arXiv subjects

Uri Ben-Ya'acov

Publications and source records attributed to Uri Ben-Ya'acov.

9 recordsLinked to original sources

arXiv2021

Observers, observations and referencing in physics theories

Is it possible to encompass the full extent of the universe within a theory based on a finite set of first principles and inference rules? The rôle of observers and observations in physics theories is considered here in the light of Gödel's incompleteness theorem. Physics theories are the sum-total that we -- humans, scientists, physicists -- can make in interpreting our observations of the universe. We are integral part of the universe, together with our observations, therefore acts of observation are also observables and should become part of the phenomena considered by the theory, especially in view of the fact that arbitrarily chosen modes of observations may essentially determine empirical results. Incompleteness arises in Gödel's theorem with self-referential propositions. Observations and interpretations are acts of referencing, and self-referencing occurs in physics whenever the observer is recognized as being part of the observed system. If self-reference appears in physics in simile to Gödel's theorem, then incompleteness seems unavoidable in physics. The article discusses observers and observations as referencing in physics, culminating with the understanding that they are hierarchically inter-related so that a universal physics theory cannot be complete.

physics.hist-ph↗

arXiv2021

Gödel's incompleteness theorem and universal physics theories

An ultimate universal theory -- a complete theory that accounts, via few and simple first principles, for all the phenomena already observed and that will ever be observed -- has been, and still is, the aspiration of most physicists and scientists. Yet, a basic principle that is embodied in the results of Gödel's incompleteness theorems is that self-referencing leads to logical conflict or failure, as in the liar paradox or Russell's paradox. In physics theories self-referencing necessarily occurs when it is realized that the observer is also a participant in the experienced phenomena -- we, humans, are part of the universe while observing it. Therefore self-referencing, and consequently logical conflicts, are unavoidable, and any theory pretending to be universal is bound to be incomplete.

physics.hist-ph↗

arXiv2019

Proper-time measurement in accelerated relativistic systems

Separate constituents of extended systems measure proper-times on different world-lines. Relating and comparing proper-time measurements along any two such world-lines requires that common simultaneity be possible, which in turn implies that the system is linearly-rigidly moving so that momentary rest frames are identifiable at any stage of the system's journey in space-time. Once momentary rest-frames have been identified, clocks moving on separate world-lines are synchronizable by light-signal communication. The synchronization relations for two clocks are explicitly computed using light-signals exchanged between them. Implications for the clock hypothesis are included. Also, since simultaneity is frame-dependent, incorrect usage of it leads to pseudo-paradoxes. Counter-examples are discussed.

physics.class-ph↗

arXiv2018

Hamilton symmetry in relativistic Coulomb systems

Hamilton's hodograph method geometrizes, in a simple and very elegant way, in velocity space, the full dynamics of classical particles in $1/r$ potentials. States of given energy and angular momentum are represented by circular hodographs whose radii depend only on the angular momentum, and hodographs differing only in the energy are related by uniform translations. This feature indicates the existence of an internal symmetry, named here after Hamilton. The hodograph method and the Hamilton symmetry are extended here for relativistic charged particles in a Coulomb field, on the relativistic velocity space which is a 3D hyperboloid $H^3$ embedded in a 3+1 pseudo-Euclidean space. The key for the simplicity and elegance of the velocity-space method is the linearity of the velocity equation, a unique feature of $1/r$ interactions for Newtonian and relativistic systems alike. Although with hodographs much more complicated than for Newtonian systems, the main features of the Hamilton symmetry persist in the full relativistic picture : (1) general hodographs may be represented as linearly displaced base energy-independent circles, (2) hodographs corresponding to same angular momentum but with different energies are connected via translations along geodesics of the velocity space. As an internal symmetry over and beyond central symmetry, the Hamilton symmetry is equivalent to the Laplace-Runge-Lenz symmetry and complements it.

physics.class-ph↗

arXiv2017

The hodograph method for relativistic Coulomb systems

Relativistic Coulomb systems are studied in velocity space, prompted by the fact that the study of Newtonian Kepler/Coulomb systems in velocity space provides a method much simpler (and more elegant) than the familiar analytic solutions in ordinary space. The key for the simplicity and elegance of the velocity-space method is the linearity of the velocity equation, which is a unique feature of $1/r$ interactions for Newtonian and relativistic systems alike, allowing relatively simple analytic discussion with coherent geometrical interpretations. Relativistic velocity space is a 3-D hyperboloid ($H^3$) embedded in a 3+1 pseudo-Euclidean space. The orbits in velocity space for the various types of possible trajectories are discussed, accompanied with illustrations.

physics.class-ph↗

arXiv2017

Back to epicycles - relativistic Coulomb systems in velocity space

The study of relativistic Coulomb systems in velocity space is prompted by the fact that the study of Newtonian Kepler/Coulomb systems in velocity space, although less familiar than the analytic solutions in ordinary space, provides a much simpler (also more elegant) method. The simplicity and elegance of the velocity-space method derives from the linearity of the velocity equation, which is the unique feature of $1/r$ interactions for Newtonian and relativistic systems alike. The various types of possible trajectories are presented, their properties deduced from the orbits in velocity space, accompanied with illustrations. In particular, it is found that the orbits traversed in the relativistic velocity space (which is hyperbolic ($H^3$) rather than Euclidean) are epicyclic -- circles whose centres also rotate -- thus the title.

math-ph↗

arXiv2017

The 'twin paradox' in relativistic rigid motion

Relativistic rigid motion suggests a new version for the so-called `twin paradox', comparing the ages of two astronauts on a very long spaceship. Although there is always an instantaneous inertial frame in which the whole spaceship, being rigid, is simultaneously at rest, the twins' ages, measured as the proper-times along their individual world lines, are different when they are located at remote parts of the spaceship. The age, or proper-time, difference depends on the distance at rest between the astronauts and the rapidity difference between start to end. The relation of the age difference with the relative Doppler shift of light signals transmitted between the astronauts, and implications for the possibility to assign common age (proper-time) to complex, spatially extended, relativistic systems, are also discussed. The condition for simultaneous arrival of light signals emitted simultaneously from the opposite ends of a rigidly accelerating spaceship is resolved.

gr-qc↗

arXiv2011

Centre-of-mass and internal symmetries in classical relativistic systems

The internal symmetry of composite relativistic systems is discussed. It is demonstrated that Lorentz-Poincaré symmetry implies the existence of internal moments associated with the Lorentz boost, which are Laplace-Runge-Lenz (LRL) vectors. The LRL symmetry is thus found to be the internal symmetry universally associated with the global Lorentz transformations, in much the same way as internal spatial rotations are associated with global spatial rotations. Two applications are included, for an interacting 2-body system and for an interaction-free many-body system of particles. The issue of localizability of the relativistic CM coordinate is also discussed.

math-ph↗

arXiv2010

Laplace-Runge-Lenz symmetry in general rotationally symmetric systems

The universality of the Laplace-Runge-Lenz symmetry in all rotationally symmetric systems is discussed. The independence of the symmetry on the type of interaction is proven using only the most generic properties of the Poisson brackets. Generalized Laplace-Runge-Lenz vectors are definable to be constant (not only piece-wise conserved) for all cases, including systems with open orbits. Applications are included for relativistic Coulomb systems and electromagnetic/gravitational systems in the post-Newtonian approximation. The evidence for the relativistic origin of the symmetry are extended to all centrally symmetric systems.

math-ph↗