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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Terrell “rotation”: should wikipedia be corrected? [closed]

There are two common misconceptions regarding the Terrell "rotation" : it's a pure rotation the Lorentz-Fitzgerald contraction is not detectable by a single detector, in which the past ...
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Can time dilation affect time taken?

Take an example of a space ship moving at speed comparable with speed of light (like 60% of c) now if spaceship launched from earth to near star does time dilation affects the time taken by space ship ...
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Is the Dirac equation really covariant under Lorentz transfromations or do we just “make” it covariant?

I often read that the Dirac equation is covariant under Lorentz transformations and that this property makes it the right equation and in some sense beautiful. The thing is, the equation $$ \left(i\...
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Simultaneity problem with train and platform observer [closed]

The problem is quite simple but there might be something I'm not getting right or I must have missed some concept. Suppose we have a train moving in $y (ĵ)$ with $ v = v(-ĵ)$. The reference event is ...
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How do slanted indices work in special relativity? [duplicate]

What is the difference between $T^{\mu}{}_{\nu}$ and $T_{\nu}{}^{\mu}$ where $T$ is a tensor?
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How electric fields and magnetic fields are connected?

I'm not a physicist, but I have been reading several sources of how electric fields and magnetic fields are connected. One question in particular (How do moving charges produce magnetic fields?) ...
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Bloch Component under Lorentz Condition

Suppose we have Gaussian state in the momentum representation $$ a(\textbf p) = (2\pi)^{-3/4}w^{3/2}exp(-\textbf{p}^2/2w^2) $$ and a state $$b(\textbf p) = K\text{sinh}(\frac{\alpha}{2}) q_z a(\...
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Nature of spacetime interval

So, in the case of special relativity, we look for transformations relating inertial coordinates that leave the spacetime interval invariant and these transformations turn out to be generated by three ...
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Spinning observer inside a solenoid paradox?

It is well known that magnetic fields are frame dependent, with an observer travelling parallel to a moving point charge experiencing no field. Similarly for a solenoid, a stationary observer on the ...
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Is length contraction a physically real phenomenon? [duplicate]

Could someone explain a bit length contraction. According to the special theory of relativity objects that travel at relativistic speeds will decrease in length. Do the atoms of the object come ...
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Thomas-Wigner rotation of a stick directly from the Lorentz Transformation

I'm trying to better understand Thomas-Wigner rotation. I understand how to calculate it for the case of a perpendicular pair of boosts. But I also want to see the rotation more directly. The effect ...
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Which particles do not fit into Wigner's picture?

In his accepted and highly upvoted answer to Why particles are thought as irreducible representation in plain English? @Valter Moretti finishes his ADDENDUM with "Finally not all particles fit ...
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Differential form of the velocity equation in non-standard configuration

I'm reading a text on special relativity ($^{\prime\prime}$Core Principles of Special and General Relativity$^{\prime\prime}$, by James H. Luscombe, Edition 2019), in which we start with the equation ...
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Transformation of the frequency of a photon after an infinitesimal coordinate transformation

I am having trouble understanding a calculation done by V. Mukhanov in his book "Physical Foundations of Cosmology". In the beginning of the chapter 9, the following arguments are stated: ...
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Proving that timelike and spacelike spacetime intervals are invariant across inertial frames

I'm trying to understand the justification for using the Minkowski metric. It's clear to me that it's the natural choice of metric given that spacetime separations denoted by $(-c^2\Delta t^2+\Delta x^...
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Absolute Space & Inertial Frames

When we solve the twin paradox we say something like the traveling twin has a Rindler Metric while the stationary twin has a Minkowski metric, or more plainly, the traveling twin experiences non-zero ...
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Degeneracy of relativistic hydrogen

According to Sakurai's Modern Quantum Mechanics, we can choose different parity for the wave functions of relativistic hydrogen atoms. However, when calculating the state degeneracy, we don't ...
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Tachyons and Speed of light [duplicate]

Hi guys I am so sorry if the question maybe odd or not right but I am not an expert in this area I do apologise in advance if the questions is actually stupid. I was a reading a bit of relativity and ...
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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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Are the $\alpha$ and $\beta$ matrices of the Dirac equation unique?

Assume we are dealing wth three spatial dimensions $d=3$ which requires 3 $\alpha$ matrices. Furthermore assume that we are looking for them in the space of 4-dimensional matrices, not in higher ...
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Experiment in General Relativity and Special Relativity [closed]

Could you give me two experiment results that are consisitent with the prediction of general relativity, but inconsistent with the prediction of special relativity + Newton’s law of Gravitation ?
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Formal definition of charge density and current sources in classical electromagnetism

Charge density and current sources are fundamental to classical electromagnetism and appear in Maxwell's equations and everything that comes after. They are intuitive, charge density is a scalar field ...
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Index notation and total differential

I understand that the gradient $\partial_i$ is covariant. Let f be a function of 3 variables So I can write the total differential as $$ df=\partial_1fdx^1+\partial_2fdx^2+\partial_3fdx^3 = \...
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Why is the concept of state kets not used in relativistic quantum mechanics?

In Sakurai's Quantum Mechanics the concept of a Hilbert space underlying classical quantum wave mechanics (Schrödinger equation) is extensively developed. But when dealing with the Dirac equation this ...
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Potential well: Why non-relativistic kinetic energy?

When studying a potential well, the energy is defined as that: $E=\frac{\pi h^2 n^2}{2ma^2}$ and then some books say $E=\frac{p^2}{2m}$. Why energy is just kinetic energy and we aren't considering ...
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Can length contraction actually be seen in the real world? Light from different parts of an object will reach an observer at different times

The following passage comes from a high school physics textbook, in a chapter about special relativity and length contraction. Specifically, an example was given about a train travelling at ...
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Invariance of Inner product between 4-velocity under general coordinate transformation

I know that inner product between 4-velocity is invariant under Lorentz transformation and I know that inner product between any 2 vectors under general coordinate transformation is invariant. ...
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What does this statement signify?

With ref. to "Introduction to Special Relativity by Robert Resnick (1968)" In the book, while explaining the Michelson Morley experiment there's a statement on pg. 21 that says "If $...
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Proper Velocity $v$ Relative Velocity

I understand the proper velocity is the velocity as measured by the traveler, and relative velocity as measured by the observer. Relative velocity is limited to $c$, but is that also true of proper ...
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Force between a second and third body is such that they are rigidly bound together to form a composite body

I am currently studying the textbook Classical Mechanics, fifth edition, by Kibble and Berkshire. In classical mechanics, we have that $$m_1 \mathbf{a}_1 + m_2 \mathbf{a}_2 + m_3 \mathbf{a}_3 = \...
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A free particle moving faster than light? [duplicate]

Say I observe a free particle at the origin at time $t=0$, for $t>0$ the particle is free and hence its wavefunction evolves in space as time passes. Now if it's wavefunction has non zero amplitude ...
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Why is it problematic to regard the Lorentz group as ${\rm SO}(4, \mathbb{C})$? [duplicate]

If the four-vector $x^\mu$ is defined as $x^\mu\equiv(ict,{\bf x})$, instead of $x^\mu\equiv (ct,{\bf x})$, the Lorentz group will be the compact(?) ${\rm SO}(4, \mathbb{C})$ group. But the Lorentz ...
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Need helps understanding Relativistic mechanics

Could anyone explain the equation for total energy and relativistic momentum, why do they have a Lorentz factor in them? I also understand that these equations are derived such that they keep the laws ...
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Is the FRW metric physically distinguishable from a metric with a speed of light that changes over time?

There are many questions on this site that ask whether the expansion of space could instead be interpreted as a speed of light that changes over time, e.g.: Has the speed of light changed over time? ...
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Relativistic electromagnetism help: Current carrying wire

I am looking at the first three pages of this file (https://www.mtholyoke.edu/courses/tdray/phys310/electromag.pdf). In the lab frame, there is an infinitely long wire stretching from left to right, ...
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Causality: Two definitions

The general definition of causality is that the principle of the 'effect never occuring before the cause', as in Wikipedia. The book 'Picturing Quantum Processes' (pg: 262) defines causality as states ...
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Proving an object is a $4$-vector given its inner product with a $4$-vector is a scalar

Theorem: Suppose $A_{\mu}$ is a $4$-vector and $B^{\mu}$ is an object with $4$ components. If $A_{\mu}B^{\mu}$ is a scalar then $B^{\mu}$ is a $4$-vector. I have been stuck on trying to prove this ...
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Lorentz transformation of Weyl fields

In the Srednicki's textbook, Chapter 35, the author states (Equation 35.28): $$ U(\Lambda)^{-1}[\psi^\dagger \bar\sigma^\mu \chi ] U(\Lambda) = \Lambda^\mu_{\,\,\nu} [\psi^\dagger \bar\sigma^\nu \chi ]...
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Rotational motion and special relativity

I was trying to solve two questions from problem book on relativity and gravitation by lightman.Questions are Calculate the nonzero components in an inertial frame S of the stress-energy tensor for ...
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A question about length contraction

I'm new to special reltivity theory and length contraction. I can't figure out the logic or algorithm of calculating lengths in length contraction problems. Let me explain where I am stuck. There is a ...
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Time difference of two simultaneous events happening in an inertial frame of reference w.r.t another inertial frame of reference that is moving?

Two simultaneous events are happening in a stationary inertial frame of reference ($S$), but they are happening at different positions. First event is happening at $x=x_1$; $t=t_1$, second event is ...
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Weinberg QFT 1 Normalization one 1 particle states p. 66

I encounter a question regarding the derivation of the normalization of 1 Particle states in Weinbergs book (Formula 2.5.14). Similar questions were asked in A question on page 65 of Weinberg's ...
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Energy momentum tensor and 4-velocity [closed]

A rope of mass per unit length $\mu$ has a static breaking strength $F$. What is the largest possible $F$ that does not violate the weak energy condition, i.e. $T^{00}$ should be positive to all ...
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Elasticity of collisions in Relativity

Is it possible that collisions which are elastic in the rest frame of reference are inelastic or partially elastic in some other constant velocity frame? If you need to invoke general relativity here, ...
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Why the use of proper time as a parameter to describe the worldline only works for *massive* particle?

In Hobson et al, General Relativity: An Introduction for Physicists (pg. 15), it was said that it is natural to describe the worldline of a massive particle by giving the four coordinates $(t,x,y,z)$...
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How to integrate the infinitesimal spacetime interval? [closed]

Consider events A and B with coordinates $(t_A,x_A,y_A,z_A)$ and $(t_B,x_B,y_B,z_B)$ respectively. The spacetime interval $\Delta s$ between them is given by $$\Delta s= \sqrt{c^2\Delta t^2-\Delta x^...
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General form of the Lorentz Transformation

My textbook says: We take the most general transformation relating the coordinates of a given event in the two systems to be of the form: $$x' = Ax +Bt$$ $$y' = y$$ $$z' = z $$ $$ t' = ...
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What does the Problem 14 from Goldstein's book on classical mechanics chapter-7 (special relativity) really mean?

I am having difficulty in understanding problem number 14 in Goldstein's Classical Mechanics, 3rd edition, chapter 7 on special relativity. Here is the problem --- A rocket of length $l_0$ in its ...
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A question from Weinberg QFT (Sec. 5.1)

I'm studying QFT on Weinberg's book. And I have a question about its notation for Lorentz transformation property of the free fields (Chap.5). In Sec. 5.1 of Vol. 1, annihilation fields $\psi_{\ell}^{...
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Do stationary charges get attracted to a current carrying wire (due to change in electric charge density caused by length contraction)?

I've seen magnetic fields getting explained away by special relativity, for it accounts for the magnetism in the electron's reference frame as an electric field caused by a greater charge density due ...