The Inconsistency of the Usual Galilean Transformation in Quantum Mechanics and How To Fix It

2001 ◽  
Vol 56 (1-2) ◽  
pp. 67-75 ◽  
Author(s):  
Daniel M. Greenberger
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Proper Time ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Twin Paradox ◽  
Moving Frames ◽  
Galilean Transformation ◽  
Rest Energy ◽  
Integral Role

Abstract It is shown that the generally accepted statement that one cannot superpose states of different mass in non-relativistic quantum mechanics is inconsistent. It is pointed out that the extra phase induced in a moving system, which was previously thought to be unphysical, is merely the non-relativistic residue of the "twin-paradox" effect. In general, there are phase effects due to proper time differences between moving frames that do not vanish non-relativistically. There are also effects due to the equivalence of mass and energy in this limit. The remedy is to include both proper time and rest energy non-relativis-tically. This means generalizing the meaning of proper time beyond its classical meaning, and introduc­ ing the mass as its conjugate momentum. The result is an uncertainty principle between proper time and mass that is very general, and an integral role for both concepts as operators in non-relativistic physics.

OBSERVABLE TIME IN QUANTUM COSMOLOGY

1995 ◽  
Vol 04 (01) ◽  
pp. 105-113 ◽  
Author(s):  
V. PERVUSHIN ◽  
T. TOWMASJAN
Keyword(s):  
Quantum Mechanics ◽  
First Principles ◽  
Quantum Cosmology ◽  
Correspondence Principle ◽  
Proper Time ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Conformal Time ◽  
Energy Factor ◽  
Definition Of

We show that the first principles of quantization and the experience of relativistic quantum mechanics can lead to the definition of observable time in quantum cosmology as a global quantity which coincides with the constrained action of the reduced theory up to the energy factor. The latter is fixed by the correspondence principle once one considers the limit of the “dust filled” Universe. The “global time” interpolates between the proper time for dust dominance and the conformal time for radiation dominance.

Nuclear Physics Methods for Problems in Relativistic Quantum Mechanics

1998 ◽  
Vol 07 (05) ◽  
pp. 559-571
Author(s):  
Marcos Moshinsky ◽  
Verónica Riquer
Keyword(s):  
Quantum Mechanics ◽  
Nuclear Physics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Negative Energy ◽  
Relativistic Quantum Mechanics ◽  
Variational Parameter ◽  
Approximate Methods ◽  
Rest Energy ◽  
Quark Models

Atomic and molecular physicists have developed extensive and detailed approximate methods for dealing with the relativistic versions of the Hamiltonians appearing in their fields. Nuclear physicists were originally more concerned with non-relativistic problems as the energies they were dealing with were normally small compared with the rest energy of the nucleon. This situation has changed with the appearance of the quark models of nucleons and thus the objective of this paper is to use the standard variational procedures of nuclear physics for problems in relativistic quantum mechanics. The 4 × 4α and β matrices in the Dirac equation are replaced by 2 × 2 matrices, one associated with ordinary spin and the other, which we call sign spin, is mathematically identical to the isospin of nuclear physics. The states on which our Hamiltonians will act will be the usual harmonic oscillator ones with ordinary and sign spin and the frequency ω of the oscillator will be our only variational parameter. The example discussed as an illustration will still be the Coulomb problem as the exact energies of the relativistic bound states are available for comparison. A gap of the order of 2mc2 is observed between states of positive and negative energy, that permits the former to be compared with the exact results.

Stochastic microcausality in relativistic quantum mechanics

1984 ◽  
Vol 14 (9) ◽  
pp. 883-906 ◽  
Author(s):  
D. P. Greenwood ◽  
E. Prugovečki
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics

Relativistic Multiple Scattering Theory

1991 ◽  
Vol 253 ◽  
Author(s):  
B. L. Gyorffy
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Schr6dinger Equation ◽  
Relativistic Effects ◽  
Relativistic Quantum Mechanics ◽  
Absolute Minimum ◽  
Crystalline Anisotropy ◽  
Symmetry Properties ◽  
Finite Set

The symmetry properties of the Dirac equation, which describes electrons in relativistic quantum mechanics, is rather different from that of the corresponding Schr6dinger equation. Consequently, even when the velocity of light, c, is much larger than the velocity of an electron Vk, with wave vector, k, relativistic effects may be important. For instance, while the exchange interaction is isotropic in non-relativistic quantum mechanics the coupling between spin and orbital degrees of freedom in relativistic quantum mechanics implies that the band structure of a spin polarized metal depends on the orientation of its magnetization with respect to the crystal axis. As a consequence there is a finite set of degenerate directions for which the total energy of the electrons is an absolute minimum. Evidently, the above effect is the principle mechanism of the magneto crystalline anisotropy [1]. The following session will focus on this and other qualitatively new relativistic effects, such as dichroism at x-ray frequencies [2] or Fano effects in photo-emission from non-polarized solids [3].

scholarly journals PROBABILITY IN RELATIVISTIC QUANTUM MECHANICS AND FOLIATION OF SPACE–TIME

2007 ◽  
Vol 22 (32) ◽  
pp. 6243-6251 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Quantum Mechanics ◽  
Wave Equations ◽  
Integral Curve ◽  
Relativistic Quantum ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Relativistic Wave ◽  
Probability Densities ◽  
The Many ◽  
Conserved Currents

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of space–time must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

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