It is shown that quantum mechanics is, like thermodynamics, a phenomenological theory i.e., not a causal theory, ( not because it is a statistical theory - statistical theories with caused probability distributions can be regarded as causal) but because pure states, i.e., probability distributions of measurement values, cannot inhere in elementary particles and therefore cannot change when their world tubes intersect and hence they cannot be regarded as interacting causally. By a causal theory is meant a theory that specifies the changes in time of the states of causally interacting entities in its domain. The areas in quantum mechanics in which causal interactions are relevant include, though not explicitly, measurement and therefore the Born rule, and, explicitly, the unitary Schrodinger time development of states. The Born rule probabilities are shown to to refer not to conjoint superpositions of eigenstates but to classical mixtures of mutually exclusive eigenvalues and the Schrodinger time development of states is shown to refer to the time development of the states of non-causally interacting elementary particles and hence cannot be regarded as as a causal time development equation, appearances to the contrary notwithstanding. The recognition that quantum mechanics is not a causal theory but a phenomenological theory like thermodynamics does not affect the way it is employed to calculate an predict and hence preserves its empirical success but it does allow a typically simple phenomenological theory explanation of entanglement and other apparently non-local phenomena.
Introducing graduate students and researchers to mathematical physics, this book discusses two recent developments: the demonstration that causality can be defined on discrete space-times; and Sewell's measurement theory, in which the wave packet is reduced without recourse to the observer's conscious ego, nonlinearities or interaction with the rest of the universe. The definition of causality on a discrete space-time assumes that space-time is made up of geometrical points. Using Sewell's measurement theory, the author concludes that the notion of geometrical points is as meaningful in quantum mechanics as it is in classical mechanics, and that it is impossible to tell whether the differential calculus is a discovery or an invention. Providing a mathematical discourse on the relation between theoretical and experimental physics, the book gives detailed accounts of the mathematically difficult measurement theories of von Neumann and Sewell.
Introducing graduate students and researchers to mathematical physics, this book discusses two recent developments: the demonstration that causality can be defined on discrete space-times; and Sewell's measurement theory, in which the wave packet is reduced without recourse to the observer's conscious ego, nonlinearities or interaction with the rest of the universe. The definition of causality on a discrete space-time assumes that space-time is made up of geometrical points. Using Sewell's measurement theory, the author concludes that the notion of geometrical points is as meaningful in quantum mechanics as it is in classical mechanics, and that it is impossible to tell whether the differential calculus is a discovery or an invention. Providing a mathematical discourse on the relation between theoretical and experimental physics, the book gives detailed accounts of the mathematically difficult measurement theories of von Neumann and Sewell.
Processes with indefinite causal order (ICO), such as the quantum switch, are an emerging resource for quantum tasks and a fundamental test bed for studies of temporal correlations in quantum mechanics. A limitation of past photonic implementations of the quantum switch, however, is their inability to perform measurements inside the switch without either destroying the superposition of causal orders or delaying readout until the after the quantum switch. Measurements where the results are read out locally are needed for several applications of ICO, but also for a loophole-free verification of ICO. Here, we overcome past limitations by introducing a
local measurement scheme and coupling the photon in the switch to a
time−delocalized ancilla system. We experimentally realize this protocol using a photonic quantum switch with post-selected linear optical logic gates. Our method ensures that the measurement apparatus interacts with the system at two distinct times and yet yields a single outcome. We use a quantum eraser measurement to preserve the ICO, which we certify by measuring a causal witness and finding a negative value of
CW≈−0.305(1). Furthermore, by explicitly realizing a time-delocalized ancilla system, our protocol not only enables a new class of quantum switch protocols requiring local readout, but also provides a general method for path-coherence-preserving measurements with broad applications beyond ICO.