Questions tagged [special-relativity]

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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Is there a distinction between rest mass and relativistic mass for photons? [duplicate]

I'm trying to reconcile how photons do and don't have mass, and the distinction seems to come from the frame of reference. As far as I understand, if you were to somehow stop a photon relative to an ...
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Sound wave in relativistic perfect fluid

I was trying to solve the following problem from the problem book on relativty: Problem 5.22. Show that the velocity of sound $v_{s}$ in a relativistic perfect fluid is given by $$v_{s}^{2}=\partial p ...
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Why is this assumption made in deriving time dilation?

My book makes the following assumptions (as far as I understood) in deriving length contraction and time dilation from Lorentz transformation : Suppose there is an inertial frame $S$ and another frame ...
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How is 1 g on a planet different from 1 g in a space ship when we look at aging?

This question has been asked before in the form of the 'Twin paradox' , and there are 42 pages of questions on this site alone when I search for 'twin paradox'. For example Does the twin paradox ...
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Natural extension of the line element for the Lagrangian to fields over 3+1 spacetime?

We are all familiar with the standard construction of the Lagrangian of a free relativistic particle: Start with the definition $$ S=\int_{\Delta t}ds. \tag{1} $$ Then use the definition of the line ...
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Can dimensions change at a speed faster than light? [closed]

This may be a stupid question as I barely know the General Theory of Relativity but people keep telling spacetime that it is a like a stretchy fabric which can be modeled like a spring. $$F = -kx$$ If ...
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Can the Lorentz Transformation Matrix be Derived using the Change of Basis Formula?

So I watched a MinutePhysics video explaining the idea of Lorentz transforms geometrically and the way he described it sounded very similar to how 3Blue1Brown explained the idea of change of basis. I ...
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Special Relativity: How do observers measure distance?

Let $(M,g)$ be a flat spacetime, $(\gamma:\mathbb{R}\rightarrow M,e)$ an observer (where $e_1(\lambda)$, $e_2(\lambda)$, $e_3(\lambda)$ together with $\dot{\gamma}(\lambda)$ form the basis of the ...
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What are the Lorentz Transformation equations when the relative velocity of an entity is in an arbitrary direction?

The Lorentz Transformation equations are generally presented as a transformation of spacetime between two observers, when they each move at a velocity $v$ along the $x$ axis relative to each other. My ...
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Are there any advantages to using split-complex numbers for spacetime algebra? [closed]

Multiplication of split complex numbers correspond to Lorentz transformations in 1+1D. Their norm is the spacetime interval. Could these numbers be a useful mathematical tool for special relativity?
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Special relativity - Einstein's transformations

I am reading 'on the electrodynamics of moving bodies' (http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdf) and have got to page 6 and become stuck. Is anyone able to ...
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How does the force of charge between particles change with velocity?

I'm sure how fast a particle moves must have some relativistic effect, or maybe also classical ones too. Suppose you fixed the positions of two charged particles. Suppose you're in a lab frame and in ...
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How to prove that both $\mu_0$ and $\epsilon_0$ don't depend on any frame of references? [duplicate]

Based on my previous question here, lets us step back a little bit. The speed of light $c=1/\sqrt{\mu_0\epsilon_0}$ is assumed as a value that does not depend on the observer because it is just a ...
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How can we conclude from Maxwell's wave equation that the speed of light is the same regardless of the state of motion of the observers?

I am reading a book titled "Relativity Demystified --- A self-teaching guide by David McMahon". He explains the derivation of electromagnetic wave equation. $$ \nabla^2 \, \begin{cases}\vec{...
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Does the twin paradox require both twins to be far away from any gravity field?

If one twin is on earth at 1 g and the other twin accelerates away from earth following a great big elliptical counterclockwise trajectory. He travels at .9 g for 20 years(according to earth time) as ...
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Physical system that is described by the conformal group's irreductible representations

I am currently studying the conformal group, i.e the 15-dimensional group that is associated with the conformal symmetry of spacetime. Before working on that group, I've work on the Poincaré Lie group....
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Simple derivation of the Maxwell's equations from the Electromagnetic Tensor

Lets start by considering the electromagnetic tensor $F^{\mu \nu}$: $$F^{\mu \nu}=\begin{bmatrix}0 & -E_x/c & -E_y/c & -E_z/c \\ E_x/c & 0 & -B_z & B_y \\ E_y/c & B_z & ...
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Analytic Continuation of the $S$-Matrix and Analytic Continuation of Spinors

Broadly speaking, what is actually being done when one analytically continues the external particles' momenta in scattering amplitudes in QFT? Some associated more detailed questions: When thinking of ...
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Regarding calculation with rigorous steps

I was studying a book called Theoretical Astrophysics by Prof T Padmanavan, and in the very first chapter, i find the expression of Net Contributing Pressure ($P$) as: $$P = \frac{1}{3} \int_{0}^{\...
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Macroscopic Limit of QED

How does one go about rigorously deriving special relativistic dynamics (both relativistic mechanics and electrodynamics) from quantum electrodynamics? Is this even possible from the mathematical ...
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Why is the current generation more interested in quantum physics? [closed]

Earlier people used to be obsessed with thermodynamics and laws describing behavior of gases, electric current, gravity. Cavendish,Kelvin, Newton and etc etc etc. But now in every movie, I see physics ...
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Is there a “non-linear limit” of the Dirac equation?

I'm just going through old protocols of oral exams students wrote up. One student writes that he was supposed to derive the "non-linear limit" of the Dirac equation during the exam. Is there ...
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1answer
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Does a Meson hit earth or not hit earth? [closed]

I am told a $\mu$ meson with an average lifespan of $2 \times 10^{-6}$ is created in the upper atmosphere at an altitude of $6000m$. When it is created, it has a velocity of $0.998c$ in a direction ...
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Relativistic density

In the non-relativistic region of the space, with matter of mass $M$, and volume $V$ the density is given by \begin{equation} \rho=\frac{M}{V} \end{equation} If we encounter an equation, for example, \...
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Is there a convention for left / right-chiral Weyl spinors?

In order to distinguish the representations of the Lorentz group, we can combine the generators for rotations ($J$) and boosts ($K$) into linear combinations, $$ A_i = \tfrac{1}{2}(J_i + \text{i}K_i),\...
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Proving a given vector to be a four-vector

How to prove that $$k=(\frac{\omega}{c} , \vec{k})$$ is a four-vector? Where $\omega$ is the frequency and $\vec{k}$ is a wave vector.
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Why projection operator is not equal to zero, as we can write 1st term as 2nd term or vice versa via raising or lowering index with metric?

$$k^2g^{\mu\nu}-k^\mu k^\nu=k^2P^{\mu\nu}(k)$$ Here 1st term can be written as 2nd term via breaking square term and then raising index.
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How to use Lorentz's Transformation properly?

I have a series of doubt about how Lorentz's Transformation are written and used commonly: First doubt: It's really common to see Lorentz transformation written this way: $$x'=\gamma x -\gamma \beta t$...
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Problem regarding quantum entanglement and special relativity

So this question is about the strange phenomenon of quantum entanglement, or "spooky action at a distance", as Einstein called it. In particular, it's about the simplest conceivable case of ...
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1answer
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What happens if we rotate one gear and this rotates another and this to another and so on. Will the last gear rotate faster than light?

what happens if we rotate a small gear attached to a larger one and the large one rotates another small one attached to a large one and the large one rotates another small attached to a large one and ...
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Are two interacting electrons in an isolated system?

From your point of view, two electrons are initially at rest. In time, they repel one another, leading to an increase in both of their kinetic energies. If they are isolated from the rest of the ...
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'Why' is the Schrödinger equation non-relativistic?

The transition amplitude for a particle currently in one spacetime point to appear up in another point doesn't respect causality which becomes one of the main reasons to abandon non-relativistic ...
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Lorentz Transformation of a Tensor

If I have the electromagnetic field tensor, then, under a Lorentz transformation: $$F^{'}_{\mu\nu} = \Lambda_{\mu}^{\alpha} \Lambda_{\nu}^{\beta} F_{\alpha\beta} $$ I know that the Lorentz matrix is ...
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Intuition for curved Lorentzian manifolds through Euclidean embedding

How can one find embeddings of parts of curved Lorentzian manifolds into low dimensions ($\leq 3$) for visualization and intuition building? For example, one can embed the space $H_2$ into $\mathbb R^{...
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Is speed of light in vacuum really constant? [closed]

According to sir maxwell the speed of light is constant irrespective of the observer. But according to sir newton anything in the universe is relative to something. If u say car is moving 10mph. Its ...
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Weinberg QFT problem 2.1: transformation of quantum states

I'm solving the following problem in Weinberg's QFT textbook: an observer sees a particle of spin 1 and mass $M$ move with momentum $\mathbf{p}$ in the $y$-direction, and spin $z$-component $\sigma$. ...
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Time reversal acting on Lorentz multiplets

Given a finite dimensional multiplet of the Lorentz group $(A,B)$, let's use the notation $|A,a,B,b\rangle$ to denote the state, how does time reversal $T$ act on this? I know that $T$ acts on $\vec{A}...
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Does “QFT in curved spacetime” combine QFT and general relativity?

From my understanding, QFT combines QM and special relativity. So doesn't QFT in curved spacetime combine QFT and general relativity? I realize that we need to quantize gravity to have the more ...
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Do these relations hold between the four-gradient and its inverse?

Does it make sense to write the following expression: $$F_{\alpha\beta}(x) :=\partial_\alpha\ \left( \partial^{-1} \right)_\beta f(x), \tag{1}$$ with $\partial_\mu := \partial/\partial x^\mu$, $\...
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Angle-preserving linear transformations in 2D space for relativity

I'm watching this minutephysics video on Lorentz transformations (part starting from 2:13 and ending at 4:10). In my spacetime diagram, my worldline will be along the $ct$ axis and the worldline of an ...
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How does following relation generates Lorentz generator?

In Schwartz book sec 10.3, Schwartz says following: The Lorentz generators when acting on Dirac spinors can be written as $$S^{\mu \nu}=\frac{i}{4}[\gamma^{\mu},\gamma^{\nu}]$$ But what I am able to ...
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Radiation in Non-inertial Frame of Reference

Consider some stationary charge in an inertial frame of reference. Consider an observer accelerating with respect to that charge. Does the accelerating observer see radiation? It would be reasonable ...
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Affect of angular momentum in gravitational force

As far as I know: The gravitational force occurs due to curve in spacetime. A curve in spacetime occurs due to energy. So my question is the increase in angular momentum is also increase in ...
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Generators of Lorentz group (algebra and action on spacetime)

My question is about the generators of the Lorentz group: signature $(-,+,+,+)$. I have found the well known Lorentz generators (intended as elements of its algebra evaluated in the identity element ...
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Ambiguous visualization of time dilation by Minkowski diagram

I wanted to visualize time dilation through Minkowski diagrams but I ended up in a fiasco. Let me show how. Consider two observers $O$ and $O^\prime$ at rest and moving with velocity $-v$ with respect ...
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What if static electromagnetic field is turned off? (in vacuum)

Lets assume that there is static electromagnetic field that has $E=17mc^2$ and $p=8mc$. At some time $t=t_0$, the field is turned off. (e.g. the electric current of coil went to zero by resistance, ...
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Null planes and luminous vectors

A null plane is defined by: \begin{equation} g(X,X) g(Y,Y) - (g(X,Y))^2 \end{equation} I have two questions regarding null planes: Finding one null plane in Minkowski's space-time. I'm not sure if ...
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Do photons move from their point of view? [duplicate]

If at light speed time doesnt exist do photons not move from their point of view? If they dont, what would happen if you took a photon and somehow stopped it would it be at the same point at its POV ...
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Terrell “rotation”: should wikipedia be corrected? [closed]

There are two common misconceptions regarding the Terrell "rotation" : it's a pure rotation the Lorentz-Fitzgerald contraction is not detectable by a single detector, in which the past ...
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Can time dilation affect time taken?

Take an example of a space ship moving at speed comparable with speed of light (like 60% of c) now if spaceship launched from earth to near star does time dilation affects the time taken by space ship ...