Toward Special-Relativity-on-a-Chip: analogue of Einstein velocity addition using optical add-drop filter (OADF)

2019 ◽  
Vol 66 (6) ◽  
pp. 679-688 ◽  
Author(s):  
Benjamin B. Dingel ◽  
Aria Buenaventura ◽  
Annelle R. Chua ◽  
Nathaniel J. C. Libatique
Author(s):  
David M. Wittman

We have introduced the ideas of special relativity in quick succession because none of those ideas can really be understood in isolation. This chapter works through examples in some detail so you can practice applying the ideas and solidifying your understanding.We start with an overview of how to use spacetime diagrams to solve problems in special relativity, then we walk through examples ofmeasuring the length of a moving object; the train‐in‐tunnel paradox; velocity addition; and how clock readings are arranged so that each observer measures the other’s clocks as ticking slowly.


Author(s):  
David M. Wittman

We now pivot from relationships between frames to look at the effect of motion on communications between specific observers.This will help us look at the twin paradox in the next chapter, and will prove crucial to understanding the effects of gravity on time. Along the way, we develop an understanding of the Doppler effect; a key tool in many areas of modern science. We find that Doppler effects are reciprocal (Alice observes the same effect on Bob’s signals as Bob observes on Alice’s signals) and that Doppler effects compound over multiple frame changes. We then use the compounding of Doppler effects to deduce the algebraic formof the velocity addition law. We show that this Einstein velocity addition law reduces to the Galilean law at low speeds.


2011 ◽  
Vol 26 (02) ◽  
pp. 139-150 ◽  
Author(s):  
SURATNA DAS ◽  
SUBHENDRA MOHANTY

Glashow and Cohen make the interesting observation that certain proper subgroups of the Lorentz group like HOM(2) or SIM(2) can explain many results of special relativity like time dilation, relativistic velocity addition and a maximal isotropic speed of light. We show here that such SIM(2) and HOM(2) based VSR theories predict an incorrect value for the Thomas precession and are therefore ruled out by observations. In VSR theories the spin-orbital coupling in atoms turn out to be too large by a factor of 2. The Thomas–BMT equation derived from VSR predicts a precession of electrons and muons in storage rings which is too large by a factor of 103. VSR theories are therefore ruled out by observations.


Author(s):  
Angel Paredes Galan ◽  
Xabier Prado ◽  
Jorge Mira

Abstract With the goal of developing didactic tools, we consider the geometrization of the addition of velocities in special relativity by using Minkowski diagrams in momentum space. For the case of collinear velocities, we describe two ruler-and-compass constructions that provide simple graphical solutions working with the mass-shell hyperbola in a 1+1-dimensional energy-momentum plane. In the spirit of dimensional scaffolding, we use those results to build a generalization in 1+2 dimensions for the case of non-collinear velocities, providing in particular a graphical illustration of how the velocity transverse to a boost changes while the momentum remains fixed. We supplement the discussion with a number of interactive applets that implement the diagrammatic constructions and constitute a visual tool that should be useful for students to improve their understanding of the subtleties of special relativity.


1971 ◽  
Vol 39 (9) ◽  
pp. 1079-1084 ◽  
Author(s):  
R. G. Newburgh ◽  
T. E. Phipps

2015 ◽  
Vol 8 (1) ◽  
pp. 1976-1981
Author(s):  
Casey McMahon

The principle postulate of general relativity appears to be that curved space or curved spacetime is gravitational, in that mass curves the spacetime around it, and that this curved spacetime acts on mass in a manner we call gravity. Here, I use the theory of special relativity to show that curved spacetime can be non-gravitational, by showing that curve-linear space or curved spacetime can be observed without exerting a gravitational force on mass to induce motion- as well as showing gravity can be observed without spacetime curvature. This is done using the principles of special relativity in accordance with Einstein to satisfy the reader, using a gravitational equivalence model. Curved spacetime may appear to affect the apparent relative position and dimensions of a mass, as well as the relative time experienced by a mass, but it does not exert gravitational force (gravity) on mass. Thus, this paper explains why there appears to be more gravity in the universe than mass to account for it, because gravity is not the resultant of the curvature of spacetime on mass, thus the “dark matter” and “dark energy” we are looking for to explain this excess gravity doesn’t exist.


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