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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Electron in a Magnetic Field: Force parallel to velocity?

According to the four-force given in this question, Force is parallel to velocity. But the Lorentz Force is perpendicular to velocity in a constant magnetic field. Is this a contradiction? [a ...
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Lorentz invariance & Noether theorem of classical ED

I want to check invariance of the action under Lorentz boosts for classical electrodynamics. The action is $$S = \int \mbox{d}^4x F_{\alpha \beta} F^{\alpha \beta} $$ I assumed that the fields ...
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Error in deriving constant acceleration relativistic distance

Bob accelerates away from Carol at proper acceleration $a$ (in light seconds per second), and Carol wants to know how far Bob has traveled when $t$ seconds pass in Bob's frame. Using ...
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36 views

Gradient of $ct'$ axis in spacetime diagrams

This is either an unimportant piece of information or it's meant to be obvious, but I can't find anywhere what the gradient of the $ct'$ axis in a spacetime diagram should be. I know that the $ct'=1$ ...
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Helicity of massive particle at high enengy

We know that massless spin-1 particle like photon only has two helicity state (-1,1), what about the helicity of massive spin-1 particle (W boson) at very high energy? Does it have helicity 0 state ...
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How do I make a slowly rotating neutron star using fortran code?

I make a slowly rotating neutron star code but I am little bit confuse, when I solved the coupled differential equation using runga-kutta 4th order method. These coupled differential equations as ...
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72 views

Derive Galilean transformation. (The meaning of the relativity)

In the book The meaning of the relativity Einstein says that in classic mechanics two postulates are previously supposed: 1.- The time is absolute. 2.- The longitude is absolute. And this implies ...
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42 views

Thought experiment on special relativity

If we were travelling in a spaceship, accelerating (arbitrary value) from a velocity 0, and we assumed that times and distances outside of the spaceship remained the same as that of ours, would we be ...
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What is wrong with this derivation of the lorentz factor

in attempting to derive the lorentz contraction, I assumed that light speed is measured the same from all inertial reference frames. The situation set up is object A is standing still, whilst object B ...
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Value of $E_x$ through an $X-\textrm{boost}$

Suppose I'm standing at the (0,0,0) point of a coordinate system and I see an electric field where $E_x=f(t,x,y,z)=\sin(x\cdot y\cdot z\cdot t)$ and at time $t_0=0$ I start moving on the x-axis at ...
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question dealing with time dilation and length contraction

In Einstein's theory of relativity and reference frames, It states that an observer on earth watching a spaceship fly at close to the speed of light heading away going towards a distance star that the ...
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How does length contraction map from a macro size object to its individual sub-atomic parts?

If an object consisting of many atoms is traveling close to the speed of light, explanations of length contraction seem to indicate the whole structure contracts. It seems easy to imagine an ...
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Finding an explicit expression for inverse of Lorentz transformation ${\Lambda^\mu}_{\nu}$

I'm studying in a module titled "Symmetries and Action Principles in Physics." I'm having a small trouble with the notation, I think, of special relativity. We have in the text In fact we may ...
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38 views

Is there a relation between time dilation and (relativistic) mass increase?

I noticed that what once called relativistic mass increase and now is called energy increase is ruled by the same formula the Lorenz factor of time dilation? The formula is too particular to suggest ...
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45 views

Relativistic oscillator vs. non relativistic oscillator

Consider a particle of mass $m$ that is constrained to move under the potential $U=k|x|$. In the case where the particle's motion is non-relativistic, the Lagrangian for the motion is ...
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67 views

How the state of elementary particles change under lorentz transformation?

Let us take three observers namely Alice, Bob and Charlie. Bob is stationary with respect to Alice, but his axes are rotated from her's.We can get Bob's coordinate axes by rotating Alice's through 60 ...
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24 views

Understanding what a tranformation on a Ray and Hilbert space

I've been referring to Chapter 2 of Introduction to Quantum Field Theory by Weinberg where he talks about symmetries and how they go about. Now, there are two points that he mentions. A ray, which by ...
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36 views

Relativity of simultaneity: light source inside and outside

(Orange are light sources and red are observers) There is a train, which is moving right. In each side, there is a light source, which emits light when the train passes certain point on a track. And ...
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A few positrons collide with a solid body at rest; what can happen?

Suppose we have a macroscopic solid object. Now we have a beam of Positrons that is injected into this solid Body at vacuum. What can happen? There will take place a pair Annihilation of electrons ...
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Need some help understanding Relativistic Notation

My question originates from what is done in the book on Quantum Field Theory book by Mark Srednicki on page 21 (if anyone has it). So say you have an inertial frame that is represented in the ...
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Does Gauss flux theorem hold in relativity?

Does the Gauss flux theorem, stated in the classical electrostatics as $\iint{\vec{E}}\cdot{\vec{dS}}=q/\epsilon_0,$ hold in the case of relative motions. For instance if we observe a charged body ...
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35 views

Electromagnetic tensor in cylindrical coordinates from scratch

I want to calculate the electromagnetic tensor components in cylindrical coordinates. Suppose I did not know that those components are given in Cartesian coordinates by $$(F^{\mu \nu})= ...
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76 views

Why did Einstein allow unphysical objects in his 1906 paper on $E=mc^2$?

In the first part of this paper, Einstein considers a "rigid cylinder", "massless cavity", as well as a "massless carrier mechanism" that is used to transport the massless cavity. These hypothetical ...
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Transformation of coordinates in relativity

I'm doing some self studying through a textbook. Here I will post the question exactly, and show what I have done to solve the problem. I'm completely convinced there is an error in the text, and I ...
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Are there (interesting) Poincare-invariant QFTs with non-invariant Lagrangian densities?

In all QFTs I know, the Lagrangian density is completely invariant under the Poincare group, $$ \mathcal L \to \mathcal L. $$ On the other hand, the action would be invariant even if the Lagrangian ...
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Linkal causality in special relativity

I have a slight variation of the barn / ladder paradox, where there is a ladder too long to fit into a barn at rest, but when moving at a sufficient speed, it is length contracted with regards to the ...
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Decay of lepton into meson and neutrino using four-momentum

I'm learning about how to use four-momentums and am working through a problem involving the decay of a charged lepton into a charged meson and neutrino. The equation would be: $L^+ \to M^+ + \nu$ ...
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If humanity was to send a probe to Proxima Centauri, how long would the travel last?

If humanity was to send a probe to the nearest star: Proxima Centauri, at a distance of 4.24 light years from our sun, what would be the optimal propulsion technology to reach the destination as soon ...
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Significance of x in the Lorentz equation for time

Why does the term x appear in the Lorentz transformation equation for time? What is its significance?
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Confusion regarding step in Einstein's 1905 paper on the electrodynamics of moving bodies

Could someone explain this step in Einstein's 1905 paper on the electrodynamics of moving bodies. I tried differentiating both sides of the first equation and still don't arrive at the second one, ...
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45 views

What Would One Observe of a Calendar on Earth, Given a Round Trip to Another Star and back?

I want to ask a clarifying series of questions on what I think is a relatively simple scenario. It's a long one but I've tried to word it as simply as I can manage while trying to do the question ...
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102 views

Equation of motion of a free particle

We know that the equation of motion of particle can be derived from the respective action. But in the book I am reading, the author is saying: ... timelike worldline of a massive particle is ...
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75 views

Electron positron collision producing mesons

An electron of an energy 9 GeV and a positron of energy E collide to produce a $B^0$ and anti-$B^0$ meson, each with a mass of 5.3 GeV. What is the minimum positron energy required to produce the ...
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Momentarily Comoving Reference Frame Question

Consider a reference frame $S'$ moving with constant velocity $\vec{V}$ relative to a second nonrotating reference frame $S$. Also consider a particle moving along a trajectory $\vec{r}$ with perhaps ...
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Construct fields from from unitary representation of Poincaré group

I am trying to understand how construct fields from unitary representation of Poincaré group and the reasoning that Weinberg give in his book is the cluster decomposition principle and Lorentz ...
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Does time dilation affect the speed of a moving object?

Imagine you are traveling at 99% of the speed of light. Will the speed of the moving object slow down for both objects and for the resting observer or either one?
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Can an event occur before or after the other one depending on what frame of reference we are in?

Two buses moving relative to each other with 30% the speed of light (4 light-min apart). Now by some mysterious way bus 1 comes to the knowledge that after 3 min-bus 2 time bus 2 is going to explode. ...
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Real and relative velocity formula

What i need is a thing more complicated than the usual relative velocity formula. Imagine a radar. You are at the center, moving at some angle, but lets make it clear, you are always at the center. ...
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35 views

Why do we sum relativistic intervals in relativistic action of a massive point-particle, and not a function from it?

Relativistic action as follows (which should explain relativistic motion of a classical particle): $$ S = C \Delta s=C\int ds $$ Where $C$ is some constant and $\Delta s$ is relativistic interval. ...
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What would be seen if a firing laser is accelerated to relativistic speeds then back?

Consider this scenario: Two identical space ships, the SS Observer and the SS Accelerator. Each ship is spherical with a band of mirrored material around the outside and contains a green laser. They ...
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Are only measurements registered as events?

When we measure an electron or some other system behaving quantum mechanically, we observe something. Now, this can be called as an event in relativity terms meaning if we live in 1-D spacetime, only ...
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What will the point of view be when you move faster than light in a medium?

In water the light become slower to the point where electron in water moving faster than light (in the same medium). So in electron frame of reference what will electron's point of view be? From what ...
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Redirectioning photons through magnetic lenses

What shape magnet/s would I need to create parallel lines from the ends of a rod shaped magnet?or what shape of magnet would create parallel lines? Is this close?
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Relativistic momentum (Lorentz boost) low velocity expansion

If I have a momenta $p^{\mu}=(E, p_x, p_y, p_z)$ and transform it via lorentz boost in x-direction with velocity v I'll get for the new 0th component $E'=\gamma E + \gamma v p_x$ why is this in the ...
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Kinematic equations of a cascading particle decay

This paper discusses different measurable quantities that can be used to search for unknown particles at particle accelartors. For the following decay it introduces the invariant mass $m_{XY}$: It ...
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51 views

A Magnetic Vortex in a Magnetic Vortex

This is not to scale. Can a magnetic vortex be compressed into a flat disk using magnetic entrapment? Can a magnetic vortex happen inside another magnetic vortex?
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Magnetic field of a circular particle accelerator

Suppose there's a $500 \ GeV$ proton beam ($q=1.6 \times 10^{-19} C$) inside a circular particle accelerator, what would be the magnetic field intensity $B$ in Teslas required to keep it stable at a ...
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Why is special relativity still in use, if general relativity is more broad?

I always thought special relativity is only there because it is the building block for "The General theory of Relativity", until recently I encountered a text from my course book given below. A ...
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Confusion in Special Relativity: Rotating frame of reference

Suppose we are observing a rotating frame from an inertial frame, free from gravity, and try to measure the circumference of a circle drawn in the rotating frame. Since our measuring rod would be ...
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Can a pair of members of a “rotating system” be characterized by one value of displacement magnitude?

There seems to be a claim (cmp. Goldstein, "Classical Mechanics", eq. (4-126); or also perceptable here) that values of "velocity", and of "speed", of some participant, say $P$, can not only be ...