Another look at what is possible and impossible in optics

Daniel Filan, J. J. Hope

In this paper we address the question of whether it is possible to obtain evidence that we are in a superposition of different worlds, as suggested by the relative state interpretation of quantum mechanics. We find that it is impossible to find definitive proof, and that if one wishes to retain reliable memories of which world one was in, no evidence at all can be found. We then show that even for completely linear quantum state evolution, there is a test that can be done to tell if you can be placed in a superposition.

Jesper Lützen

Abstract Also physics has its impossibility statements. We compare them with the mathematical impossibility theorems and look into the history of one of them: the impossibility of building a perpetual motion machine. We also consider impossibilities in twentieth-century physics, in particular in quantum mechanics. For example, Heisenberg’s uncertainty relations imply that it is impossible to measure both the place and momentum of a particle accurately. We also discuss von Neumann’s controversial proof that it is impossible to obtain a deterministic version of quantum mechanics by introducing hidden variables.

Sardar Singh

K. Hess, Hans A. De Raedt, Kristel F. L. Michielsen

In 1862, George Boole derived an inequality for variables that represents a demarcation line between possible and impossible experience. This inequality forms an important milestone in the epistemology of probability theory and probability measures. In 1985 Leggett and Garg derived a physics related inequality, mathematically identical to Boole’s, that according to them represents a demarcation between macroscopic realism and quantum mechanics. We show that a wide gulf separates the “sense impressions” and corresponding data, as well as the postulates of macroscopic realism, from the mathematical abstractions that are used to derive the inequality of Leggett and Garg. If the gulf can be bridged, one may indeed derive the said inequality, which is then clearly a demarcation between possible and impossible experience: it cannot be violated and is not violated by quantum theory. This implies that the Leggett-Garg inequality does not mean that the SQUID flux is not there when nobody looks, as Leggett and Garg suggest, but instead that the probability measures may not be what Leggett and Garg have assumed them to be, when no data can be secured that directly relate to them. We show that similar considerations apply to other quantum interpretation-puzzles such as two-slit experiments.

R. Graham, Fritz Haake