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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Is the defintion of *inertial reference frame* given by Blandford and Thorne acceptable?

Edit to add: A simple explanation of my objection to Blandford and Thorne's definition of inertial reference frame (which they use synonymously with inertial frame) is that, if I'm in free float, ...
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Wifi near the speed of light

I have a hypothetical question that hopefully makes sense considering only the rudimentary amount of knowledge I have on Relativity. Assume I am in a spaceship orbiting around a spherical satellite, ...
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Dirac spinor and Lorentz group

How does the reducibility of lorentz group ensures that there exist two types of particle i.e left-handed and right-handed (weyl spinors)?
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Apparent rotation in connection with observation of Lorentz contracted objects

My question is related to the so called invisibility of Lorentz contraction, but I am essentially concerned with part related to the apparent rotation often mentioned in explanation of the phenomenon. ...
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Can you derive the Dirac equation from the Dirac-von Neumann axioms?

The Dirac von Neumann axioms say nothing about relativistic QM, can I invoke relativistic effects and derive the Dirac equation from the Dirac von Neumann axioms? If so, how does one go about it? If ...
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Relativistic observers moving on equilateral triangle

In the laboratory frame two observers A and B are moving along sides of na equilatera; triangle with equal sides, as shown in the figure below. What is velocity of B with respect to A?
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Maximum exhaust speed of relativistic rocket?

In this document "a transparent derivation of rocket equation", the author writes (on the last page): These are the classical and relativistic rocket equations. For the relativistic case, there ...
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Lorentz transformation of Interaction therm in Weinberg book

In Weinberg book The quantum theory of fields he says that one condition for the $S$ matrix to be Lorentz invariant invariant is that the interactions therm takes the form $$V(t)=\int dx^3H(x,t)$$ ...
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Lorentz Transformations and Reversing Boost Order to Give A Different Transformation

[Question] Find the matrix for Lorentz transformation consisting of a boost of speed $v$ in the $x$-direction followed by a boost of speed $w$ in the $y'$ direction. Show that the boosts performed in ...
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Does the conservation of 3 and 4-momentum implies the conservation of relativistic energy?

In special relativity, we require 3-momentum, 4-momentum and energy to be conserved. This gives three equations. However, after solving some exercises on relativistic dynamics, I find that I usually ...
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Problems on special theory of relativity [on hold]

From an observational post E on the Earth, two ballistic missiles, each of rest length l from nose-tip to tail-end, are observed to fly past each other, with the same uniform relativistic speed c/...
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Distance a muon travels in a pion rest frame

I have a question regarding a pion at rest (with a mean life time of $2.5\times 10^{-8}$ s) which decays into a muon (of mean lifetime $2.2\times 10^{-6}$ s), and a neutrino. I've found the velocity ...
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Momentum conservation in special relativity

In my textbook Kleppner, this question is given in the problem bank. We define momentum 4-vector in Kleppner as: ...
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62 views

Can the centrifugal inertial force, acting on ultrarelativistic electron in a circular orbit, be expressed in terms of its kinetic energy?

From classical mechanics we know that centrifugal inertial force, acting on an electron in a circular orbit of radius $R$ in relatively slow motion ($v \ll c$), can be expressed in terms of its ...
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Relativistic Computer Processing Power

Modern computers generally perform one step at a time at a given frequency (I know, an over-simplification). However, if one had a computer program, and wanted to speed it up, one could get on a ship ...
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How do permanant magnets work (In terms of electric charge and relativity)

I've been reading about magnetism from the point of view of reference frames and relativity. The concept of a test charge moving next to a wire (and how the choice of reference frame will cause ...
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Is there an ambiguity between the motion of an aircraft propeller and time dilation in special relativity?

We know that the faster a propeller rotates, the faster the attached vehicle (airplane, submarine, etc.) moves. (Assume that the propeller is normal to the motion direction.) On the other hand, ...
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Tensor indices from Ramond

I'm working through Pierre Ramond's "Field Theory: A Modern Primer". I can't connect the steps in I.2. Eq 2.6 (p. 7) gives a property of two linear transformations in relation to the Minkowski metric,...
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Confusion regarding length contraction [duplicate]

I understand that length contraction is a consequence of the relativity of simultaneity. I found this spacetime diagram online: Here it's clear that what constitutes a rod for one observer, is a ...
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1answer
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What is the relativistic form of the dynamic pressure of a fluid? Is it a Lorentz-invariant quantity?

If one moves a plate through the air at a uniform velocity $v$, the pressure exerted on the area $A$ of the plate is: $$p=\frac{1}{2}\rho_{air}v^2 \space .$$ This pressure is measured by the ...
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Proof of a property of the derivative of 4-velocity

In General Relativity, An Introduction for Physicists, in between equations 8.7 and 8.8, the authors make use of the property that the contraction of the 4 velocity gives the speed of light squared ($...
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Scenario around time dilation - Astronaut spinning around earth. What time is it versus observers on earth? [on hold]

The scenario: An astronaut, in a space ship capable of accelerating from zero to C instantly ( to reduce complex math to get an easy to understand answer below ). The space ship will only travel ...
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Axiomatization of SR: can we replace light rays with timelike world-lines?

If I eliminate a lot of details and just sketch the general ideas, then a common way of presenting SR is this: Axiom 1: Clocks exist. Axiom 2: Light rays exist. This is the approach followed in, e.g....
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Is there a limit of increase of relativistic mass?

As I understand physics there is a limit for every equation in the way there must not be an infinite quantity present in it.So my question is related to the Lorentz transformations for a body that ...
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Are we really moving at the speed of light in the time dimension? [duplicate]

I have seen a vector explanation of time dilation that our net velocity in space-time is the speed of light. Most of that velocity for slow spatial speeds is in the time dimension. As you go faster ...
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Is it possible that galaxies formed from incredibly fast neutron star collisions?

In the recent Kurzgesagt youtube video there is mention of how neutron star collisions are the likely candidates for creating the heavier elements in the universe. It is also possible that it created ...
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Alice leaves Earth at .6c for 3ly then transitions away at .8c ,what will be her age difference from Earth's age [closed]

In other words Alice changes her velocity from .6c to .8c away from Earth at the 3 ly mark. Oops I just realized Dale is an expert, his answer wouldn't conflict with the answer to this question ...
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Why does not acceleration affect time dilation in addition to the time dilation caused by velocity?

In his book, Relativity: The Special and General Theory, Einstein claimed that the clocks located on a rotating disc run slower solely due to their tangential velocities as appear in the Lorentz ...
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Does Special Relativity Set a Canonical Zero of Energy?

In special relativity, one has the equation $$ E^2 = m^2 + p^2 $$ It seems like this is saying that there is an absolute zero of energy: the energy of a massless, momentumless particle. On the other ...
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Question about Einstein summation convention

I'm dealing with the following: $$\eta^{\alpha \mu} \eta_{\alpha \nu} \phi,_{\beta \mu}$$ $$\eta^{\alpha \beta} \phi,_{\alpha \beta}$$ where $\eta$ is the Minkowski metric and $\phi$ is a function ...
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1answer
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Incorporating Gravity in special relativity and in Newtonian limit [closed]

Consider the following metric: $$ds^{2} = -c^{2}dt^{2} + dx^{2}+dy^{2} + dz^{2}. \tag{1}$$ This is the Minkowski Metric which describes a spacetime without Gravitational interaction. Furthermore, ...
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Time and distance in a photon's frame of reference

Disclaimer, not a physicist. When I look at the sky I can see the star Rho Cassiopeiae. In my frame of reference, the photon hitting my retina has traveled for 4000 years and 3.78x10^16 km. In the ...
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Inertial mass, and energy required to accelerate from 100 kph to 101 kph versus 1000 kph to 1001 kph

In this article it says "It is commonly known that, if you accelerate an object, its mass will increase; however, to understand why this phenomenon occurs, we mustn’t think of the object’s mass ...
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Do physicists understand why time slows down the faster the velocity of an object? [duplicate]

Like do they understand the mechanism behind it? Is there a mechanism behind it? (for a lack of a better word) Or is it just thought to be a law without any further explanation?
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1answer
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Problem with the mass of exhaust when deriving relativistic rocket equation

In my special relativity book, there is a derivation of the velocity of a rocket. Let the rocket have rest mass $m$ (which decreases over time) and velocity $v$ in an inertial frame, and let the ...
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Hilbert space and the interval of special relativity?

One requirement of the Hilbert space is that it is normed. Furthermore, in the case of special relativity, the norm has the following problematic requirements: $$ ||u||\geq 0 \\ ||u||= 0 \implies u=0 ...
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Modern understanding of zitterbewegung?

According to my naive understanding, zitterbewegung is a property of particles obeying the Dirac equation where the expectation value of the position operator has an oscillatory component at ...
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De Broglie Dispersion Relation

So i had a question that i cant wrap my head around the dispersion relation $\omega(k)$ of Matterwaves. I start out using the Energy Relationship that was given $E^2 = c^2p^2+(m_0+c^2)^2$ including ...
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3answers
84 views

How to prove the relativistic momentum?

As far as I know, the relativistic momentum of a particle is given by the equation: $$p=\frac{m_0v}{\sqrt{1-\frac{v^2}{c^2}}}$$ where $m_0$ is the mass of the particle and $v$ is the velocity of the ...
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How the relativistic mass gain prob is overcome in Synchrotron by adjusting the frequency of electric field to accelerate particles to high KE?

Cyclotron cannot accelerate particles beyond certain KE due to relativistic mass gain. I am from Chemistry background.
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What are the rules governing worldlines?

I recently got a great answer Is the clock hand off version of the twin paradox real or fake? that tracing a clock across spacetime paths was the way to determine age difference between the worldlines....
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1answer
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Action of a relativistic charged particle in an electromagnetic field

In my Classical field theory lectures we have derived the lorentz invariant action for the motion of particles in EM fields given by: $S_{particle}=-\int mc^2 d \tau -\int eA_\mu dx^\mu $ Where we ...
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Lorentz transformations of spatial functions of coordinate time

Explicitly, my question is: Suppose we have $f(x-x_p(t))$ in our unprimed frame. We now consider a primed frame moving along the x-axis, where $x' = \gamma(x-\beta ct)$ and $ct' =\gamma(ct-\beta x).$ ...
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Lorentz transformation of fields in Srednicki

In Mark Srednicki's QFT book, he writes in the Heisenberg picture: $$e^{\frac{iHt}{\hbar}}\varphi(\vec x,0)e^{-\frac{iHt}{\hbar}}=\varphi(\vec x,t)$$ This is quite reasonable, because I can view $\...
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Why is the field commutator $[\phi(\vec x, t), \phi(\vec y, t)]$ related to causality?

It's well known that $$ \langle 0| \phi(\vec x, t) \phi(\vec y, t) |0 \rangle \neq \delta(\vec x - \vec y) . $$ It is then regularly argued that this is not a big problem since the commutator $$ \...
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Lorentz group generator in Srednicki

I'm reading through Srednicki's QFT. In Chapter 2, the author denotes an infinitesimal transformation by $$U(1+\delta \omega)=I+\frac{i}{2 \hbar}\delta \omega_{\mu \nu} M^{\mu \nu}.\tag{2.11}$$ Then ...
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Why are observers/reference frames able to see themselves moving through time but not through space?

All observers are stationary in their own reference frames. That is, their space coordinates are constant at all times (in their frame). However, they can see themselves moving through time. What ...
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A thought experiment regarding radiation pressure: A new paradox or another pseudo-paradox?

Assume a plate with dimensions $L×L$ is located vertically on the ground (normal along $x$ direction) at rest with respect to the lab observer. An electromagnetic wave of $\boldsymbol{E_y}=\boldsymbol{...
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Can you point out what is wrong with this thought experiment? [closed]

Relativity claims that the simultaneity between two (or more) observers, each traveling in different Inertial Reference Frames (IRFs) is such that “Both observers consider the clock of the other as ...
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Einstein light clock with mirrors but what if mirrors outside the train?

Einstein's light clock with mirrors experiment involves mirrors on top and bottom of a moving train and light reflecting back and forth. To a stationary observer, it would seem that the light is ...