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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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Status of experimental searches for tachyons?

Now that the dust has settled on the 2011 superluminal neutrino debacle at OPERA, I'm interested in understanding the current status of experimental searches for neutrinos. Although the OPERA claim ...
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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 constant ...
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678 views

Chirality and helicity operators for the massless bispinor rep and their generalisation on arbitrary (tensor, 4-vector etc) cases

Let's have chirality projection operator $$ \hat {C}_{\pm} = \frac{1 \pm \gamma^{5}}{2}. $$ We introduce it and called it chirality, because $$ \hat {C}_{+}\psi = \begin{pmatrix} \psi_{\alpha} \\ 0 \...
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Complexifying Lie algebras confusion

I have been studying a course on Lie algebras in particle physics and I could never understand how complexifying helps us understand the original Lie algebra. For example, consider $\mathfrak{su}(2)$...
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Is Bohmian mechanics really incompatible with relativity?

This is something I've been wondering about. For those who don't know, Bohmian mechanics is an interpretation of quantum mechanics that is in the class of what are known as "hidden variable theories", ...
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General Relativity as a Special Relativistic Field Theory

In this question, I want to consider only the classical case. I have seen the statement that general relativity can be considered as a spin-2 field living on a Minkowski background. In that case, you ...
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459 views

Chirality, helicity and their relationship for the massless case

Chirality can be interpreted as a property of Lorentz group - Lorentz transformation of field through representation $(s, 0)$ or representation $(0, s)$. For the massless particles one says, that ...
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How to derive the Klein-Nishina formula from the Dirac equation?

I'm looking for the simplest demonstration of the Klein-Nishina formula, from the Dirac equation without the field described as a quantum operator: https://en.wikipedia.org/wiki/Klein%E2%80%...
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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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What is the resolution of this Lewis-Tolman-like paradox?

Though my question stands on its own, here is a brief overview of a well-explored question, the Lewis-Tolman Lever Paradox, which I think might be helpful in finding the resolution to my question. The ...
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What type of fields are continuous spin representations?

Continuous spin representations (infinite dimensional representations of the Lorentz group) are pretty rarely discussed, and usually not in that much mathematical details. And usually it is done in a ...
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Consider two electrons released from rest at a distance $d$. How much energy is radiated?

Abraham-Lorentz? Two electrons d apart have potential energy. Release them, they will be repelled according to Coulomb's law. I could make an assumption about the associated vector potential, but I ...
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Sphere moving at relativistic velocities

I stumbled upon this exercise on a SR book: Determine how fast a sphere of diameter 2R has to move to pass through a hole of diameter d on a planar surface. If I understand correctly, this should not ...
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43 views

How do particles' varying reference frames average to a single macroscopic reference frame?

Our center of mass remains approximately in a constant inertial reference frame (our accelerations combined with our meaningful time scales are negligible compared to c). However, at the atomic and ...
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Relativistic Turning: Most efficient strategy?

Say I have a ship that can go something like 99.999997% C, and has a very, very large amount of energy at its disposal (essentially beamed to the ship from elsewhere), but not unlimited. I want to ...
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336 views

Dirac equation and particle probability density

I do know that nowadays dirac equation is interpreted as field-theoretic equation, not as particle equation. But is there any sense that dirac equation can still be said to have wavefunction that ...
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238 views

Why the Universal Covering Space of a (Spacetime) Symmetry Group?

Potential philosophical issues notwithstanding, it is commonly said that the definition of an elementary particle is an irreducible, unitary representation of the Poincaré group (times a gauge group ...
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What is the topology of phase space of $n$ free relativistic particles in center of mass frame?

Consider an ensemble of $n$ relativistic particles of fixed masses $m_i \geq 0$, $i=1,\ldots,n$ with four momenta $p_i$ such that $p_i^2=m_i^2$. In center of mass frame they sum up to $$P=p_1+\cdots+...
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Why would speed of light be directional if spacetime is discrete?

In Feynman's Simulating Physics with Computers, Feynman states that "we might change the idea that space is continuous to the idea that space perhaps is a simple lattice and everything is ...
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What's the connection between the pole contours of propagators and their causality?

Wikipedia distinguishes between three kinds of propagators for a scalar field: The Retarded propagator's contours have $\mathrm{Im}(k^0)>0$ on both poles, so its limit is completely in the first ...
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Momentum eigenstate definition in Eq (2.5.5) of Weinberg Vol. 1 clairification

This is question is related to one asked here: Questions concerning some parts of the section on one-particle states in Weinberg's first volume on QFT. In Eq (2.5.5) of Weinberg's "The Quantum ...
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General theorems on tachyon propagation?

I was reading the quite nice answer of QMechanic on the topic of compact support tachyon fields not propagating faster than light, but this case is a rather simple one, free scalar field in flat space....
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What happens to the observed thermal energy of objects at relativistic speeds?

When an object is observed to move near the speed of light, what difference in thermal energy is observed? Does time dilation imply that it's colder?
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Intrinsic CPT phase

Under charge conjugation C, spatial inversion P and time reversal T transformations, there are possible intrinsic phases (more for this on Chapter 9, The Quantum Theory of Field v1 by S. Weinberg): $$...
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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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Does a mass gain inertia against movement in all directions as it approaches the speed of light?

If a mass moves along the x axis at near the speed of light, does it take as much energy to additionally accelerate the mass along the y axis as it does to accelerate it along the x axis by the same ...
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Question about path integral step of the rindler decomposition

In most papers where I've read about Rindler decomposition and the Unruh effect ( see for example [1] or [2]) they start by saying that they want to find the wavefunction of the vacuum state in the ...
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How is time “homogeneous”?

My book$^1$ states: Let's consider a clock moving freely over a curve such as: \begin{equation} \frac{dx^i}{dt}=\text{const} \tag{1.20} \end{equation} We define the proper time $\tau$ as the ...
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How is Inönü-wigner contraction done?

I have read that little group for the massive particles is $SO(3)$ and for the massless particles is $E(2)$ in 4 dimensions. How does one take zero mass limits for the representations and show that it ...
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Rindler Coordinates Derivation

In my GR lectures we've derived Rindler coordinates by first showing that the four velocity, which we defined as $$u^{\mu} = (\gamma c, 0, 0, \gamma u),$$ as a function of proper time can be written ...
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Particle collision

At the end of Chapter 3 in Griffiths "Introduction to elementary particles", he mentions that one can benefit from a change in frames, in this case, center-of-mass (CM) frame and particle-rest frame. ...
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Why spatial infinity is a point and not an $S^2$?

First a disclaimer, this question already has been asked here, but as pointed out in comments, more detail was required. So this is a more detailed version. Let $(\mathbb{R}^4,\eta)$ be Minkowski ...
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Do relativistically-contracted electron states have the same energy and angular momentum values?

I've been reading that electron bound states are defined by four quantum numbers, $n$, $l$, $m_l$, and $m_s$, respectively the principal quantum number, the azimuthal quantum number, the magnetic ...
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Analytic cotinuation between Minkowskian and Euclidean space, and causality

We can flip between Minkowkian and Euclidean signature by Wick rotation, and it is a well defined operation, provided there are no non - trivial singularities. Now, Unitarity in Minkowskian space ...
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Is there any feature which distinguishes the Hamiltonian in the Poincare algebra?

The Poincare algebra is defined as \begin{align*} i[J^{\mu\nu},J^{\rho\sigma}]&=\eta^{\nu\rho}J^{\mu\sigma}-\eta^{\mu\rho}J^{\nu\sigma}+\eta^{\sigma\nu}J^{\rho\mu}-\eta^{\sigma\mu}J^{\rho\nu}\\ ...
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Showing path integral formalism is Lorentz-invariant without resorting to Hamiltonian formalism

I think people typically say that path integral formalism is manifestly Lorentz-invariant, because Lagrangian density is Lorentz-invariant. However, path formalism is typically defined with time ...
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Connection between contra-/covariant vectors in SR and complex numbers?

If we take a spacetime with one spatial dimension, we can write a vector as $A^\mu=(t, x)$. This is a contravariant vector, and we can calculate the covariant vector by multiplying it with the ...
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Frequency spectrum of bremsstrahlung

I have tried to find a method to derive the spectrum of the emitted radiation of accelerated relativistic charged particles but I've never found such a method in any books. Does anyone know a method ...
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What's the difference between classical rigidity and Born-rigidity?

In classical mechanics, you have the concept of a rigid body. This notion is incompatible with the theory of special relativity. In 1909, Max Born introduced the concept of Born-rigidity. He did this ...
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Books on the experimental evidence for Special Relativity?

Lately I've been interested in investigating the more intricate parts of special relativity beyond what is readily apparent on wikipedia or physics 101 videos. So, besides mathematical treatments, I ...
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263 views

Four vector potential and discrete parity transformations

I am having trouble understanding the effect of parity transformations on the four-vector gauge field (for example). I am working in three dimensions, but the analysis is probably not that different ...
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154 views

Why and how Dirac cones are “tilted”?

Given a Weyl Hamiltonian, at rest, $ H = \vec \sigma \cdot \vec{p} $, A Lorentz boost in the x-direction returns $ H = \vec\sigma\cdot\vec {p} - \gamma\sigma_0 p_x $ The second term gives rise to a ...
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Many-body relativistic classical Hamiltonian

All classical mechanics textbooks I know only discuss the one-body Hamiltonian in an external field $$H = \sqrt{m^2c^4 + c^2(\mathbf{p}-e\mathbf{A}/c)^2} + e\phi$$ Jackson in his celebrated textbook ...
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Geroch's (Splitting) Theorem & Minkowski spacetime

Reference: Topology in General Relativity (R. P. Geroch, J. Math. Phys. 8(4) April 1967) Geroch's "Splitting" Theorem (Theorem 2) applies to spacetimes with compact geometries with boundary. ...
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Reference recommendation: QFT in arbitary dimensions $D=1+d$

When I self-study the QFT, I found that many results in textbook heavily rely on the dimension $1+3$. For example, I heard "In 3+1 dim, Majorana fermion cannot have well-defined handedness. But in ...
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335 views

4-vector from a spinor

Currently reading Aitchison's book on SUSY, and on page 35 (section 2.2) he asks the reader to prove that $\bar{\Psi}\gamma^\mu\Psi=\psi^\dagger\sigma^\mu\psi+\chi^\dagger\bar{\sigma}^\mu\chi$ ...
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116 views

Better explanation of propagation of gravity

There is a nice demostration picture concerning the propagation of gravity in finite time: http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity_pathway/#Starting It says: ...
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493 views

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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295 views

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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How do the electromagnetic properties of a dielectric change at relativistic speeds?

If I have a dielectric structure moving at velocity $v = \beta c_0$ relative to an observer, how do the electromagnetic properties change under relativity. Can this induce anisotropy or other ...