Quantum Probability

John Edward Gough, Joachim Kupsch

Espen Gaarder Haug

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.

Massimo Melucci

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.

Jerome R. Busemeyer, Peter Bruza

Espen Gaarder Haug

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 more closely aligned with what de Broglie was seeking and hoping for. We show that if energy is conserved, then the corresponding total aggregate collision-event count is also conserved. Furthermore, we suggest that there must exist a probability gap above zero, that is, a lowest non-zero individual probability. Individual quantum gravity probabilities are therefore not continuous from zero to one, but instead exhibit a finite probability gap. Quantities larger than one are not single probabilities; they are aggregate collision-event counts obtained by summing many bounded individual probabilities.