Abstract: Quantum theory does not require the existence of discontinuities: neither in time (quantum jumps), nor in space (particles), nor in spacetime (quantum events). These apparent discontinuities are readily described objectively by the continuous process of decoherence occurring locally on a very short time scale according to the Schršdinger equation for interacting systems, while the observerÕs Ôincrease of informationÕ is appropriately represented by the resulting dynamical decoupling of the corresponding components of the global wave function.
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As far as is known, all properties of closed quantum systems are perfectly described by means of wave functions in configuration space (in general, wave functionals of certain fields) dynamically evolving smoothly according to the timedependent Schršdinger equation. However, the condition of being closed (or shielded
against interactions with the environment) can easily be estimated to be quite exceptional. It characterizes very
special (usually atomic) systems from which the laws of quantum mechanics were derived. When the shielding ceases, most notably during measurements, discontinuous events (Ôquantum jumpsÕ or a Ôcollapse of the wave functionÕ) seem to occur, and particle aspects seem to be observed. Such events are also known to lead to a loss of interference between different values of the ÔmeasuredÕ variables  regardless of whether any result is read from the apparatus by an observer.
Macroscopic systems are very effectively coupled to their environment in this way. They cannot avoid being Ôcontinuously measuredÕ in the sense of losing interference.1 This is obvious without any calculation, since we could never s ee macroscopic objects if they didnot continuously scatter light which thereby had to carry away ÔinformationÕ about their position and shape. The effect of such interactions is often taken into account dynamically by means of stochastic terms in the evolution of the wave function of the considered system (sometimes called ÔchoppingÕ or ÔkickingÕ) Ð equivalent to a nonunitary evolution of the density matrix.2 These terms (introduced ad hoc) are usually interpreted as representing fundamental aspects of quantum mechanics (just as the supplementary dynamics that von Neumann introduced as his Ôfirst interventionÕ to augment the Schršdinger equation in the case of measurements proper3).
Precisely such empirically justified dynamical terms can however be derived within the well established quantum mechanics of interacting systems provided the environment is properly taken into account.4 (For a recent review of this approach see Zurek.5) Joos and Zeh6 have calculated that even small dust particles or large molecules must ÔdecohereÕ (that is, lose certain interference terms) on a time scale of fractions of a second, while Zurek7 has estimated that for a normal macroscopic system the rate of decoherence is typically faster than thermal relaxation by an astounding factor of the order of 1040. In contrast, microscopic systems tend to decohere into energy eigenstates, since they interact with their environment mainly through their decay products. It is for this reason that the timeindependent Schršdinger equation is so useful for describing atomic systems. In quantum measurements proper, microscopic properties will first become correlated with macroscopically different pointer positions, the superpositions of which must then immediately decohere in the described way.
For all practical purposes, this short time scale of decoherence can be interpreted as the occurrence of dynamical discontinuities. In laser physics, shielding from the environment can be controlled by the experimenter to a great extent. Even single atoms can be brought into a position of having their decay status Ôcontinuously measuredÕ, so that quantum jumps seem to be directly visible,8 while in the opposite situation of sufficiently closed systems (single atoms in a cavity) the superposition of different decay times may become
important and lead to coherent revival of the initial decaying state.9
It turns out furthermore that decoherence preferentially destroys interference between those parts of the wave function which differ markedly in position. This leads to density matrices which are effectively equivalent to ensembles of narrow wave packets. Such
wave packets may then be interpreted as representing individual ÔparticleÕ positions (i.e., no e nsemble s of positions any more), precisely as originally envisioned by Schršdinger.10 Their spreading with time according to the Schršdinger equation is counteracted by continuing decoherence, resulting in a certain (observable) indeterminism of their quasiclassical orbits (Ôquantum Brownian motionÕ) even if recoil is neglected.6 All particle aspects observed in measurements of quantum fields (like spots on a plate, tracks in a bubble chamber, or clicks of a counter) can be understood by taking into account this decoherence of the relevant local (i.e., subsystem) density matrix. (The concept of Ôparticle n umber s Õ is of course explained by the oscillator quantum numbers of the corresponding field modes  at least for bosons.)
In fact, all classical aspects (or the apparent validity of fundamental superselection rules) seem to be d erivable in this way from the assumption of a global Schršdinger wave function(al). It is the unavoidable environment that determines which properties decohere (that is, become classical). Charge eigenstates, for example, decohere locally by being ÔkinematicallyÕ quantumcorrelated with the surrounding electromagnetic field state as required by GaussÕ law in the form of the conserved constraint [divE  4pr] Y = 0. When p air s of charges are created (and spatially separated), decoherence of the individual charges by their fields becomes a dynamical process again (equivalent to an irreversible measurementlike process once photons registrating the resulting dipole and higher moments are emitted or scattered).
I do not know of any apparent violation of the Schršdinger equation or the superposition principle that cannot at least plausibly be expected to be derivable in terms of decoherence. In spite of this success (which can hardly be an accident), this description is often considered as insufficient to explain the measurement process itself.4,11 The reservations do seem sound, since decoherence is described formally by means of the density matrix of the considered subsystem of the universe, obtained by tracing out the rest (the ÔenvironmentÕ). The concept of the density matrix (of subsystems in this case) is however justified itself only as a means for calculating expectation values or probabilities for outcomes of further measurements, that is, for the secondary quantum jumps which would have to occur, for example, when the pointer is read. This explanation of measurements therefore seems to be circular from a fundamental point of view. In the global wave function (which is interpreted as representing ÔrealityÕ in this picture) all interference terms remain present. The universe as a whole never decoheres. The description of measurements by means of merely local decoherence  so goes the usual argument  must be wrong, since one does o bserve , in contrast to this global superposition of different outcomes derived from the Schršdinger equation, that only o ne of its components (a wave packet representing a d efinite outcome) exists after every measurement.
However, this latter claim is wrong, and so is the argument. For after an observation one need not necessarily conclude that only one component now e xist s but only that only one component is o bserved . But this fact is readily described by the Schršdinger equation without any modification. Whenever an observer interacts with the measurement device in a way that corresponds to an observation of the result, his own state must be quantumcorrelated with the macroscopic pointer position (and potentially also with other observers), and hence be decohered from the beginning. Superposed world components describing the registration of different macroscopic properties by the ÔsameÕ observer are dynamically entirely independent of one another: they describe d ifferent observers. Because of the forklike structure of causality (the spreading in space of the retarded effects of local causes)12, there is no chance of their forming a superposition with respect to (or
in) a local observer any more (except, perhaps, in a recollapsing Friedmann universe).
This d ynamical consequence of decoherence explains everything that has to be explained dynamically in order to understand what can be observed by local observers. He who considers this conclusion of an indeterminism o r s pl itting o f the o bserverÕs identity , derived from the Schršdinger equation in the form of dynamically decoupling (ÔbranchingÕ) wave packets on a fundamental global configuration space, as unacceptable or ÔextravagantÕ13 may instead dynamically formalize the superfluous hypothesis of a disappearance of the ÔotherÕ components by whatever method he prefers, but he should be aware that he may thereby also create his own problems: Any deviation from the global Schršdinger equation must in principle lead to observable effects, and it should be recalled that none have ever been discovered.14 The conclusion would of course have to be revised if such effects were some day to be found. But as of now, there is no objective reason to expect them to exist; and even if they did, they need not take the form of the apparent discontinuities which are readily described by means of local decoherence according to the universal Schršdinger equation.
This is not to deny the existence of several open problems. In particular, (1) the fundamental ÔarenaÕ of wave mechanics, which may or may not correspond to a classical configuration space, can only be known once we possess a fundamental ÔTheory of EverythingÕ. Quantum gravity indicates that this arena must have an interesting metric structure (ÔsuperspaceÕ) which leads to a stationary Schršdinger equation of hyperbolic
nature (the WheelerDeWitt equation).15 (2) The precise definition of the dynamically independent components (ÔbranchesÕ) remains elusive.16 However, this specification is unimportant for understanding the o bjective part of measurements (in particular, decoherence), just as a detailed theory of conscious observers was not required for describing measurements in a classical world. Hence, in contrast to dynamical collapse models proposed in the literature,17 this branching does n ot correspond to the apparently observed quantum jumps. It only justifies their description by means of decoherence of the local density matrix, provided the usual locality of interactions remains valid. (In the orthodox interpretation, decoherence would still occur as an objective process in the measurement device even if the ÔHeisenberg cutÕ were shifted deep into the observer.) (3) In contrast to an assertion by Everett, the law of quantum probabilities cannot be derived without further (though weak) assumptions about the selection of ÔourÕ world component.18 (4) The most important underivable assumption in a kinematically nonlocal (i.e., nonseparable) quantum world seems to be the locality of the ultimate (subjective) observer in spacetime (required in some vague but essential form). Quantum decoherence is meaningful (or ÔrelevantÕ) only with respect to local p art s of the nonlocal quantum world.
None of these open problems indicates an inconsistence or limitation of the description of the whole world by means of the Schršdinger equation  only a lack of knowledge about important details (mainly about the quantum physical description of an observer). Hence, there does not seem to be any reasonable motivation (other than traditionalism) for introducing concepts like particles, quantum jumps, superselection rules, or classical properties on a fundamental level. It also appears unfortunate, therefore, that the now very popular technical concept of path integrals may suggest a fundamental role of pathsor ÔhistoriesÕ of c lassical states, although their required superposition is nothing but another representation of the Schršdinger wave function. (FeynmanÕs method could similarly be applied for computing the propagation of classical waves by sums over paths in threedimensional space, without giving these paths any physical meaning.) Quasiclassical histories19 e merge instead from the global wave function as traveling and thereby smoothly branching narrow wave packets (not as time sequences of ÔeventsÕ)
only because of the continuous action of decoherence (which leads to increasing complexity, symmetrybreaking, and finegraining into dynamically independent wave packets). This statement applies also to spacetime with its metric structure that must be part of the quasiclassical history.20 It would be insufficient simply to require decoherence just because it leads to classically plausible consequences (such as Ôconsistent historiesÕ). It thus appears becoming evident that our classical concepts describe mere shadows on the wall of PlatoÕs cave in which we are living. Using them for describing reality must lead to ÔparadoxesÕ.
Acknowledgment: I wish to thank Julian Barbour, Erich Joos and Claus Kiefer for discussions and for suggesting a number of helpful changes in the manuscript.
References
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reference here : H. D. Zeh
Institut fŸr Theoretische Physik
UniversitŠt Heidelberg
There are no Quantum Jumps, nor are there Particles!
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