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The Arrow of Time THE ARROW OF TIME Why does time never go backw�rd? The answer apparently lies not in the la,vs of nature, which hardly distinguish between past and future, but in the conditions prevailing in the early universe by David Layzer t seems easy to distinguish the past have sprung from an exceedingly dense, scopic view of the world as a system de­ I from the future: memory provides us undifferentiated state in the finite past. generating toward complete disorder nor with a record of the past, but we All these processes have a quality in the microscopic view of the world as a have no certain knowledge of the future. common: they generate order, or infor­ changing but nonevolving system of in­ When events are interpreted according mation; they transform a simpler state teracting particles and fields is required to the most fundamental laws of physics, into a more complex one. In the phrase by fundamental phYSical laws. I submit however, the distinction between past of Sir Arthur Eddington, they indicate that both views derive instead from aux­ and future all but disappears. Intuitively which way "time's arrow" is pointing; iliary assumptions about the nature and we perceive the world as being extended they define what I shall call the "histori­ origin of the universe. I propose to re­ in space but "unfolding" in time; at the cal" arrow of time. place those assumptions with others that atomic scale the world is a four-dimen­ Paradoxically, the direction of time I believe are simpler and equally con­ sional continuum extended in both space can also be defined by a class of dia­ sistent with observation. The resulting and time. We assign special significance metrically opposite processes: those that model of the universe, although differ­ to a particular moment, the present, destroy information and generate disor­ ent from the one accepted by most physi­ which we view as the crest of a wave der. If I drop a lump of sugar into a cup cists, resolves the apparent contradiction continuously transforming potentiality of hot tea and stir, the spatial concentra­ between the historical and the thermo­ into actuality and leaving in its wake the tion of the sugar molecules, the orga­ dynamic arrows of time, and it reconciles dead past. Microscopic physics gives no nized motion of the tea and the differ­ both with the almost time-symmetric special status to any moment, and it dis­ ence in temperature between the tea character of physical laws at the micro­ tinguishes only weakly between the di­ and its surroundings represent macro­ scopic level. The theory implies that the rection of the past and that of the future. scopic information, or order. As the universe is unfolding in time but not un­ Our intuitive perception of the world sugar dissolves and the tea comes to rest raveling; on the contrary, it is becoming as unfolding in time cannot be dismissed and begins to cool, that information constantly more complex and richer in as being merely subjective. It has objec­ gradually disappears. The irreversible information. tive counterparts in a variety of proc­ processes that destroy macroscopic infor­ esses, including biological, geological mation (in this example molecular diffu­ Irreversibility and astronomical ones. There is evi­ sion, viscosity and heat conduction) are dence for it in the physiological proc­ manifestations of the second law of The historical and the thermodynamic esses underlying memory, in the growth, thermodynamics. This law states that all arrows of time both derive from proc­ development and differentiation of liv­ natural processes generate entropy, a esses that always have the same direc­ ing organisms, and in organiC evolution, measure of disorder. The irreversible tion; they are defined by events that can­ where random variation and natural se­ destruction of macroscopic order defines not be undone. What makes these proc­ lection have generated an immense and what I shall therefore call the "thermo­ esses irreversible? All phenomena can constantly increaSing variety of ever dynamic" arrow of time. ultimately be described as .the interac­ more highly organized living forms. The Neither the historical nor the thermo­ tions of elementary particles; if the laws earth's crust records the vicissitudes of dynamic arrow of time can be observed that govern those interactions do not 4.5 billion years of evolutionary change, at the microscopic level. The motion of distinguish between the past and the and the cratered surfaces of the moon, a single sugar or tea molecule generates future, what is the source of the irre­ Mars and Mercury preserve a chrono­ neither information nor entropy. "Order" versibility we observe in the macroscopic logical record of similar duration. Nor­ is a macroscopic concept, a property of world? mal stars, red giants, supernovas and systems made up of many particles; it One possibility is that the underlying white dwarfs represent stages in the evo­ has no meaning when it is applied to in­ microscopic laws are not in fact perfect­ lutionary life cycle of a single star. Final­ dividual atoms or molecules. In the phys­ ly time-symmetric. Evidence that a tem­ ly, the recession of distant galaxies sug­ ics of elementary particles the world poral asymmetry exists at the level of gests that the entire universe is a product changes but does not evolve. subatomic particles can be found in the of an evolutionary process: it seems to I shall argue that neither the macro- decay of the neutral K meson. One of 56 © 1975 SCIENTIFIC AMERICAN, INC .. .. ' ', . ' . .: : 0 " ••" .: ' ' ... ' : : : . .. :', ', : . : . ... " . ... ' '. : : :-: ' ,' " . : .. ., ,,' ... '. ' .. .. , . , . : . , . ' . .' •• . .' . : , : . ": ' ',! :..' : ',: , . ' '. , : . : .. : :. ,' . ' . ' . .' . : : ., , " : . ' ', . ' . .. .. ' . .. '. : ' ,',: . ::. ' . .. : , . ... , , ... , . ', ' ... , , . : . ' . .': ' . ', . ' ' : . ' '. ' " : .: . ' ' : ' : < :: : "::: ' : ; :" :-:' :- :::' ": ' <'� :: ' ' .' ., .. - . .. ' . ' . ' .. ' - . ' , , ' . ' , , . : . :.: . " : : . , , .: . : ,: . : :: - " . ' : . , , . , . , . ' . : .' : '" ' . " ' . : : . .. ..' . ' . ;\i;;;;\::t; . '.' ' . '.: . " .... " . .�:;\<>· ii?<; •••.••. ' . .. .... ' ...' . ,,' .: . , . • . '0 • . ' . • ' . ,'. ' . .. '.'. '" . ' . " ' . ... '.' ... THOUGHT EXPERIMENT concerning the diffusion of perfume cules spontaneously reassemble and condense in the bottle. In the reveals an apparent paradox: the process as a whole always pro· bottom drawings the same experiment is depicted in microscopic ceeds in the same direction, but it is defined by microscopic events detail. Individual molecules escape the surface and follow com· each of which is freely reversible. The bottle of perfume is opened plicated zigzag trajectories that take them to all parts of the room. in a hypothetical sealed room that cannot communicate with the This sequence of events could well proceed in reverse order, since outside world. The top series of drawings, when read from left to if every molecule reversed its direction, they would all retrace their right, shows molecules beginning to escape the surface of the liq. paths and return to the bottle. A molecule following a reversed tra· uid and gradually filling the room, until eventually all the perfume jectory would obey all the laws of physics, and indeed it would be has evaporated. When the drawings are read in the opposite direc· impossible to determine by examining the path of a single mole­ tion, they represent a process never 'seen in nature: all the mole· cule whether it was part of a forward experiment or a reversed one . 57 © 1975 SCIENTIFIC AMERICAN, INC several possible decay modes of that par­ ber, 1969]. The apparent violation, how­ that define the historical and the thermo­ ticle seems to violate some symmetry of ever, is quite weak: it is observed less dynamic arrows. nature, and the usual interpretation of than 1 percent of the time. Moreover, K If the root of irreversibility is not to be the event is that the violated symmetry mesons are found only in experiments in found in the laws that govern microscop­ is time-reversal symmetry [see "Experi­ high-energy physics; they are not con­ ic events, it must derive from constraints ments in Time Reversal," by Oliver E. stituents of ordinary matter, and they on how those events take place. Laws Overseth; SCIENTIFIC AMERICAN, Octo- play no role in the macroscopic processes and constraints are complementary as- a b ONE·DIMENSIONAL THREE-DIMENSIONAL REAL SPACE REAL SPACE y 1 I .. .. x , TWO·DIMENSIONAL SIX-DIMENSIONAL / / PHASE SPACE PHASE SPACE � u o ...J W > .. v .. POSITION CONCEPT OF PHASE SPACE is employed to represent the dynamical bers for the specification of its state, since both position and state of a system of particles. Any particle can be described by a vector velocity have components on three axes. The corresponding (colored arrows), which defines its position and velocity. For a particle phase space must therefore have six dimensions. Since it is in a one·dimensional universe (a) two numbers suffice to specify these not possible to construct a real space with more than three quantities, and the state of the particle can be represented in a phase dimensions, the phase space is represented here by a three· space having two dimensions. Every possible state of the particle cor· dimensional "slice" of the six·dimensional space. In a system responds to the location of some point in the phase space. A particle made up of many particles six numbers are required to speci. with freedom
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