11 Timelessness strictly inside the Quantum Realm
Knud Thomsen, Paul Scherrer Institut, Switzerland, [email protected]
Abstract
Time is one of the undisputed foundations of our life in the real world. Here it is argued that inside small isolated quantum systems, time does not pass as we are used to, and it is primarily in this sense that quantum objects enjoy only limited reality. Quantum systems, as they are considered here, are embedded in the everyday classical world. Their preparation as well as their measurement-phases leave durable records and traces in the entropy of the environment. The Landauer Principle then gives a quantitative threshold for irreversibility. With double slit experiments and tunneling as paradigmatic examples, it is proposed that a label of timelessness offers clues for rendering a Copenhagen type interpretation of quantum physics more “realistic” and acceptable by providing a coarse but viable link from the fundamental quantum realm to the classical world in which humans live.
Keywords relational time, timelessness, records, causality in 1 real world There are at least two levels of uncertainty associated with Quantum Physics since its discovery, and they are not independent of each other. The basic quantum formalisms are well-established and they comprise intrinsic quantified uncertainty-relations. The observed behavior of quantum systems seems weird and runs in many cases completely counter to expectations directly based on everyday experience. Interpretations of quantum mechanics try to bridge that gulf. Interpretations of the formalism are many and partly mutually exclusive or even contradictory [1]. From this it ensues that on the meta level, at the “common-sense” end of the scale, disorientation and uncertainty prevail. The “meaning” of quantum physics is unclear, a comprehensive embedding in form of an understandable relation to human everyday conceptions seems beyond reach. Still, without touching the formalism, such shall be attempted to sketch in the following. The aim is to draw a crude but overarching picture, allowing to relate the world, which humans now and bodily inhabit and which is aptly described by classical physics, with its seemingly bizarre foundations in quantum mechanics [2, 3].
Keeping to the overwhelming naive observational evidence and leaving Einstein relativity aside for a start, one can coarsely outline a distinction between two major domains:
Classical world, CM massive bodies occupy single well-defined positions, there are macroscopically distinguishable states, quantities like mass, energy and momentum can assume continuous values, thermodynamics provides the foundation with global irreversibility and an undeniable arrow of time according to the Second Law of Thermodynamics, entailing causal order, measurements do not perturb the measured, and Special and General Relativity deliver the best models of the spacetime-background with Newtonian space and time as almost perfect approximations for daily use.
Quantum realm, QM many quantities like energy and spin come in discrete packets, they are quantized; in some sense mostly microscopic systems are rather fragile, isolated ones are described by linear Schrödinger equation, characterizing a unitary evolution of the wavefunction, superpositions of wavefunctions, entanglement, decoherence, reversibility, non-locality, uncertainty relations for joint measurements of non-commuting observables, measuring entails back-action to a measured system, and the Born rule applies when obtaining definitive results in the form of individual random single outcomes of measurements.
Even when starting with a rather broad notion of classical (and quantum) phenomena, some intrinsic quantum mechanical aspects, which cannot be understood in classical terms, remain [4]. It goes without saying: it is the interface / borderline between these sectors, which is most interesting. There also lies the core of the measurement problem. The Copenhagen interpretation postulates a disruptive collapse of the wavefunction whereas decoherence accounts, as the seemingly major alternative, formally stay inside quantum mechanics and expound why a result is effectively (for all practical purposes) as good as a genuine classical state [5]. Decoherence does not entirely resolve the measurement problem as the mechanism by itself does not explain the occurrence of definite outcomes according to the Born rule; the composite system remains a superposition, and at least some robust entangled states are still reversible in principle [6, 7, 8, 9]. This latter point can be remedied by considering that there are limits to arbitrary “entanglement dilution”. At some stage there are so many objects involved that states become too numerous to handle for reversal in a finite universe. For effectively indistinguishable states, there is no way of reversing a development, although entanglement can help distinguishing orthogonal product states [10, 11, 12]. The Montevideo interpretation for example suggests something like this by assuming an impact of quantum gravity, which results in fundamental limitations for the accuracy of clocks [13]. Already some time ago, Roger Penrose has estimated finite life times of superposition states of masses effected by gravity [14]. Different thresholds from criteria for entanglement can be given while limits to easily detect existing entanglement in the presence of noise have been pointed out just very recently [15, 16, 17]. Mixing these levels of QM and CM and stepping back and forth between the relevant descriptions, can easily lead to inconsistencies and contradictions. A recent thought experiment has highlighted that the three naively innocent assumptions of Universality, Consistency and Uniqueness apparently cannot be met simultaneously by plain quantum physics applied indiscriminately to itself [18]. In a short paper, it has been argued that keeping with a fundamental distinction between QM and CM and accepting the importance of a fixed Heisenberg cut, one can avoid the purported contradictions [19]. The conclusion offered was, that, indeed, quantum mechanics cannot serve as the best description for all of reality, and, that the described thought experiment features a truly shifting split; it does not implement one overall consistent setting or application of the admissible rules, in particular, with respect to time [20, 21, 22]. When a measurement has been performed and the outcome is determined (and remembered), an outside observer not knowing that outcome, can assign classical probabilities to it, but cannot put the total system including an inside classical observer in superposition; ̶ with human observers living in CM. A version of the experiment, where these are replaced by fully reversible quantum computers and thus remaining completely inside QM, would be principally different [11, 12, 19, 23]. “We just cannot have classical and quantum behavior at the same TIME” was proposed as catchphrase for epitomizing something like “timelessness” inside QM. The argument is that, with time starting anew with each collapse at the strongly asymmetric transition from QM CM, the very concept of time inside QM appears questionable [19]. At the same time, some clear transient from QM CM turns any tinkering with the Schrödinger equation unnecessary, i.e., it makes non-linear amendments redundant and allows the continuation of the peaceful coexistence between quantum mechanics and special relativity [24]. In the following, this proposal shall be somewhat detailed and some explications how this might offer an interesting perspective will be sketched including some relations to selected extant approaches and interpretations.
Time
The concept of time has a rich history itself. In CM, time is Newtonian, absolute and existing from its own nature, linearly passing without relation to anything external, without reference to any change of matter. Later, with special and general relativity, the universality and absoluteness of time has been overthrown. Interestingly, also inside QM, Newtonian time is (mostly tacitly) presupposed as fixed background causal structure, i.e., the standard Schrödinger equation works with linear time. An approach to rectify this and devise a true quantum clock (Page-Wootters mechanism) claims its success by yielding essential Newtonian behavior for subsystems while the global system is stationary [25]. There are limits; for bounded systems, no good quantum clocks can be constructed: apparently suitable quantum observables, which monotonically increase with Newtonian time, have a non-vanishing probability of running backwards [26]. This and the following leave out the very beginning of time, i.e., the first split moments where it all began with Big Bang. An embedding in overall boundary conditions like from the start of the universe shall come as later topic following the more modest and restricted aim of first outlining a link between ordinary human everyday reality and QM in the sense advocated by Anton Zeilinger [2, 27]. Time has been thought of as similar to space and, later, it has also been declared as devoid of any independent existence without space [28, 29, 30]. The discussion of absolute Newtonian space has reached an early summit when Gottfried Wilhelm Leibniz pointed out that space is only meaningful in the form of relations between positions [31]. Such ideas have later been elaborated by Ernst Mach and Albert Einstein [32, 33]. Quite the same argument can actually be raised with respect to time. Leibniz, and later amongst others Einstein, saw it as the order of successive phenomena (which need to be distinct from each other). Time in fact is relational at a very basic level, even without special or general relativity, as time is always measured relating to some type of “enduring” reference. No clock is a clock without some memory. At the same time, there are minimum requirements on traces, i.e., unrelated memory records (snapshots lacking some meta-information, e.g., involving dissipation) do not reveal their order nor their spacing. Taking a simple pendulum as example, one needs to recall that (where) the mass has started to move in order to take this as basis for monitoring any change or process. For durations spanning more than one full swing, additional information storage is required, e.g., a little friction (energy transferred to a heat reservoir and increasing entropy there) to distinguish one period from another. Building clocks based on cycles where friction is pushed into the background, some type of incremental and irreversible counting mechanism is mandatory to tell moments (periods) in time apart and keep track of any flow of time. With full identity or reversibility of repetitive states, no elapsing of time nor any direction of it can be told. Thus, even before many specific and rather involved problems with time can be identified, the notion appears a little more intricate at its conceptual foundation than commonly thought [29, 34, 35, 36]. Overall irreversibility is described by the statistical Second Law of Thermodynamics which states that the total entropy of an isolated system can never decrease over time; only in cases where all processes are reversible it stays constant. As an example, large increases in coherence times for the dephasing of a qubit are observed as a cavity is decoupled from its environment [37]. In small subsystems, where statistical unlikelihood poses not the same stringent constraint as for big systems, entropy (time) may fluctuate [38, 39, 40]. Still, isolated (quantum) systems spontaneously evolve rapidly towards the state with maximum entropy, i.e., thermodynamic equilibrium, and then stay most of the time there [41, 42]. There is a well-defined condition for connecting activity (changes in time) with changes in information. Landauer’s principal states that irreversibly erasing one bit of information in finite time means increasing entropy by at least k*ln2; according to the first statement by Rolf Landauer, irreversible erasure in finite time goes with unavoidable minimum cost in energy, for one bit [43]:
ΔE ≥ kT ln2
This energy must be dumped to the environment, i.e., transferred to a heat reservoir. Landauer’s principle has been found generally valid in a large number of experiments, actually comprising CM and specific QM settings [44, 45]. For quantum systems, basically the same principle holds as for classical systems, and instead of energy, other conserved quantities can be utilized [46, 47]. It is the sum of work required for measurement and erasure, which is principally bounded [48]. For QM, this might offer a way to locate the shifting split, which is not even new: it is the merging in the flow of control, a two(or more)-to-one mapping of states, which is decisive [43, 46, 49]. Landauer’s Principle can be derived from statistical mechanics with uncontroversial assumptions, and it is valid for non-equilibrium dynamics [49, 50]. Landauer’s Principle also dovetails with the Holevo bound stating that for n qubits only n bits of classic information are retrievable [51, 52]. John Cramer reports Erwin Schrödinger saying that a state vector would collapse as soon as some macroscopic record of the result of a measurement is made, and Werner Heisenberg suggesting collapse to occur when a quantum measurement would pass from the domain of reversible processes to the domain of thermodynamic irreversibility [53]. With the uncontrolled (!) transfer of a minimum amount of energy (or of another conserved quantity), unitary evolution of a quantum system as described by the linear Schrödinger equation is interrupted [54]. Increasing the number of scattering events, coherence is increasingly lost [55]. Classical mechanics start to reign, and the Second Law of Thermodynamics fully applies. For a specific case, the involved steps measuring an arriving particle have been described in great detail showing, in particular, energy transfer [56]. Before an interruption like this occurs, decoherence can be effective [57]. Von Neumann entropy grows with increasing decoherence in quantum systems evolving with scattering processes [11]. Lesovik et al. claim that the overwhelming complexity of preparing time-reversed entangled quantum states can be seen as lying at the origin of irreversibility [11, 12]. A full projective measurement in a quantum system irreversibly reduces the entire set of possible outcomes to a single specific one; this precludes complete reversal and thus means some loss of information and increasing total entropy. Tradeoffs between information gain and the disturbance of a quantum state are close to the heart of QM [58]. True collapse as assumed by the standard Copenhagen interpretation, an event occurring, would be accompanied by a minimum uncontrolled transfer of energy as given by Landauer’s limit. Assigning a maximum amount of information of one bit to a basic quantum system fits the picture [27, 51]. Reversible entanglement with an environment would find its end with uncontrolled energy transfer effecting one of the fully entangled partners (and only to some degree in a weak measurement). Conversely, in the absence of disturbance, entanglement can be swapped and new partners to a quantum object recruited. Avoiding entropy production, a prepared central quantum state can be recovered from the environment in a second step if they were sufficiently entangled, even if that state is destroyed specifically between start and end measurements [23]. With tightly engineered and controlled dissipation, an approximate Bell state in qubits can be produced deterministically and stabilized [59, 60]. Preventing uncontrolled energy dissipation and harnessing pure dephasing-decoherence, electron spin correlations can be coherently transferred [61].
Basic directionality
The collapse of the wave function according to the Copenhagen interpretation can be understood as asymmetric and defining a clear arrow of time each time a projective measurement is made; it points from QM CM, and it has the direction of the general thermodynamic arrow of time [56, 62, 63, 64]. The above-identified irreversibility applies to reconstructing the undisturbed quantum state leading to a specific outcome, but in particular, also to the earlier preparation stage, when and where that quantum system started out [39]. At this other end of the existence of some undisturbed quantum system, careful state preparation is required for a well-defined start which can, with the exception of Big Bang, only be conceived of as belonging to CM emphasizing an operational point of view [59, 65, 66, 67]. Here, the time-step goes from classical to quantum physics. The direction of time at that interface CM QM is the thermodynamic one, and no problem with time was seen here so far, as the Newtonian time in a laboratory seamlessly matches with the Newtonian time taken as basis for unitary evolution expressed in a linear and deterministic Schrödinger equation, which is invariant under time reversal. This might require some second thought; in particular, as deterministic details from the wave propagation are reduced to individual random detection events following the Born rule.
Just the same as measurement, preparing a quantum state, reduces many options to one; both can be understood as erasing information concerning an earlier state, which is not fully accessible and cannot be reconstructed thereafter. State preparation generally involves energy transfer to and associated entropy increase in the environment containing and constraining the quantum system, in which the special delicate state is realized [65, 66, 67, 68]. At both endpoints of a quantum mechanical system, thus some permanent traces are produced in CM, and, inside an isolated quantum system, which obeys a unitary Schrödinger equation, none in between. These records of events at the boundaries in the environment comprise all, which is principally fully accessible. Already Niels Bohr claimed that nothing at the quantum scale is real before measured, and also Archibald Wheeler emphasized: we can only compare records of the past with the present "the past is not really the past until it has been measured, …, the past has no meaning or existence unless it exists as a record in the present" [69, 70]. Contrasting the CM state immediately before preparation of a quantum system with the CM situation after the measurement, many options have been reduced to one; certainly some information has been obtained. A many-into-one mapping actually can be claimed to happen at both borders of the embedded quantum system in a CM frame. These local increases in order had a price in increasing entropy outside that limited subsystem and outside the time interval between preparation and measurement. The arrow of time thus nicely points from the preparation to the measurement of a quantum state, both in the outside CM, it effectively bypasses or bridges the quantum domain. This does not entail any circularity as a potential problem, which has been warned against by Tejinder Singh [71]; on the contrary, relatively sharp transitions (in time, but still non-instantaneous) between QM and CM break any ill-defined circular dependence even if CM can be considered the limiting case of QM. Along the same lines, decoherence accounts are released from the “blemish” of naively presupposing semi-classical time [5, 6]. Classical states enclose the QM realm at both ends, fixed and marked by enduring records, at least since when time started quickly after Big Bang with the universe in a very special highly ordered low-entropy initial condition. Such records need not be clear-cut snapshots of a situation possibly containing a detailed logging of earlier events; increases in overall entropy as in the case of a damped pendulum also qualify. It is encouraging that also Murray Gell-Mann and James Hartle in their attempt to derive classical behavior from the sophisticated application or quantum mechanics and coarse graining employ records but conclude that “generalized records of histories” need “not represent records in the usual sense of being constructed from quasi-classical variables accessible to us” [3]. Even non-measurements, i.e., measurements completely without disturbing the measured object, as first envisioned by Mauritius Renninger can be understood as relying on, in this case well-defined, CM framing [72]. Interaction-free measurement in a well-controlled set-up with an object including knowledge about its prior location can yield information about that object without changing its momentum but then the momentum of the detection device will necessarily be changed upon absorption of the involved photon [73]. Quite generally, no result is a result without knowing, what the measurement set-up was. Niels Bohr formulated a contextuality requirement: “the unambiguous account of proper quantum phenomena must, in principle, include a description of all relevant features of experimental arrangement” [74]. Archibald Wheeler spoke the “great smoky dragon” with only its tail and head sharp [75].
This embedding and framing of QM in a context of CM is claimed to mark limits and constraints for all meaningful interpretations of QM. At the same time, it preserves some overall (not tightly local) locality as well as real causality and guarantees that no information or energy is transmitted between the endpoints with a velocity faster than the speed of light [76]. It has been shown that no-signaling in time, suitable statistical noninvasive measurability, is not only necessary but also sufficient for macroscopic realism [77]. The proposal here then is that in between state preparation and measurement, in undisturbed QM, a concept of time, different from our standard one, applies. In the absence of irreversibility and permanent records, time is not “real” inside an isolated quantum system. Restricting the notion of time to its classical manifestation in CM (records), “timelessness” could be a label for the quantum world, QM. Lacking time as fundamental pillar, QM objects, no matter whether waves, particles or their paths, might even be considered “unreal” [66, 67]. “Timelessness” as such is not any new idea, it has been proposed in a specific form already by Albert Einstein. In a block universe, all of space and time is claimed to exist eternally [35, 63, 78]. Long known general findings fit nicely: the entropy in an isolated quantum system is constant, and that time is not a simple quantum observable was pointed out already by Wolfgang Pauli [79]. Time cannot be described by a Hermitian operator; but see, e.g., [80, 81]. A recent proposal of an evolving block universe acknowledges the omnipresent daily use of classical boundary conditions; the past is fixed and the future is described as open; the future simply does not exist at any experienced point in time yet (and thus, photons cannot emanate from there) [63]. Spacetime “growing” into the future as events unfold is a similar proposal by Avshalom Elitzur and Shahar Dolev [82].
Timelessness strictly inside QM, experiments with slits
According to the famous statement by Richard Feynman, Thomas Young’s double slit experiment contains the essence of QM. So, it seems only natural trying to look how a new proposal of CM-constrained QM-timelessness might shed a little light on the paradigmatic double slit experiment in some of its different versions. Packets of energy, photons or particles, arrive in single locations as particles while exhibiting wave-like interference on a screen, which is placed at the opposite side of the source far behind the slits (Fraunhofer regime). The interference pattern builds up when probes are sent one by one, and what is observed is self-interference for each single particle [83]. The same has for example also been concluded from experiments employing rather massive Fullerene buckyballs in the form of C and C [84, 85]. Richard Feynman’s path integral approach does take into account all possible routes of a probe between source and detector, not only classical trajectories where action is a minimum, but also non-classical paths [78]. Only recently, it has been confirmed by extensive simulations that in a triple-slit set-up simply assuming interference between signals from slits, open one at a time, is not fully correct [86, Deviations from the superposition principle are not attributed to a violation of Born’s rule but rather to an exquisite sensitivity to boundary conditions. Enhancing electromagnetic near-fields close to the slits by the excitation of surface plasmons accordingly strongly increases the contributions by non-classical paths [90]. Timelessness in this context would simply mean that a particle or photon can in a sense effectively explore all of the possibilities permitted by the boundary conditions. Deliberately constraining and excluding looped trajectories by adding carefully placed absorbers allows for quantitatively controlling the magnitude of the Sorkin parameters, which depend also on the Gouy phase [89, 91]. With no time passing, there is also no shortage of time, and all possible transits do contribute according to their weight. Looking in the outside CM world, the occurrence of non-classic paths can be detected as a phase shift in the recorded interference pattern [91]. Complementarity as proclaimed by Niels Bohr implies that in a single experiment a quantum object either shows wave or particle characteristics. In particular, in the double slit experiment, there is no way of determining with certainty which path a particle took and still observe a wave-like interference pattern at a screen in some distance behind the slits. Whenever complete which-path information is available in principle, classical behavior is observed and interference is destroyed. This has been found in uncountable experiments for waves and particles including heavy-weights like Fullerenes [84, 85]. For these it has been shown, that emitting enough short-wavelength thermal photons, which would allow path determination, suppresses the interference pattern and the same for collisions with gas molecules [92, 93]. It is interesting to note that the uncontrolled energy transfer to the environment in these experiments is not too different from the corresponding Landauer limit. One line of argument does not necessarily in all cases obviate or invalidate a second one. Wave-particle duality relations have been shown to be equivalent to entropic uncertainty relations [94]. Looking at the primary examples, the full determination of which way a particle travelled seems to imply the blocking or full detection of a particle and thus some non-negligible energy transfer before or rather instead of the probe hitting the final screen. In the light of the above this would just mean that collapse has occurred and QM has been left at that first occasion. Particles and wave packets, which are strongly marked in order to disclose a path, e.g., by spin, show no interference pattern. For cases with reduced information on the path, a deterioration of the interference fringes has been calculated and observed for ensemble averages; non-demolition experiments allow to explore the trade-off between particle and wave signatures, necessarily employing ensembles of probes, not specific single ones [95]. In experiments with two fully entangled probes, measuring one of the partners collapses the common state and thus collapses also the wave function of the partner [96]. If disturbance is kept to a minimum using weak measurements it is possible to observe post-selected average trajectories of single photons in a two-slit interferometer [97]. Which-way experiments with monitored momentum change along Bohmian trajectories yield a quantitative relation between the loss of visibility and the momentum disturbance accumulated during propagation of the photons [98]. With entangled quantum particles in a related experimental set-up, non-locality yields “surreal trajectories” [99].
Similar to tests of Bell’s inequality, in delayed choice experiments as conceived of by Archibald Wheeler, any change is effected after the probe has left the source, but definitively before it is recorded [76, 100]. Experiments have confirmed QM predictions employing single photons and particles, also with light from far distant quasars for random number generation closing locality loopholes [101, 102, 103]. With timelessness for the free particle/wave in between, it does not know when something happened, there is no well-defined moment in the pure QM phase, boundary conditions are effective throughout. “Erasing” afterwards means filtering applicable sub-ensembles, which reestablishes an interference, ̶ strictly for the selected ensembles. Any actual choice brings suitable coincidences to the foreground and out of the hiding among the total observed events by means of considering only relevant corresponding events. Timelessness entails non-locality, a particle and its entangled partner in a sense are everywhere, continuously, always together (if sufficiently undisturbed). Provoking an event, i.e., interrupting anywhere/anytime leads to one integral result following from the overall probability distribution and the link between fully entangled partners. In a variation of the double slit experiment, Shahriar Afshar has devised a layout, which seems to demonstrate a violation of the complementarity principle, as it is posited by the Copenhagen interpretation [104]. Particle and wave-like characteristics occur in one and the same set-up; for single photons, and it seems possible to determine their path and observing interference fringes when accumulated while not perturbing with a measurement. Actually, collapse occurs only at the detectors at the end; a grid is placed in between them and the pinholes (serving as “slits” in this set-up). These findings have been taken as argument for the transactional interpretation of QM, which proposes some hand-shake between retarded and advances waves and thus describes atemporal pseudo-time conditions between emitter and absorber [53]. John Cramer, following the work of Wheeler, Feynman, Dirac and others, observes that the square of the wave function, which is decisive according to the Born rule, is the product of the advanced and retarded wave, which can be seen as kind of echo travelling back in time. The operation of complex conjugation is Wigner’s (“irreal”) time-reversal operator. With no real time passing for the isolated and free particles in between sender and receiver, there is plenty of opportunity to take the full boundary conditions, in particular, for emission and absorption, into account; contributions of forward and backward waves are thus included. The realization of a modified Afshar experiment using a Fresnel biprism and single photons yielded results fully compatible with the standard interpretation of QM including the complementarity relation [105]. Answering an objection that the measurements would not be simultaneous, Afshar claims that complementarity is violated as both findings would refer back to what “takes place” at the pinholes when a photon passes that plane. An interpretation emphasizing the uncontrolled transfer of energy (collapse) could elucidate Afshar’s findings by the fact that the grid (the obstacle) is placed in areas, which are not crossed by the main contributing “paths”, and at these locations, no interference pattern is effectively recorded. An interference pattern is just inferred; hardly any collapse takes place there and no time-stamp clearly visible in the statistics is generated. Timelessness and full probing of all possible options for an undisturbed wave function might offer a heuristic connection to the randomness intrinsic to QM. Chance results are what happens, when from a wide range of different options, one is selected like in a lottery. In the classical world, statistics on the results for ergodic processes can be compiled by either repeating the drawing exercise over and again at different points in time or at one time from many instantiations of that distribution. Aside from principal problems to have a quantum state over time resemble a composite quantum state at a single time, both appears hard with only one particle on its way between source and detector [106]. Dropping the requirement of Hermiticity (i.e., conceding that time is not an observable) while keeping four other reasonable assumptions for a quantum state over time, allows treating quantum systems over time in the same manner as composite systems at a single time [106]. With all (timeless) potential outcomes available together, a single particle in fact might constitute something like its own ensemble (with all possible superpositions) suggesting a link to a frequentist interpretation of probability. With weak measurements, it is possible to characterize quantum trajectories, which bear some similarity with classical stochastic trajectories of particles interacting with a thermal reservoir [90, 97, 99]. In an open quantum system it is even possible to derive from measured records a statistical arrow of time in measurement dynamics consistent with the macroscopic one when comparing probability densities of forward trajectories with time-reversed ones [39]. Without contact to a heat bath, the arrow of time is constrained analogous to the case with contact; investigating fluctuation theorems, it is the measurement induced wave-function collapse inherent to information acquisition, which exhibits irreversibility [39, 40]. The Born rule can be seen as a particular way of counting configurations, emerging from the factorization property of records as defined by Henrique Gomes and a reduction to the purely classical density [78]. The difference between a classical stochastic process and a quantum one can be traced to different sum rules for probabilities as explained by Rafael Sorkin; i.e., for the QM case complex amplitudes are applicable instead of direct probabilities in CM [88]. Universality of QM is not required to derive Born’s rule from the standard QM measurement postulates with the very modest and reasonable assumption that choices in the description do not effect predictions [107]. Born’s rule has also been shown to result for picking outcomes with threshold detectors in a natural way from classical random signals for ergodic processes [108]. The proposal here to “understand” the behavior of probes in the double slit experiment then is that classical records are essential and only they constitute “real” time or time compatible with special and general relativity (for cases sufficiently far from extreme conditions at Big Bang or a possible end of times in a very far future). Classical marking points mandatorily enclose every isolated quantum system, for which no “real” time passes in between state preparation and projective measurement [75]. Records of different types have been postulated before [3, 30, 63, 78, 109, 110, 111, 112]. It is records, which can be ordered according to their occurrence in succession (where available). Records only enable and define time. The term has especially been proposed for items, which contain a whole history of events (“time capsules”), which had happened in mutually consistent histories at earlier times [30]. The existence of redundant records has been found to be a sufficient condition for redundant consistency in an attempt to explain an objective past from decoherence describing sequences of events, which take/took place in a closed quantum system [111, 112]. This is effectively the case for all records marking events as here described. Records are linked and organized in non-strict hierarchies corresponding to the past light cones of particular events. A next grade of “timelessness” could be seen in the measurements of tunneling times. QM allows particles to transcend barriers, which are too high to overcome according to the laws in CM; i.e., particles / waves tunnel through it. Inherently in QM, when there is a finite probability density attached to one side of the barrier, there is some at the other side, too. Since the discovery of QM, the question has been raised what time the tunneling process would take or whether it would take any time at all, and whether any delay might be understood as a transit time [80, 81, 113]. Introducing dissipation, the predicted as well as the observed group delay increases linearly with the barrier length as expected for classical propagation [114, 115]. The consensus now appears to be that no real time duration can be assigned to the very tunneling [116, 117]; but see, e.g., [80, 81]. This means “timelessness” of the strictly quantum effect of tunneling, zero time passing. Just the same as in each instantiation, state preparation and measurement of a tunneled particle, still would need some time. Assuming an uncertainty relation between energy and time, which is far from clear itself, it can be taken that with both of these steps some short duration would be associated [65, 118]. Time ─ energy uncertainty relations have been discussed already by the founding fathers of quantum physics and ever since. The only thing clear so far is, that time ─ energy uncertainty is not at the same level as others, e.g., position ─ momentum, and that there are many facets to the topic [80, 81, 105, 118, 119]. The very basis for the difficulties with any time ─ energy uncertainty relation might actually consist in real time being only defined at / by durable CM recording points. This does not run counter to observations and applications of time ─ energy entanglement with (emission-)time and energy taken as continuous variables [120]. Just as the same as with other pairs like polarizations in space, the entangled entities are only prepared as well as measured in the outside CM world. The situation becomes additionally intricate in cases where energy below some (Landauer) threshold is exchanged with a quantum system and/or, in particular, when this is tightly controlled to carefully minimize disturbing back-action from the environment [121]. “Collapse” need not be complete, not-involved superpositions can survive, and is not instantaneous; smooth transits have been measured in experimental set-ups implementing undisturbed conditions close to ideal [122, 123, 124]. The experimental finding of the evolution of each completed jump taking time and being continuous, coherent, deterministic and controllable might be taken as implying proper time inside a quantum system, contrary to the “timelessness” advocated here. A second look reveals that time in this experiment was not monitoring the transition directly. It was observed by looking at an auxiliary “bright” state and recorded outside in CM; (only when) knowing all limited options, the absence of an event at a sufficiently well-constrained time can yield the same information as its occurrence [72]. The quantum system inside has no durable memory of which (“dark”) state it is or has been in. Differences in time scales allow combining the randomness and discreteness of individual jumps (on a long time scale) with a coherent and continuous evolution of such jumps (over a short time scale). Assuming some type of energy ─ time uncertainty relation, the latter has to be expected whatever the exact details of that relation are [80]. Avoiding “instantaneousness” renders a “collapse” more “physical” and “real”; real effective “moments” are “thick” and have a minimum duration. At the same time, there is less need to push “collapse” and the generation of records to the epistemic and mathematical realm like in interpretations of QM as purely individual Bayesian updating. An important class of time intervals is commonly derived for the durations it takes for any reversible quantum process to unwind completely, for a QM system to return to its initial state. This would mark the other end of the scale for time as there are good arguments that this in interesting cases would take forever [41, 42]. Ideal projective quantum measurements in a finite temperature environment, which are faithful, unbiased and non-invasive, have been found to demand infinite resources [125]. Even before, the identification of a system has been shown to be at best approximate [126]. Similar considerations actually are not confined to QM as full and exact reversibility does not exist in any realistic and CM system either. A common cause is that Poincare recurrence assumes infinitively accurately determined initial conditions, which have been debunked as un-physical [56, 127]. Most recent work shows that for three black holes orbiting each other there are a fraction of constellations, which for time-symmetric unwinding would demand local precision smaller than the Planck length [128]. Long before close to an end of time, another limit is encountered. Even in cases of arbitrary accurate starting conditions, a “predictability horizon” often limits time intervals for which interesting and meaningful forecasts are possible, i.e., the range for which developments and approximate expectation values for acceptable errors can be given (Lyapunov time). Principal limits to the achievable accuracy of boundary conditions and measurements (and subsequently, predictions), both in QM and CM, could be seen as somewhat blurring the distinction between these realms. On a conceptual level, it is obvious that with two areas closely bordering each other, and one of them comprising intrinsic uncertainty, also the second one cannot exhibit infinitively sharp conditions. Stretching the frame here to its maximum, situations with effectively “infinitively long” as well as with “zero” time passing might be labeled as “timeless”. What remains in a limited middle ground would then be just “permanent” traces, entropy increased in the environment, records in their relative (causal) ordering. It matches nicely, that in the quasi-static limit any logically irreversible computation can be performed in a thermodynamically reversible manner; only if erasure is performed with a finite velocity, the erasure becomes thermodynamically irreversible [48]. Real causality is inseparably linked to processes unfolding over time. Causality does not go backwards, “events do not unhappen” is the formula coined by Lee Smolin [129]. With an identified order of classical records, their potential causal dependences are constrained; (the record of) an effect can never precede (the record of) its cause. This cannot simply be transferred to inside QM, which allows more complex and entangled connections, alas, without producing durable records inside [105, 130]. Taking into account that it is only classic records, which at the end can be unambiguously ordered in one or more light cones, findings where the future seems to influence or determine the past, thus do not disturb everyday reality. This situation can be observed in experiments and harnessed in quantum computers [101, 102, 103, 131, 132]. In an interferometer experiment, the succession of states and their influence has been brought into superposition, two stages / operations (it is not “events” involving energy exchange and leaving records) could not be ordered according to any causal relation in coincidence measurements after photons have all passed through the set-up [132]. While correlations, which could not be understood in terms of any definite order, have also been found with a task involving communication between two local partners in a framework strictly inside QM and without any global causal structure, in a classical limit global causal order always arises [133]. Starting from small isolated quantum systems, a hierarchy of scales can be built including the meshing of relevant time scales [134, 135]. “More is different” has been proclaimed by Paul Anderson and before him by Nicolai Hartmann and Hermann Haken [136, 137, 138]. Contrary to allegations by trivial accounts of reductionism, “timelessness” at a most fundamental level needs not conflict with time emerging at higher levels.
The mosaic
Taken together, contained “timelessness” might be a suitable label, which allows applying a common name for the peculiar conditions of isolated (small) systems in the underlying quantum world, which appear very strange and which are distinctly different from what we know in the one world of classical physics, in which humans bodily live. Staying in accordance with observations, with the well-established QM formalism, and also with some basic common-sense plausibility seems possible on a coarse and still meaningful level. Amending the Copenhagen interpretation rudimentarily with (at least) a quantitative physical correlate for “collapse” given by the Landauer Principle and thus anchoring QM systems in real CM, the importance of durable records is emphasized. At the same time, the role of conscious observers is set to mostly inconsequential. Thus embedded in CM and the general flow of time as witnessed by increasing overall entropy, quantum states are real to a certain extent. Isolated quantum systems can be seen as “timeless” while still constituting “objective elements of reality”. Inside QM, neither records nor the order of stages are determined; there is no causality and neither retro- causality, ─ or both (at the same no -time). It might be seen as paradox that “timelessness”, when strictly contained in QM by classic framing in the real world, animates a “timeless” static block universe, which knows only unitary quantum physics, to evolving and open. Concerning questions relating to circularity, the speed limit for light fully applies in the accessible CM world, and also a second mechanism makes sure that effective “leaps” and “jumps” cannot be truly instantaneous: some time ─ energy uncertainty relation prevents infinitively fast changes. A little light is shed even on subjective interpretations where consciousness interaction is claimed to be responsible for something like a collapse of a wave function; there might be cases when this is the first contact to CM, which triggers irreversible records, in particular, in sophisticated thought experiments.
Acknowledgments
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