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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1answer
173 views

Why and how Dirac cones are “tilted”?

Given a Weyl Hamiltonian, at rest, $ H = \vec \sigma \cdot \vec{p} $, A Lorentz boost in the x-direction returns $ H = \vec\sigma\cdot\vec {p} - \gamma\sigma_0 p_x $ The second term gives rise to a ...
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Images traveling faster than light

Please help me understand my mistake(s) in this reasoning. I will write as if I knew exactly what I'm talking about for the sake of clarity, but I of course don't. Consider observer A and its ...
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1answer
507 views

Thought experiment and possible contradiction between electromagnetism and special relativity

I have designed a simple and qualitative thought experiment through which I have encountered an inconsistency in the relativistic electromagnetism. A point charge $+q$, with respect to the lab ...
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Einstein's train experiment-Do waves from lightning flashes meet after the same number of cycles for all observers?

In Einstein's thought experiment about moving and stationary observers and two lightning flashes, let's say that we replace the lightning flashes with a pulses of mono-chromatic light, with both ...
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Compressed length of a moving body [closed]

This question is on behalf of someone else without access to a computer so any further clarification or responses may be delayed. The question comes in the form of photos of the original questions as ...
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3answers
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How to derive addition of velocities without the Lorentz transformation?

Lorentz contraction and time dilatation can be deduced without Lorentz transformation. Can you deduce also the theorem of addition of velocities $$w~=~\dfrac{u+v}{1+uv/c^2}$$ without Lorentz ...
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Proof of skewsymmetry of electromagntic function in Minkowski spacetime

I have been studying special relativity from the Gregory Naber's book: "The geometry of Minkowski spacetime" and I found a very strange proof. In Section 2.1, just before of equation 2.1.2. the book ...
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1answer
46 views

Why do electrons have rest energy?

E=mc² so inserting the value of m and c we get 0.511 MeV for electron but then what does this energy account for coz according to me electrons are not made up of any particles so this doesn't account ...
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1answer
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Special Relativity Frame Ambiguity [duplicate]

If I have some predefined coordinate system — “my rest frame,” then I pick an “inertial frame” moving at some velocity with respect to my “rest frame.” Special relativity states that in the rest frame,...
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210 views

Why $c$ is $3\times10^8$ times faster than a $1\ \mathrm{m/s}$ car? [duplicate]

The value of a dimensional constant like $c$ is often regarded as unimportant since it can be arbitrarily changed to any desired value by changing our units. For example, $c=3\times10^8$ in $\mathrm{m/...
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The spinor metric, basic spinor calculations and spinor indices

I'm currently reading the textbook "Finite Quantum Electrodynamics" by Günter Scharf, but I find myself stuck already on page 24. Background Scharf introduces the index-raising symbol (spinor metric)...
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2answers
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Why physics should be the same in all inertial frame? [on hold]

One of the postulates of special relativity is that physics should be the same in all inertial frame. Suppose we have two observers $A$ and $B$ suppose that $A$ is accelerated. Now suppose that we ...
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60 views

The imaginary time [duplicate]

Some people work with the interpretation that the time basis vector has magnitude sqrt(-1) to justify the negative sign in a -+++ Minkowski metric signature. I came across a Youtube comment that ...
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1answer
137 views

How is a pseudo-Euclidean metric superior to Minkowski's complex metric? [duplicate]

This is my second attempt to get a meaningful response from you guys on this issue. The SR invariance formula makes space-like intervals imaginary (e.g., the distance $x$ in a given frame has ...
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2answers
516 views

Minkowski's complex Euclidean space vs. the real pseudo-Euclidean version

The SR invariance formula makes space-like intervals imaginary (e.g., the distance $x$ in a given frame has interval $ix$). Yet modern physicists consider it bad form to define the distance itself as $...
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What is the length of 1 second in meters

If time is treated as a fourth dimension of spacetime, what is relation between length and time units? Or in other words, how can I convert time units to length units, for instance seconds to meters?
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Transverse Relativistic Doppler effect in Non-inertial reference frame

If I have a Non-inertial reference frame in Earth (rotating camera or just my rotating head with eyes) and I am watching the Moon. If my Non-inertial reference frame in Earth rotating with the speed ...
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Work on two charges in mutually retarded field

Consider two particles with charges $q$ and $Q$ and with an initial distance of $3L$. Now I move each charge a distance $L$ closer to the other, such that the final distance is $L$. The initial and ...
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1answer
36 views

Moving clocks observed with different observers

If a clock is moving near to speed of light with constant velocity it'll slow down, but if I were to observe from the clock will the observer on Earth slow down?
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Pseudorapidity: Derive conversion to Cartesian momenta

I am working on the ATLAS opendata as part of a lab course at my uni at the moment and stumbled upon the identity $p_{z} = p_{T}*\sinh(\eta)$ with the pseudorapidity $\eta = -\ln(\tan(\frac{\Theta}{...
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4answers
131 views

Einstein's train, considering the thunder

From Einstein's "easy" explanation https://www.bartleby.com/173/9.html (Yes, I have reviewed 8 other answers to similar questions. Please bear with me.) M is on the platform, T (aka M') is on the ...
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2answers
891 views

Trying to understand one of Einstein's thought experiments

I try to understand Einstein's Relativity: The Special and the General Theory, chapter IX., "The Relativity of Simultaneity". Here's an online version: http://www.bartleby.com/173/9.html. ...
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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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Geocentric frame of reference and superluminal speeds

I have a couple of questions on frames of reference. From my understanding, we can do math in an accelerating frame of reference as long as "fictitious" force terms are correctly added. From this ...
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Conceptual interpretation of the left- and right-handed spinor representations of the Lorentz group

I understand mathematically that the Lorentz group's Lie algrebra $\mathfrak{so(3,1)}$ (given by eqns. (33.11)-(33.13) in Srednicki's QFT book) is isomorphic to $\mathfrak{su(2) \times su(2)}$ (given ...
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Red shift of radio signals

If a radio signal is red-shifted does it still last the same amount of time? Knowing the signal wavelength is now longer but still is traveling at the speed of light one would assume the radio message ...
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6answers
702 views

What does the accelerated twin see in the twin paradox?

I am referring to the usual twin "paradox" where one twin remains on Earth while the other one takes a round trip journey on a rocket. I understand how the experience of the twins is not symmetrical, ...
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What made him think so? [duplicate]

I've been looking into Einstein's theories and was struck with this question. It's contradicting the physics what I've been taught at school. How can mass change with increase in speed and what made ...
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2answers
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Effect of finite speed of light on timings of events

In relativity when an observer records an event some distance away from him, the timing of the event he measures would be different from what he would measure if he was close to the event as light ...
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10answers
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If photons have no mass, how can they have momentum?

As an explanation of why a large gravitational field (such as a black hole) can bend light, I have heard that light has momentum. This is given as a solution to the problem of only massive objects ...
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1answer
165 views
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$z$ component of angular momentum under Lorentz transformation for massless particle

This question is related to this Helicity states. Suppose we have $k=[\omega,0,0,\omega]$. In Weinberg's book The Quantum Theory of Fields: Volume I he defines the state $|k,\sigma\rangle$ as an ...
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2answers
94 views

What is the mass of photon? [duplicate]

I'm sorry if this question is asked before, but I searched through the site and none satisfied me. In most of the books I've come across, they just write "rest mass of photon is zero." But never talk ...
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Relativistic constant acceleration in the framework of general relativity

Regarding the constant acceleration of a spacecraft towards relativistic velocities, the general equations are found at the following link: Baez However, if the distance covered is in excess of 1 ...
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2answers
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Basic Special Relativity Question [closed]

I am trying to understand the implications of c being relative to the frame of reference. Is the following analysis correct? N is on a slow train moving 3 m/s and M on the platform next to N both ...
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2answers
53 views

Relativistic Doppler Effect between rotating bodies

The Wikipedia article "Relativistic Doppler effect - One object in circular motion around the other" confused me. There they say that when the light source orbits the observer, the observation of ...
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6answers
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If clocks themselves are based on light signals, wouldn't we expect the measured speed of light to always be the same constant?

I'm trying to work out if there is an alternative starting point for the second postulate of special relativity. My main observation is that all "clocks" are, internally, based on light signals. So ...
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3answers
330 views

Gauge invariant scalar which is not Lorentz-invariant

I'm looking for examples of the following descriptions: A gauge invariant scalar which is not Lorentz-invariant A Lorentz covariant scalar For 1. I was thinking about the scalar potential $A$ (for ...
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1answer
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Proving the validity of the relativistic version of Newton's second equation

I want to verify the relativistic version of Newton's second equation $ F^\mu = m_0 A^\mu $ is true. My idea is that I expand both sides and compare the components. Left $$ F^\mu = \frac{dP^\mu}{d\...
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1answer
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What if we do double slit experiment at very near speed of light velocity of electrons?

How will relativistic effects affect the interference pattern?
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Which frame to consider for time dilation? [duplicate]

Clearly for constant motion we cannot define absolute rest or motion. So ,when dealing with time dilation problems for example twin paradox , how do we define which frame is in motion? If we ...
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1answer
70 views

Helicity states

On page 71 of Weinberg's book The Quantum Theory of Fields: Volume I, he defines the operators $$A=J_2+K_1$$and $$B=-J_1+K_2$$ where ${\mathbf{J }}=(J_1,J_2,J_3)$ are the rotation generators and ${\...
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1answer
60 views

Helicity under rotation

Suppose that the state $|p,\sigma\rangle$ (for a massless particle) has 3 momentum ${\bf p}=p_3$ (that is the momentum is in the $z$ direction) and that $J_3|p,\sigma\rangle=\sigma|p,\sigma\rangle$ ...
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2answers
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The Michelson-Morley experiment as seen by a relativistic observer

I am in a space-craft moving at .99c observing the Michelson-Morley experiment. I am perpendicular to one of the interferometer 'arms'. Due to the apparent 'reality' of Lorentz length contraction I ...
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4answers
151 views

Elapsed time between two events is greater for moving observer

Lorentz's equations show the elapsed time between two events in moving frame is greater than rest frame. But moving observer's clock ticks slower. Isn't that an inconsistency? Consider two observers, ...
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1answer
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Sagnac Effect and clocks synchronization

I read this from "The Sagnac effect and its interpretation by Paul Langevin", in cylindrical coordinates $$ ds^2=c^2t^2-dr^2-r^2d\theta^2 $$ ...This transformation means that the observer O (...
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1answer
56 views

Using Lorentz transformations with variable velocity

A particle is moving in a system of reference $S$. In its proper system of reference, say $S'$, the particle is still and it is described by the event $(c\tau,0,0,0)$. In the inertial frame $S$, the ...
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3answers
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Doesn't the speed of light limit imply the same electron can be annihilated twice?

If I understand correctly, there is a small probability the same electron to be found anywhere in the universe. Suppose that an anti-electron collides with an electron, annihilating it and producing ...
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1answer
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Why I think the Michelson-Morley experiment was originally flawed, and would have failed either way [closed]

I was recently reading about how physicists were heavily relying on the existence of Luminiferous Aether for their physics to work. I read about how the Michelson-Morley experiment attempted to prove ...
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1answer
160 views

Extreme temperatures, relativity and kinetic theory

According to kinetic theory, average kinetic energy is proportional to temperature. Supposing $k_BT/2$ per particle, can we use relativity and kinetic theory to calculate, e.g., the temperature and ...
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1answer
182 views

Why can't we measure the one-way speed of light?

I believe the problem is because we need to synchronize clocks. But ok let's assume we can't do that. Can't we just use some external reference - Eg The Sun & Solar Noon? For example given the ...