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Decoherence
The "decoherence program" of H. Dieter Zeh, Erich Joos, Wojciech Zurek, John Wheeler, Max Tegmark, and others has multiple aims 
The decoherence program hopes to offer insights into several other important phenomena:
The decoherence program finds unacceptable these aspects of the standard quantum theory:
Decoherence theorists admit that some problems remain to be addressed:
As Tegmark and Wheeler put it: The main motivation for introducing the notion of wavefunction collapse had been to explain why experiments produced specific outcomes and not strange superpositions of outcomes...it is embarrassing that nobody has provided a testable deterministic equation specifying precisely when the mysterious collapse is supposed to occur. Some of the controversial positions in decoherence theory, including the denial of collapses and particles, come straight from the work of Erwin Schrödinger, for example in his 1952 essays "Are There Quantum Jumps?" (Part I and Part II), where he denies the existence of "particles," claiming that everything can be understood as waves. Other sources include: Hugh Everett III and his "relative state" or "many world" interpretations of quantum mechanics; Eugene Wigner's article on the problem of measurement; and John Bell's reprise of Schrödinger's arguments on quantum jumps.
Decoherence advocates therefore look to other attempts to formulate quantum mechanics. Also called "interpretations," these are more often reformulations, with different basic assumptions about the foundations of quantum mechanics. Most begin from the "universal" applicability of the unitary time evolution that results from the Schrödinger wave equation. They include:
Note that these "interpretations" are often in serious conflict with one another. Where Erwin Schrödinger thinks that waves alone can explain everything (there are no particles in his theory), David Bohm thinks that particles not only exist but that every particle has a definite position that is a "hidden parameter" of his theory. H. Dieter Zeh, the founder of decoherence, sees
one of two possibilities: a modification of the Schrödinger equation that explicitly describes a collapse (also called "spontaneous localization") or an Everett type interpretation, in which all measurement outcomes are assumed to exist in one formal superposition, but to be perceived separately as a consequence of their dynamical autonomy resulting from decoherence. The Information Interpretation of quantum mechanics also has explanations for the measurement problem, the arrow of time, and the emergence of adequately, i.e., statistically determined classical objects. However, IPhi does it while accepting the standard assumptions of orthodox quantum physics. See below. We briefly review the standard theory of quantum mechanics and compare it to the "decoherence program," with a focus on the details of the measurement process. We divide measurement into several distinct steps, in order to clarify the supposed "measurement problem" (mostly the lack of macroscopic state superpositions) and perhaps "solve" it. The most famous example of probabilityamplitudewave interference is the twoslit experiment. Interference is between the probability amplitudes whose absolute value squared gives us the probability of finding the particle at various locations behind the screen with the two slits in it. Finding the particle at a specific location is said to be a "measurement." In standard quantum theory, a measurement is made when the quantum system is "projected" or "collapsed" or "reduced" into a single one of the system's allowed states. If the system was "prepared" in one of these "eigenstates," then the measurement will find it in that state with probability one (that is, with certainty). However, if the system is prepared in an arbitrary state ψ_{a}, it can be represented as being in a linear combination of the system's basic energy states φ_{n}.
ψ_{a} = Σ c_{n}  n >.
where
c_{n} = < ψ_{a}  φ_{n} >.
It is said to be in "superposition" of those basic states. The probability P_{n} of its being found in state φ_{n} is
P_{n} = < ψ_{a}  φ_{n} >^{2} = c_{n}^{2} .
Between measurements, the time evolution of a quantum system in such a superposition of states is described by a unitary transformation U (t, t_{0}) that preserves the same superposition of states as long as the system does not interact with another system, such as a measuring apparatus. As long as the quantum system is completely isolated from any external influences, it evolves continuously and deterministically in an exactly predictable (causal) manner. Whenever the quantum system does interact however, with another particle or an external field, its behavior ceases to be causal and it evolves discontinuously and indeterministically. This acausal behavior is uniquely quantum mechanical. Nothing like it is possible in classical mechanics. Most attempts to "reinterpret" or "reformulate" quantum mechanics are attempts to eliminate this discontinuous acausal behavior and replace it with a deterministic process. We must clarify what we mean by "the quantum system" and "it evolves" in the previous two paragraphs. This brings us to the mysterious notion of "waveparticle duality." In the wave picture, the "quantum system" refers to the deterministic time evolution of the complex probability amplitude or quantum state vector ψ_{a}, according to the "equation of motion" for the probability amplitude wave ψ_{a}, which is the Schrödinger equation,
δψ_{a}/δt = H ψ_{a}.
The probability amplitude looks like a wave and the Schrödinger equation is a wave equation. But the wave is an abstract quantity whose absolute square is the probability of finding a quantum particle somewhere. It is distinctly not the particle, whose exact position is unknowable while the quantum system is evolving deterministically. It is the probability amplitude wave that interferes with itself. Particles, as such, never interfere (although they may collide). Note that we never "see" the superposition of particles in distinct states. There is no microscopic superposition in the sense of the macroscopic superposition of live and dead cats (See Schrödinger's Cat). When the particle interacts, with the measurement apparatus for example, we always find the whole particle. It suddenly appears. For example, an electron "jumps" from one orbit to another, absorbing or emitting a discrete amount of energy (a photon). When a photon or electron is fired at the two slits, its appearance at the photographic plate is sudden and discontinuous. The probability wave instantaneously becomes concentrated at the location of the particle. There is now unit probability (certainty) that the particle is located where we find it to be. This is described as the "collapse" of the wave function. Where the probability amplitude might have evolved under the unitary transformation of the Schrödinger equation to have significant nonzero values in a very large volume of phase space, all that probability suddenly "collapses" (faster than the speed of light, which deeply bothered Albert Einstein) to the location of the particle. Einstein said that some mysterious "spooky actionatadistance" must act to prevent the appearance of a second particle at a distant point where a finite probability of appearing had existed just an instant earlier. Animation of a wave function collapsing  click to restart
Whereas the abstract probability amplitude moves continuously and deterministically throughout space, the concrete particle moves discontinuously and indeterministically to a particular point in space.
For this collapse to be a "measurement," the new information about which location (or state) the system has collapsed into must be recorded somewhere in order for it to be "observable" by a scientist. But the vast majority of quantum events  e.g., particle collisions that change the particular states of quantum particles before and after the collision  do not leave an indelible record of their new states anywhere (except implicitly in the particles themselves). We can imagine that a quantum system initially in state ψ_{a} has interacted with another system and as a result is in a new state φ_{n}, without any macroscopic apparatus around to record this new state for a "conscious observer." H. D. Zeh describes how quantum systems may be "measured" without the recording of information. It is therefore a plausible experimental result that the interference disappears also when the passage [of an electron through a slit] is "measured" without registration of a definite result. The latter may be assumed to have become a "classical fact" as soon as the measurement has irreversibly "occurred". A quantum phenomenon may thus "become a phenomenon" without being observed. This is in contrast to Heisenberg's remark about a trajectory coming into being by its observation, or a wave function describing "human knowledge". Bohr later spoke of objective irreversible events occurring in the counter. However, what precisely is an irreversible quantum event? According to Bohr this event can not be dynamically analyzed.
The Measurement Process
In order to clarify the measurement process, we separate it into several distinct stages, as follows:
The Measurement Problem
So what exactly is the "measurement problem?" For decoherence theorists, the unitary transformation of the Schrödinger equation cannot alter a superposition of microscopic states. Why then, when microscopic states are time evolved into macroscopic ones, don't macroscopic superpositions emerge? According to H. D. Zeh: Because of the dynamical superposition principle, an initial superposition And according to Erich Joos, another founder of decoherence: It remains unexplained why macroobjects come only in narrow wave packets, even though the superposition principle allows far more "nonclassical" states (while microobjects are usually found in energy eigenstates). Measurementlike processes would necessarily produce nonclassical macroscopic states as a consequence of the unitary Schrödinger dynamics. An example is the infamous Schrödinger cat, steered into a superposition of "alive" and "dead". The fact that we don't see superpositions of macroscopic objects is the "measurement problem," according to Zeh and Joos. An additional problem is that decoherence is a completely unitary process (Schrödinger dynamics) which implies time reversibility. What then do decoherence theorists see as the origin of irreversibility? Can we time reverse the decoherence process and see the quantumtoclassical transition reverse itself and recover the original coherent quantum world? To "relocalize" the superposition of the original system, we need only have complete control over the environmental interaction. This is of course not practical, just as Ludwig Boltzmann found in the case of Josef Loschmidt's reversibility objection. Does irreversibility in decoherence have the same rationale  "not possible for all practical purposes"  as in classical statistical mechanics? According to more conventional thinkers, the measurement problem is the failure of the standard quantum mechanical formalism (Schrödinger equation) to completely describe the nonunitary "collapse" process. Since the collapse is irreducibly indeterministic, the time of the collapse is completely unpredictable and unknowable. Indeterministic quantum jumps are one of the defining characteristics of quantum mechanics, both the "old" quantum theory, where Bohr wanted radiation to be emitted and absorbed discontinuously when his atom jumpped between staionary states, and the modern standard theory with the BornJordanHeisenbergDirac "projection postulate." To add new terms to the Schrödinger equation in order to control the time of collapse is to misunderstand the irreducible chance at the heart of quantum mechanics, as first seen clearly, in 1917, by Albert Einstein. When he derived his A and B coefficients for the emission and absorption of radiation, he found that an outgoing light particle must impart momentum hν/c to the atom or molecule, but the direction of the momentum can not be predicted! Neither can the theory predict the time when the light quantum will be emitted. Such a random time was not unknown to physics. When Ernest Rutherford derived the law for radioactive decay of unstable atomic nuclei in 1900, he could only give the probability of decay time. Einstein saw the connection with radiation emission: It speaks in favor of the theory that the statistical law assumed for [spontaneous] emission is nothing but the Rutherford law of radioactive decay.But the inability to predict both the time and direction of light particle emissions, said Einstein in 1917, is "a weakness in the theory..., that it leaves time and direction of elementary processes to chance (Zufall, ibid.)." It is only a weakness for Einstein, of course, because his God does not play dice. Decoherence theorists too appear to have what William James called an "antipathy to chance."
In the original "old" quantum mechanics, Neils Bohr made two assumptions. One was that atoms could only be found in what he called stationary energy states, later called eigenstates. The second was that the observed spectral lines were discontinuous sudden transitions of the atom between the states. The emission or absorption of quanta of light with energy equal to the energy difference between the states (or energy levels) with frequency ν was given by the formula
E_{2}  E_{1} = h ν,
where h is Planck's constant, derived from his radiation law that quantized the allowed values of energy. In the now standard quantum theory, formulated by Werner Heisenberg, Max Born, Pascual Jordan, Erwin Schrödinger, Paul Dirac, and others, three foundational assumptions were made: the principle of superposition, the axiom of measurement, and the projection postulate. Since decoherence challenges some of these ideas, we review the standard definitions.
The Principle of Superposition
The fundamental equation of motion in quantum mechanics is Schrödinger's famous wave equation that describes the evolution in time of his wave function ψ,
i δψ/δt  Hψ.
For a single particle in idealized complete isolation, and for a Hamiltonian H that does not involve magnetic fields, the Schrödinger equation is a unitary transformation that is timereversible (the principle of microscopic reversibility) Max Born interpreted the square of the absolute value of Schrödinger's wave function as providing the probability of finding a quantum system in a certain state ψ_{n}. The quantum (discrete) nature of physical systems results from there generally being a large number of solutions ψ_{n} (called eigenfunctions) of the Schrödinger equation in its time independent form, with energy eigenvalues E_{n}.
Hψ_{n} = E_{n}ψ_{n},
The discrete energy eigenvalues E_{n} limit interactions (for example, with photons) to the energy differences E_{n}  E_{m}, as assumed by Bohr. Eigenfunctions ψ_{n} are orthogonal to one another,
< ψ_{n}  ψ_{m} > = δ_{nm},
where δ_{nm} is the Dirac deltafunction, equal to 1 when n = m, and 0 otherwise. The sum of the diagonal terms in the matrix < ψ_{n}  ψ_{m} >, when n = m, must be normalized to 1 to be meaningful as Born rule probabilities.
Σ P_{n} = Σ < ψ_{n}  ψ_{n} >^{2} = 1.
The offdiagonal terms in the matrix, < ψ_{n}  ψ_{m} >, are interpretable as interference terms. When the matrix is used to calculate the expectation values of some quantum mechanical operator O, the offdiagonal terms < ψ_{n}  O  ψ_{m} > are interpretable as transition probabilities  the likelihood that the operator O will induce a transition from state ψ_{n} to ψ_{m}. The Schrödinger equation is a linear equation. It has no quadratic or higher power terms, and this introduces a profound  and for many scientists and philosophers a disturbing  feature of quantum mechanics, one that is impossible in classical physics, namely the principle of superposition of quantum states. If ψ_{a} and ψ_{b} are both solutions of the equation, then an arbitrary linear combination of these, ψ = c_{a}ψ_{a} + c_{b}ψ_{b}; with complex coefficients c_{a} and c_{b}, is also a solution. Together with Born's probabilistic interpretation of the wave function, the principle of superposition accounts for the major mysteries of quantum theory, some of which we hope to resolve, or at least reduce, with an objective (observerindependent) explanation of information creation during quantum processes (which can often be interpreted as measurements).
The Axiom of Measurement
The axiom of measurement depends on the idea of "observables," physical quantities that can be measured in experiments. A physical observable is represented as a Hermitean operator A that is selfadjoint (equal to its complex conjugate, A^{*} = A). The diagonal elements It is these intrinsic quantum probabilities that provide the ultimate source of indeterminism, and consequently of irreducible irreversibility, as we shall see. The axiom of measurement is then that a large number of measurements of the observable A, known to have eigenvalues A_{n}, will result in the number of measurements with value A_{n} being proportional to the probability of finding the system in eigenstate ψ_{n} with eigenvalue A_{n}.
The Projection Postulate
The third novel idea of quantum theory is often considered the most radical. It has certainly produced some of the most radical ideas ever to appear in physics, in attempts to deny it (as the decoherence program appears to do, as do also Everett relativestate interpretations, many worlds theories, and Bohmde Broglie pilot waves). The projection postulate is actually very simple, and arguably intuitive as well. It says that when a measurement is made, the system of interest will be found in one of the possible eigenstates of the measured observable. We have several possible alternatives for eigenvalues. Measurement simply makes one of these actual, and it does so, said Max Born, in proportion to the absolute square of the probability amplitude wave function ψ_{n}. In this way, ontological chance enters physics, and it is partly this fact of quantum randomness that bothered Albert Einstein ("God does not play dice") and Schrödinger (whose equation of motion is deterministic). When Einstein derived the expressions for the probabilities of emission and absorption of photons in 1917, he lamented that the theory seemed to indicate that the direction of an emitted photon was a matter of pure chance (Zufall), and that the time of emission was also statistical and random, just as Rutherford had found for the time of decay of a radioactive nucleus. Einstein called it a "weakness in the theory."
What Decoherence Gets Right
Allowing the environment to interact with a quantum system, for example by the scattering of lowenergy thermal photons or highenergy cosmic rays, or by collisions with air molecules, surely will suppress quantum interference in an otherwise isolated experiment. But this is because large numbers of uncorrelated (incoherent) quantum events will "average out" and mask the quantum phenomena. It does not mean that wave functions are not collapsing. They are, at every particle interaction. Decoherence advocates describe the environmental interaction as "monitoring" of the system by continuous "measurements." Decoherence theorists are correct that every collision between particles entangles their wave functions, at least for the short time before decoherence suppresses any coherent interference effects of that entanglement.
But in what sense is a collision a "measurement." At best, it is a "premeasurement." All interactions change the state of a system of interest, but not all leave the "pointer state" of some measuring apparatus with new information about the state of the system. So environmental monitoring, in the form of continuous collisions by other particles, is changing the specific information content of both the system, the environment, and a measuring apparatus (if there is one). But if there is no recording of new information (negative entropy created locally), the system and the environment may be in thermodynamic equilibrium.
Equilibrium does not mean that decoherence monitoring of every particle is not continuing. If a gas of particles is not already in equilibrium, they may be approaching thermal equilibrium. This happens when any nonequilibrium initial conditions (Zeh calls these a "conspiracy") are being "forgotten" by erasure of path information during collisions. Information about initial conditions is implicit in the paths of all the particles. This means that, in principle, the paths could be reversed to return to the initial, lower entropy, conditions (Loschmidt paradox). Erasure of path information could be caused by quantum particleparticle scattering (our standard view) or by decoherence "monitoring." How are these two related?
The Two Steps Needed in a Measurement that Creates New Information
More than the assumed collapse of the wave function (von Neumann's Process 1, Pauli's measurement of the first kind) is needed. Indelibly recorded information, available for "observations" by a scientist, must also satisfy the second requirement for the creation of new information in the universe.
Everything created since the origin of the universe over ten billion years ago has involved just two fundamental physical processes that combine to form the core of all creative processes. These two steps occur whenever even a single bit of new information is created and survives in the universe.
This twostep core creative process underlies the formation of microscopic objects like atoms and molecules, as well as macroscopic objects like galaxies, stars, and planets. With the emergence of teleonomic (purposive) information in selfreplicating systems, the same core process underlies all biological creation. But now some random changes in information structures are rejected by natural selection, while others reproduce successfully. Finally, with the emergence of selfaware organisms and the creation of extrabiological information stored in the environment, the same informationgenerating core process underlies communication, consciousness, free will, and creativity. The two physical processes in the creative process, quantum physics and thermodynamics, are somewhat daunting subjects for philosophers, and even for many scientists, including decoherence advocates.
Quantum Level Interactions Do Not Create Lasting Information
The overwhelming number of collisions of microscopic particles like electrons, photons, atoms, molecules, etc, do not result in observable information about the collisions. The lack of observations and observers does not mean that there have been no "collapses" of wave functions. The idea that the time evolution of the deterministic Schrödinger equation continues forever in a unitary transformation that leaves the wave function of the whole universe undecided and in principle reversible at any time, is an absurd and unjustified extrapolation from the behavior of the ideal case of a single perfectly isolated particle. The principle of microscopic reversibility applies only to such an isolated particle, something unrealizable in nature, as the decoherence advocates know with their addition of environmental "monitoring." Experimental physicists can isolate systems from the environment enough to "see" the quantum interference (but again, only in the statistical results of large numbers of identical experiments).
The Emergence of the Classical World
In the standard quantum view, the emergence of macroscopic objects with classical behavior arises statistically for two reasons involving large numbers:
Decoherence as "Interpreted" by Standard Quantum Mechanics
Can we explain the following in terms of standard quantum mechanics?
Let's consider these point by point.
Compare the collapse of the twoparticle probability amplitude above to the singleparticle collapse here.
To summarize: Decoherence by interactions with environment can be explained perfectly by multiple "collapses" of the probability amplitude wave function during interactions with environment particles. Microscopic interference is never "seen" directly by an observer, therefore we do not expect ever to "see" macroscopic superpositions of live and dead cats. The "transition from quantum to classical" systems is the consequence of laws of large numbers. The quantum dynamical laws necessarily include two phases, one needed to describe the continuous deterministic motions of probability amplitude waves and the other the discontinuous indeterministic motions of physical particles. The mysteries of nonlocality and entanglement are no different from those of standard quantum mechanics as seen in the twoslit experiment. It is just that we now have two identical particles and their wave functions are nonseparable . For Scholars
