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Philosophers

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Werner Heisenberg
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Presentations

Biosemiotics
Free Will
Mental Causation
James Symposium
 
The Quantum to Classical Transition

There is only one world.
It is a quantum world.
Ontologically it is indeterministic, but epistemically, our common sense and experience with large objects inclines us to see the world as deterministic
Information physics claims there is only one world, the quantum world, and that the appearance of a "quantum to classical transition" occurs for any large macroscopic object that contains a large number of atoms. For large enough systems, independent quantum events are "averaged over." The uncertainty in position and momentum of the object (Δv Δx > h / m) becomes less than observational accuracy as m gets large and h / m goes to zero.

Note that macroscopic objects are quantum objects. But the uncertainty in their position and momentum is not detectable by our measuring instruments. The classical laws of motion appear to apply perfectly to macroscopic objects, because quantum effects can be neglected.

Bohr called the discontinuous (and indeterministic) "quantum jumps" in his model for the atom the "quantum postulate."
Niels Bohr correctly insisted that classical physics plays an essential role in quantum mechanics. His Correspondence Principle allowed him to recover some important physical constants by assuming that the discontinuous quantum jumps for low quantum numbers (low "orbits" in his old quantum theory model) converged in the limit of large quantum numbers to the continuous radiation emission and absorption of classical electromagnetic theory.

We know that in macroscopic bodies with enormous numbers of quantum particles, quantum effects are averaged over. So that although the uncertainty in position and momentum of a large body still obeys Heisenberg's indeterminacy principle, the uncertainty is for all practical purposes unmeasurable and the body can be treated classically. We can say that the quantum description of matter also converges to a classical description in the limit of large numbers of quantum particles. We call this "adequate" or statistical determinism. It is the apparent determinism we find behind Newton's laws of motion for macroscopic objects. The statistics of averaging over many independent quantum events then produces the "quantum to classical transition" for the same reason as the "law of large numbers" results in the "central limit theorem" in probability theory.

Both Bohr and Heisenberg suggested that just as relativistic effects can be ignored when the velocity is small compared to the velocity of light (v / c → 0), so quantum effects might be ignorable when Planck's quantum of action h → 0. But this is quite wrong, because h is a constant that never goes to zero. In the information interpretation, it is always a quantum world. The correct conditions needed for ignoring quantum indeterminacy are when the mass of the macroscopic "classical" object is large.

Noting that the momentum p is the product of mass and velocity mv, Heisenberg's indeterminacy principle, Δp Δx > h, can be rewritten as Δv Δx > h / m. It is thus not when h is small, but when h / m is small enough, that errors in the position and momentum of macroscopic objects become smaller that can be measured. The quantum to classical transition is then when h / m becomes small.

A similar limit can be seen by analogy with optics. When the wavelength of light is large compared to the dimensions of the system, wave optics must be used and diffraction effects become important. On the other hand, when the wavelength of light is small compared to the apertures in the optical system, geometrical optics is applicable (ray tracing). Similarly, classical mechanics is applicable when the de Broglie wavelength λ = h / p is small compared to the dimensions of the experimental measurement apparatus. Once again, the quantum to classical transition is when h / p = h / mv becomes small.

Note that the macromolecules of biology are large enough to stabilize their information structures. DNA has been replicating its essential information for billions of years, resisting equilibrium and keeping its entropy very low despite the second law of thermodynamics
The creation of irreversible new information also marks the transition between the quantum world and the "adequately deterministic" classical world, because the information structure itself must be large enough (and stable enough) to be seen. The typical measurement apparatus is macroscopic, so the quantum of action h becomes small compared to the mass m and h / m approaches zero.

Decoherence Theory and the Quantum to Classical Transition
Decoherence theorists say that the quantum-to-classical transition occurs because of interactions with the environment, for example ever-present thermal photons. The cosmic microwave background is a constant source of low-energy photons. Without specifying the mechanics of the interaction between the photons and the quantum system being described, the decoherence theorists say that the photons cause the "selection" of preferred pointer positions, for example, the eigenvalues of the combined target quantum system and the measurement apparatus. They call this "einselection," a word coined from "environmentally induced superselection."

Decoherence theorists say einselection explains the appearance of wave function collapse (they deny actual collapses) and the emergence of classical descriptions of reality from quantum descriptions. Information physics agrees that classicality is an emergent property, but it is not induced in open quantum systems by their environments. Macroscopic quantum objects, with h / m so small that the uncertainty Δp Δx > h is undetectable, appear classical in both open and closed environments.

Unlike information physics, which identifies exactly how radiation interactions with matter (the emission, absorption, and scattering of photons) erase path information about correlations between the molecules of a gas, thus proving Boltzmann's H-Theorem and his assumption of "molecular chaos," decoherence arguments about environmental photons are merely "hand waving."

Decoherence theorists also say that our failure to see quantum superpositions in the macroscopic world is the measurement problem.

The information interpretation of quantum mechanics explains clearly why quantum superpositions like Schrödinger's Cat are not seen in the macroscopic world. Stable new information structures in the dying cat reduce the quantum possibilities (and their potential interference effects) to a classical actuality. Just before opening the box, quantum mechanics provides the two possibilities of "live" and "dead" cat, with calculable probabilities. Upon opening the box and finding a dead cat, an autopsy will reveal that the time of death was recorded and in some sense "observed." A human experimenter is not needed to collapse the wave function. The macroscopic cat is its own measuring apparatus and observer.

Not only do objects appear to be "classical" when they are large enough, the classical laws of motion, with their implicit determinism and strict causality, emerge when microscopic events can be ignored, but this determinism is fundamentally statistical.

Information philosophy interprets the wave function ψ as a "possibilities" function. With this simple change in terminology, the mysterious process of a wave function "collapsing" becomes a much more intuitive discussion of ψ exploring possibilities (with mathematically calculable probabilities), followed by a single actuality, at which time alternative probabilities go to zero ("collapse") instantaneously.

Information physics is standard quantum physics. It accepts the Schrödinger equation of motion, the principle of superposition, the axiom of measurement (now including the actual information "bits" measured), and - most important - the projection postulate of standard quantum mechanics (the "collapse" that so many interpretations deny).

But the conscious observer of the Copenhagen Interpretation is not required for a projection, for the wave-function to "collapse", for one of the possibilities to become an actuality. What it does require is an interaction between systems that creates irreversible and observable, but not necessarily observed, information.

Among the founders of quantum mechanics, almost everyone agreed that irreversibility was a key requirement for a measurement. Irreversibility introduces thermodynamics into a proper formulation of quantum mechanics, and this is what the information interpretation does.

Information is not a conserved quantity like energy and mass, despite the view of many mathematical physicists, who generally accept determinism. The universe began in a state of equilibrium with minimal information, and information is being created every day, despite the second law of thermodynamics
Classical interactions between large macroscopic bodies do not generate new information. Newton's laws of motion imply that the information in any configuration of bodies, motions, and force is enough to know all past and future configurations. Classical mechanics conserves information.

In the absence of interactions, an isolated quantum system evolves according to the unitary Schrödinger equation of motion. Just like classical systems, the deterministic Schrödinger equation conserves information.

Unlike classical systems however, when there is an interaction between quantum systems, the two systems become entangled and there may be a change of state in either or both systems. This change of state may create new information.

If that information is instantly destroyed, as in most interactions, it may never be observed macroscopically. If, on the other hand, the information is stabilized for some length of time, it may be seen by an observer and considered to be a "measurement." But it need not be seen by anyone to become new information in the universe. The universe is its own observer!
Compare Schrödinger's Cat as its own observer.

For the information (negative entropy) to be stabilized, the second law of thermodynamics requires that an amount of positive entropy greater than the negative entropy must be transferred away from the new information structure.

Note that despite the Heisenberg principle, quantum mechanical measurements are not always uncertain. When a system is measured (prepared) in an eigenstate, a subsequent measurement (Pauli's measurement of the first kind) will find it in the same state with perfect certainty.
What then are the possibilities for new quantum states? The transformation theory of Dirac and Jordan lets us represent ψ in a set of basis functions for which the combination of quantum systems (one may be a measurement apparatus) has eigenvalues (the axiom of measurement). We represent ψ as in a linear combination (the principle of superposition) of those "possible" eigenfunctions. Quantum mechanics lets us calculate the probabilities of each of those "possibilities."

Interaction with the measurement apparatus (or indeed interaction with any other system) may select out (the projection postulate) one of those possibilities as an actuality. But for this event to be an "observable" (a John Bell "beable"), information must be created and positive entropy must be transferred away from the new information structure, in accordance with our two-stage information creation process.

All interpretations of quantum mechanics predict the same experimental results.
Information physics is no exception, because the experimental data from quantum experiments is the most accurate in the history of science.

Where interpretations differ is in the picture (the visualization) they provide of what is "really" going on in the microscopic world - the so-called "quantum reality." The "orthodox" Copenhagen interpretation of Neils Bohr and Werner Heisenberg discourages such attempts to understand the nature of the "quantum world," because they say that all our experience is derived from the "classical world" and should be described in ordinary language. This is why Bohr and Heisenberg insisted on the path and the "cut" between the quantum event and the mind of an observer.

The information interpretation encourages visualization. Schrödinger called it Anschaulichkeit. He and Einstein were right that we should be able to picture quantum reality. But that demands that we accept the reality of quantum possibilities and discontinuous random "quantum jumps," something many modern interpretations do not do. (See our visualization of the two-slit experiment, our EPR experiment visualizations, and Dirac's three polarizers to visualize the superposition of states and the projection or "collapse" of a wave function.) Related to the Heisenberg Cut, but really quite different.

Three Examples of a "Classical" Apparatus - the Photographic Plate, a CCD, the cloud chamber.
A macroscopic object with a vast number of quantum-scale systems prepared in "metastable" states.
The Decoherence Explanation
Schlosshauer agrees there is only one world - the quantum world. But there is no universal wave function, which is a construction to prevent any new information being created and establish determinism.
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