Quantum theory of observation/The appearance of relative classical worlds in the quantum Universe
Are not classical appearances proofs that quantum physics is incomplete?
The quantum theory as presented in this book, in the manner of Everett, ie without the postulate of state vector reduction, seems contradicted by the simple observation that the world always appears to us in a way which seems to contradict the teachings of the theory. When we speak of this world as it naturally appears to us, of beings which inhabit it and of their states, we never make use of the principle of quantum superposition. On the contrary, it is forbidden. The macroscopic bodies, and our bodies in particular, with their sensory organs, always seem to have defined states which can not be superposed, and which can be determined, at least approximately, with the magnitudes of classical physics (position, velocity...). Is not this sufficient proof that Bohr is correct in asserting that measuring instruments should be considered as classical objects for the interpretation of quantum physics?
It is of course possible that quantum principles have only a limited validity, that on our macroscopic scale new effects come into play, that they are ignored by the theory and that they derogate from its principles. It is possible, but it is not necessary to explain the classical, daily renewed appearances of our world, because by following Everett we can give a quantum explanation of classical appearances.
Space and mass
The formalism of the unitary operators implicitly uses the concept of time, since a unitary operator describes a change of state, but it says nothing a priori about space and mass. It seems falsely that space and mass are essentially classical concepts, that quantum physics does not explain their existence, and that therefore it can not explain by itself the classical appearances of the world. Most quantum equations have classical equivalents and we need the second ones to understand the first. Thus presented quantum physics is not autonomous in relation to classical physics, it is only a very particular way of using concepts borrowed from classical physics.
The fundamental concepts of classical physics, space, time, mass, and derived concepts, velocity, momentum, force, angular momentum, energy ... all rest on the principle that material points have trajectories. They are defined as lines in space-time. Even the dynamics of continuous, solid or fluid media describes the trajectories of the material points which constitute the bodies in motion. But the indeterminacy relation of Heisenberg (see 2.7) prevents quantum particles from having such classical trajectories, since their position and velocity can not be exactly defined at the same time. How then can it explain all the appearances which legitimize the fundamental concepts of classical physics?
The formalism of unitary operators is quantum physics in its most general and abstract form. It makes no particular assumptions about space and its contents. It can be applied to all kinds of spaces and contents. It does not impose concepts of space and mass similar to those of classical physics, but it does not prohibit them either. Schrödinger has shown how to compute the wave functions of massive particles in ordinary space (see 1.2). It is a quantum way of giving meaning to the concepts of space and mass.
The fundamental concepts of physics, space, time, matter, and derived concepts, are not exclusively classical. All the classical theoretical constructions (inertial movements, collisions between balls, periodic oscillations, etc.) which enable to give a physical meaning, ie in terms of observable beings, to the mathematical theory, can be adapted to quantum physics. It is not necessary to assume the existence of classical trajectories of material points to give a physical meaning to the concept of momentum, for example. Quantum physics does not postulate the instantaneous velocities of classical physics but it does not prohibit the measurement of mean velocities. When classical physics reasoned on points of space or space-time, it is often enough to replace these by small regions of finite extension to obtain a reasoning equally valid in quantum physics.
Even measurements of length and duration can be explained in a quantum way (Peres 1995). We can justify the postulates on the structure of space-time on the basis of spatio-temporal measurements in quantum physics as well as in classical physics. This is why quantum physics can be considered autonomous. There is no need to justify the quantum equations from the corresponding classical equations. This correspondence is found because classical physics and quantum physics are both theories of the same space-time.
The quantum evolution of the Universe determines the classical destinies of the relative worlds
From Minkowski's space-time and the principle of quantum superposition, we can construct all the spaces of quantum states which suit us to explain natural phenomena (Weinberg 1995), or almost all, because the quantum theory of gravitation is a problem.
We can thus construct models of the Universe in which the worlds relative to the observers have a classical appearance (Joos, Zeh & ... 2003, Zurek 2003, Schlosshauer 2007). The quantum evolution of the Universe can not be identified with a classical destiny, but it is enough to determine the growth of a forest of destinies of observers and their relative worlds (cf. chapter 6). Quantum physics explains classical appearances without postulating that the Universe itself must have this appearance. It shows how classical appearances relative to observers emerge from a quantum evolution which describes a forest of multiple destinies.