Measured distribution of cloud chamber tracks from radioactive decay: a new empirical approach to investigating the quantum measurement problem

Using publicly available video of a diffusion cloud chamber with a very smallradioactive source, I measure the spatial distribution of where tracks start, and consider possibleimplications. This is directly relevant to the quantum measurement problem and its possibleresolution, and appears never to have been done before. The raw data are relatively uncontrolled,leading to caveats that should guide future, more tailored experiments. Results may suggest amodification to Born’s rule at very small wavefunction, with possibly profound implications forthe detection of extremely rare events such as proton decay. I introduce two candidate smallwavefunctionBorn rule modifications, a hard cutoff and an offset model; the data may favor theoffset model, which has a stronger underlying physical rationale. Track distributions from decaysin cloud chambers represent a previously unappreciated way to probe the foundations of quantummechanics, and a novel case of wavefunctions with macroscopic signatures.

Another Proof of Born’s Rule on Arbitrary Cauchy Surfaces

In 2017, Lienert and Tumulka proved Born’s rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born’s rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well as a given unitary time evolution between any two Cauchy surfaces, satisfying that there is no interaction faster than light and no propagation faster than light. Here, we prove Born’s rule on arbitrary Cauchy surfaces from a different, but equally reasonable, set of assumptions. The conclusion is that if detectors are placed along any Cauchy surface $$\Sigma $$ Σ , then the observed particle configuration on $$\Sigma $$ Σ is a random variable with distribution density $$|\Psi _\Sigma |^2$$ | Ψ Σ | 2 , suitably understood. The main different assumption is that the Born and collapse rules hold on any spacelike hyperplane, i.e., at any time coordinate in any Lorentz frame. Heuristically, this follows if the dynamics of the detectors is Lorentz invariant.

A Wave Nature-Based Interpretation of The Nonclassical Feature of Photon Bunching On A Beam Splitter

Born’s rule is key to understanding quantum mechanics based on the probability amplitude for the measurement process of a physical quantity. Based on a typical particle nature of a photon, the quantum feature of photon bunching on a beam splitter between two output photons can be explained by Born’s rule even without clear definition of the relative phase between two input photons. Unlike conventional understanding on this matter, known as the Hong-Ou-Mandel effect, here, we present a new interpretation based on the wave nature of a photon, where the quantum feature of photon bunching is explained through phase basis superposition of the beam splitter. A Mach-Zehnder interferometer is additionally presented to support the correctness of the presented method. As a result, our limited understanding of the quantum feature is deepened via phase basis superposition regarding the destructive quantum interference. Thus, the so-called ‘mysterious’ quantum feature is now clarified by both the definite phase relationship between paired photons and a new term of the phase basis superposition of an optical system.

Justifying Born’s Rule Pα = |Ψα|2 Using Deterministic Chaos, Decoherence, and the de Broglie-Bohm Quantum Theory

In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution ρ(x) of finding a particle at point x to the Born probability law |Ψ(x)|2. Our model is discussed in the context of Boltzmann’s kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.