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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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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Train with proper length $L$ and speed $V=\frac{3}{5}c$ is passing through a tunnel with a proper length $L$ [closed]

The time it takes for train to enter and exit the tunnel is, $$\tau=\frac{2L}{V}=\frac{2L}{\frac{3}{5}c}=\frac{2L}{1}\frac{5}{3c}=\frac{10L}{3c}$$ with respect to frame $S$ which is stationary ...
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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 so length contraction. I can't figure out the logic or algorithm of calculating lengths in length contraction problems. Let me explain where I stuck. As you ...
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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 simultaneos events are happening in a stationary inertial frame of reference (S), but they are happening at difference positions. First event is happening at $x=x_1$ $t=t1$, second event is ...
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How do we calculate the contracted distance in boat frame of reference in classical river boat problem if we consider velocities are large?

Suppose we are given velocity of boat in y direction |V(y)|=0.9c and velocity of width which will be |V(x)|= 0.5c. Now we have to calculate net displacement ( magnitude of displacement in xy plane. ...
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Energy momentum tensor and 4-velocity

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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Light from a star orbiting a black hole, as measured by a distant observer

The spectrum of a hypothetical star has an absorption line at a frequency $f_\text{emit}$. The star orbits a non-rotating black hole with a mass $M$. The circular orbit is at Schwarzschild coordinate $...
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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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Does one observe light reach infinity in finite time in AdS spacetime?

I have a question about the following passage from this article: Moschidis imagined standing in the middle of AdS space-time, which would be like standing inside a giant ball whose edge or boundary ...
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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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Space Time diagrams, [closed]

I am working through Minkowski Space Time and Vectors in Relativity and I am given the following question set of questions. I am relatively new to physics and relativity: Consider the situation in ...
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Mass and velocity from relativistic momentum [closed]

I seem to be struggling to grasp the concept of relativistic momentum and how to manipulate equations pertaining to it. I am very new to relativistic mass and momentum. The problem is as follows: A ...
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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 ...
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Why don't (or why do) current carrying wires attract a stationary charge placed at a distance?

I've learned that moving charges produce magnetic fields which in turn affect other charges in motion. After seeing explanations that point to special relativity, I am kind of confused. Can ALL ...
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Lorentz transformation: qualitative explanation

Long story short, how can I qualitatively explain what is the Lorentz transformation and why it does so? I am looking for a description of its general behavior instead of "it works due to an XYZ ...
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How to find the 3-direction Lorentz boost transformation on Dirac spinor?

I am struggling to work out correct Lorentz transformation for a boost in the 3-direction on a Dirac spinor, $u(p)$. According to Peskin & Schroeder pg. 46, I need to use the equations: $$S^{0i} ...
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Space Time Diagram - world line of a wave

My understanding so far: A wave is a vector field defined on the space-time. i.e. mathematically wave is just a mapping which for every point in the space-time maps it to a vector. A world-line is ...
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Relativistic Force and Non-tangent initial velocities

Dear physics stack exchange, I was looking over the darker non-mainstream physics wing of youtube when I came across a video with a person who gave a simple experiment to prove you could accelerate ...
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Is there a formal distinction between Lorentz boosts and the others types of transformations of the Poincaré group?

The doubt arises as space translations can be associated to homogeneity of space, time translations to homogeneity of time and classical rotations to isotropy of space. These properties of space leads ...
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Electromagnetic four-potential manipulation

I was looking at my special relativity notes and when covering EM, I was wondering if the following is true? Namely, given the four-potential $A_{\mu}$, by definition it is that: $F_{\mu \nu} = -A_{\...
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Speed of particle due to Lorentz transformation [closed]

A particle moves with speed $u$ along the $x^3-$ axis of the inertial frame with co-ordinates x so $$x^3=\frac{ux^0}{c}$$ I am trying to find the speed of the particle in the co-ordinates x' where $x'...
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Relativistic doppler effect with photons

Suppose $2$ photons move along the $x$-axis in opposite directions and collide head on. They fuse to form a single particle with rest mass $M$, which then decays to produce $2$ particles moving in ...
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Can I write the following eq. (2) with the metric tensor?

I'm a beginner at relativity, I have a question about eq 2 if its true. I know that the interval can be calculated like this in special relativity: $$ ds^2 = \eta_{\mu\nu}dx^\mu dx^\nu \tag{1} $$ ...
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Show that quantity transforms as components of vector under Lorentz transformation [closed]

If $J^\nu=\frac{\partial{H^{\mu\nu}}}{\partial x^\mu}$, and $H$ depends on position in spacetime, how can I use the chain rule to show that $J^{\nu}$ transforms as the components of a vector under ...
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What is the physical interpretation of the Lorenz gauge condition?

If we integrate both sides of the Lorenz gauge condition, $\nabla \cdot \mathbf{A} = -\frac{1}{c^2}\frac{\partial \phi}{\partial t}$, over a small volume (free of charges for simplicity), we get: $$ \...
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Resource regarding Metric Tensor in Special Relativity

I am studying Special Relativity along with the tensor notation used there. I do not know General Relativity but I have heard that Special Relativity is formulated in pseudo-flat space. I am ...
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Deriving the $0$-component of 4-momentum using the relativistic Lagrangian

My question arises from Susskinds book on Special Relativity and Classical Field Theory. (page 102 equation 3.29 to 3.30 and page 105 equation 3.34 to 3.36.) The relativistic Lagrangian for a free ...
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Help at dismissing a time dilation “paradox” [duplicate]

If Observer A moves at speed $v$ respect to observer B, then there is a time dilation given by $$t_B=t_A\gamma$$ as is known from special relativity. Here, $t_A$ is the time interval measured by A ...
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Special Relativity - Doppler Effect

The question is about problem 4.3 in Rindler's book - Relativity Special, General and cosmological, namely Problem 4.3 - In some inertial frame $S$ a ray of light travels along a straight line which ...
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Special Relativity metric and imaginary sentence [duplicate]

we know that the simple form of the metric in the special relativity is like this: $ds^2 = dr^2 - (cdt)^2$ that in this metric $dr^2 = dx^2 + dy^2 + dz^2 .$ I want to ask why we minus the time ...
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Is there any connection between special relativity and general relativity? [duplicate]

Is there any connection between special relativity and general relativity? We know that gravity causes relativistic effects according to general relativity which car similar to special-relativity. so ...
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Properties of timelike congruences in flat spacetime

I'd like to learn about (or confirm) certain properties of congruences, concerning some presumably rather simple cases, namely of timelike congruences in the setting of flat spacetimes $\mathcal S$. ...
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“Micro” explanation for time dilation? [duplicate]

I understand the explanation, for example, about a light beam reflecting between two mirrors on the space craft. But what I am looking for is what aspect of traveling at very high velocities must slow ...
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Interpretation of different types of transformations on fields in the case of Poincaré group

I have problems understanding how transformations of Lorentz or Poincaré groups act on fields. We can think about two ways of transformation of a field $\phi_r(x)$: $$\phi_r(x) \rightarrow \phi^{'}_r(...
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Special relativity and biology of human

There is something I do not understand and its pretty bother me, if I have a twin and we both in our 20's now lets assume I take a trip to space close to the speed of light, when I will come back I ...
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Tensor derivative in special relativity and fluid mechanics

I’m working through Special Relativity by V. Faraoni, and am puzzled by something in his chapters on tensors. He tells us that the partial derivative of a tensor field, e.g. $T_{\alpha, \gamma}$, is ...
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Can you demonstrate the Twin Paradox using a Schwarzschild spacetime?

Short Version: If we want to solve a problem where a particle is forced off a geodesic, can we obtain identical results if we instead solve the problem where the particle is in a different spacetime ...
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Conceptual question about special relativity in electrodynamics

I‘m currently taking Physics II and I have a conceptual question about SR in edyn. Suppose I have two electron beams with linear charge density $\lambda$ paralell two each other in a resting system $...
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Understanding Length Contraction

I am learning Length Contraction from the book Special Relativity and Classical Field Theory by Leonard Susskind. There are two frames with relative speed $v$ along the x-axis. If my frame is at rest, ...
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Minimal coupling in Dirac equation

In the framework of relativistic quantum mechanics (not QFT) the Dirac equation in presence of external electromagnetic field is obtained by means of the minimal coupling, i.e. the substitution: $$p_{...
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For this derivation of time dilation, what is the orientation of the electric and magnetic fields in each inertial frame?

I wanted to review special relativity having now completed my junior year at college and my Intro to Electrodynamics course this past semester. Since we covered Griffiths' Intro to Electrodynamics ...
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Understanding Four Force as a relativistic generalisation of Newtonian Force

I am reading Special Theory of Relativity from the Lecture Notes http://joelcorbo.com/docs/notes/special-relativity-part-2.pdf. I have a doubt in the topic Four Force in page 21. The expression for ...
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Are John Norton's and Wolfgang Rindler's notions of “inertial frame (in special relativity)” equivalent?

Among the (several) descriptions of an "inertial frame" (in the context of the Special Theory of Relativity), those by John Norton and by Wolfgang Rindler appear especially concise: "In special ...
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Is this 4-vector identity $k^\mu k^\nu = \frac{1}{4}k^2\delta^{\mu\nu}$ correct?

I've often seen the identity \begin{equation} k^\mu k^\nu = \frac{1}{4}k^2\delta^{\mu\nu} \tag{1} \end{equation} used in various derivations (for example, see Schwartz QFT pg. 625). This result ...

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