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H. Dieter Zeh

H. Dieter Zeh is one of the founders of the idea of decoherence.

Zeh taught a course on the direction of time over the past few decades at Heidelberg University. The course has been published in a textbook, The Physical Basis of the Direction of Time, that has gone through five editions.

Zermelo's Recurrence Objection to the H-Theorem

In the latest edition of his text, Zeh discusses Ernst Zermelo's recurrence objection to Ludwig Boltzmann's H-Theorem and suggests that the time-dependence of the size of the whole universe prevents such a recurrence.

Another argument against the statistical interpretation of irreversibility, the recurrence objection (or Wiederkehreinwand), was raised much later by Ernst Friedrich Zermelo, a collaborator of Max Planck at a time when the latter still opposed atomism, and instead supported the 'energeticists', who attempted to understand energy and entropy as fundamental 'substances'. This argument is based on a mathematical theorem due to Henri Poincaré, which states that every bounded mechanical system will return as close as one wishes to its initial state within a sufficiently large time. The entropy of a closed system would therefore have to return to its former value, provided only the function F(z) is continuous. This is a special case of the quasiergodic theorem which asserts that every system will corne arbitrarily close to any point on the hypersurface of fixed energy (and possibly with other fixed analytical constants of the motion) within finite time.

While all these theorems are mathematically correct, the recurrence objection fails to apply to reality for quantitative reasons. The age of our Universe is much smaller than the Poincaré recurrence times even for a gas consisting of no more than a few tens of particles. Their recurrence to the vicinity of their initial states (or their coming close to any other similarly specific state) can therefore be excluded in practice. Nonetheless, some 'foundations' of irreversible thermodynamics in the literature rely on formal idealizations that would lead to strictly infinite Poincaré recurrence times (for example the 'thermodynamical limit' of infinite particle number). Such assumptions are not required in our Universe of finite age, and they would not invalidate the reversibility objection (or the equilibrium expectation, mentioned above). However, all foundations of irreversible behavior have to presume some very improbable initial conditions...

In order to reverse the thermodynamical arrow of time in a bounded system, it would not therefore suffice to "go ahead and reverse all momenta" in the system itself, as ironically suggested by Boltzmann as an answer to Loschmidt.

This agrees with the Eddington and Layzer solutions of the recurrence problem
In an interacting Laplacean universe, the Poincaré cycles of its subsystems could in general only be those of the whole Universe, since their exact Hamiltonians must always depend on their time-dependent environment.
In a 1993 response to an article by Nicholas Gisin entitled "Wave-function approach to dissipative processes: are there quantum jumps?," Zeh argued that "quantum jumps" ("collapses" of the wave function) are only "apparent." Their appearance is caused by the loss of shielding from the environment, which "continuously monitors" a quantum system.

Zeh's work seems inspired by two 1952 articles by Erwin Schrödinger titled "Are There Quantum Jumps?" (Part I and Part II) and perhaps by John Bell's 1987 article with the same title.

Max Born replied to the Schrödinger claims, defending his statistical interpretation of quantum mechanics. Here is Zeh's position:

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 time-dependent Schrödinger 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 ('quantum jumps' or a 'collapse of the wave function') 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 'measured' 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 'continuously measured' in the sense of losing interference. This is obvious without any calculation, since we could never see macroscopic objects if they did not continuously scatter light which thereby had to carry away 'information' 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 'chopping' or 'kicking') - equivalent to a nonunitary evolution of the density matrix.' 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 'first intervention' to augment the Schrödinger equation in the case of measurements proper).

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. Joos and Zeh have calculated that even small dust particles or large molecules must 'decohere' (that is, lose certain interference terms) on a time scale of fractions of a second, while Zurek' 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 time-independent Schrödinger 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...

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 'particle numbers' 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 derivable in this way from the assumption of a global Schrödinger wave function(al). It is the unavoidable environment that determines which properties decohere (that is, become classical)...

I do not know of any apparent violation of the Schrödinger 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...

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 'environment'). 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 'reality' 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 observe , in contrast to this global superposition of different outcomes derived from the Schrödinger equation, that only one of its components (a wave packet representing a definite 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 exists but only that only one component is observed . But this fact is readily described by the Schrödinger 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 quantum correlated 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 'same' observer are dynamically entirely independent of one another: they describe different observers. Because of the fork-like structure of causality (the spreading in space of the retarded effects of local causes), 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 dynamical consequence of decoherence explains everything that has to be explained dynamically in order to understand what can be observed by local observers.

John Bell called Hugh Everett's "relative states" or "many worlds" interpretation of Q.M "extravagant"
He who considers this conclusion of an indeterminism or splitting of the observer's identity, derived from the Schrödinger equation in the form of dynamically decoupling ('branching') wave packets on a fundamental global configuration space, as unacceptable or 'extravagant' may instead dynamically formalize the superfluous hypothesis of a disappearance of the 'other' 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 Schrödinger equation must in principle lead to observable effects, and it should be recalled that none have ever been discovered. 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 Schrödinger equation.
There are no Quantum Jumps, nor are there Particles!, Physics Letters A, 172.4 (1993): 189-192. (PDF)
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