Abstract
We generalize relativistic quantum mechanics and the Standard Model of elementary particle physics by considering a finite limit for the smallest measurable length. The resulting theory of Space-Time Quantization is logically consistent and accounts for all possible particle states by means of four new quantum numbers. They specify possible variations of wave functions at the smallest possible scale in space and time, while states of motion are defined by their large-scale variations. This theory also provides insight into the nature and properties of dark matter particles. It can facilitate their detection and identification because of a very strict conservation law.
Highlights
More than 80% of all matter in our universe is dark matter (DM), it has not yet been possible to identify this type of particles
Why are wave functions and fields unable to store this information? Could this be due to the postulate that space and time are continuous? Is it a logical necessity or not? To answer this question, we considered that Nature could impose another restriction and constructed a theory of Space-Time Quantization (STQ) that generalized Relativistic Quantum Mechanics (RQM) to account for c, h and a
It is based on the fact that there are continually existing material objects. Their center of mass can only move from a point A to another point B by passing through a continuous array of intermediate points. This would be true for any point-like material particle in non-relativistic quantum mechanics, but how do we define knowledge in regard to motions? Quantum mechanics accepts that space-time coordinates can be measured with absolute precision, but it is sufficient to know the probability distribution for possible results, to calculate the average position of a point-like particle at any particular instant
Summary
More than 80% of all matter in our universe is dark matter (DM), it has not yet been possible to identify this type of particles. We considered that Nature could impose another restriction and constructed a theory of Space-Time Quantization (STQ) that generalized RQM to account for c, h and a This is the value of the smallest measurable length, which is not yet known, but it would be sufficient to show that a ≠ 0 leads to logical inconsistencies, to prove that space and time are continuous. Quantum mechanics accepts that space-time coordinates can be measured with absolute precision, but it is sufficient to know the probability distribution for possible results, to calculate the average position of a point-like particle at any particular instant. It is important in regard to principles that superluminal velocities are not excluded when a ≠ 0 , but this allows us to test the logical consistency of STQ
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