The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

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A question from “The meaning of the relativity, by A.Einstein” - Lorentz transformations [duplicate]

Let $K$ and $\bar K$ be two cartesian co-orditate systems in $\mathbb{R}^3$. The element: $$s^2=(\Delta x^1)^2+(\Delta x^2)^2+(\Delta x^3)^2$$ is an invariant in all co-ordinate system. I want prove ...
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Electric field around a moving charge

A moving charge has magnetic field around it. Is it just increased electric field in relativistic frame? If yes, does a moving charge has more electric field around it?
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Lorentz transformation and symmetries of the Lagrangian [duplicate]

Since the Lagrangian of our quantum field theories is covariant under Lorentz transformations I'm asking myself if there is any link to some symmetries (like that we get from gauge transformations ...
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Relativistic Rocket Fuel Requirements

I am trying to reconcile two different calculations of fuel for a 1g constant acceleration/deceleration trip to Alpha Centauri. One found here (http://math.ucr.edu/home/baez/physics/Relativity/SR/...
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Wave operator applied to electromagnetic field tensor

I'm trying to understand an argument in "An introduction to general relativity" by Hughston and Todd (p37). Let $F_{ab}$ be the electromagnetic field tensor, I'm trying to show: $$\Box F_{ab} = -4 \...
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Relativity paradox with mirrors and light pulses

Consider two very short light pulses emitted from the centre (C) of two mirrors A and B (as shown in the diagram). From the point of view of the lab frame, the apparatus is all moving to the left at ...
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Is there any way to justify or derive the form of the Lorentz force from relativity theory?

Lorentz force is in this form: $$\vec{F}=q[\vec{E}+\vec{u}\times\vec{B}]$$ As we know, it is Lorentz-invariant. Is there any way to justify or derive its form from relativity theory?
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Poincare Group (Wald, Chapter 4 Page 59)

In Wald's text on general relativity, he mentions that in special relativity, many different global inertial coordinate systems are possible and can be put into one-to-one correspondence with elements ...
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146 views

What is the inconsistency between Maxwell's electrodynamics and newtonian mechanics?

As far as I understand, when a modification of a theory is made it is because some observation required this modifcation. Quantum Mechanics is a nice example of that: observations of microscopic ...
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Relativistic mass of electron in a potential [closed]

An electron is accelerated through a 6 MV potential difference. what is the mass of the electron at the end of the path?
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Variation of spin in the rest frame of an electron in an external magnetic field

In Jackson's Classical Electrodynamics, the equation of motion for the angular momentum $\textbf{s}$ of an electron in an external magnetic field is given by (eq. 11.101) $$\left(\frac{d\textbf{s}}{dt}...
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Why would two inertial frames be distinguishable, if the coordinate of an event perpendicular to the motion would be different? [closed]

This question arises from the classical example: imagine a laboratory frame, and a space shuttle frame, the space shuttle moving in the laboratory frame with a constant velocity, let's say in the $x$ ...
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175 views

Is the $i$ in QM a time component in disguise?

In SR, it is possible to replace the Minkowski metric $\eta_{\mu\nu}$ with a (pseudo) euclidean metric $\delta_{\mu\nu}$ provided that time is measured in imaginary units. I was wondering if the same ...
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2answers
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Do any two points in Minkowski spacetime determine a unique line?

Any two points in a Euclidean space determine a unique line, but I wasn't sure if this result generalized to Minkowski spacetime given that the latter is not a Euclidean 4-space, but is, instead, a ...
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1answer
77 views

Will the speed of gravity and the speed of light always be the same?

I have been considering the following though experiment: If the entire sun were to disappear at once, would we feel it first due to the sudden drop in gravity or see it first? The answer I have come ...
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Does Heat Cause Time Dilation?

Since heat is defined as the movement of molecules, and because of relativity time slows for faster moving objects, would a hot object be in a slower time frame then a cooler object, because the hot ...
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632 views

Proper time for an accelerating object

As far as I have read so far, proper time is the time measured on the clock of an inertial frame moving uniformly with respect to another inertial frame. The concept and the mathematical expression ...
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Decrease in density due to relative velocity [closed]

A moving frame sees density of a spherical body decreased by 20% of its density in rest frame . What is the velocity of the moving frame ? I thought moving frame observes change in length of object ...
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1answer
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Is traveling at the speed of light the same thing as teleportation? [closed]

If I were on one side of the room and moved at the speed of light to the other side of the room, to an observer it would appear that I teleported. If time stops at that speed, it would be ...
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59 views

Lorentz force in different reference frames?

I have been introducing myself to special relativity and relativistic electrodynamics, and became curious about the similarity of the electric and magnetic forces. I'm trying to show that the combined ...
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1answer
51 views

Which one of these energy formulas is correct? [closed]

Which one of the following formulas is correct? What do they mean/represent? How are they used? $E=mc^2$ $E^2=m^2c^4+p^2c^2$ $E=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}$
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Is there any uncertainty between mass and proper length or time?

I was trying to naively draw a parallel between special relativity and the Heisenberg uncertainty principle. I try to understand uncertainty principle as a consequence of 4-position and 4-momentum ...
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Hubble's constant measured by observer approaching light speed

I recently read about expansion of the universe and I can't figure out if Hubble's law (and other models of expansion of the universe) is compatible with the theory of relativity. My question is: In ...
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1answer
51 views

Relativistic transformation of electrical current [closed]

If, in frame $S$, we have an electrically neutral wire with some current $I$, modelled as positive charges moving in $x$ direction and negative charges moving in $-x$ direction, then how would one ...
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1answer
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Dirac Equation in RQM (as opposed to QFT) is written in which representation?

In introductory Quantum Mechanics treatments it is common to see the Schrödinger's equation being written, simply as: $$-\dfrac{\hbar^2}{2m}\nabla^2\Psi(\mathbf{r},t)+V(\mathbf{r})\Psi(\mathbf{r},t)=...
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Help understanding Bell's spaceship paradox

The problem statement of Bell's Spaceship paradox is this: Two spaceships float in space and are at rest relative to each other. They are connected by a string. The string is strong, but it ...
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Reference for Reichenbach synchronisation and non-standard special relativity

My professor introduced in the last lesson a new method for clock synchronisation, which he called "Reichenbach synchronisation". In this new method, two clock A and B synchronise themself with the ...
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Parallel axes between inertial frames in Special Relativity

In "CLASSICAL ELECTRODYNAMICS" by J.D.Jackson, 3rd Edition , $\S$ 11.3, the author gives in equation (11.19) a generalization of Lorentz transformation as follows : If the axes in K and K' remain ...
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What spacelike, timelike and lightlike really mean?

Suppose we have two events $(x_1,y_1,z_1,t_1)$ and $(x_2,y_2,z_2,t_2)$, then we can define $$\Delta s^2 = -(c\Delta t)^2 + \Delta x^2 + \Delta y^2 + \Delta z^2$$ which is called the spacetime ...
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According to the theory of relativity, (relativistic) mass of an electron changes when it moves at very high speed; how and why? [duplicate]

It is given that $$ \mathbf m' = \frac{m}{\sqrt{1-\frac{v^2}{c^2}}} $$ How does (relativistic) mass change here?
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692 views

How do photons experience time? [duplicate]

I know that as velocity approaches the speed of light the time dilation shoots to infinity as shown below. 1)So I want to know how time is perceived from the point of view of the photon? 2)Since ...
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How does a photon experience space and time?

To an an external observer it appears that time has stopped for photon. But this relation is reflexive, so for an observer travelling with the photon it appears the universe has stopped everywhere. ...
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Does photon experience time? [duplicate]

According to the special theory of relativity, for all observers the speed of light is c. Any observer travelling at the speed of light c does not experience time. Hence even protons shouldn't ...
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Are we traveling through time at the speed of light? [duplicate]

In the image below the y axis represents time and x represent velocity. Point D represents velocity c, point E represents 1 second per stationary observers second. What this chart is showing is as you ...
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Calculating speed in four dimensions [closed]

If you are moving at $c$ in 3D space and $c$ in time axis too, What would be your total speed? Edit: Since question has been voted to be closed, I shall make an Edit. In 4D world all objects move ...
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How to derive addition of velocities without the Lorentz transformation?

Lorentz contraction and time dilatation can be deduced without Lorentz transformation. Can you deduce also the theorem of addition of velocities $$w~=~\dfrac{u+v}{1+uv/c^2}$$ without Lorentz ...
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Why are the electric force and magnetic force classified as electromagnetism?

I confuse the four kinds of fundamental interactions, so I think the electric force and magnetic force should not be classified as a big class called electromagnetism. Here is my evidence: The ...
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What does $v=c$ in the Lorentz transformation for time tell us?

For the simpler cases as boost in the x-direction, the time dilation formula following the Lorentz transformation for time is $$\Delta t'=\gamma(\Delta t-v\frac{\Delta x}{c^2})$$Now, we observe that ...
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1answer
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According to Einstein & Brian Greene, does the photon remain stationary in the fourth dimension? [duplicate]

According to Einstein and Brian Greene, does it logically follow that the photon remains stationary in the fourth dimension? In An Elegant Universe, Brian Greene writes: “Einstein found that ...
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Proper time of world lines in twin paradox

I was thinking about the twin paradox in Special Relativity and I thought I understood it fine, but when I view the "paradox" in a certain way, I get confused. So we have two twins, John and Jim. Let ...
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Is time an observable in Relativistic Quantum Mechanics?

Relativistic Quantum Mechanic is based, as far as I know, in the Dirac Equation. Now, the Schrödinger equation, in the abstract state space takes the form: $$i\hbar \dfrac{d|\psi(t)\rangle}{dt}=H|\...
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The path that a light beam takes in empty space

First excuse me if this question is very simple for you but for me and for my friend is not. Recently we were discussing what path a light beam will follow in a box moving at a constant velocity in ...
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1answer
49 views

Yukawa Potential in non-relativistic limit

In Peskin's book "An Introduction to Quantum Field Theory", on page 121 (section 4.7) , it tries to recover the Yukawa Potential in the nonrelativistic limit, but there's a simplification that I don't ...
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Local Phase Transformation of the Dirac equation

The Dirac Equation ("free Dirac") is a relativistic Equation of Motion (EoM) for a free ($V=0$) Spin $1/2$ particle (like an electron). The free Dirac equation is invariant under global phase ...
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69 views

Working out Length Contraction

I'm having trouble reconciling the quantitative and conceptual aspects of length contraction. This example is taken out of a book: Say a particle is moving toward us at 0.99c, relative to us. If at ...
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1answer
243 views

How does EM radiation depend on the reference frame?

In special relativity, magnetism is electrostatics in a different reference frame. This is how we explain the magnetic field being produced by moving charges (aka currents). Charges that move produce ...
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Physical reasons for metric definition in special relativity [duplicate]

I am working through "General Relativity" by Wald, and am currently going through the brief section on Special Relativity. The spacetime metric is defined as $\eta_{ab} = \sum\limits_{\mu, \nu=0}^3 \...
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Two particles of different velocities travel through a region of time-dependant acceleration. At what time do they meet afterwards? [closed]

Two projectiles: $P_{1}$ and $P_{2}$ have velocities $v_{1}$ and $v_{2}$, both propagting in the x direction and starting at $x=0$. They propagate with constant velocity over a distance $L$ and reach ...