time symmetry and the cosmological arrow of time:too soon for a definite answer?

8/19/2019 TIME SYMMETRY AND THE COSMOLOGICAL ARROW OF TIME:TOO SOON FOR A DEFINITE ANSWER?

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UNIVERSIT S PHILOSOPHIC 46, pp. 79- 98)junio 2006, Bogotá, Colombia

TIM E SYMM ETRY AND THE COSMO LOGICALARRO W O F TIM E:TOO SO ON FOR A DEFINITE

ANSWER?

EDGARESLAVA*

ABSTRACT

The text addresses a proposed solution to the question for the direction ofthe cosmological arrow of time, interpreting some of its conclusions andexposing some of its drawbacks. Some alternative answers are explored,including an extension of the so-called Gravitational Symmetry Argument.

Key words: Price, Tem poral Sym metry, Inflation, S pace-Time G eometry.

* Licenciado en Física Universidad Pedagógica Nacional; Magíster en Filosofía, PontificiaUniversidad Javeriana, Ph.D. en Filosofía, Southern Illinois University. Miembro de la SociedadColombiana de Filosofía y de la American Philosophical Association. E-mail:[email protected].


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UNIVERSITAS PHILOSOPHICA46, (pp. 79- 98 )junio 2006, B ogotá, C olombia

LA SIM ETRÍA DEL TIEMPO Y LA FLECHACOSM OLÓGICA DEL TIEM PO: ¿MUY PRONTO

UNA RESPUESTA DEFINITIVA?

ED(;AR ESLAVA

RESUMEN

E l texto aborda un a solución propuesta a la pregunta sobre la dirección de laflecha cosmológica del tiempo, interpretando algunas de sus conc lusiones yexponiendo algunos de sus problemas. Se exploran algunas respuestasalternativas, incluyendo una extensión del llamado A rgumento de la simetríagravitacional.

Palabras clave:Price, Simetría temporal, Inflación, Geometría espacio-

temporal.

* L icenciado en Física Universidad Pedagógica N acional; M agíster en F ilosofía, PontificiaUniversidad Javeriana, Ph.D. en Filosofía, Southern Illinois University. Miemb ro de la SociedadColombiana de Filosofía y de la American Philosophical Association. E-mail:[email protected].


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1. 1NTROD UCTION

THERE ARE Ivo SENSESin which the question about the arrow of time isusually formulated. On the onehand, one could be interested in know ing ifthere are differences betw een past, future and present, and how is it thatdiese three "parts" of time permeate and define w hat could be named the"temporal structure of the universe." Does time have an origin? From whereto where does time flow? A t was speed does time flow? W hat can be used

to measure the passage of time? A re past and present, and future all alike?If not, what is the difference? T hose are questions for the direction of timeitself. On the other hand, there is the question of the movement of things intime. The target of this question is the temporal organization exhibited byevents, the organization that allows us to define them as belonging to thepast, or the present, or the future. Did the b ig bang come first than the bigcrunch? A re there more events in the past that in the future? W hy can't wereverse some physical processes? These are the questions about themovement of things in time.

For about two decades, Huw Price has defended that the result of thelong history of responses to the question for the arrow of time, usually statedin tercos of thermodynamics, is that they lead us to the question about theuniverse's ¡nidal low entropy state. Such a question, as opposed to the questionfor die direction of time itself is, according to Price, thereal question worthasking. It is also the reason why any suitable response to the problem of thephysical arrow of time should move to the territory of cosmology, the placeto where it naturally belongs. The fust part of the paper addresses in somedetail Price's solution to the question for the cosmological arrow of time.Price's central claim about the cosmological arrow is current theories answerthe question about the initial low-entropy universe by appealing to what hecalls a T emporal Double S tandard. Price contends current cosmological

models explain the universe's initial state using time-asymmetric principies,making their solutions biased towards temporal asymmetry. Recognizing theorigin of diese time-asymmetric principies and their role in the currentinterpretation of the evidence becomes then a preliminary task to ob tain amore acceptable answer to the low entropy question. In fact, Price fmds asuitable answ er in tercos of a temporal symmetric model of the universe hasalready been advanced, but cosmologists simply have not given it the attention

it deserves. But, beyond the exposition of Price's view, my main goal is toshow w hat I consider to be some of its major drawbacks by exploring some

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current alternatives that seem to undermine Price's answer. As second goal

I'll set the ground for what could be some alternative paths both friends andfoes of Price's general program could follow in order to extend or limitPrice's Gravitational Symmetry Argument. But let's not spoil the end of thestory and let's go to see its beginning.

2.TRE ARENA

OUR CUR REN T vrew of the evolution of the universe is stated in terms of theBig Bang theory. The theory describes the actual universe as originating inan enormous burst of plasma that resulted from the internal tension generatedat the heart of an infinitely dense, pre-universe, singularity. From this explosionthe universe received all that it needed to develop into the actual distributionof stars, galaxies, solar systems, em pty spaces, dark matter and energy flowthat we witness today. The Big Bang theory is very successful in manyaspects. It predicts the current ratio of expansion of the universe, the existence

of a cosmic background of microwave radiation, as well as the abundanceof light chemical elements and the unification of strong, weak andelectromagnetic interactions at certain energy's scale. The experimentalconfirmation of all these results strengthened confidence in the model and itquickly became the standard model of the origin of the universe.

But the model is not problem-free. Among the problems troubling the

Big Bang scenario two are of particular importance. First, there is the "horizonproblem" (W einberg, 197 2; Thom e and W heeler, 197 3), a problem thatoriginates in the inconsistency between the large-scale homogeneity of theuniverse, as evidenced by the uniformity of the cosmic background radiation,and the expected uneven distribution of radiation that should have resultedfrom an original explosion such as the big bang. The problem here is toexplain how a very homogeneous universe resulted from a veryinhomogeneous starting point. The second problem is know n as the "densityfluctuation problem" (Guth, 198 1; Blau and Guth, 1987 ). In this case, theproblem is the difference between the large-scale homogeneity of the universeand its local inhomogeneous structure; while matter and energy seem to beevenly spread throughout the universe, its concentration in local systemssuch as galaxies, clusters and the like is very hard to explain from the bigbang m odel. These problems are complementary in that they both refer todifferent aspects of the universe's mass-energy distribution and they highlight

the same limitation in the model: the global homogeneity and the mass density

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TIME SYMM ETRY AND THE COSM OLOGICAL A RROW OF TIME 3

perturbation have to be assumed as part of the initial conditions rather than

being deduced from the model. According to the Big B ang model, the onlyway in which the universe would exhibit the distribution we observe, uniformin one scale and non-uniform in the other, is to assume that in the universeearly stages the energy distribution was dramatically smooth. From such anoriginal smoothness the actual even energy distribution is a natural result,because the formidable explosion would have expanded the universepreserving its original distribution.

A solution to the problem of the smoothness of the early universe is theso called "inflationary hypothesis." A ccording to this hypothesis (Linde, 1979;1982a, 198 2b; Guth, 1981), very dramatic physical conditions in the earlystages of the universe brought about a period of exponential expansion thatincreased the scale of the universe by a factor of about 105 times its originalscale. The extreme physical conditions of the unborn universe in its inflationaryphase "ironed out" MI the inhomogeneities that otherwise would have existed,resulting in a smooth universe. The period of inflation was followed by anequilibrium state, which ended w ith the actual bang, from w here the storycontinues as in the original, non-inflationary, big bang model.

The inflationary model solves several of the problems of the original bigbang theory. How ever, it still leaves unanswered some questions about theinitial conditions of the early universe. One set of questions belongs to what

L inde calls the problem of the uniqueness of the universe.

The essence of this problem was formulated by E instein in his talk with E.Strauss: "what I am really interested in is whether God could create theworld differently." The answer to this question in the context of theinflationary cosmology appears to be rather unexpected. Namely, thelocal structure of the universe is determined by inflation, which occursat the classicallevel. The universe after inflation becomes locally fíat,

homogeneous and isotropic. However, itsglobalstructure is determinedby quantumeffects. It proves that the large-scale fluctuations of thescalar field...created in the inflationary chaotic scenario lead to an infiniteprocess of creation and self-reproduction of inflationary parts of theuniverse. In this scenario the evolution of the inflationary universe hasno end and may have no beginning... One may say therefore that notonly could God create the universe differently, but in His wisdom Hecreated a universe which has been unceasingly producing different

universes of all types (Linde, 1987: 607).

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B ecause w e do not have a definite physical explanation of the chaotic

inflation scenario on which L inde bases his case for the possibifity for themultiplicity of universes, and because of our lack of understanding of thepossible mechanism responsible for the differences between the global andlocal features of the universe, a solution to the uniqueness problem is stillwanted. More interesting for our purposes, is another set of questionsaddressing the problem of the initial conditions of the universe. Questionslike (Ibid, 606) "W hat is the origin of the universe?" "W as it created in asingular state or has it appeared due to a quantum jump `from nothing'7' or"Which initial conditions in die new-boro universe are most natural?' stillremain open and receive different kinds of answ ers.

Reformulating the problem by asking "w hy did the classical evolutionphase of the universe start off the way it did?" (Hawkin, 1987) , Haw kingansw ers the question for the early conditions of the universe by his "no-boundary solution", a solution that, as one can see from the very formulation

of the problem, is a development of the inflationary hypothesis. According tothe no-boundary solution, the w ay to answer questions about the initial stateof the universe is to restrict the possible accounts to those in which theuniverse's original state "does not refer to any unobserved asymptotic regionand it does not involve any boundary or edge to spacetime at infinity or asingularity where one would appeal to some outside agency to set theboundary condition (Hawkin and Israel, 1987). Such a self-contained

universe would then be determined completely by the lawa of physics, withoutany resource to points where those laws get broken and w ithout any roomfor extemal influence to play a role. The no-boundary solution derives thetime-asymmetric dynamics of our present universe from a sym metric set oflaws by eliminating the possible boundary conditions that would determineasymmetric laws for the evolution of physical systems. A universe w ithoutboundaries makes recourse to asymm etric laws unnecessary by taking forgranted that the same laws are satisfied at every moment in time. Thisappeal to the symmetry of the physical laws seems to make Hawking'sproposal to imply that entropy must be low both during the initial moments ofits "classical phase," i.e., near the big bang, and during the final moments ofthat phase, i.e., during the "future" b ig crunch. In other w ords, it seems thatthe no-boundary m odel cannot offer a plausible answer to the question ofthe universe's entropy asymmetry. A ccording to Haw king, the question issolved because "the no-b oundary conditionimpliesthat the universe would

have started off in a smooth and ordered state with all the inhomogeneous

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perturbations in their ground state of minimum excitation. A s the universe

expanded, the perturbations would have grown and the universe wouldbecome more inhomogeneous and disordered (Hawkin, 1987: 648).

But implying is not the same as explaining and, therefore declares Price:the no-boundary model does not show that all, or almost all, possible universeshave at least one ordered temporal edge. Because it lacks such ademonstration, Hawking's argument becomes a clear example of the temporaldouble standard.

After all, we know that we might equally well view the problem in reverse,as a gravitational collapse towards a big crunch. In statistical terms, thiscollapse may be expected to produce inhomogeneities at the time of anytransition to an inflationary phase. Unless one temporal direction isalready privileged, the statistical reasoning is as good in one direction asthe other. Hence, in the absence of a justification for the double standard-a reason to apply the statistical argument in one direction rather than the

other, the appeal to inflation doesn't seem to do the work required of it(Price, 2004:24).

3 A N ANSWER

FOR PRICE THEN, THEproblem w ith the no-boundary model is that it assumesthe asymmetry between the temporal extremes, rather than explaining it, asit should. But, as a matter of fact, Haw king has suggested an explanation of

such an asym metry can be found in terms of an anthropic interpretation ofthe no-boundary. A ccording to Hawking's anthropic solution, while the lawsof physics define the global symmetry of the universe, they leave open thepossibility that creatures like ourselves can exist in only one of the twopossible phases of the universe, that during w hich a low entropy state isconsidered the past. In Haw king's own w ords,

Because the 'no-boundary' quantum state is CPT invariant, there willalso be histories of the universe that are CPT reverses of that describedaboye [inflationary big bang-like histories]. However, intelligent beingsin diese stories would have the opposite subjective sense of time. Theywould therefore describe the universe in the same way as aboye; it wouldstart in a smooth state, expand and collapse to a very inhomogeneousstate. The question therefore becomes: why do we live in the expandingphase? To answer this, I think one has to appeal to the weak anthropicprincipie. The probab ility is that the universe will not recollapse for a

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very long time. By that time, the stars would have burnt out and thebaryons would have decayed. The conditions would therefore not besuitable for the existence of beings like us. It is only in the expandingphase that intelligent beings can ex ist to ask the question: w hy is entropyincreasing in the same direction of time as that in which the universe isexpanding? (Hawkin, 1987: 649).

Price finds this proposal to be "exceedingly costly in ontological tercos."The anthropic principie divides the universe into two main regions, the region

in which we, intelligent creatures, have evolved, and the "rest of the universe,"where this type of intelligence did not, and could not have, evolved. It is thisdivision that makes the principie insufficient as an answer to the question forthe particular initial conditions of the universe as a whole. A t best, the modelwould be useful to explain things in the little local region we inhabit. But thequestion about the inclusive larger' universe still remains unansw ered. Price'srequest for a "cheaper" ontological model is a plea for a m odel that explainsat once local and global properties of the universe. A nd w ithout recourse tothe anthropic principie, cosmology,faces the challenge of answering thequestion of the universe's origins while being forced to acknow ledge thatnothing in physics tells us that there is a right or w rong orientation of thetemporal coordinates.

Price attempts to solve the issue by introducing what he calls theGravitational Symm etry A rgument. The gravitational symm etry argument

has three-steps: First, we ask w hat the universe might be expected to be likeafter a process of gravitational collapse, which, from a thermodynamicanalysis leads us to consider the early universe as a very inhomogeneoussystem. S econd, w e apply the temporal symmetric principle that tules theevolution of physical systems, i.e., the time-symm etric nature of the laws ofphysics, to the universe. Accordingly, we see that a commitment to the notionof the universe originating with an explosion that rapidly increased theuniverse's size and distributed its matter and energy imposes also the notionof the universe's future as sinking under its own gravity and acceleratingtoward a final crunch. Finally, we acknowledge the fact that there is nothingin physics that tells us that any particular end of this exploding-collapsinguniverse must be considered either its beginning or, its end. In short, Price'sgravitational symmetry argument is nothing but the recognition that there isno physical reason for treating the early and the late stages of the universedifferently. In other words, Price is arguing tha t our current view of the

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universe in tercos of inflation and gravitational coilapse does not

between the big bang and the big crunch situations. What cosmoldo then is to develop a m odel that uses the gravitational symm etas a founda tional p rincipie.

Looking back in history, Price finds that such a cosm ological mthe fines of the gravitational symm etry argum ent was introducedthe early 60's as part of his program of trying to con nect the exthe universe with the second law of thermodynam ics. Accordim odel, i t is the large-scale m otion of the u niverse that accouobserved tem pora l irreversibility of a physical system 's evolutithermodynam ic arrow of tim e being directly determined by the ethe un iverse. Gold p ictures the universe as originating and endingpoints, w ith a closed evolutionary pa ttem of expansion and colw ith en tropy increasing in the expand ing half of the universe'while it decreases in the collapsing h alf. It is precisely the sym mthe origin and end of the universe in Gold's model that attracts Pricei t is becau se of this sym m etry that the m odel w as not accepcom m unity of cosmologists and becam e rapidly overridden by thinflationa ry m odel.' At any rate, the m oral that Price draw s fromthat it is possible to develop a reliable interpretation of the tem poof the universe from an atem poral perspective, one in w hich pasare treated evenh and edly. From this new viewp oint, past and

sym m etric points in the tim e-like dim ension of spacetim e, w iclaim to be used as reference m arks for the physical descriptioGiven this perspective, looking stoward the p ast ' becom es as lw ay of interp reting p hysical behav iors, as look ing low ard thcurrently seen. In the case of interacting systems, this new apprthe tem pora l evolution of the system s' states describable eithefrom a com m on past or as going to a com m on future. This, nee

is precisely the sort of feature that Price w ants for any m odel oatemporal view w ould rest. Within a m odel that considers preseto be un distinguishab le, a future state of a system that bringssystems' past states might be not only unexcep tiona l bu t mightone of the expected results.

1. For a detail account of Gold's model see Gold (1967).For a history of the recept ion of themodel, see Bondi and Gold (1995 ), and Kragh (1996).

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S um marizing then, Price finds Haw king's no-boundary model to be

insufficient to account for the asymm etry between the temporal extremesof the universe it proposes, and its appeal to an anthropic principie impossibleto be used to solve the problem. Trying to do so would incur in having to payan "ontological price," higher than the benefits we could possibly derivefrom it. Price proposes to replace the Haw king's model by a fully symmetricone and sees Gold's picture to offer the expected sym metric treatment ofthe initial and final moments of the universe: the big bang and the big crunch.Only this model, states Price, accounts adequately for the physical evolution

of the universe in terms of the syrrunetry of its temporal extremes. UsingGold's model Price places himself in his desired A temporal A rchimedeanPoint, a point from where the notions of "temporal evolution to the past" and

temporal evolution to the future become nothing more that ways ofspeaking, which lacks any physical content.

4 T H E P R O B L E M S

THE RE A RE RE A SO N S TO find Price' s criticism of Hawking's no-boundarysolution appealing. One could argue that the project of contemporarycosmology rests on the attempt to explain the actual universe by retrospection.By tracing down the past of the universe, its present, as well as its future,are expected to be understood in terms of the possible original scenarios, ofinitial conditions, that would naturally evolve into a configuration like the onewe currently experience. S uch a project is based on the symmetric nature

of the physical law s, according to which the past can be extrapolated fromthe present in the very same w ay that the future can be extrapolated fromthe past. One could even follow Price and warn against the vice of thisproject, the possibility to forget that the symmetry of the physical laws impliesthat past and future should be treated alike, a problem exem plified by the acommon cosmological motto: 'when w e look far into space, we find ourselveslooking far into our past.' But if the past and the future can be both inferredfrom the present, the fact that w e cannot ge t access to the future, at leastnot via observation, should not lead us to the conclusion that the past is inany sense more fundamental than the future. B ecause of this, we seem tohave very good reasons for exploring the origin and structure of the universeby means of models that are fully committed to the symmetric character ofthe physical laws.

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TIME SYMMETRY AND THE CO SMOIAGICAL ARROW OF TIME 9

But not all are good news. Callender (1998) has shown that Price s

interpretation of Haw king's no-boundary m odel is wrong. Althougdenied by the Hawking's model, states Callender, Price understaboundary m odel as one in w hich entropy depends exclusively othe universe, w ith the co rollary that the tem poral asym m etry ethe model has been put in there by hand. Furtherm ore, Callenderto accept that both Price and Haw king m odels go after the samfinal explanation of the universe's low en tropy p ast.

My worry is that Hawking's theory may not haveanything to dowithPrice's dilemma. By ignoring the details of Hawking's project, Price hasn'trealized how alíen it is to his own project. One way to see this is toreconsider Price's corkscrew-factory analogy. This analogy is nota goodone. In three spatial dimensions, there really is a difference betweenright-handed and left-handed corkscrews, i.e. they are enantiomorphs.But as Price has cogently argued, yet seems temporally to have forgotten,from the atemporal standpoint there isno genuine differencebetweenlow-to-high and high-to-low universes. They are the same universedifferently described. But ifall the solutions are symmetric inthe sam eway(say, right handed) then the equation can't be a symmetric one. Pricecannot make sense of what he claims is Hawking's loophole' withoutresolving this puzzle. This requires delving into the details of Hawking'stheory. Once there, the philosopher will find himself in a strange newland, one brimm ing with questions that need answering beforecontemplating time's arrow (Callender, 1998: 142-143).

B ecause ofthese problem s, Ca llender declares Price's concluswell as the general program of investigating quantum cosmology simp lications for the arrow of tim e, prem ature. And these are buof the m ajor prob lem s Callend er points out abo ut Price 's amechanism underlying the low-entropy past hypothesis, his cosmquestion, the other one being the high prob ability that we do nolive in a Gold-like un iverse. In a nutshell, Callender argum ent idate scientists have not found an y of the effects that a univertowards an entropy-increasing final collapse, as Gold's, is expect(Ibid, 145-146). Without such evidence, Price's model seem s tobltowards a wall, with final resulta easily predictable, regardless oabout the p ast, or fu ture, hypotheses. Additionally (Callend er,very project for explaining the past hypothesis seem s to be undPrice's com m itm ent with the indispensability of a clear detennin


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mechanism responsible for the initial universe's low-entropy state. Relating

Price's project to that of the physicists of solving the horizon and densityfluctuation problems, C allender finds that Price holds on to the low -entropypast hypothesis while trying to explain why such a past state is obtained. Butthis seems to be a self-deflating project, for any explanation of the universe'sinitial state in terms a basic mechanism that would have produced it impliesthat the low-entropy past hypothesis cannot be used as a basic explanationany longer.

If we stick to Price's new explanandum, explaining the Past S tate itself,and it is the first state, then any kind of novel causal process that bringsthis state about would seem to require referring to a mechanism outsidespacetime— or adding more spacetime to current modeis than is warrantedby empirical evidence. But that seems to me suspiciously akin to addingsome untestable mechanism merely to satisfy one's apriori judgment ofwhat facts can be brute. Worse, why should I prefer this brute elementover the previous one? (Callender, 2004a: 251).

C allender then sees more than enough reasons to recomm end not tofollow Price's lead and to avoid getting to conclusions too b riskly, beforehaving considered all the alternatives.

Callender's serious criticisms notwithstanding, one could still be interestedin pursuing goals similar to Price's ones and try to find a mechanism that

explains the universe's low -entropy past, or developing a fully temporallysymm etric cosmological model, not necessarily directed over against theno-boundary theory. In such a sense, the lesson we are meant to learn fromthe analysis of Gold's model is that we can use it as a frame for theconstruction of a symmetric representation of the physical evolution of theuniverse in which past and future are treated evenhandedly. In other words,Gold's model fulfills the need for a temporal symm etric reference frame.Such a treatment is the heart of Price's Gravitational Symmetry Argument,for which past and future are symmetric points in the time-like dimension ofspacetime, with the same right to be taken as reference marks for the physicaldescription of events. It is in this sense that we say that the temporal evolutionof a physical system can be described as coming from a common past or asmoving towards a common future. And Gold's model fits the required profilefor a just, temporally speaking, judge of the universe's dynamics. How ever,it is worth asking what exactly the puzzle is that an appeal to Gold's modelhelps solving.

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TIME SYMMETRY AND THE COSMOLOGICAL ARR OW OF TIME 1

Given the w ay Price's conclusion is built up, it seems that the problem

was merely that of finding a cosmological model consistent with the temporalsymm etry of the laws of physics. But it is not easy to see how Gold's modelanswers the question that Price has moved to the spotlight, that for the earlyuniverse's low entropy. A ccording to Gold's, due to the relation betw eenentropy and the global structure of the universe, the initial conditions have tobe considered symm etric, temporal reverse tw ins, of the universe's finalconditions. The B ig Bang and the B ig Crunch are then indistinguishable in

terms of entropic considerations. But nothing in Gold's model seems to sayanything about the low entropy states found at the origin and the end of theuniverse. One can agree with Price in saying that there is no intrinsicasynametry that makes the universe's initial conditions more special that itsfmal ones. O ne can also, even at the cost of neglecting the conclusions ofC allender's devastating attack, agree that even if Price's analysis sinks itstill makes som e damage, or that there are escape routes from C allender's

conclusions and to continue with the original task of finding a time-symmetricframe from which the universe's initial conditions could be explained. This iswhen Gold's universes are supposed to come out to help. However, thelesson to learn from Gold's model is just that the origin and end of the universeare identical, and this still leaves unexplained the question of why thosetemporal distant ends happen to be very low-entropy states. If we ask 'howis the problem of the initial conditions solved? ' and try to find an answer

exclusively in terms of Gold's picture, we w ill not find any answer. Butacknowledging the limas of one's use of Gold's model and declaring that theproblem to be solved is only the one the model actually solves is a significantconcession. This would imply that the question about the initial conditions ofthe universe is not "the question to be solved," making the explanation of thedifference between symmetric and asymmetric models more important thanthe explanation of the universe's initial conditions. This is of course a route

Price cannot take if he is to retain the force of his argument. Therefore,Price's appeal to Gold's model turns out to be a tw o-edged sw ord. It offersa symmetric interpretative frame for cosmology, but it leaves unansweredthe question about the universe's original low-entropy state. If, in response,Price chooses to minimize the importance of answering that question, heundercuts his own criticisms of the asymmetric models he rejects.

T here is yet another problem faced by Price's answ er to the questionabout the cosmological arrow of time, coming from recent cosmologicalmodels intended to offer both a symmetric cosmological picture but which


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also make room for an objective arrow of time. Two of such models areworth mentioning here, those of Castagnino, Lombardi and Lara, and ofButterfield and Isham.

C astagnino, L ombardi and L ara (2003a; 2003b; hereafter, CL L ) addressthe question about the cosmological temporal asymmetry in terms of theproblem of determining if the basic physical asymmetry between past andfuture is conventional or substantial. Their approach to the problem of time-asymmetry shares some of Price's intuitions, in particular the idea that in

order to answ er the question abou t time's arrow it is necessary to "step outof time. Nonetheless, contrary to Price's view from nowhen , instead oftrying to disprove the existence of a physical temporal arrow, the authorsinvestigate the possibility of grounding the physical arrow of time on thedirection of time itself. Recall that Price regards questions ab out the d irectionof time itself as meaningless. By contrast, CLL think that it is perfectlymeaningful to ask whether the temporal arrow refers to a property of timeitself or whether it is just a feature of the way things are ordered in time. B ya series of geometrical arguments over the topological properties of theuniverse, as pictured by general relativity, CLL argue that there is a clearsense in w hich the direction o f time is physically determinab le, and that, infact, a global arrow of time appears as a consequence of two principies:first, the time-reversal invariance of the physical laws, i.e., the temporalsymmetry of the laws and, second, the orientability of spacetime, i.e., theexistence of a non-vanishing time-like vector field on spacetime. The firstprincipie states that the distinction between past and future, between temporaldirections, is just a m atter of convention, w hile the second states that, despiteconventions, there is a definite sense in which we can define a temporaldirection of spacetime. Using these principies CL L find not only that there isa sense in which the direction of time itself can be determined, but also thatthis temporal arrow is more fundamental than the proposed entropic,thermodynamic, arrow. After all, CLL declare, "the geometrical propertiesof the universe are more basic than its thermodynamic properties (CLL,

2003b: 886).

A long similar limes, Butterfield and Isham (1999a; 1999b) have advanceda case for the emergence of time in quantum gravity. L ike C L L , Butterfieldand Isham use a topological approach in their argument, but unlike CLL theyfind that there is no ob jective w ay to determine w hether or not the universehas an overall objective temporal direction. T heir conclusion is not that time-

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directness is a fundam ental feature of our universe, a substantiv

bu t instead that t im e as a con tinu ou s ordering of events iapproximation, valid for sufficiently large scales of time andlength (Bu tterfield and Isham , 1999a), a relativist claim.

Ap art from the technicalities of and d ifferences between altemative m odels, the prob lem they present for Price is that they dthat his dem ise of the question for the existence of an arrow of tiopposed to an arrow of things in tim e, seems to leave una ttendeimportant issues. The conflict is not merely about the consequenctechnical geom etrical or statistical considera tions. Nor is it m ereof counting, or of m aking sense of w hat w e find in the w orld. Tgoes deep er, into considerations of what coun ts as real. Price hathat he is not interested in finding any possible arrow of tim e,finds that p roblem to be of no interest at all. In this sense, Price'continuou s with those of W illiam s, Sm art, M ellor and Grum bpresuppose that what is objective about the direction of tim e itsela m atter of perspective, an anthropocentric notion, and that dierein which a global arrow of tim e itself can be ob jectively definealtemative theories offering an explicit objective accoun t of a globarrow, it seem s that this comm on p resupposition cannot sim ply bEven if these n ew alternatives do not d isprove Price's proposathey m ay b e just w rong, the fact that bo th target the question rejects forces us to see Price's altemative in a new perspective.question that Price refuses to ask may shed light on both the tempoof our universe and why its initial conditions are w hat they are. Iw e can say that diese m odels are m ore general than Price's, beaddress both questions abou t both the arrow of tim e and questiondirection of things in time.

It seems, then, that rather than closing the case Price has actuathe door for reform ulating the question for the ob jectivity of the time itself. By restating the question abou t the objective directiom ay be possible to get a better form ulation, if not a solution, to about the thermodynam ic asym m etry of experience. Such a refm ight help us clarifying the relation betw een the therm odyna mcosm ological arrows of t im e. M ay be then that such is the m aplaying the gam e following Price's rules, because the proposed fusym m etric approach that Price has offered us does no t fulfill its

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casting overwhelmingly strong doubts over the current approaches to

undermine their credibility. It still gives current approaches enough elbowroomto escape from the supposedly deathly arguments advanced from theatemporal perspective.

5 W H E R E D O W E G O F R O M T H E R E

A H R THE PRE V IOUS AN ALYSIS it is clear that we have left Price's view in thedefensive spot. In this final section I will point out some alternative routesthat could be followed for those interested in pushing forward argumentsalong the lines of Price's view, or those trying to correct some of the problem sby restating the questions under a d ifferent light. N eedless to say, this shortsection does not exhaust the alternatives at hand, but simply suggests someof the places were one could be interested in looking for som e help.

One w ay of solving the narrow aiming scope problem is to "broaden the

scope" of one's model. To do so is to extend the both the original questionsand their interpretation con text in order to include some of the alternativespreviously left behind. By such and inclusive m ove, one gets the not sm allgain of having some extra help in the route for solving questions, or, in theworse case scenario, a more complete background against which one'stempting conclusions can be tested. It could be possible, for example, todecide to expand the q uestion's horizon as to include the question about the

existence of an arrow of time itself. In such a case, if there seems to betracks leading towards the determination of such an arrow , it could be possibleto follow that lead in order to explain the arrow of things in timein term softhe arrow of time itself. Or, moving in the opposite direction, it could be thecase that what is needed is a deflated notion of the arrow of time itselfas aconsequence of the answ er to the question of things in time. If it is the casethat the arrow of time is disproved, then the question for the arrow of thingsin time would gain a new light because of, being an objective arrow, alltemporal asymm etries would have to be definedfrom it, the basic one.

T w o examples of this kind of question re-shaping are worth mentioninghere. One could follow from an adequate interpretation of contemporarystring cosmology. According to some authors (Veneziano 1999, 2000;Gasperini and V eneziano, 2003), what string analysis brings to the solution tosome of the crucial problems of the standard Big-Bang model is that they

allow for the inclusion of new tools. Som e of those tools are a proposed new



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quantum of length and a new kind of inflation (the dilation-driven inflation),

that help explaining the dynamics of the universe from the so-called pre Big-Bang scenario. In terms of the previous discussion, string analysis could beinterpreted as a way for determining the mechanism that determined boththe origin and the arrow of time. Besides its possibilities as an explanation ofan arrow of time itself, this kind of analysis could eventually lead to thedetermination of a mechanism that explains the intriguing universe's low-entropy past. A second altemative is modeled in terms of the so-called

quantum or Feynm an clocks (Hitchcock, 1999 ), according to which ratherthan being a param eter in the description of "quan tum system s", time isdefined as a lifetime, the lifetime of unstable quantum systems. A s in thecase of cosmic strings, this kind of analysis could be the answ er the pray ofthose trying to determine a mechanism from w hich the early universe's low-entropy would come from. These would be the favorable interpretation ofthe new , expanded, questions.

However, there is also the no so favorable interpretation of analyses likethese. It could be possible to interpret both the string and the quantum clocksmodels as new problems rising against an atemporal view. In such a case,both models could be said to imply that there is a place from where temporalasymmetries, physical temporal asymmetries arise, mak ing it necessary notjust to expand the question about the things in time but to reformulate it fromthe now naturally asymmetric universe. Of course, our current interpretation

of physical laws as temporally symm etric should also have to be revised,making the few known counter-examples the norm rather than the exception.

Evidently, given the highly speculative character of these models it is stilltoo early to take sides on this dispute, but the thing to be learned from themis that the resource to altemative questions and routes is w orth exploring,even if answ ers are not just around the com er. Besides, the inclusion of

such new models and kinds of analysis could help solving not just the limitedaiming scope problem, but could also be pan of the solution to the weaponinadequacy problem . Gold's universes could becom e cases of a broaderstring theory, or examples of large quantum clocks, or whatever one's favoritemodel indicates they are, mak ing their use justifiable after their requiredcontextualization in a less restricted interpretative frame.

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