Related papers: Three +1 Faces of Invariance
We revisit, qualify, and objectively resolve the seemingly controversial question about what is the number of dimensional fundamental constants in Nature. For this purpose, we only assume that all we can directly measure are space and time…
Relativistic length contraction is revisited and a simple but new thought experiment is proposed in which an apparent asymmetric situation is developed between two different inertial frames regarding detection of light that comes from a…
Based on the principle of relativity and the postulate on universal invariant constants ($c,l$) as well as Einstein's isotropy conditions, three kinds of special relativity form a triple with a common Lorentz group as isotropy group under…
In quantum geometry, we consider a set of loops, a compact orientable surface and a solid compact spatial region, all inside $\mathbb{R} \times \mathbb{R}^3 \equiv \mathbb{R}^4$, which forms a triple. We want to define an ambient isotopic…
The developments of special relativity and quantum mechanics marked the beginning of the modern physics age. The former has taught us that while space and time are frame dependent notions, there is a quantity -- the space-time interval --…
We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The…
Double Special Relativity theories are the relativistic theories in which the transformations between inertial observers are characterized by two observer-independent scales of the light speed and the Planck length. We study two main…
Time can be defined as the duration between events. It is irreversible. When used as a variable in quantifying the changing properties of matter, this irreversibility of time is incompatible with Newton's deterministic mechanics and with…
The dimensional structure of space-time is investigated according to physical and mathematical methods. We show that ther are various empirical and theoretical restrictions on the number of independent dimensions of space-time, consequently…
An interpretation of the inertial mass increase due to an object's velocity which is derived from the theory of special relativity is discussed. A Lorentz transformation of the reference time causes the inertial mass increase. It is assumed…
Scale invariance has received very little attention in physics. Nevertheless, it provides a natural conceptual foundation for a relational understanding of the universe, where absolute size loses meaning and only dimensionless ratios retain…
Contrary to our immediate and vivid sensation of past, present, and future as continually shifting non-relational modalities, time remains as tenseless and relational as space in all of the established theories of fundamental physics. Here…
Current approaches to the problem of inertia attempt to explain the inertial properties of matter by expressing the inertial mass appearing in Newton's second law of motion in terms of some other more fundamental interaction. One…
The time ordering of two spacelike separated events is arbitrary, when all inertial frames are taken into account, but for three or more events it is not generally so. We determine the structure of possible time orderings, or chronologies,…
If space is compact, then a traveller twin can leave Earth, travel back home without changing direction and find her sedentary twin older than herself. We show that the asymmetry between their spacetime trajectories lies in a topological…
Using the Hilbert-Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned. (These definitions are based on definitions…
As a basis for epistemological study of ``time,'' we analyze three suspect phenomena introduced by modern physics: non-locality, asymmetric aging and advanced interaction. It is shown that all three arise in connection with what has to be…
Though many experiments appear to have confirmed the light speed invariance postulate of special relativity theory, this postulate is actually unverified. This paper resolves this issue by first showing the manner in which an illusion of…
The invariant is one of central topics in science, technology and engineering. The differential invariant is essential in understanding or describing some important phenomena or procedures in mathematics, physics, chemistry, biology or…
The theory of relativistic {\em location systems} is sketched. An interesting class of these systems is that of relativistic {\em positioning systems,} which consists in sets of four clocks broadcasting their proper time. Among them, the…