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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Fate of largest scale structures?

In $\Lambda\mathrm{CDM}$, structures form "bottom up" with larger structures forming later. Structures are generally speaking supported by the velocity dispersion of their constituent objects (e.g. ...
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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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2answers
174 views

Upper limits for jerk and higher derivatives in physics

Is there an upper limit for jerk in physics? What about higher derivatives? A consequence of special relativity is that no material body can reach or exceed the speed of light in vacuum (due to ...
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700 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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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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467 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 ...
7
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1answer
692 views

Hidden momentum

I'm trying to learn about hidden momentum. After reading what I could find with a google search, I understand that it is equal to the momentum carried by radiation, calculated with the Poynting vector....
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208 views

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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230 views

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%...
5
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1answer
189 views

Planck length at relativistic speeds?

Im currently in high school so sorry if the answer to this question seems obvious but i’m only just learning about this stuff. I’ve been learning about special relativity, in particular length ...
5
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386 views

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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348 views

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 ...
5
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1answer
443 views

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 ...
4
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1answer
108 views

Connection between gauge invariance and Lorentz invariance

This question is presented in the context of Weinberg's QFT book treatment, in particular considering the electromagnetism chapter. It begins in chapter 5 where Weinberg argues that in order to have ...
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94 views

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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121 views

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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44 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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60 views

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 ...
4
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339 views

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 ...
4
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6answers
805 views

Time dilation and uniform motion

Assume a period of uniform relative motion (no acceleration) of a spaceship in reference frame, B, going 80% of light speed observed from my reference frame, A, when it passes by Earth (my references ...
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354 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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511 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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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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154 views

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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108 views

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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153 views

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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285 views

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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118 views

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 ...
3
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1answer
114 views

Can we talk about velocity field and acceleration field in 1D?

It's well know that a charged particle radiate when it is accelerated. We can rely on two different formulas. The first one it's from Jefimenkos : $$\mathbf{E}(\mathbf{r}, t) = \frac{1}{4 \pi \...
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Twin Paradox in String Theoretical Backgrounds / Compactifications

It is a common exercise while learning special relativity to work out the resolution to the twin paradox. As an extension, I have looked at the twin paradox with compact dimensions, i.e. having an ...
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Question about the travel time of a ship “using” a warp drive metric

I - The Warp Drive metric: The Warp Drive is a geometry in a spacetime $(\mathcal{M},g)$ given (in geometrized coordinates $c=G=1$) by the following metric tensor: $$ ds^{2} = -dt^{2}+ (dx-v_{s}f(...
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1answer
132 views

Relative speed when getting close to the speed of light

I was thinking about the relative speed of an observation reference frame and an object which has been accelerated to a speed close to the speed of light. I'm by no mean an expert and the last physics ...
3
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38 views

Effectively Lorentz-invariant interacting Lagrangians in solid state?

Are there any known examples in solid state physics when an essentially non-relativistic system in certain regime may be described by a relativistically invariant Lagrangian with an interaction? ...
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50 views

Has this group something to do with the cone of light?

Consider the group $V=(-1,1)$ with addition $+_{rel}:V\times V\to V$ defined as: $$v+_{rel}w=\frac{v+w}{1+vw}$$ This group is analogous to the relativistic velocities where the speed of light equals ...
3
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2answers
107 views

Why would a spinor transform under Lorentz transformations?

From my understanding of spinors, they arise as projective representations of $SO_0(1,3)$ that do not correspond to representations of $SO_0(1,3)$. But still one says here - and virtually everywhere - ...
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55 views

Timelike, spacelike etc. for higher-order tensors

Vectors $V^\mu$ in relativity can be classified into those which are timelike, spacelike and null. A similar classification is available for tensors: A tensor $$T^{\mu_1\mu_2...\mu_p}_{\phantom{\mu_1\...
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Proper time for a relativistic particle in quantum mechanics?

It is an often cited fact that a muon falling through the atmosphere at great speed has a decay time longer than the one we would observe in the same particle at rest due to relativistic effects, and ...
3
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32 views

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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56 views

In Einstein's 1905 paper on electrodynamics, what he meant by energy of electromotive force?

In his 1905 paper, Einstein says that when the magnet is in motion and conductor stationary, changing magnetic field in space develops electric field "of certain definite energy", and this starts ...
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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 ...
3
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1answer
68 views

Faster than light speed transfer of certain event

I am CS/Math person I am not quite sure what it means in physics information cannot be transferred faster than light (FTL). I tried to understand the proof of no transfer theorem but I lacked the ...
3
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1answer
95 views

When do Lorentz transformations take straight field lines to straight field lines?

If you look at elementary examples, it seems like a Lorentz transformation takes a field pattern with a lot of straight field lines to another field pattern with a lot of straight lines. Examples: an ...
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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 ...
3
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2answers
149 views

Klein Gordon equation in the nonrelativistic and semiclassical limit in a Wigner approach

I would like to analyse the semiclassical and nonrelativistic limit of the Klein-Gordon equation, \begin{equation} \frac{1}{c^2} \partial_t^2 \phi - \Delta \phi + \frac{M^2 c^2}{\hbar^2} \phi =0. ...
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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. ...