scholarly journals Einstein's Elevator: World Lines, Michelson-Morley Experiment and Relativistic Paradox

2021 ◽  
Author(s):  
Mathieu Rouaud
Keyword(s):  
Black Hole ◽  
Large Scale ◽  
Thought Experiment ◽  
Free Fall ◽  
Classical Case ◽  
Frame Of Reference ◽  
Qualitative Aspect ◽  
First Time ◽  
Morley Experiment ◽  
Faster Than Light

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation, and for the first time the worldlines equations are given. We consider a uniformly accelerated reference frame in rectilinear translation, and we show that the trajectories of the particles are semi-ellipses with the center on the event horizon. The frame of reference is non-inertial, the space-time is flat, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, especially the experiment with the accelerated Michelson-Morley interferometer is solved, and we described an experiment where a new relativistic paradox appears --- a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical. The concepts of metric, coordinated velocity and horizon are discussed, and the analogy with the black hole is made.

scholarly journals World Lines in Einstein's Elevator

2021 ◽  
Author(s):  
Mathieu Rouaud
Keyword(s):  
Black Hole ◽  
Special Relativity ◽  
Large Scale ◽  
Thought Experiment ◽  
Free Fall ◽  
Classical Case ◽  
Frame Of Reference ◽  
Qualitative Aspect ◽  
Morley Experiment ◽  
Faster Than Light

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation, and we show that the trajectories of the particles are semi-ellipses with the center on the event horizon. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, such as the deviation of trajectories, the desynchronization of a falling clock, the accelerated Michelson-Morley experiment, and, finally, an experiment where a paradox appears — a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical. The concepts of metric, coordinated velocity and horizon are discussed, and the analogy with the black hole is made.

scholarly journals World Lines in Einstein's Elevator

2021 ◽  
Author(s):  
Mathieu Rouaud
Keyword(s):  
Black Hole ◽  
Special Relativity ◽  
Large Scale ◽  
Thought Experiment ◽  
Free Fall ◽  
Classical Case ◽  
Frame Of Reference ◽  
Qualitative Aspect ◽  
Morley Experiment ◽  
Faster Than Light

We all have in mind Einstein’s famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation, and we show that the trajectories of the particles are ellipses centered on the event horizon. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, such as the deviation of trajectories, the desynchronization of a falling clock, the accelerated Michelson-Morley experiment, and, finally, an experiment where a paradox appears — a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical and pedagogical. The study helps the student to become familiar with the concepts of metric, coordinate velocity, horizon, and, to do the analogy with the black hole.

scholarly journals World Lines in Einstein's Elevator

2021 ◽  
Author(s):  
Mathieu Rouaud
Keyword(s):  
Black Hole ◽  
Special Relativity ◽  
Reference Frame ◽  
Large Scale ◽  
Thought Experiment ◽  
Michelson Interferometer ◽  
Free Fall ◽  
Classical Case ◽  
Frame Of Reference ◽  
Qualitative Aspect

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation and we show that the trajectories of the particles are ellipses centered on the horizon of the events. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian and the computations are performed within the framework of special relativity. Some experimental consequences are discussed such as trajectory deviation, desynchronization of a falling clock and the Michelson interferometer. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the box where the interest is above all theoretical and pedagogical. The study helps the student to become familiar with the concepts of metric, coordinate velocity, horizon, and, to do the analogy with the black hole.

scholarly journals Worldlines in the Einstein's Elevator

2021 ◽  
Author(s):  
Mathieu Rouaud
Keyword(s):  
Black Hole ◽  
Special Relativity ◽  
Reference Frame ◽  
Thought Experiment ◽  
Free Fall ◽  
Classical Case ◽  
Space Time ◽  
Frame Of Reference ◽  
Exact Calculation ◽  
Qualitative Aspect

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation and we show that the trajectories of the particles are ellipses centered on the horizon of the events. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian and the computations are performed within the framework of special relativity. The deviation, compared to the classical case, is important close to the horizon, but small in the box, and the interest is above all theoretical and pedagogical. The study helps the student to become familiar with the concepts of metric, coordinate velocity, horizon, and, to do the analogy with the black hole.

Scheming

2018 ◽  
Author(s):  
Seán Damer
Keyword(s):  
Social Class ◽  
Housing Policy ◽  
Large Scale ◽  
Class Structure ◽  
Local Council ◽  
Housing Scheme ◽  
Post War ◽  
First Time ◽  
The Voice ◽  
House Building

This book seeks to explain how the Corporation of Glasgow, in its large-scale council house-building programme in the inter- and post-war years, came to reproduce a hierarchical Victorian class structure. The three tiers of housing scheme which it constructed – Ordinary, Intermediate, and Slum-Clearance – effectively signified First, Second and Third Class. This came about because the Corporation uncritically reproduced the offensive and patriarchal attitudes of the Victorian bourgeoisie towards the working-class. The book shows how this worked out on the ground in Glasgow, and describes the attitudes of both authoritarian housing officials, and council tenants. This is the first time the voice of Glasgow’s council tenants has been heard. The conclusion is that local council housing policy was driven by unapologetic considerations of social class.

What is the meaning of the pullback Schwarzschild metric?

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Black Hole ◽  
Thought Experiment ◽  
Schwarzschild Metric

We propose a thought experiment regarding the pullback Schwarzschild metric, considering that there is no interior of a black hole.

scholarly journals Shell-crossing in a ΛCDM Universe

2020 ◽  
Vol 501 (1) ◽  
pp. L71-L75
Author(s):  
Cornelius Rampf ◽  
Oliver Hahn
Keyword(s):  
Dark Matter ◽  
Perturbation Theory ◽  
Large Scale ◽  
Cold Dark Matter ◽  
Three Dimensional ◽  
Random Initial Data ◽  
Recursion Relations ◽  
Indispensable Tool ◽  
First Time ◽  
Very High

ABSTRACT Perturbation theory is an indispensable tool for studying the cosmic large-scale structure, and establishing its limits is therefore of utmost importance. One crucial limitation of perturbation theory is shell-crossing, which is the instance when cold-dark-matter trajectories intersect for the first time. We investigate Lagrangian perturbation theory (LPT) at very high orders in the vicinity of the first shell-crossing for random initial data in a realistic three-dimensional Universe. For this, we have numerically implemented the all-order recursion relations for the matter trajectories, from which the convergence of the LPT series at shell-crossing is established. Convergence studies performed at large orders reveal the nature of the convergence-limiting singularities. These singularities are not the well-known density singularities at shell-crossing but occur at later times when LPT already ceased to provide physically meaningful results.

3.17% efficient Cu2ZnSnS4–BiVO4 integrated tandem cell for standalone overall solar water splitting

2021 ◽  
Author(s):  
Dingwang Huang ◽  
Kang Wang ◽  
Lintao Li ◽  
Kuang Feng ◽  
Na An ◽  
...  
Keyword(s):  
Water Splitting ◽  
Large Scale ◽  
Tandem Cell ◽  
Solar Water ◽  
Solar Water Splitting ◽  
First Time

3.17% efficient Cu2ZnSnS4–BiVO4 integrated tandem cell and a large scale 5 × 5 cm integrated CZTS–BiVO4 tandem device for standalone overall solar water splitting was assembled for the first time.

scholarly journals On the formation and stability of fermionic dark matter halos in a cosmological framework

2020 ◽  
Author(s):  
Carlos R Argüelles ◽  
Manuel I Díaz ◽  
Andreas Krut ◽  
Rafael Yunis
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Space Distribution ◽  
Coarse Grained ◽  
Dark Matter Halos ◽  
The Core ◽  
The Galaxy ◽  
Gravitating Systems ◽  
The Given ◽  
First Time

Abstract The formation and stability of collisionless self-gravitating systems is a long standing problem, which dates back to the work of D. Lynden-Bell on violent relaxation, and extends to the issue of virialization of dark matter (DM) halos. An important prediction of such a relaxation process is that spherical equilibrium states can be described by a Fermi-Dirac phase-space distribution, when the extremization of a coarse-grained entropy is reached. In the case of DM fermions, the most general solution develops a degenerate compact core surrounded by a diluted halo. As shown recently, the latter is able to explain the galaxy rotation curves while the DM core can mimic the central black hole. A yet open problem is whether this kind of astrophysical core-halo configurations can form at all, and if they remain stable within cosmological timescales. We assess these issues by performing a thermodynamic stability analysis in the microcanonical ensemble for solutions with given particle number at halo virialization in a cosmological framework. For the first time we demonstrate that the above core-halo DM profiles are stable (i.e. maxima of entropy) and extremely long lived. We find the existence of a critical point at the onset of instability of the core-halo solutions, where the fermion-core collapses towards a supermassive black hole. For particle masses in the keV range, the core-collapse can only occur for Mvir ≳ E9M⊙ starting at zvir ≈ 10 in the given cosmological framework. Our results prove that DM halos with a core-halo morphology are a very plausible outcome within nonlinear stages of structure formation.

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