by JA Wheeler · 1989 · Cited by 1270 — its ultimate significance from bits, binary yes-or-no indications, a conclusion which we epitomize in the phrase, it from bit. 19.1 Quantum Physics Requires a New

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19INFORMATION, PHYSICS, QUANTUM: THESEARCH FOR LINKSJohn Archibald Wheeler * tAbstractThis report reviews what quantum physics and information theory have to tell usabout the age-old question, How come existence? No escape is evident from fourconclusions: (1) The world cannot be a giant machine, ruled by any preestablishedcontinuum physical law. (2) There is no such thing at the microscopic level asspace or time or spacetime continuum. (3) The familiar probability function orfunctional, and wave equation or functional wave equation, of standard quantumtheory provide mere continuum idealizations and by reason of this circumstanceconceal the information-theoretic source from which they derive. (4) No element inthe description of physics shows itself as closer to primordial than the elementaryquantum phenomenon, that is, the elementary device-intermediated act of posing ayes-no physical question and eliciting an answer or, in brief, the elementary act ofobserver-participancy. Otherwise stated, every physical quantity, every it, derivesits ultimate significance from bits, binary yes-or-no indications, a conclusion whichwe epitomize in the phrase, it from bit.19.1 Quantum Physics Requires a New View of RealityRevolution in outlook though Kepler, Newton, and Einstein brought us [1-4], andstill more startling the story of life [5-7] that evolution forced upon an unwillingworld, the ultimate shock to preconceived ideas lies ahead, be it a decade hence,a century or a millenium. The overarching principle of 20th-century physics, thequantum [8] Š and the principle of complementarity [9] that is central idea of thequantum Š leaves us no escape, Niels Bohr tells us, [10] from “a radical revisionof our attitude as regards physical reality” and a “fundamental modification ofall ideas regarding the absolute character of physical phenomena.” TranscendingEinstein’s summons [11] of 1908, “This quantum business is so incredibly importantand difficult that everyone should busy himself with it,” Bohr’s modest words directus to the supreme goal: Deduce the quantum from an understanding of existence.’Reproduced from Proc. 3rd Int. Symp. Foundations of Quantum Mechanics, Tokyo, 1989,pp.354-368.copyright of this paper is held by the author.

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310JOHN ARCHIBALD WHEELERHow make headway toward a goal so great against difficulties so large? Thesearch for understanding presents to us three questions, four no’s and five clues:Three questions,Ł How come existence?Ł How come the quantum?Ł How come “one world” out of many observer-participants?Four no’s,Ł No tower of turtlesŁ No lawsŁ No continuumŁ No space, no time.Five clues,Ł The boundary of a boundary is zero.Ł No question? No answer!Ł The super-Copernican principle.Ł “Consciousness”Ł More is different.19.2 “It from Bit” as Guide in Search for Link ConnectingPhysics, Quantum and InformationIn default of a tentative idea or working hypothesis, these questions, no’s and cluesŠ yet to be discussed Š do not move us ahead. Nor will any abundance of cluesassist a detective who is unwilling to theorize how the crime was committed! Awrong theory? The policy of the engine inventor, John Kris, reassures us, “Starther up and see why she don’t go!” In this spirit [12-47] I, like other searchers [48-51]attempt formulation after formulation of the central issues, and here present a wideroverview, taking for working hypothesis the most effective one that has survived thiswinnowing: It from bit. Otherwise put, every it Š every particle, every field offorce, even the spacetime continuum itself Š derives its function, its meaning, itsvery existence entirely Š even if in some contexts indirectly Š from the apparatus-elicited answers to yes or no questions, binary choices [52], bits.THE SEARCH FOR LINKS311It from bit symbolizes the idea that every item of the physical world has atbottom Š at a very deep bottom, in most instances Š an immaterial source andexplanation; that what we call reality arises in the last analysis from the posing ofyes-no questions and the registering of equipment-evoked responses; in short, thatall things physical are information-theoretic in origin and this is a participatoryuniverse.Three examples may illustrate the theme of it from bit. First, the photon. Withpolarizer over the distant source and analyzer of polarization over the photodetectorunder watch, we ask the yes or no question, “Did the counter register a click duringthe specified second?” If yes, we often say, “A photon did it.” We know perfectlywell that the photon existed neither before the emission nor after the detection.However, we also have to recognize that any talk of the photon “existing” duringthe intermediate period is only a blown-up version of the raw fact, a count.The yes or no that is recorded constitutes an unsplitable bit of information. Aphoton, Wootters and Zurek demonstrate [53, 54], cannot be cloned.As second example of it from bit, we recall the Aharonov-Bohm scheme [55] tomeasure a magnetic flux. Electron counters stationed off to the right of a doubly-slit screen give yes-or-no indications of the arrival of an electron from the sourcelocated off to the left of the screen, both before the flux is turned on and afterward.That flux of magnetic lines of force finds itself embraced between Š but untouchedby Š the two electron beams that fan out from the two slits. The beams interfere.The shift in interference fringes between field off and field on reveals the magnitudeof the flux,(phase change around perimeter of the included area)= 2vr x (shift of interference pattern, measured in number of fringes)= (electron charge) x (magnetic flux embraced)/fie(19.1)Here H = 1.0546 x 10 27 gcrn2/s is the quantum in conventional units, or in ge-ometric units [4, 16] Š where both time and mass are measured in the units oflength Šfi=fic = 2.612 x 10~66 cm2 = the square of the Planck length, 1.616 x10~33 = what we hereafter term the Planck area.Not only in electrodynamics but also in geornetrodynamics and in every othergauge-field theory, as Anandan, Aharonov and others point out [56, 57] the differ-ence around a circuit in the phase of an appropriately chosen quantum-mechanicalprobability amplitude provides a measure of the field. Here again the concept of itfrom bit applies [38]. Field strength or spacetime curvature reveals itself throughshift of interference fringes, fringes that stand for nothing but a statistical patternof yes-or-no registrations.When a magnetometer reads that it which we call a magnetic field, no referenceat all to a bit seems to show itself. Therefore we look closer. The idea behind th«operation of the instrument is simple. A wire of length I carries a current i through

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312JOHN ARCHIBALD WHEELERTHE SEARCH FOR LINKS313Fig. 19.1. Symbolic representation of the “telephone number” of the particular one of the2″ conceivable, but by now indistinguishable, configurations out of which this particularblackhole, of Bekenstein number N and horizon area 4NHlogs2, was put together. Symbol,also, in a broader sense, of the theme that every physical entity, every it, derives from bits.Reproduced from JGST, p.220.a magnetic field B that runs perpendicular to it. In consequence the piece of copperreceives in the time t a transfer of momentum p in a direction z perpendicular tothe directions of the wire and of the field,p – Blit= (flux per unit z) x (charge, e, of the elementary carrier of current)x (number, N,of carriers that pass in the time t)(19.2)This impulse is the source of the force that displaces the indicator needle of themagnetometer and gives us an instrument reading. We deal with bits wholesalerather than bits retail when we run the fiducial current through the magnetometercoil, but the definition of field founds itself no less decisively on bits.As third and final example of it from bit we recall the wonderful quantumfinding of Bekenstein [58-60] Š totally unexpected denouement of earlier classicalwork of Penrose [61] Christodoulou [62] and Ruffini [63] Š refined by Hawking [64,65] that the surface area of the horizon of a blackhole, rotating or not, measuresthe entropy of the blackhole. Thus this surface area, partitioned in imagination(Fig. 19.1) into domains each of size 4fUoge2, that is, 2.77 times the Planck area,yields the Bekenstein number, N; and the Bekenstein number, so Thorne and Zurekexplain [66] tells us the number of binary digits, the number of bits, that would berequired to specify in all detail the configuration of the constituents out of whichthe blackhole was put together. Entropy is a measure of lost information. To nocommunity of newborn outside observers can the blackhole be made to reveal outof which particular one of 2N configurations it was put together. Its size, an it, isfixed by the number, N, of bits of information hidden within it.The quantum, H, in whatever correct physics formula it appears, thus serves aslamp. It lets us see horizon area as information lost, understand wave number oflight as photon momentum and think of field flux as bit-registered fringe shift.Giving us its as bits, the quantum presents us with physics as information.How come a value for the quantum so small as H = 2.612 x 10~66 cm2? As wellas ask why the speed of light is so great as c = 3 x 1010 cm/s! No such constantas the speed of light ever makes an appearance in a truly fundamental accountof special relativity or Einstein geometrodynamics, and for a simple reason: Timeand space are both tools to measure interval. We only then properly conceivethem when we measure them in the same units [4, 16]. The numerical value ofthe ratio between the second and the centimeter totally lacks teaching power. Itis an historical accident. Its occurrence in equations obscured for decades one ofNature’s great simplicities. Likewise with H\y equation that contains an Hfloats a banner, “It from bit”. The formula displays a piece of physics that wehave learned to translate into information-theoretic terms. Tomorrow we will havelearned to understand and express all of physics in the language of information. Atthat point we will revalue H = 2.612 x 10~66 cm2 Š as we downgrade c = 3 x 1010cm/s today Š from constant of Nature to artifact of history, and from foundationof truth to enemy of understanding.19.3 Four No’sTo the question, “How come the quantum?” we thus answer, “Because what wecall existence is an information-theoretic entity.” But how come existence? Itsas bits, yes; and physics as information, yes; but whose information? How doesthe vision of one world arise out of the information-gathering activities of manyobserver-participants? In the consideration of these issues we adopt for guidelinesfour no’s.First no: “No tower of turtles,” advised William James. Existence is not a globesupported by an elephant, supported by a turtle, supported by yet another turtle,and so on. In other words, no infinite regress. No structure, no plan of organization,no framework of ideas underlaid by another structure or level of ideas, underlaidby yet another level, by yet another, ad infinitum, down to a bottomless night. Toendlessness no alternative is evident but loop [47, 67], such a loop as this: Physics

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314JOHN ARCHIBALD WHEELERTHE SEARCH FOR LINKS315gives rise to observer-participancy; observer-participancy gives rise to information;and information gives rise to physics.Existence thus built [68] on “insubstantial nothingness”? Rutherford and Bohrmade a table no less solid when they told us it was 99.9 percent emptiness.Thomas Mann may exaggerate when he suggests [69] that ” we are actuallybringing about what seerns to be happening to us,” but Leibniz [70] reassures us,”Although the whole of this life were said to be nothing but a dream and the physicalworld nothing but a phantasm, I should call this dream or phantasm real enoughif, using reason well, we were never deceived by it.”Second no: No laws. “So far as we can see today, the laws of physics cannothave existed from everlasting to everlasting. They must have come into being atthe big bang. There were no gears and pinions, no Swiss watch-makers to putthings together, not even a pre-existing plan Only a principle of organizationwhich is no organization at all would seem to offer itself. In all of mathematics,nothing of this kind more obviously offers itself than the principle that ‘the boundaryof boundary is zero.’ Moreover, all three great field theories of physics use thisprinciple twice over This circumstance would seem to give us some reassurancethat we are talking sense when we think of physics being” [32] as foundation-freeas a logic loop, the closed circuit of ideas in a self-referential deductive axiomaticsystem [71-74].Universe as machine? This universe one among a great ensemble of machineuniverses, each differing from the others in the values of the dimensionless constantsof physics? Our own selected from this ensemble by an anthropic principle of oneor another form [75]? We reject here the concept of universe as machine not leastbecause it “has to postulate explicitly or implicitly, a supermachine, a scheme,a device, a miracle, which will turn out universes in infinite variety and infinitenumber” [47],Directly opposite to the concept of universe as machine built on law is the visionof a world self-synthesized. On this view, the notes struck out on a piano by theobserver-participants of all places and all times, bits though they are, in and bythemselves constitute the great wide world of space and time and things.Third no: No continuum. No continuum in mathematics and therefore no con-tinuum in physics. A half-century of development in the sphere of mathematicallogic [76] has made it clear that there is no evidence supporting the belief in the ex-istential character of the number continuum. “Belief in this transcendental world,”Hermann Weyl tells us, “taxes the strength of our faith hardly less than the doc-trines of the early Fathers of the Church or of the scholastic philosophers of theMiddle Ages” [77]. This lesson out of mathematics applies with equal strengthto physics. “Just as the introduction of the irrational numbers is a convenientmyth [which] simplifies the laws of arithmetic so physical objects,” Willard VanOrman Quine tells us [78] “are postulated entities which round out and simplifyour account of the flux of existence The conceptual scheme of physical objectsis a convenient myth, simpler than the literal truth and yet containing that literaltruth as a scattered part.”Nothing so much distinguishes physics as conceived today from mathematics asthe difference between the continuum character of the one and the discrete charac-ter of the other. Nothing does so much to extinguish this gap as the elementaryquantum phenomenon “brought to a close,” as Bohr puts it [10] by “an irreversibleact of amplification,” such as the click of a photodetector or the blackening ofa grain of photographic emulsion. Irreversible? More than one idealized experi-ment [38] illustrates how hard it is, even today, to give an all-inclusive definition ofthe term irreversible. Those difficulties supply pressure, however, not to retreat toold ground, but to advance to new insight. In brief, continuum-based physics, no;information-based physics, yes.Fourth and last no: No space, no time. Heaven did not hand down the word”time”. Man invented it, perhaps positing hopefully as he did that “Time is Nature’sway to keep everything from happening all at once” [79]. If there are problems withthe concept of time, they are of our own creation! As Leibniz tells us, [80] ” timeand space are not things, but orders of things ;” or as Einstein put it, [81] “Timeand space are modes by which we think, and not conditions in which we live.”What are we to say about that weld of space and time into spacetime whichEinstein gave us in his 1915 and still standard classical geometrodynamics? On thisgeometry quantum theory, we know, imposes fluctuations [13,14, 82]. Moreover, thepredicted fluctuations grow so great at distances of the order of the Planck lengththat in that domain they put into question the connectivity of space and deprivethe very concepts of “before” and “after” of all meaning [83]. This circumstancereminds us anew that no account of existence can ever hope to rate as fundamentalwhich does not translate all of continuum physics into the language of bits.We will not feed time into any deep-reaching account of existence. We mustderive time Š and time only in the continuum idealization Š out of it. Likewisewith space.19.4 Five CluesFirst clue: The boundary of a boundary is zero. This central principle of algebraictopology [84], identity, triviality, tautology, though it is, is also the unifying themeof Maxwell electrodynamics, Einstein geometrodynamics and almost every versionof modern field theory [42], [85-88]. That one can get so much from so little, almosteverything from almost nothing, inspires hope that we will someday complete themathematization of physics and derive everything from nothing, all law from nolaw.Second clue: No question, no answer. Better put, no bit-level question, no bit-

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316JOHN ARCHIBALD WHEELER.THE SEARCH FOR LINKS317level answer. So it is in the game of twenty questions in its surprise version [89].And so it is for the electron circulating within the atom or a field within a space.To neither field nor particle can we attribute a coordinate or momentum until adevice operates to measure the one or the.other. Moreover any apparatus thataccurately [90] measures the one quantity inescapably rules out then and there theoperation of equipment to measure the other [9, 91, 92]. In brief, the choice ofquestion asked, and choice of when it’s asked, play a part Š not the whole part,but a part Š in deciding what we have the right to say [38, 43].Bit-registration of a chosen property of the electron, a bit-registration of thearrival of a photon, Aharonov-Bohm bit-based determination of the magnitude of afield flux, bulk-based count of bits bound in a blackhole: All are examples of physicsexpressed in the language of information. However, into a bit count that one mighthave thought to be a private matter, the rest of the nearby world irresistibly thrustsitself. Thus the atom-to-atom distance in a ruler Š basis for a bit count of distanceŠ evidently has no invariant status, depending as it does on the temperature andpressure of the environment. Likewise the shift of fringes in the Aharonov-Bohmexperiment depends not only upon the magnetic flux itself, but also on the chargeof the electron. But this electron charge Š when we take the quantum itself tobe Nature’s fundamental measuring unit Š is governed by the square root of thequantity e2/He – 1/137.036, a “constant” which Š for extreme conditions Šis as dependent on the local environment [93] as is a dielectric “constant” or theatom-to-atom spacing in the ruler.The contribution of the environment becomes overwhelmingly evident when weturn from length of bar or flux of field to the motion of alpha particle through cloudchamber, dust particle through 3°K-background radiation or Moon through space.This we know from the analyses of Bohr and Mott [94], Zeh [95, 96], Joos andZeh [97], Zurek [98-100] and Unruh and Zurek [101]. It from bit, yes; but the restof the world also makes a contribution, a contribution that suitable experimentaldesign can minimize but not eliminate. Unimportant nuisance? No. Evidence thewhole show is wired up together? Yes. Objection to the concept of every it frombits? No.Build physics, with its false face of continuity, on bits of information! Whatthis enterprise is we perhaps see more clearly when we examine for a moment athoughtful, careful, wide-reaching exposition [102] of the directly opposite thesis,that physics at bottom is continuous; that the bit of information is not the basic en-tity. Rate as false the claim that the bit of information is the basic entity. Instead,attempt to build everything on the foundation of some “grand unified field theory”such as string theory [103, 104] Š or in default of that, on Einstein’s 1915 and stillstandard geometrodynamics. Hope to derive that theory by way of one or anotherplausible line of reasoning. But don’t try to derive quantum theory. Treat it assupplied free of charge from on high. Treat quantum theory as a magic sausagegrinder which takes in as raw meat this theory, that theory or the other theoryand turns out a “wave equation,” one solution of which is “the” wave function forthe universe [14, 102, 105-107]. From start to finish accept continuity as right andnatural: Continuity in the manifold, continuity in the wave equation, continuity inits solution, continuity in the features that it predicts. Among conceivable solutionsof this wave equation select as reasonable one which “maximally decoheres,” onewhich exhibits “maximal classicity” Š maximal classicity by reason, not of “some-thing external to the framework of wave function and Schrodinger equation,” butsomething in “the initial conditions of the universe specified within quantum theoryitself.”How compare the opposite outlooks of decoherence and it-from-bit? Removethe casing that surrounds the workings of a giant computer. Examine the bundlesof wires that run here and there. What is the status of an individual wire? Math-ematical limit of bundle? Or building block of bundle? The one outlook regardsthe wave equation and wave function to be primordial and precise and built oncontinuity, and the bit to be idealization. The other outlook regards the bit to bethe primordial entity, and wave equation and wave function to be secondary andapproximate Š and derived from bits via information theory.Derived, yes; but how? No one has done more than William Wootters towardsopening up a pathway [108, 109] from information to quantum theory. He putsinto connection two findings, long known, but little known. Already before theadvent of wave mechanics, he notes, the analyst of population statistics R. A. Fisherproved [110, 111] that the proper tool to distinguish one population from another isnot the probability of this gene, that gene and the third gene (for example), but thesquare roots of these probabilities; that is to say, the two probability amplitudes,each probability amplitude being a vector with three components. More precisely,Wootters proves, the distinguishability between the two populations is measured bythe angle in Hilbert space between the two state vectors, both real. Fisher, however,was dealing with information that sits “out there”. In microphysics, however, theinformation does not sit out there. Instead, Nature in the small confronts us witha revolutionary pistol, “No question, no answer.” Complementarity rules. Andcomplementarity as E.C.G. Stueckelberg proved [112, 113] as long ago as 1952,and as Saxon made more readily understandable [114] in 1964, demands that theprobability amplitudes of quantum physics must be complex. Thus Wootters derivesfamiliar Hilbert space with its familiar complex probability amplitudes from the twindemands of complementarity and measure of distinguishability.Try to go on from Wootters’s finding to deduce the full blown machinery ofquantum field theory? Exactly not to try to do so Š except as idealization Š isthe demand laid on us by the concept of it from bit. How come?Probabilities exist “out there” no more than do space or time or the position ofthe atomic electron. Probability, like time, is a concept invented by humans, andhumans have to bear the responsibility for the obscurities that attend it. Obscurities

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318JOHN ARCHIBALD WHEELERthere are whether we consider probability defined as frequency [115] or defined a laBayes [116-119]. Probability in the sense of frequency has no meaning as appliedto the spontaneous fission of the particular plutonium nucleus that triggered theNovember 1, 1952 H-bomb blast.What about probabilities of a Bayesian cast, probabilities “interpreted not as fre-quencies observable through experiments, but as degrees of plausibility one assignsto each hypothesis based on the data and on one’s assessment of the plausibilityof the hypotheses prior to seeing the data” [120]. Belief-dependent probabilities,different probabilities assigned to the same proposition by different people [121]?Probabilities associated [122] with the view that “objective reality is simply aninterpretation of data agreed to by large numbers of people?”Heisenberg directs us to the experiences [123] of the early nuclear-reaction-ratetheorist Fritz Houtermans, imprisoned in Kharkov during the time of the Stalinterror, ” the whole cell would get together to produce an adequate confession [and] helped them [the prisoners] to compose their ‘legends’ and phrase themproperly, implicating as few others as possible.”Existence as confession? Myopic but in some ways illuminating formulation ofthe demand for intercommunication implicit in the theme of it from bit!So much for “No question, no answer.”Third clue: The super-Copernican principle [47]. This principle rejects now-centeredness in any account of existence as firmly as Copernicus repudiated here-centeredness. It repudiates most of all any tacit adoption of here-centeredness inassessing observer-participants and their number.What is an observer-participant? One who operates an observing device andparticipates in the making of meaning, meaning in the sense of F011esdal [124],”Meaning is the joint product of all the evidence that is available to those whocommunicate.” Evidence that is available? The investigator slices a rock and pho-tographs the evidence for the heavy nucleus that arrived in the cosmic radiation of abillion years ago [38]. Before he can communicate his findings, however, an asteroidatomizes his laboratory, his records, his rocks and him. No contribution to meaning!Or at least no contribution then. A forensic investigation of sufficient detail andwit to reconstruct the evidence of the arrival of that nucleus is difficult to imagine.What about the famous tree that fell in the forest with no one around [125]? Itleaves a fallout of physical evidence so near at hand and so rich that a team of up-to-date investigators can establish what happened beyond all doubt. Their findingscontribute to the establishment of meaning.”Measurements and observations,” it has been said, [102] “cannot be funda-mental notions in a theory which seeks to discuss the early universe when neitherexisted.” On this view the past has a status beyond all questions of observer-participancy. It from bit offers us a different vision: “Reality is theory” [126]; “theTHE SEARCH FOR LINKS319past has no evidence except as it is recorded in the present” [127]. The photon thatwe are going to register tonight from that four billion-year old quasar cannot be saidto have had an existence “out there” three billion years ago, or two (when it passedan intervening gravitational lens) or one, or even a day ago. Not until we have fixedarrangements at our telescope do we register tonight’s quantum as having passedto the left (or right) of the lens or by both routes (as in a double slit experiment).This registration like every delayed-choice experiment [21, 40], reminds us that noelementary quantum phenomenon is a phenomenon until, in Bohr’s words [10], “Ithas been brought to a close” by “an irreversible act of amplification.” What we callthe past is built on bits.Enough bits to structure a universe so rich in features as we know this world tobe. Preposterous! Mice and men and all on Earth who may ever come to rank asintercommunicating meaning-establishing observer-participants will never mount abit count sufficient to bear so great a burden.The count of bits needed, huge though it may be, nevertheless, so far as wecan judge, does not reach infinity. In default of a better estimate, we follow fa-miliar reasoning [128] and translate into the language of the bits the entropy ofthe primordial cosmic fireball as deduced from the entropy of the present 2.735°K(uncertainty <0.05°K) microwave relict radiation [129] totaled over a 3-sphere ofradius 13.2 x 109 light years (uncertainty <35%) [130] or 1.25 x 1028 cm and ofvolume 27T2 radius3,(number of bits) = (log^e) x (number of nats)= (log^e) x (entropy /Boltzmann's constant,/:)= 1.44 x [(Sir4/45)(radius. kT/Kc)3]= 8 x 1088(19.3)It would be totally out of place to compare this overpowering number with the num-ber of bits of information elicited up to date by observer-participancy. So warnsthe super-Copernican principle. We today, to be sure, through our registering de-vices, give a tangible meaning to the history of the photon that started on its wayfrom a distant quasar long before there was any observer-participancy anywhere.However, the far more numerous establishers of meaning of time to come have alike inescapable part Š by device-elicited quesstions and registration of answer Šin generating the "reality" of today. For this purpose, moreover, there are bil-lions of years yet to come, billions on billions of sites of observer-participancy yetto be occupied. How far foot and ferry have carried rneaning^making communica-tion in fifty thousand years gives faint feel for how far interstellar propagation isdestined [131, 132] to carry it in fifty billion years.Do bits needed balance bits achievable? They must, declares the concept of"world as system self-synthesized by quantum networking" [47]. By no predictiondoes this concept more clearly expose itself to destruction, in the sense of Pop-per [133]. PAGE - 8 ============ 322JOHN ARCHIBALD WHEELER(1) the 0-or-l sharpness of definition of bit number nineteen in a string of binarydigits, or (2) the accordion property of a mathematical theorem, the length of which,that is, the number of supplementary lemmas contained in which, the analyst canstretch or shrink according to his convenience.Four. Survey one by one with an imaginative eye the powerful tools that math-ematics Š including mathematical logic Š has won and now offers to deal withtheorems on a wholesale rather than a retail level, and for each such techniquework out the transcription into the world of bits. Give special attention to one andanother deductive axiomatic system which is able to refer to itself [159], one andanother self-referential deductive system.Five: From the wheels-upon-wheels-upon-wheels evolution of computer pro-gramming dig out, systematize and display every feature that illuminates the level-upon-level-upon-level structure of physics.Six: Capitalize on the findings and outlooks of information theory [160-163],algorithmic entropy [164], evolution of organisms [165-167] and pattern recogni-tion [168-175]. Search out every link each has with physics at the quantum level.Consider, for instance, the string of bits 1111111 and its representation as thesum of the two strings 1001110 and 0110001 Explore and exploit the connec-tion between this information-theoretic statement and the findings of theory andexperiment on the correlation between the polarizations of the two photons emittedin the annihilation of singlet positronium [176] and in like Einstein-Podolsky-Rosenexperiments [177], Seek out, moreover, every realization in the realm of physics ofthe information-theoretic triangle inequality recently discovered by Zurek [178].Finally: Deplore? No, celebrate the absence of a clean clear definition of theterm "bit" as elementary unit in the establishment of meaning. We reject "thatview of science which used to say, 'Define your terms before you proceed.' Thetruly creative nature of any forward step in human knowledge," we know, "is suchthat theory, concept, law and method of measurement Š forever inseparable Š areborn into the world in union [179]." If and when we learn how to combine bits infantastically large numbers to obtain what we call existence, we will know betterwhat we mean both by bit and by existence.A single question animates this report: Can we ever expect to understand ex-istence? Clues we have, and work to do, to make headway on that issue. Surelysomeday, we can believe, we will grasp the central idea of it all as so simple, sobeautiful, so compelling that we will all say to each other, "Oh, how -could it havebeen otherwise! How could we all have been so blind so long!"AcknowledgementsFor discussion, advice or judgment on one or another issue taken up in this review,I am indebted to Nandar Balazs, John D. Barrow, Charles H. Bennett, DavidTHE SEARCH FOR LINKS323Deutsch, Robert H. Dicke, Freeman Dyson and the late Richard P. Feynman aswell as David Gross, James B. Hartle, John J. Hopfield, Paul C. Jeffries, BernulfKanitscheider, Arkady Kheyfets and Rolf W. Landauer; and to Warner A. Miller,John R. Pierce, Willard Van Orman Quine, Benjamin Schumacher and Frank J.Tipler as well as William G. Unruh, Morton White, Eugene P. Wigner, William K.Wootters, Hans Dieter Zeh and Wojciech H. Zurek. For assistance in preparationof this report I thank E. L. Bennett and NSF grant PHY245-6243 to PrincetonUniversity. I give special thanks to the sponsors of the 28-31 August 1989 conferenceISQM Tokyo '89 at which the then current version of the present analysis wasreported.This report evolved from presentations at Santa Fe Institute Conferences, 29May-2 June and 4-8 June 1989 and at the 3rd International Symposium on Founda-tions of Quantum Mechanics in the Light of New Technology, Tokyo, 28-31 August1989, under the title "Information, Physics, Quantum: The Search for Links;" andheaded "Can We Ever Expect to Understand Existence?", as the Penrose Lectureat the 20-22 April 1989 annual meeting of Benjamin Franklin's "American Philo-sophical Society, held at Philadelphia for Promoting Useful Knowledge," and theAccademia Nazionale dei Lincei Conference on La Verita nella Scienza, Rome, 13October 1989; submitted to proceedings of all four in fulfillment of obligation andin deep appreciation for hospitality. Preparation for publication assisted in part byNSF Grant PHY 245-6243 to Princeton University.DiscussionA discussion followed:N. G. van Kampen: Did you mean to say that the observer influences the ob-served object?J. A. Wheeler. The observer does not influence the past. Instead, by his choiceof question, he decides about what feature of the object he shall have the right tomake a clear statement.J.P. Vigier. Two problems.1. The first is that the QSO raise lots of unsolved problems, i.e. Š strangequantized N0/log(l + z) relation Š correlation with galaxies (Arp) Š angu-lar correlation with brightest nearby galaxies (Burbidge et al.)2. The second is that the idea (Einstein et al.) of the reality of fields has led(assuming that "particles" are field singularities) to the only known justifica-tion of the geodesic law. To contest it is to make the meaning of dynamicalbehaviour purely observer-dependent, i.e., to kill the reality of the physicalworld. 174 KB – 15 Pages