PoS(QG-Ph)038 http://pos.sissa.it/ † ∗ [email protected] Speaker. A footnote may follow. This paper contains a critique ofstructures the from standard quantum inflationary fluctuations account of inpurely the philosophical the origin in early of nature, universe. cosmological but This Iinterpretational prefer critique aspects to of can view the be it, theory thought rather,with -which as experiments- to on quite arising the be firm obviously from grounds the lie required by need atdiscussion the to the unique is features put followed basis of by the the of a problem proposal any at hand. toaspects comparison This complement of that the treatment standard to account deal of withinduced the the collapse unsatisfactory problem, of the using quantum Penrose’s states ideas of aboutanalysis matter the was fields. quantum The first formalism gravity introduced developed to in carryconfront (1) out some and this of leads the to details unexpected ofmost predictions the promising and proposal path to with towards novel observations. quantum avenues In gravity phenomenology. to my view, this is, therefore, the ∗ † Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c

From Quantum to Emergent Gravity: TheoryJune and 11-15 Phenomenology 2007 Trieste, Italy Daniel Sudarsky Instituto de Ciencias Nucleares UNAM E-mail: The seeds of cosmic structures asQuantum a Gravity Phenomena door to PoS(QG-Ph)038 Daniel Sudarsky ? If the answer to 1 2 Draft Version – – November 26, 2007 This point is sometimes characterized as the “transition from the quantum regime to the classical regime", but I 1 find this a bitdescription misleading: ought most to be people quantum would always,accuracy but agree by there that are their regimes there classical in are whichthe counterparts certain physical no representing quantities state, the classical can the be corresponding or underlying described expectation dynamics, quantum to the values. a regimes. quantity sufficient This The of depends interest, fundamental of and the course context on in which we might want to use it. The seeds of cosmic structures as a door to Quantum Gravity phenomena 1. The Problem The inflationary theory of the originits of successes structure (2; 3), in has our a universe,geneous very although and unsettling generally isotropic aspect: acclaimed (H.&I.) it early for does state not of accountstate. the What for universe do to the we its transition late, mean from anisotropic by a and that?does homo- in-homogeneous Isn’t in this, precisely, calculating what the the spectrum account we ofto read primordial this in fluctuations? question books and We depends will articles very see stronglyan that on issue the what which answer one is one strongly expects gives correlated ait with physical is one’s theory not. views to about The be what noteworthy able quantumthese point to mechanics issues is, deliver, is are however, and approached that what have despiteimpinge implications what on that it transcend our might the understanding seem purely of atus philosophical one first aspects go of sight, and the back the fundamental to way questionsing the in calculations questions modern of raised: cosmology. the But spectrum does let ofH.&I. the primordial early standard fluctuations, state really of inflationary account the scenario, for universethe to the and above its transition the question late, from depends anisotropic accompany- a on and one’s inhomogeneousa view state categorical of assertion, quantum that theory, why the does answerwould this is be article in led start the to with take negative? such My aboutare point quantum not will mechanics, one in be that seeking that physicists a the wouldat justification views like to hand, that to answer and/or one take, in are are the not not positive, onefor one quantum that that gravity. would would allow justify one its toThis use consider article in will the the be sort situation devoted, of to issuesdescription a raised large of in extent, the the to richness deal search with inview the of perspective issues that the above, but can essence will be ofmore include a achieved quantum profound brief if physics. questions, one We but will takessurprising that, see a insights in that about stricter the not attempting ontological nature only to ofthe will quantum deal early gravity we universe. with and The gain their them, fact the relevance that we totranscend issues right the will such that to understanding can domain be of ask initially and led be enter deemedcome to the to as new realm be a merely of and philosophical, shock observational can to scientificof people inquire, questions. can belonging However, be these to expected questions thethis to are generations author indeed of that some this physicists manuscript of trained may the nottrend. contribute hardest to to ones, the ask changing and that of it the type is above mentioned the unfortunate hope of 2. What is quantum physics? It must be surely pretentious beyondcists belief that to have raise devoted this issue theirquantum in lives physics the to compatible. company These the of efforts prestigious evenopment have physi- more of been the complex concentrated mathematical problem in language the and of the highly making subtleties nontrivial that gravitation devel- arise and in constructing plausible theoret- PoS(QG-Ph)038 Daniel Sudarsky By this, I am referring to the 3 Draft Version – – November 26, 2007 Quantum physics as a complicated theory of statistical physics. The seeds of cosmic structures as a door to Quantum Gravity phenomena ical models applicable to quantum gravity.of Perhaps, that it challenge, is the that enormity havingleft of absorbed as the the relatively task attention much and less of the explored the difficulty These the most are issues related brilliant which to minds I the will in so bepuzzled our called rising. “measurement field, physicists problem have and in quantum philosophers mechanics" ofWe a will physics subject however focus that from has here the on one timewhich particular is of instance a the of subject of inception that the has ofcourse problem: received the notable the much cosmological exceptions theory less setting, to attention (4). the fromHartle assessment the (6), above, physics represented and community. There by others are thinkers whoHaving of like have said R. faced all Penrose, these (5) this, and J. I relatedjust must issues to nevertheless with make try very my to open position and answerpostures clear critical the taken to minds. question in the posed, this reader, ifencountered manuscript. and for on To help no the do him subject: other this understand reason, I thea) will hows and go whys through of someposition the that of holds the that postures quantum thatof mechanics acquires identical I meaning systems. have only In as thisby it view, one is quantum applied must mechanics. to accept Let an thatthat ensemble us a atoms single not atom in get in isolation confused isolationits do by is interactions not not the with described exist. correct distant The atoms, butvacuum point and state simply is specially is distracting known with to whether, argument interact the to with electromagnetic theof the atom, field a quantum extent which, mechanics single is to even applicable atom. in which toanything the its Again, we description about what do the can neglect atom, we weis mean must simply by make whether that, it applying if interactbe the we expected with formalism know to a of that yield measuring correct quantum in device?that results mechanics order as Well, this to to the it is treat be pertains question a the the ablethat subsequent nonsensical to isolated this measurements.? question, say atom One statement as can might is these think notto results really having are accurate: been always for prepared statistical instancethe in in if one its the in nature. ground atom the The state, ground (say,angular point the of state is momentum probability hydrogen) is of eigenstate was zero. measuring is known Furthermore,hamiltonian any the equally the energy predictions probability zero. are other of not In than observing statistical atmust fact, the all, be atom for but 100% something in any deterministic to a and observable the precise! high and If commuting thus description so, it with of there becomes that the blatantly single falsesystem. the atom What notion by is that its quantum true, mechanics usual ofwe can quantum course, not can mechanical is be make that, state, applied with to in certainty single applyingboth are very the by limited, theory the with to nature the aMoreover, extent of single in of the relation system, such with system’s the limitations the dynamics, predictions being issue andquantum determined that concerns by physics, us the would in way this be article, the admittingtheory taking in system from a addressing posture was the questions like concerning initially beginning this, the prepared. about thatwere unique universe we to to accept have which we no that have somehow right access,Note, there even to moreover, if that exists employ we we an such should ensemble bewareone of from universe. universes confusing Furthermore, to statistics if of which a universes weelement and quantum of have statistics state the no within serves ensemble access. only toin be to that described? represent case Perhaps, an with it our ensemble, can universe? how not is be each described at all ? What do we do PoS(QG-Ph)038 Daniel Sudarsky . According to this view, With this I am referring to . Within this view of quantum theory, the state 4 become insurmountable once we leave the laboratory and Draft Version – – November 26, 2007 . We must acknowledge, however, that in situations where one can not point to the 2 Quantum theory gives perfectly well defined and rigorous predictions, which are in general of a statistical nature, 2 Quantum physics as an non-completable description of the world. Quantum physics as a theory of human knowledge once we have identifiedgeneral the the time state at which of theidentifications measurement the occurs. are The system made in the and the standard thus observablenon-rigorous. treatments the of that line the is situation of at reasoning going hand connecting no to such the explicit be formalism measured, to the which predictions must is include best described in as of a quantum system does notsystem. reflect something Such about view, the naturally system, rises butsomething the just that question what pertains we what to know is about the there the system?system to The and be answer the known comes measuring about in devices, the the butmeaning form then, of system the of: what if word correlations is correlation not implies between the some the meaning sortone of of object coincidence these with of correlations?. some certain conditions The other pertaining conditions usual to describes pertaining such to correlation, the there second must object. be However,the if some objects. a meaning quantum Are to state not the these, conditions then, pertainingthe the to object? aspects each If we one that answer of are in described the negative,that by it the can must quantum mean not that mechanical be there state are casted for furtherthe in descriptions positive the of we the quantum are object mechanical again taking state aitself. vector. Perhaps view On we whereby the are the other just state going hand, vector innonsense, says if circles. let something we For us about those answer just the who say in read object that these in if considerationsevolution we of as follow the philosophical this universe view, in we the have absence noin of right sapient to that beings, consider universe, and questions much of about less the the tousing consider conditions a the quantum that emergence, theory. I are would necessary takestates it for even in the further: any what eventual model would evolution of be of quantum the justification gravity, humans, ifc) for while considering we took such view of quantum physics? The seeds of cosmic structures as a door to Quantum Gravity phenomena b) any posture that effectively, iftheory containing not it explicitly, exists or states:“The will theory everphysicists do" that, is . while This not incomplete, openly view and advocating will such be noas posture, considered we will as complete direct all being us know held to how by " use the quantum whilehas many mechanics reminding " ever us been with a observed. stern While voice this thatour no is colleagues violation with that of not quantum by doubt mechanics this, atext they literally book, refer, correct that of statement, essentially course, we rely to mustsevere on remind the interpretational to rules issues the as Copenhagen found that in interpretation,consider applying any which quantum quantum as theory mechanics to we something all likewe the know, universe raises should itself content ourselvespredictions using its tools, andclassical-quantum making, dividing line, in where the we situationobservables can that at not are hand, identify to the non-rigorous bewhich system measured, and the the the measurements entity apparatus, are nor carryingscheme to the out specifying be those how thought measurements to as andpertaining taking make the to the time place, the early at we desired universe in have, predictions.making terms in predictions. That of fact, quantum However, is, theory, according no we in to clearly haveshould the no dealing defined be clear colleagues with content and arguing with specific the for the rules questions suchto for fact agree that practical with the posture, observations. predictions The we have issue in is, of fact course, been that made, in and the that absence of they a do well seem defined set of rules, PoS(QG-Ph)038 Daniel Sudarsky ! They must first 3 Here we are not referring The view that quantum mechanics 5 Draft Version – – November 26, 2007 For those that shiver upon the last statement let me recall a theory about venereal diseases that was popular in 3 Quantum physics as a complete description of the world. Quantum physics as part of a more complete description of the world. ancient Rome: venereal diseases comeMercury, from which Venus, the constantly Goddess challenged ofMercury Love, the had obviously. a The Goddess’s substance celestial for associated enemysubstances the with of containing him, Venus attention mercury was that should of could help be theleast in found among Sun fighting on the the Earth: practitioners (Apollo). of diseases the Fortunately medicine) metal associatedthe that mercury. for with most certain It Venus. mercury humans, common And was salts then it of did evident wasphysics the provide that a substantial with venereal relief known diseases for ancient fact those of ( Rome’s infectedpredictions at the with medical are time. not arguments. I enough. My do point not, of is course, only pretend to to illustrate compare the any statement theory of I modern made above: correct The seeds of cosmic structures as a door to Quantum Gravity phenomena that are explicit to theonly point the where explicit a algorithm computer andor could, the not, in explicitly such principle, "predictions" stated arrive do inputs, to orsome we the do unjustified have predictions not, choices, no using follow manipulations way from and the towhich theory. arguments ascertain the We have whether can predictions been not have be used been surebe as obtained. whether actual part predictions. or Correct of This not predictions the is are quite processarriving not to clear, by particularly, the enough when predictions the are argumentative soor connections loose used that not. no in Specially one suspect can are, bethis sure of point whether course, we these those should are "predictions" be in aware that facthad that predictions are, already long in before concluded fact, inflation the retrodictions, wasabout form invented, and the Harrison of on nature and the of Zel’dovich (7) the primordial large spectrum, scaled) structure based of on our rather universe. broadto observations an extension of therid theory the theory into from some is sortthe not of theory its hidden would indeterminism, require variable but something type, thean that as so removes external called the the observer, measurement problem need problem. etc. we forusing Completing There want a a external to scheme are, based measurement for on apparatus, sums instance,something over like ideas decoherent the histories dynamical like proposed reduction by generalization models J. proposedideas of by Hartle of Ghirardi, (6), quantum R. Rimini others & Penrose physics invoking Weber about (8),of and the the the role two of aspects gravitation of in physicalof modifying reality quantum these (5). mechanics The issues in present carried the manuscript,Penrose’s as merging out generic well ideas. in as the collaboration original with treatment e) A. Perez and H.faces Shalmann no open (1),are issues inspired and that, on holders in of particular, the these measurement views problem hasalong one been the can solved. so Among further the called identify "manysolution two world to main the interpretation currents: measurement of problem, those quantum andquantum that mechanics" those mechanics that subscribe and has hold to consider a been this ideas view solvedthe that to by many the be the world measurement interpretation a consideration problem does in of very "decoherence".mapping little between Let to ameliorate what us the in first measurement that note problem,be approach that as would call there be is "measurements" called a in the thein splittings Copenhagen the of latter interpretation. worlds, interpretation Thus and has what every aof would question corresponding the that one measurement can in problem the be manyunder made the worlds what issues interpretation. circumstances would For does the be. it case mechanism when occur? as What does a constitutes a solution a to world trigger? the splitting Concerning measurement occur? the problem I decoherence why, would and like to start by quoting the postures PoS(QG-Ph)038 Daniel Sudarsky E. Joos (11). 6 Arnold Neumaier (9). Draft Version – – November 26, 2007 once one has understood why certain interferences can not be observed in practice, , M. Schlosshauer (10). The seeds of cosmic structures as a door to Quantum Gravity phenomena that in these regards are helddispel by the several widespread people notion that that such have"Many considered is physicist the the consensus nowadays issue view: at think length thatsurement in problem. decoherence order But provides to this a is fully an" satisfying illusion." answer ...note to that the the mea- matrix formal is identification easily of misinterpreted thetoo.. as .. reduced implying the density that total matrix the compositequantum system with state mechanics is a of still that the mixed described no by system state individualsystem a definite can density ..." superposition, state be it can viewed follows be from as attributed"Does the mixed decoherence to rules solve one of the measurement of problem? (the Clearlycertain not. parts) objects What of appear decoherence classical the tells when us observed, ishave But that what to is apply an the observation? usual At probabilityIn some rules stage of fact, we Quantum we still Theory." willand see acute. that Nonetheless, when most dealing researchersas with the in cosmology paradigm the the where field problem the seemproblem becomes direct at to even application hand take more of finds some vexing the its versionsome standard justification. degree of forms of Significantly, decoherence in-satisfaction of the of diversity quantum some ofBefore mechanics researchers engaging precise to with on approaches the the the views indicates cosmological of case, othersand let (12). can us not review briefly do. what decoherenceDecoherence is, is and the what can process byronment which a (as system are that all is physicalinto not systems isolated, the except but the degrees in universe interaction of itself) withthan freedom "looses" an supersedes or of envi- the " laws such transfers" of environment. coherence thought quantum It physics. to is It offer is, a explanations therefore, wellof that clear the studied that, go in principles effect beyond principle, of that what it quantumditions can follows can physics. in not be rather which Its be directly the main inferred quantum achievementas interferences from is isolated, expected the to from become application allow the observationally for idealized suppressedenvironment. the consideration as of studying the a the system result con- ofThe basic the recipe system’s for interaction an analysis with1) of the Divide decoherence D.O.F. in : a system given + situation2) environment follows ( Compute the identify Reduced following inaccessible Density steps: or matrix irrelevant (trace3) D.O.F.). over Perform environment suitable D.O.F.). time average so4) that Regard the the off-diagonal diagonal matrix density elements matrix vanish. The as Problems: describing a statistical ensemble. it is tempting to conclude that onethere has understood is the nothing "emergence left of of classicality", the and soto that called therefore be " a measurement simplistic problem" and in misguided quantumin conclusion, mechanics. fact, as This at turns indicated least out by two the veryI) quotations serious The listed problems basis above. with There problem: considering are decoherence it inthe is step this clear 3) light: that of the the program diagonal above, willof nature be the of lost, in system the general, at reduced upon hand. a density change Thisselects matrix of a is obtained basis so for taken in called the to pointer Hilbert mean basis space which thatof underscores the decoherence. the nature aspects The that of point have the of become system-environment classical course interaction as is a that result this leaves one with the usual situation whereby, if the PoS(QG-Ph)038 π "As axis? z Daniel Sudarsky about the π D’Espagnat (18). . Now consider taking the trace over the z 7 around π direction. Take this state and rotate it by and angle y + ( the vectors in 3-D space are given in cartesian coordinates (x, y, z)). Let Draft Version – – November 26, 2007 ) 0 , 0 , D = ( axis. Now consider the superposition of the initial and the rotated states. The resulting X ~ z 3. The exacerbated problem: applying quantum physics to theWe should early point universe out that someis researchers something in mysterious the in field, such theHartle as standard (16), (6) account have that of acknowledged have the that pointed emergence there ogy, of out and structure, of the and course need people R. to likemeasurement Penrose, generalize J. who problem quantum in in mechanics his quantum to lastinflation, mechanics deal book comparing (17) with to it has cosmol- the with stressed problem the thecay. problem of relevance In of of breakdown my the the of breakdown view, general this of the analogy sphericalproblem H.&I. is symmetry does during even in not more a emphasize severe particle than the inon de- point ordinary the that, situations, strict because, in Copenhagen in interpretation the that as cosmological case,As a context, we an source can example the of that not safe exhibits even quite practical rely clearly rules. the the deepening following of quotation the from problem in a this well context, known let’s consider thinker on these sort of issues in quantum theory: Obviously yes. Can a mathematical manipulation withthe no state physical of process the counterpart system? ever change Answering yes would take you to the view discussed in b). long as we remain within the realmwill of mere appear predictions to concerning us) what we and shall refrainobserve observe from them (i.e. stating " what anything no concerning break “things in as theHowever, in they linearity must of the be quantum cosmological before dynamics setting, we isto we necessary. " think need to about deal the precisely state with of this situation: affairs we of need the universe before the emergence of the conditions spin D.O.F. The resulting densityclassical? Of matrix course is not. Is diagonal. the Can state still we invariant say under rotations that of the magnitude situation has become state is clearly symmetric under rotations by about the the particle have its spin pointing in the The seeds of cosmic structures as a door to Quantum Gravity phenomena selected basis is, say, thethus position one basis, can the not momentum argue that ofII)The classicality the definite has system outcomes really problem: remains emerged. here undetermined the and interpretation problem of is the the mixed absence state of described sufficient byand justification the in density for regarding matrix the a as single describing system a asin statistical being ensemble the in diagonal definite elements yet of unknown stateculations the among rather density the indicates matrix. ones that The represented the system resultbut must that be where emerges regarded from the as the coexisting interferences in decoherencesuppressed. in the cal- various Selecting the alternatives, among observables these associated alternatives can withcoexistence" be interpretations. the viewed In as particular deciding order pointer between toclassicality basis the argue one " being that choice would vs decoherence have really tomentally leads advocate confirmed aspects the to of "choice" the quantum interpretation, emergence mechanicsus of but such to well as opt the for known, the violation and "coexistence" of experi- The interpretation Bell next (14; inequalities, example, 15). force from ordinary non-relativisticthe quantum situation mechanics, we serves face: as consider a acentered clear single at analogy particle of in a state corresponding to a minimal wave packet PoS(QG-Ph)038 , or Daniel Sudarsky matrix element when?, why? S 8 matrix element between the "in" vacuum and the other vectors in the S Draft Version – – November 26, 2007 . The seeds of cosmic structures as a door to Quantum Gravity phenomena that make us possible, beforemeasurement. we existed and beforeIn we the cosmological ever setting, carried we out seekevolution a an that historical, follows observation that the is or a lawstheory time of development, of physics description cosmology?). (would of Such this cosmic description be,emergence should perhaps, explain of too how the did much primordial WE to arise,living ask density organisms, in of fluctuations, humans, a a cultures, of path physical etc.. covering galaxies, Such the abilities an stars, of account and the should late planets, not evolved rely andsible. creatures on eventually From to the this explain measurement perspective, the (in) one emergence canbased of not on conditions justify the identifying that current, some make or D.O.F even them as permanent,the pos- limitations irrelevant primordial environment, of density humans, in fluctuations, the for analysisvalue. doing of so the emergence leads of to aFurthermore, circular one argument might with no bethe explanatory asked, explanations when of attempting these toquantum delicate physics follow points, does some to not of describe accept ouruniverses the one universe, was. or standard as The it argument more versions here was of of seems neverbe H.&I., to the rely only used following on a to notions: the certain notion describe 1)that ensemble of of thought aspects such would of ensemble indicate of our that universes it universe could is thatwhat the is superposition could represented of by not the the be states H.&I. of quantum describedif state. all we in The the have problem two universes isolation. is systems, in that The each the this of ensemble, described line is which by not of is the quantum described superposition mechanics: by of a the quantumproduct two state, in quantum the the states composite direct ( system product it of is is the not and described corresponding that Hilbert by spaces). the their 2) direct appearances that or to our "tensor" the universefreedom. is contrary This still are H.&I., posture the makes result us oforigin and our of our inability the to limitations, observe conditions a all fundamental thatuniverse the stopped part makes degrees being of our of H.&I. the ", existence explanation without possible. of being 3) able the to That even "it address issues does such not as matter when the due to what? I find it quite remarkableI that would many physicists call seem technical to pseudo-answersterized look to as for, the calculation or that problem. content while These themselves technicallyacceptance approaches with, correct of can what an fail be interpretational to scheme address globally of the charac- thetext. issue formalism, These at which often hand is include not by pseudo-analogies, justified the that inproblems implicit the is, which present comparisons con- superficially of the seem presentthat complete problem they analogies with are other but missing crucial that aspects,lenge. upon particularly The careful those danger that examination make of reveal the thepoint problem analysis’ where at all by hand aspects such analogy of a is the chal- analogyConsider, that have for they been instance, often explicitly exposed fail a and to recent canlies therefore dissect article at be the (19) examined. the problem which origin to proposes ofof the an particle the analogy creation anisotropies between out and of the inhomogeneities thecess process vacuum known in that in as the the the early presence Schwinger universe, of process a with (20). sufficiently In the intense that process electric calculation, field, one a evaluates pro- the between the "in" vacuum andand the the "out" unity vacuum, as and aand measure interprets the of observation the that particle difference the creation. between This the identification result would be justified by unitarity PoS(QG-Ph)038 is a will i . But ( one i i as the A 1 | t B 2 | out i| ; B | +) A , 2 |h Daniel Sudarsky ψ ( , in the absence of a ) i − 0 ) and we ask about the | , i 1 0 U ψ , ( | in | ( where U is the unitary evo- i B (of course this might not be easy | i U out ; ). Analogously, we assume the electric 1 +) t , 2 ψ ( , ) in the vacuum state ( 9 , if it was originally prepared in the state − 1 i , of the number of pairs at a certain time, we are not t 1 A | centered at ψ ( ) | << t S t ( | ∆ . The probability interpretation is only valid in conjunction respectively. This question has a very well defined answer in i 2 B 0; | h ψ measurement and 1 ψ . Let us assume that that electric field points in the x direction. We now as- Draft Version – – November 26, 2007 2 t , among other things, because the initial state is invariant under translations i out ; +) , 2 ψ plane, the hamiltonian preserves this invariance but the state ( z , , ) y − , 1 ψ ( not in general share such invariance.calculation Thus, while to we yield are the perfectly justifiedvacuum prediction in when for viewing contemplating the probability the S for matrix the observation of pair creation out of the in the probability amplitude for observing thein system the in single the particle state states containingin an quantum theory, electron which and is a simply to positron, compute but that isthe quite system, a in the different absence issue).| of However, let a us measurement, note has a that well we defined can probability not of assume being that in the state justified in regarding the state of a field as being anything but measurement. Again some of the mostthe conspicuous right to and use clear unjustified contradictions interpretationalB-EPR(21) that extrapolations, setup can arise while be when entertaining seen we the byorientation notion give considering in that ourselves the the standard the absence two (or particlesdecide might before) to trace have a over a measurement the particular is spinD.O.F. spin of D.O.F. carried of the out other one particle, (22). of a the We diagonalthat could, particles density the of matrix, for particle and the instance, has be EPR one tempted pair to of andI’ll interpret the obtain, try this two for as to spins indicating the convince orientations. spin the But readerverse we know offers that this the this leads "Laboratory is to not " contradictions. worth necessarily where pointing “just some out philosophy", of that, and the in that fact, issues the the can, motivations early at for uni- least inflation in itself are principle, often be criticized studied. as It being is "too probability of finding the systemthis in assumes the that state an observation, or measurement(non-degenerate) eigenstate. is In carried the out absence for of an a observableby measurement, for the the which unitary system evolution must of be in thewith the state a state given measurement. To see the problems that entailtive the scheme extrapolation of into quantum unjustified mechanics, realms letby of us noting the consider that standard in we interpreta- must more imagine detailthe the the problem electric Schwinger field of process: to the we be electron start turnedand filed if on the at in system some interaction was finite prepared with time, invalue an for its of otherwise, eternal the vacuum state, full electric or hamiltonian, filed, the it would state wouldwould remain corresponding not be in to make stationary, that the any state minimal sense for eigen- . all Sois times let and often us the interested assume issue that in of the pair considering electricthis creation such field taking is process turned place to on during be at a carried somefield time long out to interval adiabatically be turned , off so at we can imagine lution operator ) before acontext, measurement we is have no carried right out. to Similarly view the in state the of early the universe universe inflationary as anything but sume that the system is prepared at a time The seeds of cosmic structures as a door to Quantum Gravity phenomena "out" Hilbert space, such asinterpreted a as specific the state probability with ofstandard a pair quantum single creation mechanics in pair such postulate of state. of electron This the and would projection positron, in postulate, would turn, be indicating be that justified by the PoS(QG-Ph)038 = R (4.1) µν g ) 2 / 1 ( Daniel Sudarsky − µν R might play a central role in 4 i µν T h G π 8 = µν in the semi-classical Einstein’s equation which Q µν + 10 Q R µν g ) 2 / 1 during the collapse of the quantum mechanical wave function ( − µν only R Draft Version – – November 26, 2007 whereas the other fields are treated in the standard quantum field theory (in curved i µν T Here the suggestion is that such theory is not just the result of the standard type of quantization as applied to h 4 G π gravity, but something involving a radical change in our paradigm of physical theories. 8 is supposed to become nonzero of the matter fields. Thus we write space-time) fashion. This is supposedcollapse to hold of at the all wave times functiongravitational except degrees when occurs, of a at freedom quantum must which gravity be time,the induced taken into semi-classical the account, approximation. excitation with The of the possible corresponding theformally breakdown breakdown represented fundamental of of by quantum the the presence semi-classical of approximation a is term 4. What to do? Our approach. As we have seen,state we for need the a universe paradigm toan a that external state will system that allow is to usobservers neither carry to to isotropic select out consider nor a a homogeneous, a set but of measurement transitionapproach degrees without will and from of relying follow freedom without in a on to this reliance H.&I. be casefunction considered on the as suggestions collapse our unobservable, by is and own Roger an so Penrose limitations forth. that actualcertain Our as quantum dynamical collection mechanical of process wave states, where breaking, aMoreover, in system these the ideas is process, suggest forced the that to unitary the jump evolution fundamental of into theory quantum one of mechanics. gravity of a The seeds of cosmic structures as a door to Quantum Gravity phenomena philosophical". the actual physics of collapse, by forbiddingof certain freedom types to of exist superpositions of for gravitational more degrees allow than us a to very carry brief a time. detailed Theseinspired analysis ideas on of are them. the The certainly issues idea a at behind bit hand,both the too so scheme the we schematic we will to modification will consider of be a using our concretethe is theory formalism that of fundamental the gravitation quantum degrees and gravity of requires thatsimple gravitation of way, but quantum are instead mechanics. the not latter In appear related thistheory. as scheme effective to The degrees of degrees the freedom of metric of a freedomas degrees non-quantum of effective susceptible of other to freedom fields a in whetherwhen quantum any or contrasting treatment not this on fundamental paradigm are theirgravitational with realms. to own, the be an well considered assumption established thatThese successes ideas would leave of room avoid to quantum problems consider, theorywould therefore, be situations in appropriate where but a non- a quantum classical treatment treatmentsemi-classical of of gravity other gravitation that fields would be we justified. will Thatimation assume is would to the realm break be of down valid in for association mostto with be of part the the of quantum time. the mechanical However, underlying this jumpsIn quantum approx- that accordance theory are with containing the considered gravitation. ideas above wetion will use with a quantum semi-classical fields description of as gravitation reflected in interac- in the semi-classical Einstein’s equation PoS(QG-Ph)038 ≈ has 2 I V (5.3) (5.2) (5.4) (5.1) H . 5 with but the metric ( with units of , L G η I 1 Daniel Sudarsky H . This era is sup- 0 − are, the scalar field V ), and ) , and the potential ) L 2 a / η 3 ˙ 1 , ) = ( ) / , 0 )] L η 3 1 at the "present cosmo-  φ / ( φ a j a ( ( M = , negative and very small in ( 0 V dx − i a occurs during the inflationary η − = a dx times Length = 0 ab will have units of length i j ˙ φ i g M δ η x ) . φ , , b ]) 0 η Ψ has units of 0 ∇ 2 φ φ [ φ − ] = a V 1 φ 2 ∇ [ a 2 V 2 / + ( φ 1 2 ∂ + 2 η 2 − 0 a ˙ ] d 11 φ (with units of Mass ) g ( [ + ¯ h Ψ . G 0 R ˙ 2 φ π G ˙ 4 a a δφ + π 1 for the inflaton’s potential. One then splits both, metric 2 1 + = ( 16 0 , and the homogeneous scalar field + V 2 2 [  − φ ˙ 0 j a a g ¨  φ 3 2 = − dx ) field in the slow roll regime so i 1 but will keep φ √ η will be dimensionless. The field 0 x , ( = dx a φ 4 g a during these latter periods is, of course, different but we will ignore c i j d δ ) δ = Z η + 2 + ( 0 2 a Draft Version – – November 26, 2007 = g ds η S d = − g  2 ) η ( a and with the scalar 3 stands for the inflaton and L = / 2 GV φ M ) ds 3 We will be using units where ) explicitly throughout the manuscript. The coordinates in the metric / 5 after the Gospel π M / 8 The background solution correspondsing to a the conformal standard time, inflationary has, cosmology during which the written inflationary us- era, a scale factor components, such as the scaleunits factor of and scalar field into(‘fluctuation’), a i.e. spatially homogeneous (‘background’)Th part equations governing and the an background unperturbedment in-homogeneous Friedmann-Robertson part universe with line ele- equation, and Friedmann’s equation L where ( The starting point of the analysis is as usual the action of a scalar field coupled to gravity The seeds of cosmic structures as a door to Quantum Gravity phenomena Thus, we consider the development of thestructure state emerge of to the be universe initially during described the by a timesome H.& at stage, I. which the state the for quantum seeds the state of gravitational and offor matter the the D.O.F.. At matter gravitational fields D.O.F. reaches is a forbidden,is stage and triggered. whereby a This the quantum new corresponding collapse state state of ofinitial the the state, matter and matter field by fields its wave does connection function to nosemi-classical the longer gravitational equation need D.O.F. leads now to accurately to share described a by the geometry Einstein’s symmetries that of is the no longer homogeneous and isotropic. 5. The inflationary origin of cosmic structures: the amended story, or the story posed to give rise tofields, a and reheating then period to whereby a the standardThe hot universe functional big is form bang repopulated of cosmology with leading ordinarysuch up matter details to on the the present cosmological account time. thatregime. most The of overall the normalization change in oflogical the the time". value scale The of inflationary factor regime will would be end for set a so value of absolute terms. The perturbed metric can be written PoS(QG-Ph)038 )+ (5.8) (5.9) (5.5) (5.7) (5.6) η ( . R k  ˆ I π , ). k R k integer and † i ˆ − ) = a . n ) ) η Daniel Sudarsky ( η η k ( and ˆ k ik π , ¯ k g
) ± 0 ( k 3 with + η , and ( − I , , k 2 ) k R ˆ , exp π δ k η 1 x ~ ˆ · k 2 a ( k I ~ − ) i with k = 0 e ˆ r η k y i , k i i ( k k † − k ~ ± δ ˆ ∑ g a for )+ ) 3  3 1 i η η L 2 . To avoid some distracting infrared ) = n ( ( which, as we pointed out are hermi- 1 ¯ a hL , k R π η √ ) ¯ ˙ / k g ( φ 2 ˆ ˙ y ) = η φ ± k δ ( x + ] = s 0 g I δ = ,~ , ) = k I k ˆ R ˆ k ) = a η L a η = = i ˆ . It is convenient to work with the rescaled ) ( , π ( η ) k ˙ I k I φ , ( η y π , and decompose the real field and momentum ˆ a ( k ( R δφ [ , δ L ˆ k k y π ) 0 and ˆ g . ˙ π are, therefore, hermitian operators. Note that the φ η 0 ) 12 , ˙ φ ) G ≡ ik η
0 π ) ( η G k ± I ( , 4 , ( π η I − ) , , R k , satisfying ( 4 k R y k k = η  k ˆ δ ˆ ( I ~ π π exp , = k Ψ k R ˆ y + s 2  † x 0 ~ · ˆ are identical in the real case (and identical, up to a sign, in the k a k k ∇ , and i ~ and i ) k k η e k δ ) η − † − ( η ± ˆ k k a 3 ~ ( ¯ ∑ y ) 1 I , 3 ¯ η and hL R k  1 + L ( y I k k k , ¯ y 2 R 1 of the operators ˆ ] = k 0 ˆ ) = R k + Draft Version – – November 26, 2007 √ 6 a ˆ and its conjugate momentum x ) a k ,~ ˆ , a η R k ) η ( ˆ ) = a δφ ( k η [ ˆ y y a η ( ( into their real and imaginary parts ˆ k  ) y = ) 2 ± k ( y η 1 ≡ y ( √ k ) ˆ π η stands for the relevant perturbation and is called the Newtonian potential. ( ) = where k Ψ y η ) and ( I η ) An imprecise measurement of an observable is one in which one does not end with an exact eigenstate of that , ( 6 R η I k k ( ˆ y ˆ k π ˆ i tian operators and thus reasonable observables. Theseabout field the operators field contain (we complete ignore information here, for simplicity, the relations between the modes We note that the operators ˆ operators corresponding to imaginary case). We, now, proceed to calculate the commutator, and we will find out that any of them are standard: Next, we specify the waycollapse we to will model the the end collapse,imprecise of measurement and inflation. follow the We field will evolution assume through that this the collapse is somehow analogous to an Now we consider the quantumfield theory variable of the field observable but rather withcertain a particle’s state position which and ismomentum only momentum defined peaked so to around as a thebound. to limited eigenvalue. extent, end Thus, and up we which, with could of a consider course, measuring state does a that not is entail a a conflict wave with packet Heisenberg’s with uncertainty both position and where we introduced the abbreviation As we will beanalogy interested with a in “measurement", considering it is a convenient toquantum kind work with mechanics of Hermitian operators, are self which in induced the ordinary y collapse ones which susceptible operates of in direct close measurement. Thus we decompose both operators as problems we set the problem in a finite box of side where the sum is over the wave vectors The seeds of cosmic structures as a door to Quantum Gravity phenomena where The perturbation of the scalar field leadsEinstein’s to equations a at perturbation lowest of order the lead energy momentum to tensor, and thus where ˆ PoS(QG-Ph)038 . Ξ for i I , i after (6.1) (6.2) k R ) (5.11) (5.10) (5.12) (5.13) ˆ i a η h ( Θ I | , = R ) I , y ( R k k , respectively. ˆ . d π 2 0 Daniel Sudarsky ) h ) I , ) y R k ( . k d ˆ ) and π ) , 3 i ∆ 2 η ) ( ( / ¯ hL , k 3 η ( 2 g ( 2 while their corresponding / I | ( , ¯ hL 3 k and , individually are distributed R ℜ g 0 k ) | 2 0 q 2 ¯ hL y y ) | ) ( k = ) k 2 √ ˆ ˆ c π k q y 0 / | i η ∆ 1 ) = I ( ( c , k k Ξ R i i and η ) g i ) ) = ( ( | y ) y k ( I k k 2 ( η 2 0 , , y ˆ y η ( ˆ ) π R k | π ( ) I h I x , h 1 I y , ) we obtain ˆ , , , ( ) R k R k R 0 k ˆ a = π x ) ˆ π y h / 2 0 ( = k ) s 5.10 ∆ ) = ˆ 2 π I 0 ( , 2 0 h i R I ) are given by: ak = ( ) , I y , / R i 13 ( k R k s η k ˙ ˆ ˆ ˆ ( φ π y y , h δ , ∆ ∆ ) − h ) ( ( 3 I s , . Let us introduce the following quantity: R q q k ¯ y hL after the collapse. It turns out that, for the goals at hand, all I I ) = = 1 2 d ( , , , , i ) 2 R R k k η | Ψ ( x x η k Θ . In the vacuum state, ˆ 2 k | ( i y | k ∇ = = Ψ ) Θ y | ( 2 I Θ Θ , / i i ℜ R k 1 ) ) ˆ 2 a c c k k | √ η η Θ = ( ( ( h I I 2 0 , , = ) we have, of course,: R k R = I , and using the result in Eq. ( Draft Version – – November 26, 2007 ˆ ) Ξ , y i I y i I , h R ( , 0 k ) R k k | ˆ R k ˆ π y d η h d ( ∆ I ( , R are selected randomly from within a Gaussian distribution centered at zero with k ˆ y I 2 , h , R k x , I 1 , , R k be any state in the Fock space of ˆ x i Ξ | collapse: However, since they are mutually non-commuting, theirIn distributions are our certainly collapse not model, independent. we docommutativity not want and to make distinguish one the over following the other, assumption so we about will the ignore the (distribution non- of) state(s) Now we will specify the rules accordingwill to be which simplicity collapse and happens. naturalness. Again, atWhat this we point have our to describe criteria is thewe state need to specify according to Gaussian distributions centered at 0 with spread the state that resulted from theWe should collapse keep for in all mind that later this times. specificand recipe for natural the ones, collapse is and just that anIn other example fact, among possibilities the in simple do (1) an exist, alternative and recipethe those was fine may considered, tuning that lead problem seems to that to different generically be predictions. affect quite inflationary promising models in dealing (23). with 6. Analysis of the Phenomenology Now, we must put togetherquantum our mechanics description semi-classical of description the ofversion inflaton of of the field. the perturbed We Einstein’s gravitational recall equation D.O.F. that that, and in this our the entails case, the reduces semi-classical to: Thus, the expectation values of the modes are expressible as The Fourier components at the conformal time spread one. Here, we must emphasizerandom that variables, our and universe thus corresponds each to of aabove, these single we quantities realization solve has for of a these single specific value. From the equations For the vacuum state uncertainties are where The seeds of cosmic structures as a door to Quantum Gravity phenomena Let PoS(QG-Ph)038 = ν / (6.3) (6.5) (6.7) (6.4) (6.6) ) ν ( ∆ ] Daniel Sudarsky Θ i ) η ) to write ( I ) 6.4 indicates the direction , y ( ) k 0, and the space-time is ˆ ˆ k ˆ k π ( h i lm ) = Y + ) and ( η ) ( Θ , D k i x ~ 6.3 · ) R k Ψ | ~ i . From this quantity, one extracts η k e ~ | 7 ( , ) . ) R k (( ~ ) ( l Ω η y j ( 2 k ( F l ˆ k d i π a h 1 ∗ π Ψ 2 lm x )[ 4 ~ · Y 3 2 ) k ) ~ i ¯ hk L k ~ D e ( ak x / ,~ F r k s ~ ) D k ∑ ( 14 k η 3 , leads through the black body radiation formula to 2 ( √ − 1 ( 2 k L ) Ψ k k Ψ = sU ( = Θ Z k ν U ) = ~ i ∑ / x ) ) k ,~ = ~ ν ∑ η ( η ( ) = a lm ( ) ∆ 1 y x . This quantity is identified with the temperature fluctuations on 2 α ( k Ψ ,~ ) ˆ 3 π ¯ D h η L h x ( ) ,~ 2 Ψ r D . s η ak Ψ ( / = s = Ψ ( T Draft Version – – November 26, 2007 lm − / represents the aspects of the evolution of the quantity of interest associated ) α ) T k ( ) = ( ∆ η U ( k . It is in this expression that the justification for the use of statistics becomes clear. k Ψ ~ is the spherical Bessel function of the first kind, and where ) x ( l j and therefore T The gravitational change in frequency / 7 ) T ( which no longer vanishes, indicatinghomogeneous that at the after corresponding this scale. We time nowtonian can the potential reconstruct universe the using became space-time value anisotropic of the and New- in- To evaluate the expected value for the quantity of interest we use ( of the vector The quantity we are inble fact of considering harmonic is oscillators, the eachwhat result one is, of contributing in with the effect, a combinedobservational a complex contributions number quantity. of two To to an dimensional proceed the ensem- random further, sum,displacement. walk we leading This whose must to we total evaluate do with the displacement the mosttion corresponds help likely of of to the value the the imaginary for most ensemble likely such of value total universes, and with the the identifica- ensemble mean value. Note that this is used here only as a where the surface of last scattering, by regardingthe those gravitational as potential due well to from the which gravitational the red photons shift emerge associated with which can be usedessentially, to through extract its imprint the on quantitiessurface the of of last temperature scattering: observational fluctuations, interest. the “Newtonian The potential" measured on quantity the is still homogeneous and isotropic at the corresponding scale, while after the collapse we have ∆ The seeds of cosmic structures as a door to Quantum Gravity phenomena Where the expectation value is theThus, one before corresponding the to collapse, the the appropriate state state of is the the quantum vacuum field. and, therefore, where the factor with the physical processes occurringclude, during among the others, period the acoustic from oscillations re-heatingwe of to are the exploring decoupling, plasma in which and this which in- work. are notThen, central after to some the algebra issues one finds PoS(QG-Ph)038 the (6.9) (6.8) c k (6.10) η and the , that is, k U Daniel Sudarsky , , dx ) 3 dk k x 3 ) ∆ appears in the present analysis k x 2 ) . ) ( ( k D D 2 l ( j R R | sin C ) , the observational spectrum should k ) ~ D | k C is essentially independent of z R (( / k / 2 l z j x 1 ( ) C k 4 + ( 2 ( ). Next we note, in order to get a reasonable x ) 2 C ∞ ) 4 D 2 k ),we note that the appearance of the time of ob- k ) has become encoded in: R ∆ k → / ) ( 15 ( x 6.9 k a ( ( U sin F U ) as Z 2 k 1. This is a rather strong conclusion which could repre- z Z − 2 . / ¯ h 0 a k 2 represents the conformal time of observation, and 2 2 ¯ h a π s ) = 2 2 π → η s k + ( 2 ( η = 1 C . = can be made more useful by changing the variables of integration L ≡ . . with . L L ) . 2 M . k | k 2 M c k 2 M ( | | lm η C lm α lm | α = α | Draft Version – – November 26, 2007 | k z , k z − η k leading to = D . In fact, the standard answer, in the absence of late time physical effects such as plasma k k ∆ / kR z = = x c k the time of collapse ofη the different modes should depend on the mode’s frequency according to and not in the standard treatments,not despite be the expected fact to that the hide systemrequires any is a real linear feature. simple and To analogy. linear address I averages thisoscillator can believe issue, initially that prepared going it on beyond is the a providedfocusses highly calculation by on excited itself the carrying eigen-state consideration averages of of of the quantitiestrace a hamiltonian. extracted simple If of directly all harmonic any from our oscillatory the treatment behavior initialor state in inaccurate we time. will measurement However, find if of no coherent we the state, consider position, the the time which state of resultingwill is the be of considered of measurement a relevance to or and partial from collapse be thatthe of point naturally relevant the onwards physical described oscillations quantities. initial in by state time into can a be the expected coherent for state various of oscillations, would correspond to spectrum, there seems to be only one simple option: that where have no dependence on the sizeTurning of our the attention surface of to last the scattering expressionservation in could, Eq. in ( principle, leadwhich to is concerns, thought as to that lie shouldexpected in to be be a taken negligible regime as because where ( thetially in inflation time our small has of convention) negative that long decoupling, number conformal ended. ( time In would i.e. be practice, a its an effects exponen- can be sent relevant information about whatever theto actual mechanism tests of on collapse the is, feasibility andTo of end leads, different this mechanisms as section, for we we the consider will physical areason see, collapse. question behind raised the during fact the that talk, the by oscillatory W. behavior Unruh. reflected He in asked about the conformal time of collapse of the mode This expression reveals that, ifremaining one signatures ignores of late the time collapse physics process processes represented represented in in The last expression for to The seeds of cosmic structures as a door to Quantum Gravity phenomena calculational tool to extract thethe most ensemble likely and no value call of for the themagnitude existence "random of of walk". this its No elements quantity. Taking is other the invoked. Now role continuum we limit, is compute and given the after expected to some algebra (1) we find, where some of the information contained in PoS(QG-Ph)038 . 2 ) ρ 0 ˙ φ (7.2) (7.1) (7.4) (7.3) , with )( y k . ), (after , π x ak ) ) 3 . Now we / 2 η p 5.5 d ( ) ) ak 2 ¯ M hG 2 ( to a laplacian / ( k π s ) Daniel Sudarsky 4, and thus we x )) y / η 3 π , = ( . Clearly, we must x )( ) = ( by considering two k ) ( ¯ y η hkL η 2 , ) Ψ ( , ( ) π ) η k ( = 1 would be, in accordance η , ( ( k 0 ( I k ˙ 2 k φ ) | ( Ψ E 2 ) and I k ( k ) η E > ) Σ y , 0 1 y k x ˙ π ( φ ( π ) ) )( 3 1 ( < η L ( . / | Ψ ) 2 1 1 ) ( k Z 0 ) by ˙ y φ = ( = ) π )( x x η 3 )( 3 ( 2 ak ) d d ) ) 2 / 0 3 ( k ) a ak y − ) k ¯ hG ( k π ( / η 16 π , ix 1 ( )( x e ( k ( k η Σ ) ( Σ Z 2 ) ( 2 ) 0 1 ˙ ( ρ φ η ) = ) ) ) ( y k 3 η ) η π 0 2 ( L , ( k ( I . Then the relevant energy is given by : x / ) y E ( y a ) π ( π 1 0 ( represents the density perturbation associated with a collapse into ( ˙ G φ 0 ) Ψ ˙ 3 π 2 φ ( 4 − ) Z ρ a η ( = ) = ) = 1 k ( Draft Version – – November 26, 2007 η ( , and ˙ Ψ dV δφ ), we estimate ) 0 ) E 0 k 2 1 , ˙ ( φ ( k to replace the laplacian expressed in the comoving coordinates 2 . Note that in this section we are ignoring the overall sign of this energy which ρ Σ 2 ) ) 5.11 − ) 1 − 2 6 a ( ( refer to the two different realizations chosen. Recalling that a L Ψ ) = / as the Newtonian potential and, consequently, the right hand side of Eq. ( 2 represents the Newtonian potential that would have arisen if the system had collapsed 1 ρ Z ( , we find ) , 0 1 Ψ ˙ ) ( φ 1 ) = ) = ( ( G Ψ η π η ( ( 4 I E E = Using equation ( where s being a gravitational binding energyterms would of naturally the Fourier be expansion negative. leading We to next : express this energy in the alternative where into the alternative interpret associated with coordinates measuring physical length )Therefore, should be identified with matter density which can be interpreted as thedifferent sum alternatives. According of to the all contributions the of considerationslapse each we as mode have occurring made, to independently, we so the view the interaction each triggerto energy mode’s for the of col- the scheme collapse based of on mode reaches Penrose’s the ideas, ‘one-graviton the level’, condition namely, that that this it energy equals the value of the Planck Mass representatives of the possible collapsedthe states vacuum. on opposite We sides will of denote the the Gaussian two associated with alternativesa by rescaling by the indices Penrose has advocated, for amight long be time, a that the dynamicalmight collapse process be of related independent quantum to of gravitational mechanical interaction. waveinto observation, More functions one precisely, and of according that to two this quantum the suggestion,tion mechanical collapse underlying alternatives energy would mechanism between take the place alternatives whentivation exceeds for the a gravitational the interac- certain present work threshold.history came In of from fact, the Penrose’s much universe. ideas of and the hisA initial questions very mo- regarding naive the realization quantum each of mode Penrose’s would ideas collapse in byrealizations. the the In action present of our setting the case, could gravitational one be interaction could between obtained estimate its as own the follows: possible interaction energy The seeds of cosmic structures as a door to Quantum Gravity phenomena 7. A version of ‘Penrose’s mechanism’ for collapse in the cosmological setting obtain: PoS(QG-Ph)038 and (7.5) (7.6) (7.7) c z during the , at the very k η Daniel Sudarsky corresponding to 45 − , 10 c z is the so called slow roll ≈ 2 is that the above expression at the last scattering surface ≡ c k ) k a 2 a V / 1 / 0 ) 1 ˜ could conceivable have appeared V V − ( ) )( . a ˜ π 2 ¯ h V ) 6 ( / 0 ε p , and thus the scale factor at the time of 2 and the slow rolling of the background Pl √ V k kl 8 I of the mode / )( M ) 1 c H . k c ε k − . Similarly, in our case, the energy created in z )( 1 = η / / η 2 − a 3 ω = / ( ¯ h = − 12 ly 1 c ) ) k 2 I ( a p 2 10 η ¯ hG H 17 / = ( − M ≡ 9 π 1 I 1 ( 10 ε − H ) has been set so its value today is 1), the modes that are ( was c k ≈ 2 ) = a k ) η 0 k ), an increasing function of conformal time η , we have for those modes I , 5 k H − ¯ hV ( 7.5 ( I of the size of the surface of last scattering (corresponding to a ). Moreover, we note that, as the energy of mode E 9 π = ( 3 to find c k − 7.5 0 = a V k ) c ˙ k a η / 3 , and, thus, leads to a roughly scale invariant spectrum of fluctuations in a = k k Draft Version – – November 26, 2007 )( z 3 / . Thus, we find: to be of order 10 p 1 ( ˜ M V − × = (recall that the scale factor ε 0 4 ˙ φ − stands for the Planck length, and 10 p l ≈ 103 e-folds of total expansion, or something like 80 e-folds before the end of inflation in a = e Thus, the condition determining the time of collapse recall that the time of collapse is determined by reaches the value slow roll regime is, as shown in Eq. ( the collapse of each modefield is considerations, finite. the However, and sum in over completeis all analogy in modes with both, gives the infinite the standard if present quantum case thehas no and number relation the of with ordinary modes the quantum is universe’s field infinite. "size". Note theory This that case, the an ultraviolet formalism problem allowswhen and do us the to relevant look modes collapse? closer In into order the to collapse answer this issuecollapse question of and we the to use modes the ask with value wave for for number instance: The seeds of cosmic structures as a door to Quantum Gravity phenomena use the specific expressions for the scale factor which is independent of accordance with observations. It is worthon pointing out simple that dimensional this result grounds, is as far from the trivial dimensionless or expected factor early times the condition for collapse wouldexpands not that have such been point be would fulfilled, be andOne it attained. is question only as that the universe wasfiniteness raised of energy during created during the each presentation collapseIn and this of its independence regard, this of we the talk note "size"of by of that the the T. the universe. vacuum Jacobson, calculation energy concerns of ofmode of the the a the energies quantum quantum field above field is is essentiallyinfinitude in an analogous of Minkowski harmonic the to oscillator universe, space-time, is its the a in vacuum calculation finite energy, its regardless quantity of : ground the state: as each where scalar field with the incorrect power in Eq.( Thus, taking standard type of inflationary scenarios. Thus,for in it this to scheme include inflation the must complete have description at of least the 90 regime e-folds we are considering and to account also for parameter of the inflationary model. Aswas the value of the scalerelevant factor to say scales of orderfraction 10 of a degree in today’s sky) have N PoS(QG-Ph)038 , k = H k (7.8) a / c k a would be ) for mode k ( H k C Daniel Sudarsky η . Therefore this latter 1 . − I 2 / H 1 − ) ˜ V ( 2 / 1 ) 3 π 32 / 3 ( p kl will remain in any reasonable collapse scheme. . These dependences will, in turn, lead to slight k 18 6.9 ) = I ) H k ( π C 2 ( / k ) = H k η ( a ≡ , which leads to the appearance of the metric fluctuations. The point is i H k Draft Version – – November 26, 2007 , which would ordinarily be a very large number, indicating that the collapse a µν 2 / T 1 h − ) ˜ V ( 2 / 1 ) 3 π 6 )( ε / 16 A particularly robust source of thisseen effect in is in associated the with the expression finite for time the of function decoupling as can be exactly a constant, and that some dependence of that the energy momentumof tensor the contains quantum linear matter and field quadratic fluctuations, terms which in are the the expectation source values terms determining the geometric deviations from the standard form of theas spectrum the before the plasma inclusion oscillations. of This, theCMB in late time spectrum turn, physics that can such could, be conceivable, expected be toHowever, searched the leave for most some striking observationally. prediction traces of in the the scheme,very is observational strong the absence suppression. of The tensor modes, reasonversion or at of for least Einstein’s this their equation can and be itsand understood role anisotropies in by in describing the considering the metric thetaken manner arise semiclassical in to in which be our the scheme. an inhomogeneities Asas effective indicated the description in fundamental of the D.O.F. the introduction, susceptibledegrees gravitational the to of metric D.O.F., freedom be (which in is described in the the atare present classical the context described regime, are quantum quantum represented level. and mechanically by It and the not at which, inflaton is field) as the thus the a quantum the ones result level, that matter of undergoof a effective view fundamental quantum is aspect collapse that of gravitation (the gravitation at readertheories, the should quantum and recall level that, will that be in our drasticallynontrivial particular, point different value from it for standard will quantum not involve universal unitary evolution). This leads to a time would be much later thanmode. the time of “horizon exiting"Thus, or we find crossing that out, a of naive the realizationto of corresponding supply Penrose’s the ideas seems, element at that firstseeds we sight, of to argued be is cosmic a missing structure good in candidate universe. from the However, quantum more standard research fluctuations accounts along of during these thethe the scheme lines emergence would inflationary is of imply necessary a regime the second to in collapse findcollapse of the modes could out, already disrupt early for collapsed, in and instance, a whether whether such substantial secondary way the observational spectrum. 8. Predictions and discussion It is quite clear that it would be very hard to find a scheme in which the function The seeds of cosmic structures as a door to Quantum Gravity phenomena the collapse of the modes thatThe are usual of requirements the of order inflation ofso put the magnitude the present of lowest requirement the bound is surface at not ofThis something substantially last result stronger. like scattering can 60 be itself. e-folds directly of compared with inflation the so called, time of “horizon crossing" corresponding to the physical wavelength reaching the Hubble distance Thus, the ratio of scale( factors at collapse and at horizon crossing for a given mode is time is determined from: PoS(QG-Ph)038 Daniel Sudarsky , 2317, (2006) [arXiv: gr-qc/0508100]. 23 while no similar first order terms appear as source 19 i ˙ φ δ h 0 ˙ φ Draft Version – – November 26, 2007 Classical and Quantum Gravity Sudarsky, [1] “On the Quantum Origin of the Seeds of Cosmic Structure" A. Perez, H. Sahlmann, and D. The seeds of cosmic structures as a door to Quantum Gravity phenomena perturbations. And a close examination reveals that,first in order the contributions case proportional of to the scalar perturbations, we have of the tensor perturbations ( i.e. ofthe the tensor gravitational modes waves). At had the not time been ofsupport detected, the to in writing the contrast of prediction with this above. the article, scalarNext modes, we a consider fact briefly that the seems relationship to betweenfor the lead a present analysis quantum and theory the programsconflict of that search gravity. between The the first present thingdegrees analysis to of with freedom note are any is not program thatthe necessarily that there other directly hand, is, tied contemplates a with in that conflict the principle,to the could observable no be arise space-time fundamental intrinsic if geometry. quantized On the on quantumwould equal gravity require footing theory a required and quantum the description, in geometricin leading all D.O.F. to the circumstances a present, where situation and that the similara would matter contexts, theory invalidate degrees of the of applicability the quantum of gravity semi-classical freedom of that Einstein’s the is equations. circumstances posed The in by which challenge the that for the semiclassical present cosmological approach analysis situation would is at be to hand justified provide (which )mechanism would while an of include at characterization collapse the that same we time are provideThe an attributing search to explanation for for some manifestations the unknown of effective aspect quantum ofa aspects quantum of long gravity. gravitation, time, after has being practically transformed,researchers ignored have as for become of strongly attracted late, even into byinterpretation. some such It ideas an of seems doubtful attractive that consistency enterprise in andhave unclear this that been "Gold a Rush", ignored. large at The number least case of process, some of proved very the interesting to and emergence be direct of observationallybe avenues the accessible, inexorably seeds in tied, of seems which cosmic to gravitysurprising, be structure, and at the the quantum most least only physics glaring within known seem example.could the to On be quantum the called other gravity "purely hand, community, philosophicalconfronted it that, considerations", with is would observations, something naturally and lead that quite which to give started analysisaspects rise of as that to the predictions can what emergent that be proposals. could, directly The inof lesson principle, we aspects invalidate draw of from quantum this gravity casethem. one is This that has is, in to of the face course search the true, forgravity, clues in where most any there obscure scientific are issues enterprise so head but fewguiding on it pointers principles. is rather beyond more than the so ignore need in of a consistency field as such one a quantum of the few reliable 9. Acknowledgments I wish to thank thethe conference grant organizers 43914-F for of CONACyT the . hospitality. This work was supported in part by References PoS(QG-Ph)038 Found. , 2726, 1 , Daniel Sudarsky et. al.Astrophys. , 97, (2003). et. al. Phys. Rev. 148 Phys. Rev. D Physics meets philoso- , (Oxford University Press , 135, (2003); “Power Spec- 148 , , 1p (1972). 160 Astrophys. J. Suppl. Century", J. B. Hartle, [arXiv: gr-qc/9701022]; st 20 Astrophys. J. Supp. The Emperor’s New Mind , , L11, (1996); “First Year Wilkinson Micorowave , 257, (2003)[arXiv: quant-ph/0302164]; 464 et. al. , 1267 (2004), [arXiv: quant-ph/0312059, page 9]. 379 , 135-142 (2003), [arXiv: quant-ph/0112095]ã Why ÒmodalÓ 76 34 , 1777, (1985). Mon. Not. Roy. Astron. Soc. 31 Callender, C. (ed.) (2001). , , 470, (1986). Phys. Rept , 1899, (1985); “Fluctuations in the Inflationary Universe", S. W. Hawking Draft Version – – November 26, 2007 , 180, (1983); “Origin of Structure in the Universe" J.J. Halliwell and S. W. D 34 32 , 5-19 (1993) and the review of approaches to the problem presented in A. Rev. Mod. Phys. 6 et. al. Astrophys. J. , 1, (2003); “First Year Wilkinson Micorwave Anisotropy Probe (WMAP) Ob- B 224 Phys. Rev. D 148 Phys. Rev. , 042001, (2001); G. Hinshaw Phys. Rev. D 63 , “Generalized Quantumqc/0510126]. mechanics for Quantum Gravity", J. B. Hartle, [arXiv: gr- Bassi G. C. Ghirardi, trum of Primordial InhomogeneityK.M. Determined Gorski from four Year COBE DMR SKY Maps", of Phys. Lett. 1989); R. Penrose, On Gravity’s Role inphy Quantum at State the Reduction, Planck in scale (1970); Y. B. Zel´dovich Anisotropy Probe (WMAP) Observations: Preliminary Results" C.L. Bennett ics see for instancepretations the of classical quantum reference mechanics “PhilosophySons, in of New historical York quantum 1974); perspective" mechanics. or M.Peres The the (Kluwer, Jammer, inter- more Academic ( Publishers, recent 1993). John “Quantum “TheOmnes, Wiley Theory: Interpretation ( and Concepts of Princeton Quantum and University Mechanics" Press Methods", R. ence 1994), A. has and not the Solved more the specificStud. Measurement critiques Hist. Problem: “ Philos. A Mod. Why Phys. Response Decoher- tointerpretations PW of Anderson" quantum - mechanics S. don’t L. solve Adler the measurement problem A Elby, Weber, http://www.mat.univie.ac.at/ neum/physics-faq.txt. Schlosshauer, servations: Foreground Emission", C. Bennett et al. D J. Suppl. Pi Nucl. Phys. Hawking, [5] “The Emperor’s New Mind", R. Penrose, [7] “Fluctuations at the threshold of classical cosmology" E. R. Harrison, [6] “Quantum Cosmology Problems for the 21 [4] For reviews abut the various approaches to the measurement problem in quantum mechan- [8] “A Unified Dynamics For Micro And Macro Systems", G. C.[9] Ghirardi, A. Arnold Rimini, Neumaier, and in T. the "theoretical physics FAQ" at his University of Wien, webpage: [2] “Quantum Mechanics of the scalar field in the new inflationary Universe", A. Guth and S.-Y. [3] “Cosmological parameters From First results of Boomerang" A.E. Lange [10] “Decoherence, the measurement problem and interpretations of quantum Mechanics" M. The seeds of cosmic structures as a door to Quantum Gravity phenomena PoS(QG-Ph)038 , 49 Int. Phys. , 255 88 Daniel Sudarsky , 664, (1951). 82 Phys. Rev. Lett. , 2912,(1989); “Ori- 39 , 377 (1996) [arXiv: gr- , , 199 (2005) [arXiv:hep- 13 669 Phys. Rev. Nucl. Phys. Proc. Suppl. Phys. Rev. D , 171 (1993) [arXiv:gr-qc/9303036]; “The 2 Moscow 1990, Proceedings, Quantum gravity Class. Quant. Grav. , 374 (1999) [arXiv:gr-qc/9812043]; Lect. Notes Phys. 21 551 , 1924 (1997) [arXiv:gr-qc/9702018]; “Decoherence 56 , 133, (2000). 282 Int. J. Mod. Phys. D Nucl. Phys. B Phys. Rev. D Draft Version – – November 26, 2007 , 1281, (2003), [arXiv:quant-ph/0211163]; “Decoherence during inflation: Phys. Lett. A 42 , 063506 (2005) [arXiv:gr-qc/0506051]; “Inflationary Cosmological Perturbations , 203, (1992); “Decoherence Funtional and Inhomogeneities in the Early Universe", 72 215 R. Laflamme and A. Matacz gin of Classical Structure(2000) [arXiv:astro-ph/0006252]; From “Semiclassicality Inflation", and C.turbations", decoherence D. Kiefer of Polarski and Cosmological A.A. Starobinsky, per- Rep. self-induced approach to decoherence inJ. cosmology,” Theor. M. Phys. Castagnino and O. Lombardi, The generation of classicalRev. inhomogeneities,” D F. C. Lombardo and D. Lopez Nacir, Phys. (QC178:S4:1990), p. 456-472. (see High EnergyInvariant Cosmological Physics Perturbations" Index R. 30 Branderberger (1992) H. No. Feldman 624); and V. “Gauge Mukhavov, of Quantum Mechanical Origin" J. Martin, qc/9504030]; “ Environment Induced Superselectionment In Induced Cosmology", Superselection W.H. In Zurek, Cosmology Environ- in th/0406011]; “ Best Unbiased Estimatesishchuk for and Microwave J. background Martin, Anisotropies", L.P. Gr- herence Theoretical, Experimental and ConceptualE. Problems" Joos, Eds. C. P. Blanchard, Keifer and D. I. Giulini, O. Stamatescu ( Springer 1999) [arXiv: quant-ph/9908008]. in Quantum Cosmology atKiefer, the and onset I.V. Mishakov, of Inflation", A.O. Barvinsky, A.Y. Kamenshchik, C. th/07043540]. 9, (1982). Press 1996). tial States", J.qc/961101904030] . Lesggourges, David Polarski and Alexei1987). A. Starobinsky [arXiv: gr- The seeds of cosmic structures as a door to Quantum Gravity phenomena [11] E. Joos, in "Elements of Environmental Decoherence", proceedings of the conference Deco- [12] “Decoherence in Quantum Cosmology", J.J. Halliwell, [19] “Inflationary perturbations: The Cosmological Schwinger effect" J. Martin,[20] [arXiv: “On Gauge hep- Invariance and Vacuum Polarization" J. Schwinger [16] “Cosmology and Astrophysics Through Problems", T. Padmanabhan (Cambridge University [17] "The Road to Reality", R. Penrose ( Ed.[18] Alfred A. B. Kopf- D’Espagnat, New York, 2006). [13] “Quantum To Classical Transition of Cosmological Perturbations for Non Vacuum[14] Ini- “Speakable and Unspeakable in Quantum Mechanics", J. S. Bell (Cambridge University Press [15] “A New violation of Bell’s inequalities" A. Aspect, P. Grangier, G. Roger, PoS(QG-Ph)038 Daniel Sudarsky J. Phys. Conf. Ser. , 38, (1985). 32 Physics Today 22 Draft Version – – November 26, 2007 , 012029, (2007) [arXiv: gr-qc/0612005] . cepts and Methods" (Kluwer Academic Publishers, 1993) 68 The seeds of cosmic structures as a door to Quantum Gravity phenomena [21] See for instance discussions about the EPR experiment in A. Peres “[22] Quantum Theory: “Is Con- the Moon There when nobody Looks?" D. Mermin [23] “The Seeds of Cosmic structure as a door to New Physics" D. Sudarsky,