Both Albert Einstein and Louis de Broglie were dissatisfied with the type of quantum probabilities found in standard quantum mechanics. We have recently introduced a new formulation of quantum mechanics in which the quantum gravity probabilities are much more closely aligned with what de Broglie was seeking and hoping for. We show that if energy is conserved, then these new types of quantum gravity probabilities must also be conserved. Furthermore, we suggest that there must exist a probability gap above zero—that is, a lowest non-zero probability. In other words, quantum gravity probabilities are not continuous from zero to one, but instead exhibit a finite probability gap.
The paper shows that ranking information units by quantum probability differs from ranking them by classical probability provided the same data used for parameter estimation. As probability of detection (also known as recall or power) and probability of false alarm (also known as fallout or size) measure the quality of ranking, we point out and show that ranking by quantum probability yields higher probability of detection than ranking by classical probability provided a given probability of false alarm and the same parameter estimation data. As quantum probability provided more effective detectors than classical probability within other domains that data management, we conjecture that, the system that can implement subspace-based detectors shall be more effective than a system which implements a set-based detectors, the effectiveness being calculated as expected recall estimated over the probability of detection and expected fallout estimated over the probability of false alarm.
This paper develops the Quantum Probability Density Function (QPDF) method to describe the evolution of quantum probability density functions in space and time. The QPDF method has been applied to derive QPDF equations for quantum scalar particles. The formulations relate probability theory and quantum uncertainty and thereby provide insight into the quantum theory and the quantum fluid approach of quantum mechanics. The QPDF approach can be applied to problems in quantum communications, quantum imaging, and quantum computing.