arXiv subjects

Elliott Tammaro

Publications and source records attributed to Elliott Tammaro.

4 recordsLinked to original sources

arXiv2026

Associating Trajectories with Quantum Processes by Equivalent Spectra

Quantum mechanics abandoned the classical notion of a particle trajectory, yet trajectories remain conceptually appealing for resolving foundational issues in quantum mechanics. Bohmian mechanics offers one route to associating trajectories with quantum processes, but it requires explicit non-locality to remain consistent with EPR-type experiments, placing it in tension with special relativity. We propose an alternative approach: rather than deriving trajectories from a quantum guidance equation, we search for classical trajectories whose radiated frequency spectra match those of quantum processes such as atomic transitions. Using the Liénard-Wiechert potentials, we compute the electric and magnetic fields generated by a point charge along a given trajectory, numerically solving the retarded-time and from these fields obtain the power spectrum of emitted radiation. By fitting the parameters of a chosen family of trajectories, we identify "equivalent spectrum" trajectories that reproduce a target frequency distribution, including ones of quantum mechanical origin. We discuss the implications of this method and propose future work to determine whether equivalent spectrum trajectories belong to a family governed by a differential equation, which would constitute a quantum-equivalent equation of motion.

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arXiv2023

Considering a superposition of classical reference frames

A ubiquitous feature of quantum mechanical theories is the existence of states of superposition. This is expected to be no different for a quantum gravity theory. Guided by this consideration and others we consider a framework in which classical reference frames may be in superposition relative to one another. Mirroring standard quantum mechanics we introduce a complex-valued wavefunctional, which takes as input the transformations between the coordinates, $Ψ[x(x')]$, with the interpretation that an interaction between the reference frames may select a particular transformation with probability distribution given by the Born rule - $P[x(x')] = \text{probability distribution functional} \equiv \vert Ψ[x(x')] \vert^2$. The cases of two and three reference frames in superposition are considered explicitly. It is shown that the set of transformations is closed. A rule for transforming wavefunctions from one system to another system in superposition is proposed and consistency with the Schrodinger equation is demonstrated.

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arXiv2014

Structural Instability and Quantum Lying in the Many-worlds (Relative State) Interpretation

The stability of dynamical systems against perturbations (variations in initial conditions/model parameters) is a property referred to as structural stability. The study of sensitivity to perturbation is essential because in experiment initial conditions are not fixed, nor are model parameters known, to arbitrarily high precision. Additionally, if a physical system under study exhibits stability (insensitivity to initial conditions) then a theoretical description of the system must exhibit structural stability. Consequently, stability can be a useful indicator of the correctness of a theoretical formulation. In this work the many-worlds interpretation is considered. It is first demonstrated that the interpretation admits a class of special states, herein referred to as "quantum liar states," because they indicate disagreement between the recorded result of a measurement and the actual state of a system. It is then demonstrated that the many-worlds interpretation is not structurally stable against the introduction of quantum liar states.

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arXiv2014

Why Current Interpretations of Quantum Mechanics are Deficient

Quantum mechanics under the Copenhagen interpretation is one of the most experimentally well verified formalisms. However, it is known that the interpretation makes explicit reference to external observation or "measurement." One says that the Copenhagen interpretation suffers from the measurement problem. This deficiency of the interpretation excludes it as a viable fundamental formalism and prevents the use of standard quantum mechanics in discussions of quantum cosmology. Numerous alternative interpretations have been developed with the goals of reproducing its predictive success while obviating the measurement problem. While several interpretations make distinct, falsifiable, predictions, many claim to precisely reproduce the results of standard quantum mechanics. The sheer number of interpretations raises several issues. If the experimental predictions are identical, how are they to be assessed? On what grounds can an interpretation be said to trump another? Without recourse to experimental findings, one may continue to assess an interpretation on its logical structure, self-consistency, and simplicity (number and plausibility of its assumptions). We argue, and where possible, demonstrate, that all common interpretations have unresolved deficiencies. Among these deficiencies are failures to resolve the measurement problem, fine-tuning problems, logical/mathematical inconsistencies, disagreement with experiment, and others. Shortcomings as severe as these call into question the viability of any of the common interpretations. When appropriate, we indicate where future work may resolve some of these issues.

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