Unitary Mechanics Research Articles

A no-go theorem for the persistent reality of Wigner\u2019s friend\u2019s perception

The notorious Wigner’s friend thought experiment (and modifications thereof) has received renewed interest especially due to new arguments that force us to question some of the fundamental assumptions of quantum theory. In this paper, we formulate a no-go theorem for the persistent reality of Wigner’s friend’s perception, which allows us to conclude that the perceptions that the friend has of her own measurement outcomes at different times cannot “share the same reality”, if seemingly natural quantum mechanical assumptions are met. More formally, this means that, in a Wigner’s friend scenario, there is no joint probability distribution for the friend’s perceived measurement outcomes at two different times, that depends linearly on the initial state of the measured system and whose marginals reproduce the predictions of unitary quantum theory. This theorem entails that one must either (1) propose a nonlinear modification of the Born rule for two-time predictions, (2) sometimes prohibit the use of present information to predict the future—thereby reducing the predictive power of quantum theory—or (3) deny that unitary quantum mechanics makes valid single-time predictions for all observers. We briefly discuss which of the theorem’s assumptions are more likely to be dropped within various popular interpretations of quantum mechanics.

Emergent phase space description of unitary matrix model

We show that large N phases of a 0 dimensional generic unitary matrix model (UMM) can be described in terms of topologies of two dimensional droplets on a plane spanned by eigenvalue and number of boxes in Young diagram. Information about different phases of UMM is encoded in the geometry of droplets. These droplets are similar to phase space distributions of a unitary matrix quantum mechanics (UMQM) ((0 + 1) dimensional) on constant time slices. We find that for a given UMM, it is possible to construct an effective UMQM such that its phase space distributions match with droplets of UMM on different time slices at large N . Therefore, large N phase transitions in UMM can be understood in terms of dynamics of an effective UMQM. From the geometry of droplets it is also possible to construct Young diagrams corresponding to U(N) representations and hence different large N states of the theory in momentum space. We explicitly consider two examples: single plaquette model with TrU2 terms and Chern-Simons theory on S3. We describe phases of CS theory in terms of eigenvalue distributions of unitary matrices and find dominant Young distributions for them.

Does the myosin V neck region act as a lever?

Recent research efforts from several groups have addressed the question of whether the amplitude of myosin's unitary step size is proportional to the length of the neck region. Unconventional myosin V, which has an extended neck region with 6IQ motifs, provides a natural template by which to test the lever arm model via mutational analysis. The most stringent test requires that a series of single-headed molecules from the same myosin class be analyzed. Here we characterized the unitary mechanics of three single-headed fragments of myosin V expressed in the baculovirus/insect cell system. Each construct consisted of the motor domain (MD) and a variable number of IQ motifs (MD2IQ, MD4IQ and MD6IQ) that bind calmodulin, followed by an epitope tag so that the molecule can be attached to the nitrocellulose surface via an antibody. The results show a correlation between the unitary step size and the number of IQ motifs, confirming that the myosin neck region acts as a lever. The step size of MD2IQ is twice that observed from single-headed subfragments of class II myosins with the same neck length. Our results are discussed in relation to data obtained concurrently from other laboratories with similar constructs.

A statistical theory of the detector in unitary quantum mechanics

The general approach to the theory of statistical measurements in any quantum theory is considered and is shown to contain great difficulties in particular cases. In unitary quantum mechanics a particle is represented by a periodically disappearing and reappearing wave packet, on which vacuum fluctuations are superimposed in some random way. Thus the problem of detecting a particle may be simplified and reduced to finding the packet by means of a threshold device (called detector). This problem is solved in the most general case. It is shown that the optimal detector (which minimizes the error) has to possess a threshold energy which is equal to one-fourth of the registered particle energy. The probabilities of particle detection in unitary quantum mechanics and in ordinary quantum mechanics are shown to be different by two orders of magnitude, which can be tested experimentally.

A statistical theory of measurements in unitary quantum mechanics

The paper is concerned with a statistical problem on the detection of particles by macroinstruments in unitary quantum mechanics. Requirements of macroinstruments whose error is minimal are defined. The wave function in unitary quantum mechanics is interpreted. The probabilities of particle detection in unitary quantum mechanics and in conventional quantum mechanics are shown to be different by two orders of magnitude, which can be tested experimentally.

The Case Against Quantum Duality

(1) The idea that diffraction of matter particles can only be understood in terms of a temporary wave transformation or ‘double manifestation’ is an uneconomical ad hoc hypothesis, shattered already in 1923 by the unitary quantum theory of diffraction of Duane which in 1926 became part of the quantum mechanics, with a statistical interpretation of wave-like appearances.(2) Bohr's re-interpretation of Heisenberg's uncertainty of prediction as an indeterminacy of existence rests on an illegitimate literal translation of a wave result into particle language which is at variance with experience as well as with the statistical interpretation.(3) The fact that one can transform the simple and unitary particle mechanics into a complicated wavelike form is only a weak substitute for genuine dualism — as if one would see dualism in the transformability from the geo- to the heliocentric reference system.(4) The strongest argument against a symmetry of the particle and the wave theory of matter is the explainability of the former in terms of simple postulates of invariance, leaving the wave formalism as a purely ad hoc construction.