American Journal of Physics

Physical Quantities in Different Reference Systems According to Relativity

A. Gamba

Published Feb 1, 1967• 69 citations

Abstract

The relativistic transformation of measurements from one observer S to another observer S′ is valid, of course, only when both observers are measuring the same physical quantity. What is the same quantity is, however, not a trivial problem in relativity. As a matter of fact, two different definitions have already been used in the literature, without realizing that they were not equivalent. Some of the pitfalls of such a confusion are discussed.

DOI: 10.1119/1.1973974

Related papers

Basics of Relativistic System Theory

Volker Achim Weberruß

In order to observe a physical system, a reference frame is needed, in which case the physical situation measured by an observer depends on the choosen reference frame.

Vieweg+Teubner eBooksJan 1, 19930 citations

Physics of Unitary Transformations

K. Kong Wan

A physical theory often admits different mathematical descriptions. Classical mechanics has three familiar formulations: the traditional Newton’s formulation, the Lagrange’s and the Hamilton’s formulations. It is easy to see that these are physically equivalent. Quantum mechanics also admits many different formulations. This chapter discusses how different mathematical descriptions of a probability theory based on a Hilbert space can be physically equivalent. The prescription does not single out a unique Hilbert space nor a unique set of unit vectors and operators for the description of a given quantum system. This non-uniqueness does not matter since operators and unit vectors themselves are not physically measurable quantities. Two different mathematical descriptions of a quantum system are physically equivalent if the unit vectors and selfadjoint operators for the representation of states and observables in the two descriptions are related by a simultaneous unitary transformation.

Jul 9, 20190 citations

Das Problem der Irreversibilität im Rahmen eines verallgemeinerten Entropiebegriffs

Folker Engelmann, Marc Roy Feix, Ettore Minardi +1 more

In view of the fact that physical measurements represent transmission of information, a general definition based on the measure of “lack of knowledge” in information theory can be introduced for different entropies each of them corresponding to one particular kind of measurement. By means of this entropy concept the problem of the consistency of microscopic reversibility and macroscopic irreversibility is studied. Under certain conditions it can be shown that the reversible microscopic equation of motion leads to the result that all entropies corresponding to “reduced” quantities, i.e. to quantities which do not determine the microscopic state of the system completely, can never decrease. However, it is to be noted that this behaviour is symmetric in time, in the classical as well as in the quantum mechanical case. Irreversibility is so related on the one hand to incomplete description of a system, but on the other also to the fact that theoretical statements can be verified by experiments in the future only. The validity of the results obtained within the framework of ensemble theory for a single physical system is discussed. As applications of the general ideas a system of free particles and the BOLTZMANN gas are treated.

Zeitschrift für Naturforschung ANov 1, 19614 citations

Theory of Relativity or Quantum Mechanics

Valentin Malinov

Why scientists stating that the Theory of Relativity and Quantum Mechanics they are not compatible, and one of them probably is wrong?

Dec 1, 20200 citations

A note on the foundation of relativistic mechanics. I: Relativistic observables and relativistic states

Carlo Rovelli C

Is there a version of the notions of "state" and "observable" wide enough to apply naturally and in a covariant manner to relativistic systems? I discuss here a tentative answer.

arXiv:gr-qc/0111037Nov 13, 200116 citations

From the principle of least action to the conservation of quantum information in chemistry. Can one generalize the periodic table?

Vasil Dinev Penchev

In fact, the first law of conservation (that of mass) was found in chemistry and generalized to the conservation of energy in physics by means of Einstein’s famous “E=mc2”. Energy conservation is implied by the principle of least action from a variational viewpoint as in Emmy Noether’s theorems (1918): any chemical change in a conservative (i.e. “closed”) system can be accomplished only in the way conserving its total energy. Bohr’s innovation to found Mendeleev’s periodic table by quantum mechanics implies a certain generalization referring to the quantum leaps as if accomplished in all possible trajectories (according to Feynman’s interpretation) and therefore generalizing the principle of least action and needing a certain generalization of energy conservation as to any quantum change. The transition from the first to the second theorem of Emmy Noether represents well the necessary generalization: its chemical meaning is the generalization of any chemical reaction to be accomplished as if any possible course of time rather than in the standard evenly running time (and equivalent to energy conservation according to the first theorem).The problem: If any quantum change is accomplished in all possible “variations (i.e. “violations) of energy conservation” (by different probabilities), what (if any) is conserved?An answer: quantum information is what is conserved. Indeed, it can be particularly defined as the counterpart (e.g. in the sense of Emmy Noether’s theorems) to the physical quantity of action (e.g. as energy is the counterpart of time in them). It is valid in any course of time rather than in the evenly running one. That generalization implies a generalization of the periodic table including any continuous and smooth transformation between two chemical elements.

May 19, 20207 citations