Reconstruction of Quantum Theory

Abstract

What belongs to quantum theory is no more than what is needed for its derivation. Keeping to this maxim, we record a paradigmatic shift in the foundations of quantum mechanics, where the focus has recently from interpreting to reconstructing quantum theory. Several historic and contemporary reconstructions are analyzed, including the ones due to Hardy, Rovelli, and Clifton, Bub and Halvorson. We conclude by discussing the importance of a novel concept of intentionally incomplete reconstruction.1 What is wrong with interpreting quantum mechanics?Ever since the first days of quantum mechanics physicists as well as philosophers tried to interpret it, understanding this task as a problem of giving to the new physical theory a clear meaning. One of the principal reasons why one has always felt the need for interpretations has to do with the puzzling aspect of the formalism of quantum mechanics, usually referred to as the measurement problem. Reversible unitary evolution of the wave function, according to standard quantum mechanics, at the moment of measurement is replaced by an irreversible transformation known as wavefunction collapse. First and foremost, interpretations of quantum mechanics aimed at making sense of this surprising change in the theory's dynamics, sometimes taking the collapse at face value and claiming its fundamental irreducible role, or sometimes going to another extreme and denying the collapse altogether. However, looking globally, the enterprize of interpreting quantum mechanics failed: today we still have no consensus on what the meaning of quantum theory is. None of the proposed answers has won overall acceptance. Perhaps the most remarkable manifestation of the failure to interpret quantum mechanics is the attitude taught to most young physicists in 1 lecture rooms and research laboratories in the last half century, "Shut up and calculate!" [37] Why did attempts at a univocal interpretation fail? Many answers are possible, and among them we favor two, both showing that there is an intrinsic deficiency in the idea of interpreting a physical theory with the help of philosophical instruments only.The first answer is that to a physical theory one would naturally like to give a physical meaning in the Greek sense of ϕύσις, i.e. we-as part of the physicists' audience-expect to be told a true story about nature. This is because we casually tend to apply physical theory to the phenomenal world to learn something about the latter, and not the world to physical theory in order to invent a meaning of the theory. Physical theory is above all a tool for predicting the yet unobserved phenomena; so employing existing knowledge and experience of the world to interpret physics runs counter to its basic function as a scientific theory. However, notwithstanding such an against-the-grain direction in which a philosophical interpretation operates, the former does not necessarily lead to formal contradiction that would invalidate the interpretation program logically; more modestly but perhaps no less irr...

Reconstruction and Reinvention in Quantum Theory

“…14 Third, while all of the above can be understood in traditional realist terms, the abundance of accounts of reinvention and (to a lesser extent) reconstruction does leave the traditional realist in the (admittedly familiar) position of having to choose, or at any rate, believing that there is a correct choice (which could be 'none of the above'). I conclude by suggesting that, in contrast to the cheap instrumentalism of yesteryear, 15 the 'instrumentalism' that many philosophers presume is intended when the word is used, an instrumentalism content with the unanalyzed statement that theories are 'instruments', there is a philosophically respectable position which seeks to engage with this instrument through both reinvention and reconstruction, not, of course, in order to understand the secrets of the unobserved physical world, but to understand why this instrument behaves the way it does in light of the uses to which we put it. The assumption that makes this view essentially opposed to traditional realism is that, according to it, the inputs to these reinventions and reconstructions (e.g., the axioms in a reinvention, the presumptions about the nature of physical quantities in a reconstruction) reflect not the fundamental facts about the physical world, but fundamental facts about the manner in which we seek to understand the physical world.…”

“…This point perhaps echoes a similar point (arrived at from a somewhat different angle) made by Grinbaum[15]: "Philosophical and linguistic justification, and mathematical derivation, play here a game of mutual onslaught and retreat which, ultimately, leads to the advance of science" 15. I'm not convinced that anybody ever really thoughtfully believed in cheap instrumentalism.…”

“…I have left out of the discussion the 'partial reconstructions' identified by Grinbaum[15,16], such as the 'toy models' of Spekkens[23]. In this work, researchers produce models that reconstruct a portion of quantum theory, intentionally leaving the rest out for the purpose of investigating some one (or few) principles independently of the rest of quantum theory.…”

(Almost) C*-algebras as sheaves with self-action

“…In spirit, this approach is similar to the existing reconstructions of quantum mechanics from operational axioms [10]. In recent years, a wide range of reconstruction theorems with a large variety of choices for the axioms have been derived, as pioneered by Hardy [11,12].…”

On classical cloning and no-cloning

“…Although we will not need the added generality of Poisson structures in our 24 That is to say, the Poisson bracket satisfies Leibniz's law in both arguments. 25 Here we use the 'wedge' notation to indicate that each fiber of the bundle is the antisymmetrized tensor product of two tangent spaces of M .…”