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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The Klein-Gordon equation and the sign of the mass term

A derivation of the Klein-Gordon equation starts with the following lagrangian for a scalar field ϕ: $$ L=\frac{1}{2}g^{ab}(∇_a\phi)(∇_b\phi)-V(\phi) $$ If we plug this lagrangian in the Euler-...
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Deaccelerating to the Speed of Light

The trajectory of an observer with a uniform proper acceleration $a$ (Rindler) in an inertial frame $(t,z)$ can be described by the hyperbola \begin{equation} \left(z+\frac{\gamma_{0}}{a}\right)^{...
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Interference pattern of relativistic particles

I wanted to know if it is possible to perform a double slit experiment with electrons travelling at 0.99c as the wavelength is very short.
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Photoelectric Effect combined with Doppler Redshift

Suppose we were standing in the vacuum with a photoelectric effect experiment. If we had a source of EM radiation emitting photons with a high enough frequency, we would begin to observe said effect ...
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Extending relativistic action for a particle to a relativistic field [duplicate]

The action for a relativistic particle is given by $$S_R = -m\int\sqrt{dx^\mu dx_\mu} = -m \int_{t_1}^{t_2} \sqrt{1-\dot{\mathbf{x}}} dt$$ where I have parametrized using time in the last equality. ...
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Linear momentum of an EM wave

In my optics textbook, the derivation of the expression for the linear momentum of a plane wave shocks me as rather sloppy, but I don't know if I should be so shocked. It goes as follows: Let a plane ...
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Determining the time elapsed between two events in

I want to determine the time a photon needs in order to cover a distance, say $l_0$, where $l_0$ is the length of a spaceship (reference system S'). So, the photon is going from one end of the ...
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2D SR angle transformation [closed]

A couple of days ago I encountered a problem on special relativity. It said There are 2 observers A and B. B is emitting $k$ balls per unit time per unit angle from it in all directions from its ...
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The behavior of $\sin {\omega t}$ at relativistic frequencies

The product $\omega t$ is a dimensionless quantity and the same is true for $\sin{\omega t}$. If they are dimensionless, then they are identical between the rest and relativistic frames because there ...
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Repulsive force between electrons at relativistic speeds

What happens to the repulsive force between two electrons, once one of the electrons travel at relativistic speeds? Let's consider two electrons in an atom with magnetic dipole moment, one of which is ...
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Relativistic mass and relativistic charge

Let a particle with a mass $m$ and a charge $q$ move with a speed $v$ close to the speed of light ($v\approx c$). Then, the special theory of relativity tells us the particle's relativistic mass would ...
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Proper treatment of springs in special relativity

I've looked on-line for a simple treatment of springs under tension/compression while moving at relativistic velocities parallel to the direction of tension/compression and could not find one. There ...
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Do supertranslations act in a physically nontrivial way?

I'm currently reading arXiv: 1703.05448 [hep-th]. In this question, I'm interested in a statement made on page 67 of the pdf (76 of the printed book, if you prefer to check in it). There, the author ...
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Does a dimensional analysis of Einstein’s equation describe a rapidly expanding area? [closed]

The speed of light, C, is measured in meters per second. C squared, therefore is measured in meters squared per second squared, a rapidly expanding area. So my interpretation of is that as a photon is ...
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A mathematical issue in the resolution of Bell's spaceship paradox

I am referring to https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox and explanations based on diagrams like The reasoning for a resolution of Bell's spaceship paradox is mainly that the ...
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Transform final momentum $p_b^{'fin}$ in CM frame back to lab frame (Taylor Classical Mechanics)

Referring to page 646 of Taylor Classical Mechanics, I have a question regarding the step to transform final momentum in CM frame back to lab frame. Example 15.10: An Elastic Head-On Collision ...
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Was the Hafele-Keating experiment a bad result? [closed]

The result on the eastward journey came close to breaching the error margin. Time was measured in microseconds, modern clocks are more precise. With modern equipment the Hafele-Keating experiment ...
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Equivalence of speed and time flow

Is it right to assume that in 4-dimensional spacetime the speed of any object is constant? I mean a stationary object travels straight to the future but any spatial movement simply means that the ...
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How do Maxwell's equations follow from the action of Lorentz generators on field strength?

Following Warren Siegel's book on Field theory (pg. 223), one might derive the action of Lorentz generators $S_{ab}$ on an antisymmetric 2-tensor field strength $F_{cd}$ which arises for example in ...
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Confusion regarding Special Relativity and Relativity of Velocity? [duplicate]

Suppose that there are two points in an empty space A and B and observers at A and B having clocks: If A were to be traveling near speed of light, when clock at A passes 1 hour, observer at A ...
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Extreme confusion with the Lorentz transformation law for vector fields

Let $\Lambda$ be a Lorentz transformation represented as $4 \times 4$ matrix. Then, following What does it mean to transform as a scalar or vector? , it seems that a vector field $f : \mathbb{R}^4 \...
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How to show causality for a Klein-Gordon field in 1+1 dimensions using field commutators?

For a non-interacting massive scalar field $\phi$ in an $n+1$ dimensional minkowskian spacetime, the field commutator between two event points is $$ [\phi(x),\phi(y)] = \int \frac{\mathrm{d}^n p}{(...
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Complete absortion of a photon by an atom (from the perspective of conservation laws)

It is very simple to show that an isolated charged particle cannot completely absorb a photon, since that would contradict the conservation of linear momentum or energy: consider a system where the ...
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Reason Why 1 Coulomb was redefined in SI unit system?

Since current can be calculated as $I = q/t$, the original definition of 1 Coulomb in SI unit system was that it is such amount of charge which flows through wire cross-section having current of $1 A$ ...
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Relativity - how do you calculate the duration of this trip from various reference frames?

Let's have following scenario: A spaceship departs from the Earth and constantly accelerates in a straight line for 60 000 000 seconds at 1g (10 m/s^2), then immediately starts decelerating at 1g for ...
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Relativistic heat equation and form of "relativistic kinetic energy"

I'm reading a paper (https://arxiv.org/abs/1507.05030) on a proposed form for the relativistic heat equation derived by optimal transport from a relativistic cost function. In particular, the paper ...
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If you have two clocks moving toward each other and they both stop when they meet does it point to a paradox?

Say they both decelerate at the same rate also. If clock A sees clock B as slower than itself and clock B see clock A as slower than itself due to relativity isn't this a paradox because when they ...
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Two different observations by different frame of references? How are both observations true and exists simultaneously?

Consider the scenario wherein an electron undergoes acceleration in free space, eventually emitting radiation. Two distinct observers are involved: one accelerates alongside the electron, while the ...
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Do the Lorentz transformations imply a free particle is moving in opposite directions simultaneously in the primed frame, or accelerating? [closed]

Consider the following two points, or events as they are more commonly called, in SpaceTime: Event 1: $(x,t) = (0,0)$ Event 2: $(x,t) = (a,0)$ As you can see they are merely two separate locations, ...
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How would a spacecraft travelling near light speed say 0.9c compensate for time dilation in radio communication from spacecraft to earth?

For a spacecraft travelling at 0.9 c for 5 seconds, only 5 seconds would have passed for an observer on Aircraft, while 26.31 second would pass for a stationary observer watching from Earth. In a ...
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Value of $p^{2}$ for little groups

I am looking at Weinberg, The Quantum Theory of Fields, Volume 1 page 66. In this table, the author mentions various little groups of the Lorentz group. Orthochronous Lorentz transformations must ...
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Can I justify that the Electric Field intensity will double for the case described using the following relativistic and quantum mechanic argument?

If one is heading towards the source of a constant amplitude EM wave at a speed that makes the frequency twice that of another observer, then the amplitude of the E (electric field amplitude) will ...
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Thought experiment on a spinning neutron star [closed]

Consider a typical neutron star spinning at a rate of 250-300 revs per sec and say we attach a long rod to it (semi-infinite) and is made of some ideal material (unbreakable etc). What effects would ...
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How does relativistic Doppler effect conserve energy?

Say I have a laser traveling at the stationary observer at relativistic speed, so the laser wavelength gets blueshifted. To conserve total energy emitted, according to the observer, the laser emits ...
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Paradox in the observation of ripple

What I am going to speak about may not be a paradox but i see a contradiction here so I used used the word "paradox". To begin with, let there be 2 charges A and B which are stationary with ...
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Can something exceed the speed of light relative to a moving object? [duplicate]

If you fire two light beams in opposite directions, won't one of the beams be moving away from the other at twice the speed of light? Doesn't that mean you and a friend can travel at 51% of the speed ...
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Equation for relative Kinetic energy

Relative Kinetic energy is given by K.E = ($\gamma$-1)$m_0$c²; where $m_0$ is rest mass but can it also be given by this K.E= $\frac{1}{2}\gamma m_0v²$; where v is velocity of particle can it?
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How do I find numerical solutions to geodesics when given initial four-position, initial four-velocity and a metric? (for a ray tracer)

I've had the idea to try and code a ray tracer that obeys laws of special/general relativity. In order to predict the motion of objects in the scene I'd need to compute geodesics with a user specified ...
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Attempt to give a semi-classical clue for gravitational wave [closed]

We begin with a general concept. We want to know under what circumstances a typical field and its reflection can generate an oscillation or wave. A periodic field from the source S is travelling to ...
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Generalization of Newton's First Law?

One might express Newton's first law as, A body with position $\mathbf{x}(t)=\left(x(t),y(t),z(t)\right)$ will obey $\dfrac{\partial^2 \mathbf{x}(t)}{\partial t^2}=\mathbf{0}$, unless influenced by ...
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Mass in de Broglie Formula

Regarding de Broglie formula $$\lambda= h/mv$$ here m is relative mass or rest mass?
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Why aren‘t other metals colored?

From an online lecture, I heard that $d$ orbitals cause metals to have a peak in their reflectivity curve at some wavelength. This is generally the case for most metals. However, the peak lies mostly ...
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Non-orthogonal frames

Fix $4$-dimensional Minkowskian spacetime $(\mathbb{R}^4, \eta)$. As in my previous posts, a reference frame is then simply a choice of basis vectors $\{e_{\mu}\}\subset \mathbb{R}^4$ such that $\{e_0\...
Relativity's user avatar
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What role does inertial frame play in general relativity?

The study of geometric aspect of Special Relativity is all about the geometry of Minkowski spacetime $(M,\langle,\rangle)$, a flat spacetime whose curvature vanishes at everywhere. The (Minkowski/...
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Does the interval pseudometric say that elapsed time is negative spatial distance?

Quick review (skip it): In the formula from 8th grade, you figured out the length of the long side of the triangle using this equation: And in three dimensions: This gives the length of the line ...
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Columns, rows, dotted, undotted, $SL(2, \mathbb{C})$ reps, and building Dirac spinors from Weyl spinors

I'm looking through Introduction to Supersymmetry by Muller-Kirsten and Wiedemann, along with any other resource I can find. I'm specifically trying to understand the concepts and notations for ...
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Do the Lorentz transformations lead to negative amounts of time? [closed]

Consider the following two points, or events as they are more commonly called, in SpaceTime: Event 1: $(x,t) = (0,0)$ Event 2: $(x,t) = (a,0)$ As you can see they are merely two separate locations, ...
lee pappas's user avatar
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Confusion about length contraction of gaps in relativity [closed]

I am trying to understand if gaps contract in the same way as solid objects in SR and casually the answer seems to be yes, but there seems to be circumstances where this is not always true. Consider ...
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A conceptual difficulty about the Ehrenfest paradox

I had always understood that the well-known effects of SR- such as time dilation, length contraction and so on- were properties of the geometry of spacetime so that they applied to spacetime in an ...
Marco Ocram's user avatar
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A confusion about the inner product keeps disturbing me [duplicate]

I get very confused about the concept of inner product. When an inner product is defined in a vector space, $\mathbb{V}$, don't we define it as an operation between two vectors from $\mathbb{V}$ ...
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