Two QM papers by Gabriele Carcassi

Recently, two papers by the same author appeared on arXiv which offer some clarity to some of the aspects of quantum mechanics. Whilst there is sometimes an effort among authors toward hyperbolic romanticization of the “mysteries” of quantum mechanics, this author instead offers some welcome and insightful perspective on QM. The papers do not offer anything “new” in the usual sense that one might expect; instead, these papers offer conceptual approaches which are both enlightening and pedagogically instructive.

“Classical Mechanics as the many-particle limit of quantum mechanics” [1]:

We derive the classical limit of quantum mechanics by describing the center of mass of a system constituted by a large number of particles. We will show that in that limit the commutator between the position and velocity of the center of mass is infinitesimal, which allows both to be known with great precision. We then show how the infinitesimal commutator allows for the definition of functions of position and velocity, and how the commutator reduces to a Poisson bracket.

“How Einstein’s quantum hypothesis requires a departure from classical mechanics” [2]:

The aim of this work is to show how Einstein’s quantum hypothesis leads immediately and necessarily to a departure from classical mechanics. First we note that the classical description and predictions are in terms of idealized measurements that are exact, instantaneous, non-perturbative, independent of each other and process agnostic. If we assume we cannot arbitrarily reduce the strength of a signal, measurements are ultimately perturbative to some degree. We show how a physical description in which the best measurement conceivable, i.e. the ideal measurement, perturbs the system leads to all the concepts present in quantum mechanics including conjugate variables, probabilistic predictions and measurements connected to symmetries.

 

The latter paper is of particular interest, for its focus on, and treatment of, measurements which “are ultimately perturbative to some degree”. This, of course, is not new but is still a topic with deep conceptual consequences, as the author notes:

Some people, typically ones that only give only a superficial reading, argue that this work does not provide anything new: there is no new math developed, no new physical concepts, no new prediction. This shows a misunderstanding on our aim, which is to better understand a theory that is already now established for almost a century: it is unlikely that some important piece is missing. It is more likely, instead, that we do have all the pieces but we have not assembled them in a way that allows the big picture to emerge.

 

References

[1] Carcassi, G. “Classical Mechanics as the many-particle limit of quantum mechanics”. arXiv.0902.141.

[2] Carcassi, G. “How Einstein’s quantum hypothesis requires a departure from classical mechanics”. arXiv.0902.2680.

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