Related papers: The probability in the relativistic m+1 space-time
In this two-part essay, we distinguish several senses in which general relativity has been regarded as "locally special relativistic". Here, in Part 1, we focus on senses in which a relativistic spacetime has been said to be "locally…
We find the probability density function $\mathcal{P}(V_{\texttt{r}})$ of the relativistic relative velocity for two colliding particles in a non-degenerate relativistic gas. The distribution reduces to Maxwell distribution for the relative…
By pursuing the deep relation between the one-dimensional Dirac equation and quantum walks, the physical role of quantum interference in the latter is explained. It is shown that the time evolution of the probability density of a quantum…
We show that the relativistic signatures on the transition probability of atoms moving through optical cavities are very sensitive to their spatial trajectory. This allows for the use of internal atomic degrees of freedom to measure small…
The appearance of linear spaces, describing physical quantities by vectors and tensors, is ubiquitous in all of physics, from classical mechanics to the modern notion of local Lorentz invariance. However, as natural as this seems to the…
We consider a massive particle of arbitrary spin and the basis vectors that carry the unitary, irreducible representations of the Poincar\'e group. From the complex coefficients in normalizable superpositions of these basis vectors, we…
We study the action and the dynamics of a relativistic particle, uncharged or charged, in multiscale spacetimes. Invariance under reparametrizations and Poincar\'e symmetries uniquely determine the action and the line element to be the…
Quantum Action Principle formulated earlier is used as a ground for a probabilistic interpretation of one-particle relativistic quantum mechanics. In this new approach the probability "flows" in the Minkowsky space being dependent on an…
We present a new method for describing quantum measurements in relativistic systems that applies (i) to any QFT and for any field-detector coupling, (ii) to the measurement of any observable, and (iii) to arbitrary size, shape and motion of…
Quantum measurement predictions are consistent with relativity for macroscopic observations, but there is no consensus on how to explain this consistency in fundamental terms. The prevailing assumption is that the relativistic structure of…
The space-time features of the relativistic dynamics are analyzed in the framework of the time dependent propagator theory. The adiabatic hypothesis is substituted by the disturbative adiabatic hypothesis, resulting with the corresponding…
Quantum theory is a mathematical formalism to compute probabilities for outcomes happenning in physical experiments. These outcomes constitute events happening in space-time. One of these events represents the fact that a system located in…
We consider a particle moving in a one dimensional potential which has a symmetric deterministic part and a quenched random part. We study analytically the probability distributions of the local time (spent by the particle around its mean…
In Minkowski spacetime, we consider an isolated system made of two pointlike bodies interacting at a distance, in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic…
This work proposes a view of probability as a relative measure rather than an absolute one. To demonstrate this concept, we focus on finite outcome spaces and develop three fundamental axioms that establish requirements for relative…
Time measurements are routinely preformed in laboratories, nevertheless their theoretical account presents some difficulties and for actual experiments an approximate, semiclassical expression is always used. Here, we will discuss their…
Measurements of a weighted energy density average taken in the vacuum state of a conformal field theory in $1+1$ dimensions are randomly distributed with vanishing expectation value. The probability distribution is computed in closed form…
Constructing observables that describe the localization of relativistic particles is an important foundational problem in relativistic quantum field theory (QFT). The description of localization in terms of single-time observables leads to…
We extend previous work on quantum stress tensor operators which have been averaged over finite time intervals to include averaging over finite regions of space as well. The space and time averaging can be viewed as describing a measurement…
We show that probability is locally conserved in discrete time quantum walks, corresponding to a particle evolving in discrete space and time. In particular, for a spatial structure represented by an arbitrary directed graph, and any…