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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What is the covariant version of the dipole moment?
Magnetic dipoles in a rest frame behave as a mixture of dielectric dipoles and magnetic dipoles in another moving frame. However this is sometimes controversial due to Mansuripur's paradox (see ...
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What's the difference between Lorentz transformation properties of Hermitian and Dirac adjoint lepton doublets?
If the lepton doublet transforms like a left-handed Weyl spinor under Lorentz transformations,
$$
L \longrightarrow exp\left[\frac{1}{2}(i\theta_j\sigma^j - \beta_j\sigma^j)\right]L = \Lambda_{sL}L,
$$...
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Dimension of a vector space of all tensors of rank $(k,l)$ in 4D
Dual vector space is the set of all linear functionals defined on a given vector space. The vector space and dual vector space is isomorphic and hence have the same dimension. A rank $(k,l)$ tensor is ...
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Time dilation and contradiction
Suppose we have a reference $R$ and a reference $R'$ with velocity $v \ne 0$ respect to $R$ then we know that:
$$\Delta t = \gamma \Delta t'$$
but respect to $R'$ the reference $R$ has also velocity $...
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Original Einstein papers on theory of relativity
I am looking for definitive way to get einstein original paper on theory of relativity which is both papers of special relativity and general relativity. I am software engineer with graduation in ...
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Relation between Lorentz transformations in QFT and GR [duplicate]
I often have difficulty expressing certain doubts because I am not (not even my self, yes) fully aware of what's going on that bothers me, so forgive me if the question isn't the clearest.
I noticed ...
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What is the velocity in the Lorentz equation relative to when considering a vacuum?
The Lorentz Equation
$\mathbf{F}=q(\mathbf{E}+\mathbf{v} \times \mathbf{B})$
involves a velocity vector $\mathbf{v}$. What is this velocity relative to? Based on e.g. this resource, it seems that when ...
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Gravity vs. EM: action at a distance
Countless texts point to Newton's theory $\nabla^2\phi = 4\pi G\rho$, and remark that the problem here is that a distribution of mass determines the potential instantaneously everywhere, which is ...
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Does Special Relativity apply to waves or particles?
I know that Special Relativity is a classical theory, so perhaps it applies to light waves, but I'm not too sure. The question I want to ask is, does Special Relativity set a bound on particle ...
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Time dilation calcs don't match values cited in recent media
Been reading a lot lately about how space agencies are talking about setting up timekeeping on the Moon and sync that with Earth's system. Nearly every article I read cites: time on the Moon runs ...
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Proving that commutator algebra of Dirac matrices are isomorphic to that of matrix generators of lorentz group
In the exercise 2.6 for Supergravity by Freedman and van Proyen I am asked to Use (2.4) to show that the commutator algebras of $\sigma_{\mu \nu}$ and $\bar{\sigma}_{\mu \nu}$ are isomorphic to (1.34)
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Relativity, communication and reference frames [closed]
Quick question here.
Does communication in special relativity involve sending signals from contrasting reference frames? I gather reference frames aren't really physical things, they're mathematical ...
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Finding how velocity changes with proper acceleration in a different direction
The velocity of a body relative to an inertial frame moving with a constant proper acceleration is a well-known problem, whose solution as $v(t) = c\tanh(gt/c)$ (where $t$ is proper time and $g$ is ...
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Twins paradox, Christmas photo album edition [closed]
Twin A leaves Earth in a spaceship while Twin B stays on Earth. They both agree that at the one year anniversary of their separation, according to their local clock, they will take a photo of ...
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Could inhomogeneties and/or topological defects break the fundamental symmetries of the universe?
I have heard that some types of inhomogeneties and topological defects (like cosmic strings) in cosmology have been proposed to be able to break fundamental symmetries of nature such as the Poincaré, ...
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Contraction of distances in explanation of relativity of simultaneity in special relativity
I was going through my old college notes on special relativity and found a reasoning that a professor used to explain why the simultaneity of events is relative. But I believe there is a mistake in ...
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How to interpret the soft theorem consequence that the gravitational charge of massless particles is $2E$?
In Weinberg's 1964 paper "Photons and Gravitons in S-Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass" where he proved the leading soft photon ...
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Lorentz transformation and special relativity: Why the equations must be linear? [duplicate]
I'm reading Einstein's paper on special relativity (On the electrodynamics of moving bodies 1905), it gives a derivation of the lorentz transformation. In the derivation, he compares the stationary ...
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Experimental evidence that a particle experiences time?
It is a famous fact that massless particles don't experience time, i.e. have no well-defined proper time. Conversely, massive particles can meaningfully be assigned a proper time parameter; they do ...
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Why Lorentz transf. representation in spin 1/2 particles Hilbert space is not a unitary operator? [duplicate]
Weinberg introduces the idea of Lorentz group representation describing how vectors in the Hilbert space of definite momentum states should change due to a L.T. It is understandable that to preserve ...
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Lorentz/rotational invariance parameter doesn't vanish on boundaries
As I know Stress-Energy tensor is defined as Noether current under arbitrary coordinate transformations $\boldsymbol{x} \rightarrow \boldsymbol{x}+\epsilon(\boldsymbol{x})$.
$$
\delta_\epsilon S=\int_{...
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Is there a Lorentz invariant electromagnetic quadrupole moment tensor?
I'm familiar with the electric and magnetic quadrupole moment tensors. However, I'm bothered that these objects are tensors only in the sense of spatial rotations. After all, Maxwell's equations and ...
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Would everything we see be delayed if light slowed down to 1ms?
I don't know much about physics, though it certainly interests me. so I apologize if this is a dumb question, but if we somehow slowed down the speed of light around us. (like we somehow made air have ...
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What is the three-parameter family of time translation Killing field in Minkowski spacetime?
In section 5.1 of Wald's Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, there are two paragraphs before the discussion of Unruh effect as follows.
Let us reconsider the ...
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Stuck on thought experiment about light [duplicate]
Say we have a very long fluid pipe with the width of a few astronomical units, and that this pipe is perfectly resistant to sustain the stress of a perfectly incompressible fluid going through it ...
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Does Special Relativity assume a finite $c$?
Does SR explicitly assume $c$ to be finite?
If so, by what statement in Einstein's original paper is this implied?
If not, what to make of equations containing $c$? (e.g., $E = mc^2$)
Formulating the ...
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Can there be a repulsion between an electron beam and a proton beam depending on the beam's velocities?
We have two beams side-by-side: an electron beam and a proton beam. I understand that there will be a force of attraction between them (opposite charges).
But can this force turn repulsive if:
the ...
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How does the Kennedy-Thorndike experiment test for time-dilation?
From the Wikipedia page (as of 3/6/2023),
The Kennedy–Thorndike experiment, first conducted in 1932 by Roy J. Kennedy and Edward M. Thorndike, is a modified form of the Michelson–Morley experimental ...
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Can transverse waves be both mechanical and non-mechanical?
Transverse waves need a medium for particles to propagate perpendicular to the wave right? Then how can transverse waves be non mechanical which do not require any medium?
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How does special relativity affect absorption spectra? [closed]
Metal reflects radio waves but absorbs UV.
Suppose a spaceship was burning towards Earth near the speed of light and a dish on Earth sent out a radar pulse. From Earth's perspective, the photons reach ...
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Would an object travelling close to the speed of light gather a lot of energy?
Quick disclaimer: I don't know much about physics, so I don't really know what I'm talking about.
The idea
The idea is that an object traveling fast enough in space will be receiving more radiation ...
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Invariant nature of mass and particle annihilation [closed]
Since mass is a Lorentz invariant, it can never change to preserve the vectorial nature of the four-momentum and the other four vectors. Thus the only interpretation of the energy-mass equation that I ...
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Question on the value of speed of light, non-inertial frames and equivalence principle
One of the axioms of special relativity concerns on the value of speed of light measuread by a family of inertial observers. They must measure $c$.
Now, the global inertial frame is lost if the ...
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Acceleration perpendicular to constant velocity in special relativity
In newtonian mechanics, if a body is experiences an acceleration that is perpendicular to the direction of motion at all times, it moves in a circle and the magnitude of it's velocity does not change....
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How to determine the electric and magnetic fields from $*F=q\sin \theta d\theta \wedge d\phi$?
I have the 2-form $*F=q\sin \theta d\theta \wedge d\phi$, how can I determine the eletric and magnetic fields from that?
I have tried wrtting F in the vector potential form for them finding the ...
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Confusion about Lorentz invariance of scalar product
I am a bit confused about the way that Lorentz invariance of the scalar product $A^\mu g_{\mu\nu}B^\nu$ is proved. Usually, the proof would go like this (see also e.g. this Physics SE question). The ...
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Principle of relativity and the train and ball example
I have a question about the theory of relativity. I took a lesson on brilliant.org, maybe you have heard about this educational platform.
And the example with the ball and the train is completely ...
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How do projective representations act on the QFT vacuum?
Let $U:\mathcal{G}\to \mathcal{U}(\mathcal{H})$ be a unitary projective representation of a symmetry group $\mathcal{G}$ on a Hilbert space $\mathcal{H}$. It satisfies the composition rule:
$$U(g_1)U(...
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Projective representations of the Lorentz group can't occur in QFT! What's wrong with my argument?
In flat-space QFT, consider a spinor operator $\phi_i$, taken to lie at the origin. Given a Lorentz transformation $g$, we have
$$\tag{1} U(g)^\dagger \phi_i U(g) = D_{ij}(g)\phi_j$$
where $D_{ij}$ is ...
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Can a rotating body see it's own reflection?
So my question is this: Say I'm able to get close to, but not achieve the speed of light. I want to look at the back of my head in the mirror, would it be possible to turn around before the light from ...
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Classical EM wave energy proportional to frequency ( valid argument)?
I remember coming up with this argument as an undergrad and it came back to me the other day. I was curious: is the argument a valid one?
The following is purely classical.
Consider a plane ...
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ONLY non-relativistic limit of general relativity
From my study of GR I learnt that to reach the “Newtonian” limit of the Einstein field equation we have to assume:
weak field $g_{\mu\nu} = \eta_{\mu\nu} + \epsilon h _{\mu\nu}$ with $\epsilon <&...
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Relativistic particle in circular motion
Imagine a relativistic particle in a circular motion, e.g. electron in magnetic field. We can easily obtain the centripetal acceleration in laboratory frame using : $$F= evB = \frac{dp}{dt} = \frac{d(\...
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Minkowski inner product
I'm elementary in physics and I have a question about a notation. In the book, the author says that the rotation group is the set of linear transformations on $\mathbb{R}^n$ preserving the inner ...
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Velocity addition formula in non-inertial frames
I am a beginner in SR, so the following may seem to be basic. I cannot find any answer in the text books. If there is any, I would appreciate the reference.
The well-known thought experience used to ...
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Do generators of translations transform as *covariant* vectors under a homogeneous Lorentz transformation?
Using the composition law of Poincaré transformations, it is easy to see (cf. e.g. Ref. 1 this answer) that under a Lorentz transformation
$$\underbrace{U(\Lambda,0)P^\mu U(\Lambda,0)^{-1}}_{P'^{\mu}}=...
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Question about Time Dilation [closed]
I was studying about Time dilation and I wondered, does Time seem less for a moving body, or does it seem less for a resting body, both relative to each other, or does both occur at same time?
Meaning ...
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Is Time Dilation Directional Under Special Relativity, What Fundamental Concept Am I Missing Here?
I'm starting college this summer and trying to learn physics. Special relativity is new. I thought I was getting a handle on it but nope... I'm just trying to nail the concepts down to give the math ...
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Field representations - problem with differential
So when we talk about scalar fields in spacetime, we set that $\phi(x) \rightarrow \Lambda\phi(x)\equiv\phi'(x'). $ So that in the same event, the field value is the same for different frames $\phi'(...
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Light-like interval and simultaneity [closed]
Why if the interval between two events is light-like then there is no frame of reference where the events occur at either the same time? If I assume that the 2 events happen at the same time, I arrive ...
