The quantum orthodoxy attests that all dynamical degrees of freedom should be quantized, including those associated with the centers of mass of composite/complex systems, such as protons/pebbles. By assuming that the centers of mass of protons/pebbles should be quantized, one implies the existence of a corresponding Fock space, since, according to the present lore, quantum mechanics is a consequence of quantum field theory. Despite the fabulous success of quantum mechanics, it is unreasonable to assume the existence of annihilation and creation operators for pebbles. Fortunately, there are strong reasons to doubt that wave mechanics can describe the centers of mass of systems at or above the Planck scale, thereby jeopardizing the construction of the corresponding Fock space. We argue that isolated (free) systems with masses exceeding the Planck mass would have their centers of mass governed by classical (rather than quantum) mechanics, despite harboring macroscopic quantum phenomena as observed in the laboratory. Here, we briefly revisit (i) the arguments for the need for a Heisenberg cut delimiting the boundary between the quantum and classical realms and (ii) the kind of new physics expected at (the uncharted region of) the Heisenberg cut.
Journal reference
Brazilian Journal of Physics, vol.56, article number 192, 2026
The quantum orthodoxy attests that all dynamical degrees of freedom should be quantized, including those associated with the centers of mass of composite/complex systems, such as protons/pebbles. By assuming that the centers of mass of protons/pebbles should be quantized, one implies the existence of a corresponding Fock space, since, according to the present lore, quantum mechanics is a consequence of quantum field theory. Despite the fabulous success of quantum mechanics, it is unreasonable to assume the existence of annihilation and creation operators for pebbles. Fortunately, there are strong reasons to doubt that wave mechanics can describe the centers of mass of systems at or above the Planck scale, thereby jeopardizing the construction of the corresponding Fock space. We argue that isolated (free) systems with masses exceeding the Planck mass would have their centers of mass governed by classical (rather than quantum) mechanics, despite harboring macroscopic quantum phenomena as observed in the laboratory. Here, we briefly revisit (i) the arguments for the need for a Heisenberg cut delimiting the boundary between the quantum and classical realms and (ii) the kind of new physics expected at (the uncharted region of) the Heisenberg cut.
Harmonizing classical and quantum worlds is a major challenge for modern physics. A significant portion of the scientific community supports the notion that classical mechanics is an effective theory that arises from quantum mechanics. Recently, the present authors have argued that this should not be the case, as quantum mechanics is not trustworthy for describing the center of mass of systems with masses m much larger than the Planck mass MP. In this vein, a simple gravitational self-decoherence model was proposed, describing how the center of mass of quantum systems would classicalize for m∼MP. Here, we show that our model does not prevent macroscopic systems (with classical centers of mass) from harboring quantum internal vibrations (as has been observed in the laboratory).
WHAT TO LOOK FOR Although the classical theory developed in Chapter 2 can be used to describe a great many phenomena in the real world, there is little doubt that the proper description of the world is quantum. To a large measure we perceive the world classically and we must find ways to uncover the underlying quantum theory. The process of “quantization” normally consists of turning a classical theory into a corresponding quantum theory. In turn, the “classical limit” is the process by which a quantum theory is brought to its associated classical theory. The parameter ħ = 1.0545 × 10 −27 (≃ 10 −27 ) erg-seconds (cgs units), referred to as Planck's constant, sets the scale of quantum phenomena. In many applications it will prove useful to use “natural” units in which ħ = 1 just so that formulas are less cumbersome. For most typical formulations of quantum mechanics the classical limit means the limit that ħ → 0, and in this text we shall have many occasions to use this definition as well. In addition, we shall also learn to speak about the classical and quantum theories simultaneously coexisting – as they do in the real world – without the need to take the limit ħ → 0. There are three generally accepted “royal” routes to quantization, due principally to Heisenberg, Schrödinger, and Feynman, respectively, and we shall exploit them all. In each case we begin with a single degree of freedom ( N = 1).
Newton’s force law [Formula: see text] is derived from the Schrödinger equation for isolated macroscopic bodies, composite states of e.g. [Formula: see text] atoms and molecules, at finite body temperatures. We first review three aspects of quantum mechanics (QM) in this context: (i) Heisenberg’s uncertainty relations for their center of mass (CM), (ii) the diffusion of the CM wave packet, and (iii) a finite body temperature which implies a metastable (mixed-) state of the body: photon emissions and self-decoherence. They explain the origin of the classical trajectory for a macroscopic body. The ratio between the range [Formula: see text] over which the quantum fluctuations of its CM are effective, and the body’s (linear) size [Formula: see text], [Formula: see text] or [Formula: see text], tells whether the body’s CM behaves classically or quantum mechanically, respectively. In the first case, Newton’s force law for its CM follows from the Ehrenfest theorem. We illustrate this for weak gravitational forces, a harmonic-oscillator potential, and for constant external electromagnetic fields slowly varying in space. The derivation of the canonical Hamilton equations for many-body systems is also discussed. Effects due to the body’s finite size such as the gravitational tidal forces appear in perturbation theory. Our work is consistent with the well-known idea that the emergence of classical physics in QM is due to the environment-induced decoherence, but complements and completes it, by clarifying the conditions under which Newton’s equations follow from QM, and by deriving them explicitly.
Quantum mechanics is the theoretical framework that describes physical phenomena on the microscopic scale. In particular, it is used in those situations in which Planck's constant h , approximately equal to 6.62 × 10 -34 Js, cannot be assumed to be negligible, despite its apparently tiny magnitude. Macroscopic phenomena, on the other hand, involve magnitudes that are so large that h can be set equal to zero without appreciable error. As an illustration of this in the macroscopic context, consider the following example: a ladybug ( Hippodamia convergens ) of mass 1 g moves radially at a speed of 0.01 ms -1 on a turntable rotating at 10 rpm. In the rotating frame of reference, the ladybug has a kinetic energy of about an erg, and, in the laboratory frame, its angular momentum is roughly 10 -5 Js when it is at a distance of 0.1 m from the center of the rotating turntable. The latter angular momentum is of the order of 10 28 h . Thus, relative to this value, h is well approximated by zero and, indeed, only classical mechanics is needed to describe the ladybug's motion. In contrast to the preceding example, an electron in the “2p” level of hydrogen has an energy of about 10 -25 J and an angular momentum whose magnitude is approximately h /(2π) = ħ (pronounced “h-bar”). Here, h cannot be ignored and only a quantum description can accurately account for the properties of this system.
Quantum mechanics is a relatively new branch of physics as compared to the other branches.Many of its concepts are a bit confusing, which is quite obvious, because it completely destroys the classical intuitions of physicists as well as students.But some of its concepts have a classical mechanical analogy and one such concept is the concept of expectation value of observables or operators in quantum mechanics.In a way it is related to the concept of centre of mass in classical mechanics.So, in this paper, first, a review of this concept and its correspondence with centre of mass and later the reason behind the naming of this concept is discussed in brief.
Philosophical debate on the measurement problem of quantum mechanics has, for the most part, been confined to the non-relativistic version of the theory. Quantizing quantum field theory, or making quantum mechanics relativistic, yields a conceptual framework capable of dealing with the creation and annihilation of an indefinite number of particles in interaction with fields, i.e. quantum systems with an infinite number of degrees of freedom. I want to show that a solution to the standard measurement problem is available if we exploit the properties of the infinite quantum models available in this broader conceptual framework. There is a qualitative difference between quantum systems with an infinite number of degrees of freedom and quantum systems with a finite number of degrees of freedom. In the infinite case, there exist many unitarily inequivalent irreducible Hilbert space representations of the algebra of observables of the system. In the finite case, there is only one such representation.