On Logical Analysis of Relativity Theories

The aim of this paper is to give an introduction to our axiomatic logical analysis of relativity theories.Comment: 19 pages, 1 figure

A logic road from special to general relativity

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we ``derive'' an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist

Axiomatizing relativistic dynamics without conservation postulates

A part of relativistic dynamics (or mechanics) is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein's famous E=mc^2. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated

Three Different Formalisations of Einstein’s Relativity Principle

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 equivalent by introducing a small number of additional, intuitively acceptable axioms

Naptej, fürdőruha… + helyi termék? A helyi termékek iránti kereslet a Balatont turisztikai céllal felkeresők körében = Suntan lotion, swimwear… + local products? The demand for local products among leisure travellers to Lake Balaton

Napjainkban egyre több figyelmet kap az egészség, az egészséges életmód, melynek szerves része az egészséges, helyi alapanyagokra épülő étkezés. A nem élelmiszer jellegű termékek esetében is reneszánszát éljük a helyben, kis mennyiségben készült produktumoknak. Mindezen tendenciák éreztetik hatásukat a Balaton térségében: az elmúlt években zajlott fejlesztések kedveznek a helyi termékek iránti kereslet növekedésének – az igényeket a vendéglátóhelyek, a piacok és a fesztiválok autentikus termékekkel, szolgáltatásokkal, jó minőségű ajándéktárgyakkal igyekeznek kielégíteni. A helyi termékek autentikusan reprezentálhatják a célterületet, támogatják a fenntartható termelést és fogyasztást, és a turisztikai élménynek is van egy kézzelfogható eleme. Kutatásunk fókuszában a Balatont turisztikai céllal felkeresők állnak. A kvantitatív megkérdezés azt vizsgálta, hogy az utazók számára a helyi termékek mennyire vonzóak, vásárolnak-e és ha igen, hol az utazás során. Az utazók háromnegyede 2-3 helyi terméket vásárolt a Balatonnál, a termék típusától függően eltérő helyszíneken. A vásárlás helyszínét megvizsgálva arra teszünk javaslatokat, hogy a helyi termékek esetében az értékesítési csatornák közül milyen kombinációk alkalmazhatóak leghatékonyabban a nyári időszakban pihenési, kikapcsolódási céllal a Balatonhoz utazó látogatók körében. = Health and healthy life-style are gaining importance in today’s world, and eating habits, including local ingredients and products, are often in focus. Non-food and local (not mass-produced) products are also enjoying a ’renaissance’, with their low-volume items. All of these trends influence tourism around Lake Balaton: recent developments support the increased demand for local products – catering establishments, markets and festivals aim to meet the demands with authentic products, services and good quality souvenir items. Local products are an authentic representation of the destination, support sustainable production and consumption. At the same time, tourist experience includes ‘tangible’ factors. Our research focuses on the leisure travellers to Lake Balaton. The quantitative survey’s main objective is to map what kind of local products are bought and where do travellers buy them when visiting the lake and surroundings. Results show that three-quarters of the travellers buy 2-3 local products in various places (depending on the type of the product) during their trip to Lake Balaton. Mapping the places for buying local products (differentiating food and non-food items) may help in the selection of successful distribution channels in order to reach summer holiday tourists – who are still the dominant segment – during their vacation

GROUPS OF WORLDVIEW TRANSFORMATIONS IMPLIED BY ISOTROPY OF SPACE

Given any Euclidean ordered field, Q, and any 'reasonable' group, G, of (1+3)-dimensional spacetime symmetries, we show how to construct a model M-G of kinematics for which the set W of worldview transformations between inertial observers satisfies W = G. This holds in particular for all relevant subgroups of Gal, cPoi, and cEucl (the groups of Galilean, Poincare and Euclidean transformations, respectively, where c is an element of Q is a model-specific parameter corresponding to the speed of light in the case of Poincare transformations).In doing so, by an elementary geometrical proof, we demonstrate our main contribution: spatial isotropy is enough to entail that the set W of worldview transformations satisfies either W subset of Gal, W subset of cPoi, or W subset of cEucl for some c > 0. So assuming spatial isotropy is enough to prove that there are only 3 possible cases: either the world is classical (the worldview transformations between inertial observers are Galilean transformations); the world is relativistic (the worldview transformations are Poincare transformations); or the world is Euclidean (which gives a nonstandard kinematical interpretation to Euclidean geometry). This result considerably extends previous results in this field, which assume a priori the (strictly stronger) special principle of relativity, while also restricting the choice of Q to the field R of reals.As part of this work, we also prove the rather surprising result that, for any G containing translations and rotations fixing the time-axis t, the requirement that G be a subgroup of one of the groups Gal, cPoi or cEucl is logically equivalent to the somewhat simpler requirement that, for all g is an element of G: g[t] is a line, and if g[t] = t then g is a trivial transformation (i.e. g is a linear transformation that preserves Euclidean length and fixes the time-axis setwise)