相关论文: Standardizing distance and time

Two pseudo-Riemannian metrics are called projectively equivalent if their unparametrized geodesics coincide. The degree of mobility of a metric is the dimension of the space of metrics that are projectively equivalent to it. We give a…

Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…

A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…

A little error was eliminated from Hertz equations. New Hertz equations do not contradict to all electromagnetic experiments. Therefore Hertz electrodynamics is the alternative to Einstein electrodynamics. It means that the question about…

Stationary extended frames in general relativity are considered. The requirement of stationarity allows to treat the spacetime as a principal fiber bundle over the one-dimensional group of time translations. Over this bundle a connection…

After a review of the chrono-geometrical structure of special relativity, where the definition of the instantaneous 3-space is based on the observer-dependent convention for the synchronization of distant clocks, it is shown that in a class…

Authors derive the Lorentz-Einstein transformation for the space-time coordinates starting with a one-space dimension approach. They add to the results the invariance of the space coordinates measured perpendicular to the direction of…

Theoretical and observational arguments are listed in favor of a new principle of relativity of units of measurements as the basis of a conformal-invariant unification of General Relativity and Standard Model by replacement of all masses…

The properties of light in the presence of electromagnetic and gravitational fields are compared. Once one takes account of the fact that clock rates vary with distance from a massive object, it is argued that in an absolute sense light…

The Equivalence Principle (EP) is not one of the ``universal'' principles of physics (like the Action Principle). It is a heuristic hypothesis which was introduced by Einstein in 1907, and used by him to construct his theory of General…

This article is an attempt for a new vision of the basics of Physics, and of Relativity, in particular. A new generalized principle of inertia is proposed, as an universal principle, based on universality of the conservation laws, not…

In general relativity, the picture of spacetime assigns an ideal clock to each worldline. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of…

The measurement of distance between two objects is generalized to the case where the objects are no longer points but are one-dimensional. Additional concepts such as non-extensibility, curvature constraints, and non-crossing become central…

The starting point of quantum mechanics is the relationship between energy and momentum: energy is proportional to the squared momentum! As a result, energy and momentum have not been treated equally. The wave equation required by…

We present three natural but distinct formalisations of Einstein's special principle of relativity, and demonstrate the relationships between them. In particular, we prove that they are logically distinct, but that they can be made…

Since antiquity, from Euclid of Alexandria to Galileo Galilei to Immanuel Kant to Hermann Minkowksi to Albert Einstein, the question of the nature of space and time has occupied scientists and philosophers. In the four-dimensional…

The nexus between the gravitational field and the space-time metric was an essential element in Einstein's development of General Relativity and led him to his discovery of the field equations for the gravitational field/metric. I will…

Relativity and quantum mechanics are generalized by considering a finite limit for the smallest measurable distance. The value a of this quantum of length is unknown, but it is a universal constant, like c and h. It depends on the total…

The principle of equivalence is used to examine covariant descriptions of quantum phenomena within the global exterior of geometries described using Painlev\'e- Gullstrand coordinates, which are everywhere non-singular away from their…

Time series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often…