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 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.

A review of de Broglie particle–wave mechanical systems

2020 ◽  
Vol 25 (10) ◽  
pp. 1763-1777
Author(s):  
James M Hill
Keyword(s):  
Quantum Mechanics ◽  
Dark Energy ◽  
Special Relativity ◽  
Wave Energy ◽  
Particle Energy ◽  
De Broglie Wave ◽  
De Broglie Waves ◽  
Energy Formula ◽  
Work Done ◽  
Math Phys

The existence of the so-called ‘dark’ issues of mechanics implies that our present accounting for mass and energy is incorrect in terms of applicability on a cosmological scale, and the question arises as to where the difficulty might lie. The phenomenon of quantum entanglement indicates that systems of particles exist that individually display certain characteristics, while collectively the same characteristic is absent simply because it has cancelled out between individual particles. It may therefore be necessary to develop theoretical frameworks in which long-held conservation beliefs do not necessarily always apply. The present paper summarises the formulation described in earlier papers (Hill, JM. On the formal origin of dark energy. Z Angew Math Phys 2018; 69:133-145; Hill, JM. Some further comments on special relativity and dark energy. Z Angew Math Phys 2019; 70: 5–14; Hill, JM. Special relativity, de Broglie waves, dark energy and quantum mechanics. Z Angew Math Phys 2019; 70: 131–153.), which provides a framework that allows exceptions to the law that matter cannot be created or destroyed. In these papers, it is proposed that dark energy arises from conventional mechanical theory, neglecting the work done in the direction of time and consequently neglecting the de Broglie wave energy [Formula: see text]. These papers develop expressions for the de Broglie wave energy [Formula: see text] by making a distinction between particle energy [Formula: see text] and the total work done by the particle [Formula: see text], that which accumulates from both a spatial physical force [Formula: see text] and a force [Formula: see text] in the direction of time. In any experiment, either particles or de Broglie waves are reported, so that only one of [Formula: see text] or [Formula: see text] is physically measured, and particles appear for [Formula: see text] and de Broglie waves occur for [Formula: see text], but in either event both a measurable and an immeasurable energy exists. Conventional quantum mechanics operates under circumstances such that [Formula: see text] vanishes and [Formula: see text] becomes purely imaginary. If both [Formula: see text] and [Formula: see text] are generated as the gradient of a potential, the total particle energy is necessarily conserved in the conventional manner.

scholarly journals Double-Slit Electron Interference Experiment with Zero Propagation Distance Using Electron Biprism

2019 ◽  
Vol 25 (S2) ◽  
pp. 944-945 ◽  
Author(s):  
Ken Harada ◽  
Tetsuji Kodama ◽  
Tetsuya Akashi ◽  
Yoshio Takahashi ◽  
Keiko Shimada ◽  
...  
Keyword(s):  
Propagation Distance ◽  
Interference Experiment ◽  
Electron Interference ◽  
Double Slit

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.

Lorentz Invariance as a Dynamic Symmetry

1987 ◽  
Vol 42 (12) ◽  
pp. 1428-1442 ◽  
Author(s):  
F. Winterberg
Keyword(s):  
Special Relativity ◽  
Background Radiation ◽  
Clock Synchronization ◽  
Lorentz Invariance ◽  
Superconducting Gravimeter ◽  
Time Dilation ◽  
Dynamic Symmetry ◽  
Lorentz Contraction ◽  
Absolute Motion ◽  
Dynamic Interpretation

If all the forces of nature can be reduced to those which follow from a linear combination of a scalar and vector potential, as in electrodynamics, Lorentz invariance can be derived as a dynamic symmetry. All that has to be done is to assume that there is an all pervading substratum or ether, transmitting those forces through space, and that all physical bodies actually observed are held together by those forces. Under this assumption bodies in absolute motion through the substratum suffer a true contraction equal to the Lorentz contraction, and as a result of this contraction clocks in absolute motion go slower by the same amount. The velocity of light appears then to be equal in all inertial reference systems, if Einstein’s clock synchronization convention by reflected light signals is used and which presupposes this result. The Lorentz contraction and time dilation measured on an object at rest relative to an observer who gained a velocity by an accelerated motion is there explained as an illusion caused by a true Lorentz contraction and time dilation of the observer.Both the special relativistic kinematic interpretation and this alternative dynamic interpretation give identical results only in the adiabatic limit where the accelerations are small, because if the Lorentz contraction is a real physical effect, it must take a finite time. However, to break the peculiar interaction symmetry with the ether, and which in the dynamic interpretation is the cause for the Lorentz invariance, the accelerated motions must involve rotation. Only then can non-adiabatic relativity-violating effects be observed and which would establish a preferred reference system at rest with the ether. Under most circumstances relativity-violating effects resulting from such a dynamic interpretation of special relativity would be very small and difficult to observe, a likely reason why they have evaded their detection in the past. For the rotating earth a residual sideral tide has been observed with a superconducting gravimeter, and which could be explained by an “ether wind” of about 300 km /sec at rest with the cosmic microwave background radiation. However, because of the observational uncertainties in measuring the terrestrial tides no definite conclusion can be drawn. A number of new experiments are therefore needed to decide the question regarding a possible weak violation of special relativity.

Hot electron interference by 40 nm-pitch double slit buried in semiconductor

1997 ◽  
Vol 35 (1-4) ◽  
pp. 337-340
Author(s):  
H. Hongo ◽  
Y. Miyamoto ◽  
M. Suhara ◽  
K. Furuya
Keyword(s):  
Hot Electron ◽  
Electron Interference ◽  
Double Slit

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.

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