scholarly journals Moving Unstable Particles and Special Relativity

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Eugene V. Stefanovich
Keyword(s):  
Special Relativity ◽  
Reference Frame ◽  
Unstable Particle ◽  
Internal Variables ◽  
Dirac Theory ◽  
Decay Probability ◽  
Unstable Particles ◽  
Interacting Systems

In Poincaré-Wigner-Dirac theory of relativistic interactions, boosts are dynamical. This means that, just like time translations, boost transformations have a nontrivial effect on internal variables of interacting systems. In this respect, boosts are different from space translations and rotations, whose actions are always universal, trivial, and interaction-independent. Applying this theory to unstable particles viewed from a moving reference frame, we prove that the decay probability cannot be invariant with respect to boosts. Different moving observers may see different internal compositions of the same unstable particle. Unfortunately, this effect is too small to be noticeable in modern experiments.

scholarly journals DOUBLE SPECIAL RELATIVITY WITH A MINIMUM SPEED AND THE UNCERTAINTY PRINCIPLE

2012 ◽  
Vol 21 (02) ◽  
pp. 1250010 ◽  
Author(s):  
CLÁUDIO NASSIF
Keyword(s):  
Special Relativity ◽  
Reference Frame ◽  
Uncertainty Principle ◽  
Vacuum Energy ◽  
Background Field ◽  
Uncertainty Relations ◽  
Minimum Speed ◽  
Fundamental Understanding ◽  
Low Energies ◽  
Preferred Reference Frame

The present work aims to search for an implementation of a new symmetry in the spacetime by introducing the idea of an invariant minimum speed scale (V). Such a lowest limit V, being unattainable by the particles, represents a fundamental and preferred reference frame connected to a universal background field (a vacuum energy) that breaks Lorentz symmetry. So there emerges a new principle of symmetry in the spacetime at the subatomic level for very low energies close to the background frame (v ≈ V), providing a fundamental understanding for the uncertainty principle, i.e. the uncertainty relations should emerge from the spacetime with an invariant minimum speed.

scholarly journals Complex-Mass Definition and the Structure of Unstable Particle’s Propagator

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Vladimir Kuksa
Keyword(s):  
Spectral Function ◽  
Unstable Particle ◽  
Unstable Particles ◽  
Spinor Fields ◽  
Complex Mass ◽  
Special Case ◽  
Mass Definition

The propagators of unstable particles are considered in framework of the convolution representation. Spectral function is found for a special case when the propagator of scalar unstable particle has Breit-Wigner form. The expressions for the dressed propagators of unstable vector and spinor fields are derived in an analytical way for this case. We obtain the propagators in modified Breit-Wigner forms which correspond to the complex-mass definition.

scholarly journals The relativistic foundations of synchrotron radiation

2017 ◽  
Vol 24 (4) ◽  
pp. 898-901 ◽  
Author(s):  
Giorgio Margaritondo ◽  
Johann Rafelski
Keyword(s):  
Electromagnetic Field ◽  
Synchrotron Radiation ◽  
Special Relativity ◽  
Reference Frame ◽  
Lorentz Transformation ◽  
Doppler Shift ◽  
Time Dilation ◽  
Common Belief ◽  
Research Discipline ◽  
Radiation Properties

Special relativity (SR) determines the properties of synchrotron radiation, but the corresponding mechanisms are frequently misunderstood. Time dilation is often invoked among the causes, whereas its role would violate the principles of SR. Here it is shown that the correct explanation of the synchrotron radiation properties is provided by a combination of the Doppler shift, not dependent on time dilation effects, contrary to a common belief, and of the Lorentz transformation into the particle reference frame of the electromagnetic field of the emission-inducing device, also with no contribution from time dilation. Concluding, the reader is reminded that much, if not all, of our argument has been available since the inception of SR, a research discipline of its own standing.

scholarly journals Common Pedagogical Issues with De Broglie Waves: Moving Double Slits, Composite Mass, and Clock Synchronization

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Robert L. Shuler
Keyword(s):  
Special Relativity ◽  
Reference Frame ◽  
Kinematic Analysis ◽  
Clock Synchronization ◽  
Pedagogical Issues ◽  
De Broglie Waves ◽  
Independent Analysis ◽  
Electron Interference ◽  
Similarity And Difference ◽  
Double Slit

This paper addresses gaps identified in pedagogical studies of how misunderstanding of De Broglie waves affects later coursework and presents a heuristic for understanding the De Broglie frequency of composite. De Broglie’s little known derivation is reviewed with a new illustration based on his description. Simple techniques for reference frame independent analysis of a moving double slit electron interference experiment are not previously found in any literature and cement the concepts. Points of similarity and difference between De Broglie and Schrödinger waves are explained. The necessity of momentum, energy, and wavelength changes in the electrons in order for them to be vertically displaced in their own reference frame is shown to be required to make the double slit analysis work. A relativistic kinematic analysis of De Broglie frequency is provided showing how the higher De Broglie frequency of moving particles is consistent with Special Relativity and time dilation and that it demonstrates a natural system which obeys Einstein’s clock synchronization convention of simultaneity and no other. Students will be better prepared to identify practical approaches to solving problems and to think about fundamental questions.

scholarly journals FACTORIZED FORMULA FOR THE CROSS-SECTION OF TWO-PARTICLE SCATTERING

2008 ◽  
Vol 23 (27n28) ◽  
pp. 4509-4516 ◽  
Author(s):  
V. I. KUKSA
Keyword(s):  
Cross Section ◽  
Intermediate State ◽  
Factorization Method ◽  
Phenomenological Analysis ◽  
Unstable Particle ◽  
Specific Structure ◽  
Particle Scattering ◽  
Unstable Particles ◽  
The Cross ◽  
Exact Factorization

We applied the factorization method to the processes of two-particle scattering with an unstable particle in the intermediate state. It was shown, that in the framework of this method, the cross-section can be represented in the universal factorized form for an arbitrary set of particles. An exact factorization is caused by a specific structure of unstable particles propagators. Phenomenological analysis of the factorization effect is performed.

Accelerated frames

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Euclidean Space ◽  
Special Relativity ◽  
Reference Frame ◽  
Inertial Frame ◽  
Physical Space ◽  
Minkowski Spacetime ◽  
Curvilinear Coordinates ◽  
Accelerated Frames

This chapter shows how, within the framework of special relativity, Newtonian inertial accelerations turn into mere geometrical quantities. In addition, the chapter states that labeling the points of Minkowski spacetime using curvilinear coordinates rather than Minkowski coordinates is mathematically just as simple as in Euclidean space. However, the interpretation of such a change of coordinates as passage from an inertial frame to an accelerated frame is more subtle. Hence, the chapter studies some examples of this phenomenon. Finally, it addresses the problem of understanding what the curvilinear coordinates actually represent. Or, similarly, it considers the question of how to realize them by a reference frame in actual, ‘relative, apparent, and common’ physical space.

scholarly journals Time in the Special Theory of Relativity

2011 ◽  
Author(s):  
Steven Savitt
Keyword(s):  
Special Relativity ◽  
Reference Frame ◽  
Inertial Frame ◽  
Special Theory ◽  
Inertial Reference Frame ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Crucial Element ◽  
Most Significant Change ◽  
Conventionality Of Simultaneity

Restricted to special relativity, this chapter observes that the most significant change in the concept of time is certainly the relativity of simultaneity. What events are simultaneous with some event for one observer are different from those that are simultaneous with respect to an object traveling in a different inertial frame. Many believe that this relativity can play a role in an argument for eternalism. This chapter critically surveys these arguments before taking on the implications of relativity for the metaphysics of time. It also tackles the conventionality of simultaneity. Many philosophers of science, especially during the early days of relativity, felt that simultaneity is not only relative but also conventional—there is a crucial element of choice in deciding what events are simultaneous for any other in a given inertial reference frame, so that there is no fact of the matter about what is simultaneous.

scholarly journals A SIMPLER SOLUTION OF THE NON-UNIQUENESS PROBLEM OF THE COVARIANT DIRAC THEORY

2013 ◽  
Vol 10 (07) ◽  
pp. 1350027 ◽  
Author(s):  
MAYEUL ARMINJON
Keyword(s):  
Reference Frame ◽  
Reference Frames ◽  
Uniqueness Problem ◽  
Diagonal Form ◽  
Dirac Theory ◽  
Tetrad Field ◽  
Gauge Transformations ◽  
Gamma Field ◽  
Preferred Reference Frame ◽  
Generally Covariant

Although the standard generally covariant Dirac equation is unique in a topologically simple spacetime, it has been shown that it leads to non-uniqueness problems for the Hamiltonian and energy operators, including the non-uniqueness of the energy spectrum. These problems should be solved by restricting the choice of the Dirac gamma field in a consistent way. Recently, we proposed to impose the value of the rotation rate of the tetrad field. This is not necessarily easy to implement and works only in a given reference frame. Here, we propose that the gamma field should change only by constant gauge transformations. To get that situation, we are naturally led to assume that the metric can be put in a space-isotropic diagonal form. When this is the case, it distinguishes a preferred reference frame. We show that by defining the gamma field from the "diagonal tetrad" in a chart in which the metric has that form, the uniqueness problems are solved at once for all reference frames. We discuss the physical relevance of the metric considered and our restriction to first-quantized theory.

scholarly journals Why the Tsirelson Bound? Bub’s Question and Fuchs’ Desideratum

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 692 ◽  
Author(s):  
William Stuckey ◽  
Michael Silberstein ◽  
Timothy McDevitt ◽  
Ian Kohler
Keyword(s):  
Information Theory ◽  
Special Relativity ◽  
Reference Frame ◽  
Quantum Correlations ◽  
Quantum Information Theory ◽  
Quantum States ◽  
The World ◽  
Preferred Reference Frame ◽  
Bell Basis ◽  
Tsirelson Bound

To answer Wheeler’s question “Why the quantum?” via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., “Why the Tsirelson bound?” We show that the quantum correlations and quantum states corresponding to the Bell basis states, which uniquely produce the Tsirelson bound for the Clauser–Horne–Shimony–Holt (CHSH) quantity, can be derived from conservation per no preferred reference frame (NPRF). A reference frame in this context is defined by a measurement configuration, just as with the light postulate of special relativity. We therefore argue that the Tsirelson bound is ultimately based on NPRF just as the postulates of special relativity. This constraint-based/principle answer to Bub’s question addresses Fuchs’ desideratum that we “take the structure of quantum theory and change it from this very overt mathematical speak ... into something like [special relativity].” Thus, the answer to Bub’s question per Fuchs’ desideratum is, “the Tsirelson bound obtains due to conservation per NPRF”.

scholarly journals Target Selection for Reaching and Saccades Share a Similar Behavioral Reference Frame in the Macaque

2003 ◽  
Vol 89 (3) ◽  
pp. 1456-1466 ◽  
Author(s):  
Hansjörg Scherberger ◽  
Melvyn A. Goodale ◽  
Richard A. Andersen
Keyword(s):  
Reference Frame ◽  
Target Location ◽  
Target Selection ◽  
Arm Movements ◽  
Quantitative Measure ◽  
Arm Movement ◽  
Saccade Target ◽  
Internal Variables ◽  
Coordinate Frame ◽  
Selection For

The selection of one of two visual stimuli as a target for a motor action may depend on external as well as internal variables. We examined whether the preference to select a leftward or rightward target depends on the action that is performed (eye or arm movement) and to what extent the choice is influenced by the target location. Two targets were presented at the same distance to the left and right of a fixation position and the stimulus onset asynchrony (SOA) was adjusted until both targets were selected equally often. This balanced SOA time is then a quantitative measure of selection preference. In two macaque monkeys tested, we found the balanced SOA shifted to the left side for left-arm movements and to the right side for right-arm movements. Target selection strongly depended on the horizontal target location. By varying eye, head, and trunk position, we found this dependency embedded in a head-centered behavioral reference frame for saccade targets and, somewhat counter-intuitively, for reach targets as well. Target selection for reach movements was influenced by the eye position, while saccade target selection was unaffected by the arm position. These findings suggest that the neural processes underlying target selection for a reaching movement are to a large extent independent of the coordinate frame ultimately used to make the limb movement, but are instead closely linked to the coordinate frame used to plan a saccade to that target. This similarity may be indicative of a common spatial framework for hand-eye coordination.

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