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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Do the Lorentz transformations contradict reality by implying time had no beginning? [closed]

Consider the following two points, or events as they are more commonly called, in SpaceTime: Event 1: $(x,t) = (0,0)$ Event 2: $(x,t) = (a,0)$ Take t=0 to correspond to the first moment in time. As ...
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Acceleration in flat space-time and gravitational redshift

Consider two observers in flat space-time, of which one, called Terrence, is stationary, while the other, called Stella, moves in an accelerated way. I am particularly interested in the case where ...
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Why does $S$-matrix theory end up being a covariant formalism when it is not obvious that it is?

A principle of QFT that is frequently invoked, repeated, and potentially subject to rigorous verification is that the theory in question must exhibit Lorentz covariance and be invariant under the ...
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How did the author get these three expressions?

I am reading Nonplanar Relativistic Flow by Peter G. Eltgroth, Phys. Fluids 15, 2140–2144 (1972) doi. I do not understand how the author arrives at expressions (12), (13) and (14) at page 2. Equation (...
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Is there a general methodology for causal nets of observables regardless of kinematics?

The typical definition of a causal net of observables in quantum theory is to consider, for the case of a (globally hyperbolic) spacetime $M$, the category of open sets $O(M)$ ordered by inclusion, in ...
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Why is the derivative necessary to connect left and right-hand spinors?

I am studying Weyl and Dirac spinors. Suppose we have two Weyl fermions $\eta, \chi$ transforming under $(1/2,0)$ representation of the Lorentz group. I learned that to construct Lorentz invariant ...
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Fundamental invariants of a Lorentz tensor

As answered in this question, an antisymmetric tensor on 4D Minkowski space has two Lorentz-invariant degrees of freedom. These are the two scalar combinations of the electromagnetic tensor (as proven ...
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Finite dimensional irreducible projective representations of $SO^+(1,3)$

Conventions: Take the Minkowski metric tensor to have signature $(+, -, -, -)$. Use Hermitian (instead of skew-symmetric) generators of rotations $J_i$ and anti-Hermitian (instead of symmetric) ...
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Minkowski metric derivation [duplicate]

Can we derive the Minkowski metric from the Einstein field equations? I am still feeling unclear about the general relativity.
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Is the square modulus of the cross product between three-vectors a Lorentz invariant?

Is the square modulus of the cross product between two vectors $\vec{v_1}$ and $\vec{v_2}$ ,i.e., $(\vec{v_1}\times\vec{v_2})^2$, a Lorentz invariant or not? The result of a cross product between two ...
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Could relativity be consistent if there are multiple light-like fields with different invariant speeds?

My understanding of real physical theory of electromagnetism goes like this: The Maxwell equations can be used to derive the speed of light; $$\nabla\cdot\textbf{E}=0$$ $$\nabla\cdot\textbf{B}=0$$ $$\...
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Help with the Minkowski space-time metric

I've been trying to learn how to multiply two tensors in order to go from $$g_{\mu\nu} dr^\mu dr^\nu$$ to $$c^{2}\,dt^2-dx^2-dy^3-dz^2$$ But I can't figure it out. $g_{\mu\nu}$ is a $4\times4$ matrix, ...
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How far can we go in space?

I'm a noob in physics & math, so I'm just looking for a scientific answer for a small fiction project. My question is : How far can we realistically go in space, if we managed to "use" ...
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Special Relativity: Inner product invariance under Lorentz transformations [closed]

I have the following $$ \Lambda = \begin{pmatrix} \:\:\:\gamma & -\dfrac{\gamma v}{c} & \:\:\:0 & \:\:\:0\:\:\:\\ -\dfrac{\gamma v}{c}& \:\:\:\gamma & \:\:\:0 & \:\:\:0\:\:\: \\...
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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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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 also 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, ...
lee pappas's user avatar
1 vote
1 answer
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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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1 answer
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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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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 ...
Blackhole927's user avatar
1 vote
2 answers
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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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