generic ones which escape collapse into the dense black hole fluid phase.

##### Gia Dvali, PhD

New York University

e-mail | web site | publications

**Black Hole Constraints on the Particle Species**

We explain how black hole physics imposes a stringent bound on the masses and the number of particle species. This bound sheds a new light on some fundamental problems, such as the inexplicable weakness of gravity, and the origin of dark matter in the Universe.

##### Leonard Parker, PhD

University of Wisconsin, Milwaukee

e-mail | web site | publications

**Time's Arrow and the Strength of Inflation**

One of the features marking the beginning of our universe is a very brief period of time during which the scale of the universe underwent a huge exponential expansion. This cosmological inflation was likely caused by a scalar field referred to as the inflaton field. Entropy was pumped into our universe in part by the amplification of quantized perturbations of the inflaton field, which later became ingrained in the large-scale structure of our universe and in small anisotropies of the cosmic microwave background (CMB). Inflation successfully predicts the spectrum of these observed CMB anisotropies. To better understand the origin of time's arrow, we need to know the strength of the fundamental mechanism governing the inflaton field as its entropy increases. Therefore, it is important to relate as precisely as possible the well-observed amplitude of CMB anisotropies to the strength of the initial inflationary mechanism. Here we discuss a quantum effect that could be important in determining how the forces that give rise to inflation are related to the amplitude of perturbations of the inflaton field.

##### Jorge Pullin, PhD

Louisiana State University

e-mail | web site | publications

**Quantum Mechanics with Real Clocks**

When one uses a realistic time variable in quantum mechanics, the description loses unitarity. We discuss the implications of this for the black hole information puzzle, ultimate quantum computation, and the measurement problem in quantum mechanics.

##### Robert M. Wald, PhD

University of Chicago

e-mail | web site | publications

**The Arrow of Time and the Initial Conditions of the Universe**

The existence of a thermodynamic arrow of time in the present universe implies that the initial state of the observable portion of our universe at (or near) the Big Bang must have been very "special." We argue that it is not plausible that these special initial conditions have a dynamical origin.

##### Eva Silverstein, PhD

Stanford University

e-mail | web site | publications

**Time Evolution and Dimension in String Theory**

The density of states of perturbative string theory—in particular the rate of growth of the Hagedorn density of states—decreases with time in generic expanding spacetime solutions. In these backgrounds, ordinary late-time cosmology is preceded by a phase with additional degrees of freedom in a precise sense that is dictated by the consistency of the theory. In the simplest cases these new degrees of freedom build up new spatial dimensions in a novel way. Other, special backgrounds begin in a phase with essentially no degrees of freedom, and give a perturbative string mechanism for an old idea from Euclidean quantum gravity. After an overview of these developments, we will explore their implications for the arrow of time in cosmology.

##### Gary Horowitz, PhD

University of California, Santa Barbara

e-mail | web site | publications

**String Theory Insights into the Arrow of Time**

In string theory, there is strong evidence that time is an emergent phenomena. I will briefly review the arguments for this, and suggest that the origin of the arrow of time is intimately connected to the origin of time itself. A model based on AdS/CFT will be described which naturally leads to an arrow of time.

##### Paul Davies, PhD

Arizona State University

e-mail | web site | publications

**Hidden Assumptions and Unaddressed Problems of Time Asymmetry**

Attempted solutions to the arrow of time problem have the air of pushing the bump in the carpet around. The problem is so deep-rooted, and has persisted in physics in its present form for so long (at least 150 years), that it may be time to re-examine the fundamental assumptions that underpin it. Among these assumptions is Newtonian dualism—that the laws of physics are independent of the states of the world. The concept of physical laws as infinitely precise, immutable, transcendent Platonic relationships, decoupled from physical states, has been challenged in recent years, most notably by Wheeler's "it from bit" dictum. I will describe some work on finite-resource cosmological models and discuss how it demands a new paradigm for approaching the arrow of time problem. I will also mention some issues often shrugged aside in discussions of time asymmetry, such as a proper definition of gravitational entropy, T-violation in particle physics and the cognitive problem of time's passage.

##### Katherine Freese, PhD

University of Michigan

e-mail | web site | publications

**Phantom Bounce**

An oscillating model for the universe is proposed, in which the universe cycles through a series of expansions and contractions. In the contracting phase, the arrow of time moves in the direction of an ever shrinking universe, reversing the standard history. In our model, "phantom" energy (with pressure less than the negative of the energy density) grows rapidly and dominates the late-time expanding phase. The universe's energy density is so large that the effects of quantum gravity are important at both the beginning and the end of each expansion (or contraction). The bounce can be caused by high energy modifications to the Friedmann equation, which make the cosmology nonsingular. The classic black hole overproduction of oscillating universes is resolved due to their destruction by the phantom energy.

##### Chris Williams

Chris Williams is Executive Web Editor at the New York Academy of Sciences.