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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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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43 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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A couple of questions on mass increase

I found these experimental data on mass increase. Data of the Bertozzi experiment show close agreement with special relativity. Kinetic energy of five electron runs: 0.5, 1, 1.5, 4.5, 15 MeV ...
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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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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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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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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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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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24 views

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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55 views

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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68 views

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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44 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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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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67 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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24 views

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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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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44 views

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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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 ...
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Is static gauge quantization of the particle equivalent to covariant quantization?

In the covariant quantization one is able to get directly (from the constraint $p^\mu_\mu+m^2=0$) the Klein-Gordon equation. But if one uses the parametrization $\tau=X^0$ then the Schrodinger ...
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Michelson-Morley expression for relative phase

I am trying to find the relative phase when ether is propagating vertically versus when ether is propagating horizontally. The question is written below When the light (of wavelength) is split at the ...
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Given the intervals of a punctured flat spacetime how to reconstruct the intervals of the complete flat spacetime?

A set $\mathcal S$ of events can be characterized as a flat unbounded spacetime through a function $s^2 : \mathcal S \times \mathcal S \rightarrow \mathbb R$ which assigns spacetime interval values to ...
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Is there a bound on spacelike intervals between the trajectories of a pair of chronometrically rigid participants in flat spacetime?

Considering, in flat spacetime, two participants, $A$ and $B$, who were "chronometrically rigid" with respect to each other (i.e. $A$ found constant ping duration with respect to $B$, and $B$ found ...
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Luminosity and entropy of a relativistic shell

I am looking to understand more about gamma ray bursts. The review I am reading through describes in equations (111), (112) the luminosity of a relativistic plasma shell, in an inertial frame at rest ...
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angle between spacelike and timelike vector

What is the significance of the fact that the angle between a spacelike and a timelike vector has a real part of pi/2?
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What are some ways to measure variations in the speed of light in vacuum?

To avoid confusion, I am not talking about measuring differences in the speed of light in vacuum as a result of a particular Lorentz boost. What I mean is, suppose the "constant speed of light" were ...
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61 views

Are photons just electric waves in an electron's frame of reference?

They say that electrons emit photons when they jump to a lower orbit. But the way electrons should see it, there's no any emission, really. There's just rapid change in electric field due to a rapid ...
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Distance and Time

I understand that if an object is 10 light years away then the light I am seeing from that object is actually from 10 years ago. If this is the case, which a few posts on this forum seem to concur, ...
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Will objects heat up and become hidden at relativistic speed?

Let us assume there is a mirror travelling at extremely relativistic speeds, perhaps few picometers away from speed of light, and let us assume we have a very thin detector which is very small perhaps ...
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Inelastic cross section derivation

I am trying to derive the inelastic cross section (the mass changes). I looked up the elastic derivation on Peskin's book (are there any alternatives?): $$d \sigma = \frac{1}{2 E_a 2 E_b \left| ...
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Inverse Lorentz transformation of four-velocity

Consider two frames. In the first frame $K'$ a particle executes uniform circular motion. Frame $K'$ travels with constant velocity along the axis of the circle (take z-axis) w.r.t. the observer's ...