Doppler Boosting and Cosmological Redshift on Relativistic Jets
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From Relativistic Time Dilation to Psychological Time Perception
From relativistic time dilation to psychological time perception: an approach and model, driven by the theory of relativity, to combine the physical time with the time perceived while experiencing different situations. Andrea Conte1,∗ Abstract An approach, supported by a physical model driven by the theory of relativity, is presented. This approach and model tend to conciliate the relativistic view on time dilation with the current models and conclusions on time perception. The model uses energy ratios instead of geometrical transformations to express time dilation. Brain mechanisms like the arousal mechanism and the attention mechanism are interpreted and combined using the model. Matrices of order two are generated to contain the time dilation between two observers, from the point of view of a third observer. The matrices are used to transform an observer time to another observer time. Correlations with the official time dilation equations are given in the appendix. Keywords: Time dilation, Time perception, Definition of time, Lorentz factor, Relativity, Physical time, Psychological time, Psychology of time, Internal clock, Arousal, Attention, Subjective time, Internal flux, External flux, Energy system ∗Corresponding author Email address: [email protected] (Andrea Conte) 1Declarations of interest: none Preprint submitted to PsyArXiv - version 2, revision 1 June 6, 2021 Contents 1 Introduction 3 1.1 The unit of time . 4 1.2 The Lorentz factor . 6 2 Physical model 7 2.1 Energy system . 7 2.2 Internal flux . 7 2.3 Internal flux ratio . 9 2.4 Non-isolated system interaction . 10 2.5 External flux . 11 2.6 External flux ratio . 12 2.7 Total flux . -
Simulating Gamma-Ray Binaries with a Relativistic Extension of RAMSES? A
A&A 560, A79 (2013) Astronomy DOI: 10.1051/0004-6361/201322266 & c ESO 2013 Astrophysics Simulating gamma-ray binaries with a relativistic extension of RAMSES? A. Lamberts1;2, S. Fromang3, G. Dubus1, and R. Teyssier3;4 1 UJF-Grenoble 1 / CNRS-INSU, Institut de Planétologie et d’Astrophysique de Grenoble (IPAG) UMR 5274, 38041 Grenoble, France e-mail: [email protected] 2 Physics Department, University of Wisconsin-Milwaukee, Milwaukee WI 53211, USA 3 Laboratoire AIM, CEA/DSM - CNRS - Université Paris 7, Irfu/Service d’Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France 4 Institute for Theoretical Physics, University of Zürich, Winterthurestrasse 190, 8057 Zürich, Switzerland Received 11 July 2013 / Accepted 29 September 2013 ABSTRACT Context. Gamma-ray binaries are composed of a massive star and a rotation-powered pulsar with a highly relativistic wind. The collision between the winds from both objects creates a shock structure where particles are accelerated, which results in the observed high-energy emission. Aims. We want to understand the impact of the relativistic nature of the pulsar wind on the structure and stability of the colliding wind region and highlight the differences with colliding winds from massive stars. We focus on how the structure evolves with increasing values of the Lorentz factor of the pulsar wind, keeping in mind that current simulations are unable to reach the expected values of pulsar wind Lorentz factors by orders of magnitude. Methods. We use high-resolution numerical simulations with a relativistic extension to the hydrodynamics code RAMSES we have developed. We perform two-dimensional simulations, and focus on the region close to the binary, where orbital motion can be ne- glected. -
(Special) Relativity
(Special) Relativity With very strong emphasis on electrodynamics and accelerators Better: How can we deal with moving charged particles ? Werner Herr, CERN Reading Material [1 ]R.P. Feynman, Feynman lectures on Physics, Vol. 1 + 2, (Basic Books, 2011). [2 ]A. Einstein, Zur Elektrodynamik bewegter K¨orper, Ann. Phys. 17, (1905). [3 ]L. Landau, E. Lifschitz, The Classical Theory of Fields, Vol2. (Butterworth-Heinemann, 1975) [4 ]J. Freund, Special Relativity, (World Scientific, 2008). [5 ]J.D. Jackson, Classical Electrodynamics (Wiley, 1998 ..) [6 ]J. Hafele and R. Keating, Science 177, (1972) 166. Why Special Relativity ? We have to deal with moving charges in accelerators Electromagnetism and fundamental laws of classical mechanics show inconsistencies Ad hoc introduction of Lorentz force Applied to moving bodies Maxwell’s equations lead to asymmetries [2] not shown in observations of electromagnetic phenomena Classical EM-theory not consistent with Quantum theory Important for beam dynamics and machine design: Longitudinal dynamics (e.g. transition, ...) Collective effects (e.g. space charge, beam-beam, ...) Dynamics and luminosity in colliders Particle lifetime and decay (e.g. µ, π, Z0, Higgs, ...) Synchrotron radiation and light sources ... We need a formalism to get all that ! OUTLINE Principle of Relativity (Newton, Galilei) - Motivation, Ideas and Terminology - Formalism, Examples Principle of Special Relativity (Einstein) - Postulates, Formalism and Consequences - Four-vectors and applications (Electromagnetism and accelerators) § ¤ some slides are for your private study and pleasure and I shall go fast there ¦ ¥ Enjoy yourself .. Setting the scene (terminology) .. To describe an observation and physics laws we use: - Space coordinates: ~x = (x, y, z) (not necessarily Cartesian) - Time: t What is a ”Frame”: - Where we observe physical phenomena and properties as function of their position ~x and time t. -
Uniform Relativistic Acceleration
Uniform Relativistic Acceleration Benjamin Knorr June 19, 2010 Contents 1 Transformation of acceleration between two reference frames 1 2 Rindler Coordinates 4 2.1 Hyperbolic motion . .4 2.2 The uniformly accelerated reference frame - Rindler coordinates .5 3 Some applications of accelerated motion 8 3.1 Bell's spaceship . .8 3.2 Relation to the Schwarzschild metric . 11 3.3 Black hole thermodynamics . 12 1 Abstract This paper is based on a talk I gave by choice at 06/18/10 within the course Theoretical Physics II: Electrodynamics provided by PD Dr. A. Schiller at Uni- versity of Leipzig in the summer term of 2010. A basic knowledge in special relativity is necessary to be able to understand all argumentations and formulae. First I shortly will revise the transformation of velocities and accelerations. It follows some argumentation about the hyperbolic path a uniformly accelerated particle will take. After this I will introduce the Rindler coordinates. Lastly there will be some examples and (probably the most interesting part of this paper) an outlook of acceleration in GRT. The main sources I used for information are Rindler, W. Relativity, Oxford University Press, 2006, and arXiv:0906.1919v3. Chapter 1 Transformation of acceleration between two reference frames The Lorentz transformation is the basic tool when considering more than one reference frames in special relativity (SR) since it leaves the speed of light c invariant. Between two different reference frames1 it is given by x = γ(X − vT ) (1.1) v t = γ(T − X ) (1.2) c2 By the equivalence -
Massachusetts Institute of Technology Midterm
Massachusetts Institute of Technology Physics Department Physics 8.20 IAP 2005 Special Relativity January 18, 2005 7:30–9:30 pm Midterm Instructions • This exam contains SIX problems – pace yourself accordingly! • You have two hours for this test. Papers will be picked up at 9:30 pm sharp. • The exam is scored on a basis of 100 points. • Please do ALL your work in the white booklets that have been passed out. There are extra booklets available if you need a second. • Please remember to put your name on the front of your exam booklet. • If you have any questions please feel free to ask the proctor(s). 1 2 Information Lorentz transformation (along the xaxis) and its inverse x� = γ(x − βct) x = γ(x� + βct�) y� = y y = y� z� = z z = z� ct� = γ(ct − βx) ct = γ(ct� + βx�) � where β = v/c, and γ = 1/ 1 − β2. Velocity addition (relative motion along the xaxis): � ux − v ux = 2 1 − uxv/c � uy uy = 2 γ(1 − uxv/c ) � uz uz = 2 γ(1 − uxv/c ) Doppler shift Longitudinal � 1 + β ν = ν 1 − β 0 Quadratic equation: ax2 + bx + c = 0 1 � � � x = −b ± b2 − 4ac 2a Binomial expansion: b(b − 1) (1 + a)b = 1 + ba + a 2 + . 2 3 Problem 1 [30 points] Short Answer (a) [4 points] State the postulates upon which Einstein based Special Relativity. (b) [5 points] Outline a derviation of the Lorentz transformation, describing each step in no more than one sentence and omitting all algebra. (c) [2 points] Define proper length and proper time. -
The Challenge of Interstellar Travel the Challenge of Interstellar Travel
The challenge of interstellar travel The challenge of interstellar travel ! Interstellar travel - travel between star systems - presents one overarching challenge: ! The distances between stars are enormous compared with the distances which our current spacecraft have travelled ! Voyager I is the most distant spacecraft, and is just over 100 AU from the Earth ! The closest star system (Alpha Centauri) is 270,000 AU away! ! Also, the speed of light imposes a strict upper limit to how fast a spacecraft can travel (300,000 km/s) ! in reality, only light can travel this fast How long does it take to travel to Alpha Centauri? Propulsion Ion drive Chemical rockets Chemical Nuclear drive Solar sail F = ma ! Newton’s third law. ! Force = mass x acceleration. ! You bring the mass, your engine provides the force, acceleration is the result The constant acceleration case - plus its problems ! Let’s take the case of Alpha Centauri. ! You are provided with an ion thruster. ! You are told that it provides a constant 1g of acceleration. ! Therefore, you keep accelerating until you reach the half way point before reversing the engine and decelerating the rest of the way - coming to a stop at Alpha Cen. ! Sounds easy? Relativity and nature’s speed limit ! What does it take to maintain 1g of accelaration? ! At low velocities compared to light to accelerate a 1000kg spacecraft at 1g (10ms-2) requires 10,000 N of force. ! However, as the velocity of the spacecraft approaches the velocity of light relativity starts to kick in. ! The relativistic mass can be written as γ x mass, where γ is the relativistic Lorentz factor. -
Arxiv:1909.09084V3 [Physics.Hist-Ph] 16 Jul 2020 IX
Defining of three-dimensional acceleration and inertial mass leading to the simple form F=M A of relativistic motion equation Grzegorz M. Koczan∗ Warsaw University of Life Sciences (WULS/SGGW), Poland (Dated: July 20, 2020) Newton's II Law of Dynamics is a law of motion but also a useful definition of force (F=M A) or inertial mass (M =F/A), assuming a definition of acceleration and parallelism of force and accel- eration. In the Special Relativity, out of these three only the description of force (F=dp/dt) does not raise doubts. The greatest problems are posed by mass, which may be invariant rest mass or relativistic mass or even directional mass, like longitudinal mass. This results from breaking the assumption of the parallelism of force and standard acceleration. It turns out that these issues disappear if the relativistic acceleration A is defined by a relativistic velocity subtraction formula. This basic fact is obscured by some subtlety related to the calculation of the relativistic differential of velocity. It is based on the direction of force rather than on a transformation to an instantaneous resting system. The reference to a non-resting system generates a little different velocity subtrac- tion formulae. This approach confirms Oziewicz binary and ternary relative velocities as well as the results of other researchers. Thus, the relativistic three-dimensional acceleration is neither rest acceleration, nor four-acceleration, nor standard acceleration. As a consequence, inertial mass in any direction of the force has the same value as relativistic mass. In other words, the concepts of transverse mass and longitudinal mass, which depend on velocity, have been unified. -
The Lorentz Factor and the Probability Density by Boris S
Global Journal of Science Frontier Research: A Physics and Space Science Volume 17 Issue 3 Version 1.0 Year 2017 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Inc. (USA) Online ISSN: 2249-4626 & Print ISSN: 0975-5896 The Lorentz Factor and the Probability Density By Boris S. Dizhechko Abstract- New Cartesian physics based on the identity of space and matter and makes the principle of uncertainty Heisenberg by a principle of physical irrationality of points of space- matter from which naturally follows a probabilistic way of describing the developments in quantum mechanics. New Cartesian physics relates the probability of an event in quantum mechanics with the factor of Lorentz of the special theory of relativity, which turns idle geometric space in the physical, in which space moves. GJSFR-A Classification: FOR Code: 020399p TheLorentzFact orandtheProbabilityDensity Strictly as per the compliance and regulations of: © 2017. Boris S. Dizhechko. This is a research/review paper, distributed under the terms of the Creative Commons Attribution- Noncommercial 3.0 Unported License http://creativecommons.org/licenses/by-nc/3.0/), permitting all non commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. The Lorentz Factor and the Probability Density Boris S. Dizhechko Abstract - New Cartesian physics based on the identity of New Cartesian physics, based on identity of space and matter and makes the principle of uncertainty space and matter, argues that space is moving and Heisenberg by a principle of physical irrationality of points of movement is the main vortex, i.e. the circumference. -
A Solution of the Interpretation Problem of Lorentz Transformations
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 30 July 2020 doi:10.20944/preprints202007.0705.v1 Article A Solution of the Interpretation Problem of Lorentz Transformations Grit Kalies* HTW University of Applied Sciences Dresden; 1 Friedrich-List-Platz, D-01069 Dresden, [email protected] * Correspondence: [email protected], Tel.: +49-351-462-2552 Abstract: For more than one hundred years, scientists dispute the correct interpretation of Lorentz transformations within the framework of the special theory of relativity of Albert Einstein. On the one hand, the changes in length, time and mass with increasing velocity are interpreted as apparent due to the observer dependence within special relativity. On the other hand, real changes are described corresponding to the experimental evidence of mass increase in particle accelerators or of clock delay. This ambiguity is accompanied by an ongoing controversy about valid Lorentz-transformed thermodynamic quantities such as entropy, pressure and temperature. In this paper is shown that the interpretation problem of the Lorentz transformations is genuinely anchored within the postulates of special relativity and can be solved on the basis of the thermodynamic approach of matter-energy equivalence, i.e. an energetic distinction between matter and mass. It is suggested that the velocity-dependent changes in state quantities are real in each case, in full agreement with the experimental evidence. Keywords: interpretation problem; Lorentz transformation; special relativity; thermodynamics; potential energy; space; time; entropy; non-mechanistic ether theory © 2020 by the author(s). Distributed under a Creative Commons CC BY license. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 30 July 2020 doi:10.20944/preprints202007.0705.v1 2 of 25 1. -
Testing the Validity of the Lorentz Factor Y Wang, X Fan, J Wang Et Al
Physics Education PAPER • OPEN ACCESS Related content - A MRPC prototype for SOLID-TOF in JLab Testing the validity of the Lorentz factor Y Wang, X Fan, J Wang et al. - Prototyping a 2m × 0.5m MRPC-based To cite this article: H Broomfield et al 2018 Phys. Educ. 53 055011 neutron TOF-wall with steel converter plates M Röder, T Aumann, D Bemmerer et al. - Aging test of a real-size high rate MRPC for CBM-TOF wall View the article online for updates and enhancements. Y Wang, X Fan, H Chen et al. This content was downloaded from IP address 128.141.192.149 on 04/01/2021 at 10:56 IOP Physics Education Phys. Educ. 53 P A P ER Phys. Educ. 53 (2018) 055011 (10pp) iopscience.org/ped 2018 Testing the validity of the Lorentz © 2018 IOP Publishing Ltd factor PHEDA7 H Broomfield1, J Hirst1, M Raven1, M Joos2,4, T Vafeiadis3, 055011 T K Chung1, J Harrow1, D Khoo1, T Kwok1, J Li1, H Mandelstam1, J Martin-Halls1, R Perkins1, A Singh1, H Broomfield et al J Southwell1, A Tsui1, K Tsui1, D Townsend1 and H Watson1 1 Colchester Royal Grammar School, Colchester, United Kingdom Testing the validity of the Lorentz factor 2 CERN, Geneva, Switzerland 3 Aristotle University of Thessaloniki, Thessaloniki, Greece Printed in the UK E-mail: [email protected] PED Abstract The CERN Beamline for Schools Competition gives high school students the 10.1088/1361-6552/aaccdb opportunity to perform an experiment of their design using the T9 facility. Our team, ‘Relatively Special’, was fortunate enough to be joint winners of this global event and travel to CERN for a unique adventure. -
Section 5 Special Relativity
North Berwick High School Higher Physics Department of Physics Unit 1 Our Dynamic Universe Section 5 Special Relativity Section 5 Special Relativity Note Making Make a dictionary with the meanings of any new words. Special Relativity 1. What is meant by a frame of reference? 2. Write a short note on the history leading up to Einstein's theories (just include the main dates). The principles 1. State Einstein's starting principles. Time dilation 1. State what is meant by time dilation. 2. Copy the time dilation formula and take note of the Lorentz factor. 3. Copy the example. 4. Explain why we do not notice these events in everyday life. 5. Explain how muons are able to be detected at the surface of the Earth. Length contraction (also known as Lorentz contraction) 1. Copy the length contraction formula. Section 5 Special Relativity Contents Content Statements................................................. 1 Special Relativity........................................................ 2 2 + 2 = 3................................................................... 2 History..................................................................... 2 The principles.......................................................... 4 Time Dilation........................................................... 4 Why do we not notice these time differences in everyday life?.................................... 7 Length contraction................................................... 8 Ladder paradox........................................................ 9 Section 5: -
Synchrotron Radiation
Synchrotron Radiation The synchrotron radiation, the emission of very relativistic and ultrarelativistic electrons gyrating in a magnetic field, is the process which dominates much of high energy astrophysics. It was originally observed in early betatron experiments in which electrons were first accelerated to ultrarelativistic energies. This process is responsible for the radio emission from the Galaxy, from supernova remnants and extragalactic radio sources. It is also responsible for the non-thermal optical and X-ray emission observed in the Crab Nebula and possibly for the optical and X-ray continuum emission of quasars. The word non-thermal is used frequently in high energy astrophysics to describe the emission of high energy particles. This an unfortunate terminology since all emission mechanisms are ‘thermal’ in some sense. The word is conventionally taken to mean ‘continuum radiation from particles, the energy spectrum of which is not Maxwellian’. In practice, continuum emission is often referred to as ‘non-thermal’ if it cannot be described by the spectrum of thermal bremsstrahlung or black-body radiation. 1 Motion of an Electron in a Uniform, Static Magnetic field We begin by writing down the equation of motion for a particle of rest mass m0, charge ze and Lorentz factor γ = (1 − v2/c2)−1/2 in a uniform static magnetic field B. d (γm0v) = ze(v × B) (1) dt We recall that the left-hand side of this equation can be expanded as follows: d dv 3 (v · a) m0 (γv) = m0γ + m0γ v (2) dt dt c2 because the Lorentz factor γ should be written γ = (1 − v · v/c2)−1/2.