Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBrownian motion at the speed of light: a Lorentz invariant family of processes
64
0
0.0
(
0
)
Authors
Maurizio Serva
Ask ChatGPT about the research
No Arabic abstract
We recently introduced a new family of processes which describe particles which only can move at the speed of light c in the ordinary 3D physical space. The velocity, which randomly changes direction, can be represented as a point on the surface of a sphere of radius c and its trajectories only may connect the points of this variety. A process can be constructed both by considering jumps from one point to another (velocity changes discontinuously) and by continuous velocity trajectories on the surface. We followed this second new strategy assuming that the velocity is described by a Wiener process (which is isotropic only in the rest frame) on the surface of the sphere. Using both Ito calculus and Lorentz boost rules, we succeed here in characterizing the entire Lorentz-invariant family of processes. Moreover, we highlight and describe the short-term ballistic behavior versus the long-term diffusive behavior of the particles in the 3D physical space.
rate research
Read More
We expand the IST transformation to three-dimensional Euclidean space and derive the speed of light under the IST transformation. The switch from the direction cosines observed in K to those observed in K-prime is surprisingly smooth. The formulation thus derived maintains the property that the round trip speed is constant. We further show that under the proper synchronization convention of K-prime, the one-way speed of light becomes constant.
We report on a test of Lorentz invariance performed by comparing the resonance frequencies of one stationary optical resonator and one continuously rotating on a precision air bearing turntable. Special attention is paid to the control of rotation induced systematic effects. Within the photon sector of the Standard Model Extension, we obtain improved limits on combinations of 8 parameters at a level of a few parts in $10^{-16}$. For the previously least well known parameter we find $tilde kappa_{e-}^{ZZ} =(-1.9 pm 5.2)times 10^{-15}$. Within the Robertson-Mansouri-Sexl test theory, our measurement restricts the isotropy violation parameter $beta -delta -frac 12$ to $(-2.1pm 1.9)times 10^{-10}$, corresponding to an eightfold improvement with respect to previous non-rotating measurements.
This work presents an experimental test of Lorentz invariance violation in the infrared (IR) regime by means of an invariant minimum speed in the spacetime and its effects on the time when an atomic clock given by a certain radioactive single-atom (e.g.: isotope $Na^{25}$) is a thermometer for a ultracold gas like the dipolar gas $Na^{23}K^{40}$. So, according to a Deformed Special Relativity (DSR) so-called Symmetrical Special Relativity (SSR), where there emerges an invariant minimum speed $V$ in the subatomic world, one expects that the proper time of such a clock moving close to $V$ in thermal equilibrium with the ultracold gas is dilated with respect to the improper time given in lab, i.e., the proper time at ultracold systems elapses faster than the improper one for an observer in lab, thus leading to the so-called {it proper time dilation} so that the atomic decay rate of a ultracold radioactive sample (e.g: $Na^{25}$) becomes larger than the decay rate of the same sample at room temperature. This means a suppression of the half-life time of a radioactive sample thermalized with a ultracold cloud of dipolar gas to be investigated by NASA in the Cold Atom Lab (CAL).
The structure of the Lorentz transformations follows purely from the absence of privileged inertial reference frames and the group structure (closure under composition) of the transformations---two assumptions that are simple and physically necessary. The existence of an invariant speed is textit{not} a necessary assumption, and in fact is a consequence of the principle of relativity (though the finite value of this speed must, of course, be obtained from experiment). Von Ignatowsky derived this result in 1911, but it is still not widely known and is absent from most textbooks. Here we present a completely elementary proof of the result, suitable for use in an introductory course in special relativity.
We considered the generalization of Einsteins model of Brownian motion when the key parameter of the time interval of free jumps degenerates. This phenomenon manifests in two scenarios: a) flow of the fluid, which is highly dispersing like a non-dense gas, and b) flow of fluid far away from the source of flow, when the velocity of the flow is incomparably smaller than the gradient of the pressure. First, we will show that both types of flows can be modeled using the Einstein paradigm. We will investigate the question: What features will particle flow exhibit if the time interval of the free jump is inverse proportional to the density of the fluid and its gradient ? We will show that in this scenario, the flow exhibits localization property, namely: if at some moment of time $t_{0}$ in the region gradient of the pressure or pressure itself is equal to zero, then for some time T during t interval $[ t_{0}, t_0+T ]$ there is no flow in the region. This directly links to Barenblatts finite speed of propagation property for the degenerate equation. The method of proof is very different from Barenblatts method and based on Vespri - Tedeev technique.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
