Any theory, to be theoretically complete, must permit thought-experiments, consistent with that theory, that fix the values of all the numbers that the theory requires to make its predictions.One crucial set of numbers required by all known physical theories is the set of values assigned to internal properties such as mass and charge ratios.For instance, it must be possible, completely within the theory of classical mechanics, to construct a thought-experiment that determines the values of the masses and charges of a set of bodies and that does not require prior knowledge of the values of the masses and charges of other bodies.Thus, a beam balance cannot be used to determine the ratio of the masses of the first two particles considered because the mass and charge distributions of the beam are crucial, but, by hypothesis, are unknown.Within classical mechanics (CM), special relativity (SR), and general relativity (GR), it is possible to construct thought-experiments that will determine standard clocks, standard rods, force-free volumes, and inertial frames, and that then will determine the values of the mass and charge (ratios) of particles.For instance, C M can test for a force-free volume and an inertial frame within which to perform a two-body Machian experiment, and then it can apply the set of equations:Any theory, to be theoretically complete, must permit thought-experiments, consistent with that theory, that fix the values of all the numbers that the theory requires to make its predictions.One crucial set of numbers required by all known physical theories is the set of values assigned to internal properties such as mass and charge ratios.For instance, it must be possible, completely within the theory of classical mechanics, to construct a thought-experiment that determines the values of the masses and charges of a set of bodies and that does not require prior knowledge of the values of the masses and charges of other bodies.Thus, a beam balance cannot be used to determine the ratio of the masses of the first two particles considered because the mass and charge distributions of the beam are crucial, but, by hypothesis, are unknown.Within classical mechanics (CM), special relativity (SR), and general relativity (GR), it is possible to construct thought-experiments that will determine standard clocks, standard rods, force-free volumes, and inertial frames, and that then will determine the values of the mass and charge (ratios) of particles.For instance, C M can test for a force-free volume and an inertial frame within which to perform a two-body Machian experiment, and then it can apply the set of equations:

Annals of the New York Academy of SciencesDec 1, 19860 citations

Quantum Mechanics and the Special and General Theory of Relativity

Erkki Brändas

Advances in quantum chemistryJan 1, 20087 citations

Relativistic coupling of internal and centre of mass dynamics in classical and simple bound quantum mechanical systems

D. E. Krause, Inbum Lee

Abstract Although special relativity and quantum mechanics revolutionised physics in the early 20th century, the consequences of combining these two theories are still being explored a hundred years later, usually using the formidable theoretical machinery of quantum field theory. However, a formalism accessible to undergraduates has been recently developed which shows how the centre of mass and internal dynamics of classical and quantum systems is relativistically coupled with interesting consequences. Here we explore some of the implications of this coupling, first classically, where we find that the dynamics of the system is time dilated when moving relative to another inertial frame. We then apply the dynamics to a quantum 2-level atom bound in a one-dimensional infinite potential well, and show that the coupling produces collapses and revivals in quantum interference. This example provides an illustration of how the combination of special relativity and quantum mechanics can be studied in situations familiar to most undergraduates.Abstract Although special relativity and quantum mechanics revolutionised physics in the early 20th century, the consequences of combining these two theories are still being explored a hundred years later, usually using the formidable theoretical machinery of quantum field theory. However, a formalism accessible to undergraduates has been recently developed which shows how the centre of mass and internal dynamics of classical and quantum systems is relativistically coupled with interesting consequences. Here we explore some of the implications of this coupling, first classically, where we find that the dynamics of the system is time dilated when moving relative to another inertial frame. We then apply the dynamics to a quantum 2-level atom bound in a one-dimensional infinite potential well, and show that the coupling produces collapses and revivals in quantum interference. This example provides an illustration of how the combination of special relativity and quantum mechanics can be studied in situations familiar to most undergraduates.

European Journal of PhysicsApr 18, 20174 citations

Symmetry groups in quantum mechanics

Alexander Semenovich Holevo

The spatially-temporal structure which we are going to introduce is a distinctive feature in the description of mechanical objects. In classical mechanics the motion of point masses is described in a frame of reference which consists of a spatial Cartesian coordinate system and a clock. The distinguished class is formed by the so called inertial frames which are characterized by the property that a free point mass performs uniform rectilinear motion with respect to such a frame. It follows that the coordinates (ξ, τ) and (ξ′, τ′) of a point mass in any two inertial frames of reference are related by the Galilei transformation 3.1.1 $\xi ' = R\xi + x + v\tau , \tau ' + \tau + t,$ where R is an orthogonal matrix (rotation) which describes the orientation of the new spatial axes with respect to the old ones, x is the vector of the spatial shift of the origin, ν is the relative velocity, and τ is the time shift showing the difference between the readings of the two clocks.The spatially-temporal structure which we are going to introduce is a distinctive feature in the description of mechanical objects. In classical mechanics the motion of point masses is described in a frame of reference which consists of a spatial Cartesian coordinate system and a clock. The distinguished class is formed by the so called inertial frames which are characterized by the property that a free point mass performs uniform rectilinear motion with respect to such a frame. It follows that the coordinates (ξ, τ) and (ξ′, τ′) of a point mass in any two inertial frames of reference are related by the Galilei transformation 3.1.1 $$ \xi ' = R\xi + x + v\tau , \tau ' + \tau + t, $$ where R is an orthogonal matrix (rotation) which describes the orientation of the new spatial axes with respect to the old ones, x is the vector of the spatial shift of the origin, ν is the relative velocity, and τ is the time shift showing the difference between the readings of the two clocks.

Edizioni della Normale eBooksJan 1, 20113 citations

\xi ' = R\xi + x + v\tau , \tau ' + \tau + t,

where R is an orthogonal matrix (rotation) which describes the orientation of the new spatial axes with respect to the old ones, x is the vector of the spatial shift of the origin, ν is the relative velocity, and τ is the time shift showing the difference between the readings of the two clocks.