Citation for this page in APA citation style.           Close


Mortimer Adler
Rogers Albritton
Alexander of Aphrodisias
Samuel Alexander
William Alston
Louise Antony
Thomas Aquinas
David Armstrong
Harald Atmanspacher
Robert Audi
Alexander Bain
Mark Balaguer
Jeffrey Barrett
William Belsham
Henri Bergson
George Berkeley
Isaiah Berlin
Richard J. Bernstein
Bernard Berofsky
Robert Bishop
Max Black
Susanne Bobzien
Emil du Bois-Reymond
Hilary Bok
Laurence BonJour
George Boole
Émile Boutroux
Michael Burke
Joseph Keim Campbell
Rudolf Carnap
Ernst Cassirer
David Chalmers
Roderick Chisholm
Randolph Clarke
Samuel Clarke
Anthony Collins
Antonella Corradini
Diodorus Cronus
Jonathan Dancy
Donald Davidson
Mario De Caro
Daniel Dennett
Jacques Derrida
René Descartes
Richard Double
Fred Dretske
John Dupré
John Earman
Laura Waddell Ekstrom
Herbert Feigl
John Martin Fischer
Owen Flanagan
Luciano Floridi
Philippa Foot
Alfred Fouilleé
Harry Frankfurt
Richard L. Franklin
Michael Frede
Gottlob Frege
Peter Geach
Edmund Gettier
Carl Ginet
Alvin Goldman
Nicholas St. John Green
H.Paul Grice
Ian Hacking
Ishtiyaque Haji
Stuart Hampshire
Sam Harris
William Hasker
Georg W.F. Hegel
Martin Heidegger
Thomas Hobbes
David Hodgson
Shadsworth Hodgson
Baron d'Holbach
Ted Honderich
Pamela Huby
David Hume
Ferenc Huoranszki
William James
Lord Kames
Robert Kane
Immanuel Kant
Tomis Kapitan
Jaegwon Kim
William King
Hilary Kornblith
Christine Korsgaard
Saul Kripke
Andrea Lavazza
Keith Lehrer
Gottfried Leibniz
Michael Levin
George Henry Lewes
David Lewis
Peter Lipton
C. Lloyd Morgan
John Locke
Michael Lockwood
E. Jonathan Lowe
John R. Lucas
Alasdair MacIntyre
Ruth Barcan Marcus
James Martineau
Storrs McCall
Hugh McCann
Colin McGinn
Michael McKenna
Brian McLaughlin
John McTaggart
Paul E. Meehl
Uwe Meixner
Alfred Mele
Trenton Merricks
John Stuart Mill
Dickinson Miller
Thomas Nagel
Otto Neurath
Friedrich Nietzsche
John Norton
Robert Nozick
William of Ockham
Timothy O'Connor
David F. Pears
Charles Sanders Peirce
Derk Pereboom
Steven Pinker
Karl Popper
Huw Price
Hilary Putnam
Willard van Orman Quine
Frank Ramsey
Ayn Rand
Michael Rea
Thomas Reid
Charles Renouvier
Nicholas Rescher
Richard Rorty
Josiah Royce
Bertrand Russell
Paul Russell
Gilbert Ryle
Jean-Paul Sartre
Kenneth Sayre
Moritz Schlick
Arthur Schopenhauer
John Searle
Wilfrid Sellars
Alan Sidelle
Ted Sider
Henry Sidgwick
Walter Sinnott-Armstrong
Saul Smilansky
Michael Smith
Baruch Spinoza
L. Susan Stebbing
Isabelle Stengers
George F. Stout
Galen Strawson
Peter Strawson
Eleonore Stump
Francisco Suárez
Richard Taylor
Kevin Timpe
Mark Twain
Peter Unger
Peter van Inwagen
Manuel Vargas
John Venn
Kadri Vihvelin
G.H. von Wright
David Foster Wallace
R. Jay Wallace
Ted Warfield
Roy Weatherford
William Whewell
Alfred North Whitehead
David Widerker
David Wiggins
Bernard Williams
Timothy Williamson
Ludwig Wittgenstein
Susan Wolf


Michael Arbib
Walter Baade
Bernard Baars
Gregory Bateson
John S. Bell
Charles Bennett
Ludwig von Bertalanffy
Susan Blackmore
Margaret Boden
David Bohm
Niels Bohr
Ludwig Boltzmann
Emile Borel
Max Born
Satyendra Nath Bose
Walther Bothe
Hans Briegel
Leon Brillouin
Stephen Brush
Henry Thomas Buckle
S. H. Burbury
Donald Campbell
Anthony Cashmore
Eric Chaisson
Jean-Pierre Changeux
Arthur Holly Compton
John Conway
John Cramer
E. P. Culverwell
Charles Darwin
Terrence Deacon
Lüder Deecke
Louis de Broglie
Max Delbrück
Abraham de Moivre
Paul Dirac
Hans Driesch
John Eccles
Arthur Stanley Eddington
Paul Ehrenfest
Albert Einstein
Hugh Everett, III
Franz Exner
Richard Feynman
R. A. Fisher
Joseph Fourier
Philipp Frank
Lila Gatlin
Michael Gazzaniga
GianCarlo Ghirardi
J. Willard Gibbs
Nicolas Gisin
Paul Glimcher
Thomas Gold
Brian Goodwin
Joshua Greene
Jacques Hadamard
Patrick Haggard
Stuart Hameroff
Augustin Hamon
Sam Harris
Hyman Hartman
John-Dylan Haynes
Donald Hebb
Martin Heisenberg
Werner Heisenberg
John Herschel
Art Hobson
Jesper Hoffmeyer
E. T. Jaynes
William Stanley Jevons
Roman Jakobson
Pascual Jordan
Ruth E. Kastner
Stuart Kauffman
Martin J. Klein
Simon Kochen
Hans Kornhuber
Stephen Kosslyn
Ladislav Kovàč
Rolf Landauer
Alfred Landé
Pierre-Simon Laplace
David Layzer
Benjamin Libet
Seth Lloyd
Hendrik Lorentz
Josef Loschmidt
Ernst Mach
Donald MacKay
Henry Margenau
James Clerk Maxwell
Ernst Mayr
John McCarthy
Ulrich Mohrhoff
Jacques Monod
Emmy Noether
Abraham Pais
Howard Pattee
Wolfgang Pauli
Massimo Pauri
Roger Penrose
Steven Pinker
Colin Pittendrigh
Max Planck
Susan Pockett
Henri Poincaré
Daniel Pollen
Ilya Prigogine
Hans Primas
Adolphe Quételet
Juan Roederer
Jerome Rothstein
David Ruelle
Erwin Schrödinger
Aaron Schurger
Claude Shannon
David Shiang
Herbert Simon
Dean Keith Simonton
B. F. Skinner
Roger Sperry
John Stachel
Henry Stapp
Tom Stonier
Antoine Suarez
Leo Szilard
Max Tegmark
William Thomson (Kelvin)
Peter Tse
Vlatko Vedral
Heinz von Foerster
John von Neumann
John B. Watson
Daniel Wegner
Steven Weinberg
Paul A. Weiss
John Wheeler
Wilhelm Wien
Norbert Wiener
Eugene Wigner
E. O. Wilson
H. Dieter Zeh
Ernst Zermelo
Wojciech Zurek
Fritz Zwicky


Free Will
Mental Causation
James Symposium
The Arrow of Time
The laws of nature, except the second law of thermodynamics, are symmetric in time. Reversing the time in the dynamical equations of motion simply describes everything going backwards. The second law is different. Entropy must never decrease in time, except statistically and briefly.

Many natural processes are apparently irreversible. Irreversibility is intimately connected to the direction of time. Identifying the physical reasons for the observed irreversibility, the origin of irreversibility, would contribute greatly to understanding the apparent asymmetry of nature in time, despite nature's apparently perfect symmetry in space.

In 1927, Arthur Stanley Eddington coined the term "Arrow of Time" in his book The Nature of the Physical World. He connected "Time's Arrow" to the one-way direction of increasing entropy required by the second law of thermodynamics. This is now known as the "thermodynamic arrow."

In his later work, Eddington identified a "cosmological arrow," the direction in which the universe is expanding, as shown by Edwin Hubble about the time Eddington first defined the thermodynamic arrow.

There are now at least five other proposed arrows of time (discussed below). We can ask whether one arrow is a "master arrow" that all the others are following, or perhaps time itself is just a given property of nature that is otherwise irreducible to something more basic, as is space.

Given the four-dimensional space-time picture of special relativity, and given that the laws of nature are symmetric in space, we may expect the laws to be invariant under a change in time direction. The laws do not depend on position in space or direction, they are invariant under translations and rotations, space is assumed uniform and isotropic. But time is not just another spatial dimension. It enters into calculations of event separations as an imaginary term (multiplied by the square root of minus 1). Nevertheless, all the dynamical laws of motion are symmetric under time reversal.

So the basic problem is - how can macroscopic irreversibility result from microscopic processes that are fundamentally reversible?

Long before Eddington, scientists asked deep questions about the direction of time. Perhaps the first to explore the connection with physics was Ludwig Boltzmann, who with James Clerk Maxwell investigated the statistical motions of the atoms and molecules of gases.

If the laws of nature are time symmetric, perhaps the "arrow of time" is to be found in the "initial" conditions, although this may be a circular concept, since "initial,"current," and "final" states are all defined with respect to time. Since the dynamical laws are time reversible, scientists as early as Isaac Newton understood that one could calculate all the motions of a system by assuming "final conditions" and working backwards in time.

Nevertheless, most physicists have assumed the universe must have begun in a highly ordered (low entropy) state and it has been "running down" (entropy or disorder increasing) ever since. In the nineteenth century, this was called the "heat death" of the universe. This view has the unfortunate implication that all the information in the current universe was present at the beginning, which is friendly to some theological ideas like pre-destination, but distinctly unfriendly to ideas of human free will.

Boltzmann assumed that the universe was infinitely old and that our current state is the consequence of a massive statistical fluctuation away from equilibrium and maximum entropy, a condition to which we must ultimately return.

Would time itself be reversed if we could make the entropy decrease? That is unlikely, since entropy decrease anywhere (creating negative entropy or negentropy, a term coined by Leon Brillouin) must be accompanied by an increase elsewhere, to satisfy the second law. Otherwise we could use the local reduction in the entropy to build a perpetual motion machine.

Put another way, if we could reverse the time, would entropy decrease? What can time reversal really mean? A thought experiment suggests not. Consider a closed perfume bottle inside a large empty container. Remove the bottle top and what would happen assuming that time is flowing backwards? It seems likely that the perfume molecules would leave the bottle whatever time is doing.

For Aristotle, time was a measure of motion and change and for practical purposes, many scientists have thought that time reversal is approximated by the reversal of all the velocities or momenta of material particles at an instant, starting from their current positions.

If we could reverse the motions of every material body (a practical impossibility, and perhaps a violation of Heisenberg's uncertainty principle), would that make the entropy decrease? Ludwig Boltzmann agreed that it might, but only for a while. His intuition was that a system could not return to a highly ordered original state, such as every molecule back in the perfume bottle.

J. Willard Gibbs thought otherwise, if the detailed path information in all the macroscopic motions is still available as microscopic information (if information is a conserved quantity), then reversal of all the motions should be exactly like a movie played backwards.

The fundamental question of information philosophy is cosmological and ultimately metaphysical. What is the process that creates information structures in the universe?

Given the second law of thermodynamics, which says that any system will over time approach a thermodynamic equilibrium of maximum disorder or entropy, in which all information is lost, and given the best current model for the origin of the universe, which says everything began in a state of equilibrium some 13.75 billion years ago, how can it be that living beings are creating and communicating new information every day? Why are we not still in that state of thermal equilibrium?
It is perhaps easier for us to see the increasing complexity and order of information structures on the earth than it is to notice the increase in chaos that comes with increasing entropy, since the entropy is radiated away from the earth into the night sky, then away to the cosmic microwave background sink of deep space.

David Layzer is a Harvard cosmologist who in the early 1970's made it clear that in an expanding universe the entropy would increase, as required by the second law of thermodynamics, but that the maximum possible entropy of the universe might increase faster than the actual entropy increase. This would leave room for an increase of order or information at the same time the entropy is increasing!

Layzer pointed out that if the equilibration rate of the matter (the speed with which matter redistributes itself randomly among all the possible states) was slower than the rate of expansion, then the "negative entropy" or "order" (defined as the difference between the maximum possible entropy and the actual entropy) would also increase. Claude Shannon identified this negative entropy with information, though visible structural information in the universe may be less than this "potential" for information.

Layzer called the direction of information increase the "historical arrow."

In a 1975 article for Scientific American called The Arrow of Time, Layzer wrote:

the complexity of the astronomical universe seems puzzling.
This is the fundamental question of information philosophy
Isolated systems inevitably evolve toward the featureless state of thermodynamic equilibrium. Since the universe is in some sense an isolated system, why has it not settled into equilibrium? One answer, favored by many cosmologists, is that the cosmological trend is in fact toward equilibrium but that too little time has elapsed for the process to have reached completion... I shall argue that this view is fundamentally incorrect. The universe is not running down, and it need not have started with a marked degree of disequilibrium; the initial state may indeed have been wholly lacking in macroscopic as well as microscopic information.

Suppose that at some early moment local thermodynamic equilibrium prevailed in the universe. The entropy of any region would then be as large as possible for the prevailing values of the mean temperature and density. As the universe expanded from that hypothetical state the local values of the mean density and temperature would change, and so would the entropy of the region. For the entropy to remain at its maximum value (and thus for equilibrium to be maintained) the distribution of energies allotted to matter and to radiation must change, and so must the concentrations of the various kinds of particles. The physical processes that mediate these changes proceed at finite rates; if these "equilibration" rates are all much greater than the rate of cosmic expansion, approximate local thermodynamic equilibrium will be maintained; if they are not, the expansion will give rise to significant local departures from equilibrium.

This is the Layzer's seminal theory of the growth of order in the universe
These departures represent macroscopic information; the quantity of macroscopic information generated by the expansion is the difference between the actual value of the entropy and the theoretical maximum entropy at the mean temperature and density.

In his 1989 book The Emperor's New Mind, Roger Penrose speculated on the connection between information, entropy, and the arrow of time.

Recall that the primordial fireball was a thermal state — a hot gas in expanding thermal equilibrium. Recall, also, that the term 'thermal equilibrium' refers to a state of maximum entropy. (This was how we referred to the maximum entropy state of a gas in a box.) However, the second law demands that in its initial state, the entropy of our universe was at some sort of minimum, not a maximum!

What has gone wrong? One 'standard' answer would run roughly as follows:

True, the fireball was effectively in thermal equilibrium at the beginning, but the universe at that time was very tiny. The fireball represented the state of maximum entropy that could be permitted for a universe of that tiny size, but the entropy so permitted would have been minute by comparison with that which is allowed for a universe of the size that we find it to be today. As the universe expanded, the permitted maximum entropy increased with the universe's size, but the actual entropy in the universe lagged well behind this permitted maximum. The second law arises because the actual entropy is always striving to catch up with this permitted maximum.
Penrose's "standard" answer is a clear reference to the pioneering work of Harvard cosmologist David Layzer, especially his 1975 Scientific American article "The Arrow of Time." Layzer explained the the growth of order in the universe as the maximum possible entropy of the expanding universe increasing faster than the actual entropy, because the equilibration rates for matter and radiation are slower than the expansion rate.
Other Arrows of Time
The Radiation Arrow
Whether they be electromagnetic waves or waves in water, we only observe wavelike disturbances that propagate outwards in space away from the disturbance. These waves are described by what is called the retarded potential. In his 1909 discussion of waves and particles, Albert Einstein described the possibility of incoming spherical waves:
According to our prevailing theory, an oscillating ion generates a spherical wave that propagates outwards. The inverse process does not exist as an elementary process. A converging spherical wave is mathematically possible, to be sure; but to approach its realization requires a vast number of emitting entities. The elementary process of emission is not invertible. In this, I believe, our oscillation theory does not hit the mark. Newton's emission theory of light seems to contain more truth with respect to this point than the oscillation theory since, first of all, the energy given to a light particle is not scattered over infinite space, but remains available for an elementary process of absorption.
In 1945, John Wheeler and his student Richard Feynman attempted to symmetrize Maxwell's equations for electromagnetic fields with an "Absorber Theory of Radiation," that combined retarded (outgoing waves) and advanced potentials (incoming spherical waves) for radiation. They later described the theory as a mistake.

The Cosmological Arrow (expansion of the universe)
We can define a cosmological direction of time as the direction in which the universe is expanding. There are excellent reasons for seeing this as the most fundamental of all arrows, even the one driving some of the others. Without expansion, a static universe would settle into thermal equilibrium and there would be no changes. There would be no entropy increase to show Eddington's thermodynamic arrow. There would be no information increase, as seen in Layzer's historical arrow.

Without the cosmological arrow, all the other arrows could not be realized.

Davies, P.C.W 1977 The Physics of Time Asymmetry, University of California Press.

Gold, T. 1967 The Nature of Time, Cornell University Press.

Reichenbach, H, 1956 The Direction of Time, University of California Press.

Zeh, H.D. 2010 The Physical Basis of the Direction of Time 5th ed., Springer-Verlag Berlin.

Chapter 4.6 - Neuroscience Chapter 5.2 - Consciousness
Part Four - Freedom Part Six - Solutions
Normal | Teacher | Scholar