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 an equivalent of Rindler coordinates for an object in centripetal motion?

Rindler coordinates are a parametrization of (a subset of) Minkowski space that are "natural" for an object experiencing constant acceleration - more specifically, an object experiencing ...
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Representation Theory of $SL(2,\mathbb R)$

The representation theory regarding the finite-dimensional representations of $SL(2,\mathbb C)$ is well-understood; namely, they all decompose into irreducibles $V_n$, $\dim(V) = n > 0$. ...
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Ephemeris calculations: Light time correction of the moon

I am currently trying to calculate apparent positions from raw JPL data. I've got it pretty much figured out, but there is one thing that's bugging me: Has the light time correction of the moon to be ...
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Electron in rotating frame

Suppose there is a stationary electron in an inertial frame $S$. Then there is only a static Coulomb field relative to $S$. However, according to a rotating frame $S'$, whose angular velocity relative ...
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What is the general definition of symmetry in quantum mechanics

Consider a quantum system with Hilbert space $\mathcal{H}$ and Hamiltonian $H$. Let $G$ be a Lie group and $U$ a unitary representation of $G$ on $H$. What are the most general conditions that $H$, $G$...
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Actions for relativistic point-particles of higher spin

To describe the behavior of a relativistic point-particle, we have the standard action $$S=\int d\tau \bigg[\frac{1}{e} \dot X^\mu\dot X_\mu +m^2 e\bigg],$$ where $e$ is the worldline einbein. Then, ...
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Minkowski as a Quotient Space

I've read many times, in many articles or books that one can obtain the four dimensional Minkowski space $\mathbb{M}^4$ as the quotient space $$ISO(3,1)/SO(3,1),$$ and equivalently de Sitter and ...
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Analogue of helicity in higher dimensions and concrete formula

Consider Poincare group $ISO(1,d-1)$ in some dimension $d>4$. There are two Casimirs. Let's look at massless one-particle states: the little group is $ISO(d-2)$, and if we restrict to finite ...
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Uses of the Angular Momentum 4-Tensor

The angular momentum 4-tensor has 6 independent components, three angular momentum components and three new guys. Some call these new guys the 'boosts', but since they are the conjugate momentum of ...
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Why parity exchanges right handed and left handed spinors

Reading through David Tong lecture notes on QFT. On pages 94, he shows the action of parity on spinors. See below link: QFT notes by Tong In (4.75) he confirms that parity exchanges right handed ...
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A question about the emergence of 'spin' from relativistic QM

I know that quantum-spin is not equivalent to the spinning of a classical object about an axis passing through it, although there are some similarities. I also know that spin naturally emerges out of ...
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Ohm's Law for Accelerated Conductors

My questions are about the Ohm's law for a moving conductor in a stationary magnetic field. As we know this law is stated based on following relation with respect to the fixed frame of reference ...
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Coincidence of spacetime events & Lorentz invariance

Am I correct in thinking that if two spacetime events are coincident in one frame of reference, then they are coincident in all frames of reference, i.e. coincidence of spacetime events is a Lorentz ...
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Linearity of Lorentz Transformations from Principle of Relativity

Many derivations of the Lorentz transformations assume they must be linear maps on $\mathbb R^4$, where we identify the components of $\mathbb R^4$ with orthogonal coordinate systems associated to ...
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How to calculate the Euler equation for fluids in the newtonian limit from the stress-energy tensor?

I have been working through the exercises of Schutz's a first course in general relativity. In chapter 7 of the book there is a question about the conservation of the spatial components of stress-...
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Can we describe a relativistic quantum field theory in a "particles with position" framework _if_ we constain it somehow?

EDIT: I'm rewriting this with a different mathematical formalism that I think may be more appropriate and hopefully this will be clearer. Yes, another conceptual question regarding quantum theory. It ...
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When observer sees source in actual nearest position, there is a transverse Doppler effect due to time dilation. From the view point of observer, the source experience a shorter time by $1/\gamma$, ...
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No-interaction theorem in classical relativistic mechanics

In classical relativistic Hamiltonian mechanics there is a so-called "no-interaction theorem" (see, for example, this article for a proof). Roughly, it states that if we have an $N$-body ...
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Time reverse transformation of 4-potential and its relation to Lorentz transformation

Until now, I thought electromagnetic potential $A^{\mu}(x)$ transform like $x^{\mu}$ under the Lorentz transformation: $$A^{\mu}(x)=\Lambda^{\mu}_{\ \nu}A^{\nu}(x).$$ But according to time reversal ...
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Infinite dimensional representation of generators of the Lorentz group

I was reading Schwichtenberg's "Physics from Symmetry 2nd Edition". In Section 3.7.11, there is the discussion on the infinite dimensional representations. If we consider a transformation of ...
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Magnetism through Relativity

If relativity tells that from a moving charge's frame (observing current carrying wire) protons contract in length and its charge density increases making the charge experience a electrostatic force. ...
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How can we prove that a non-linear equation of motion for a classical scalar field satisfies causality?

Let $\phi$ be a real-valued scalar field in $N$-dimensional spacetime with coordinates $(t,\vec x)$, and consder the equation of motion  (\partial_t^2-\nabla^2)\phi(t,\vec x)+V'\big(\phi(t,\vec x)\...
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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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Time dilation of induced dipolar gravitational fields

In gravitoelectromagnetism, changing gravitomagnetic fields can induce standard gravitational fields, much in the same way that changing magnetic fields induce electric fields. This analogy extends to ...
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