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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What is the difference between the $Spin(3,1)$ group and the $SO(3,1)$ group?

What is the difference between the $Spin(3,1)$ group and the $SO(3,1)$ group?
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Speed of light invariance (once again)

The answer to this very good question seems to be favored by a large amount of users. Yet it seems to imply that the constancy of the speed of light and its finiteness stems from the underlying ...
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Observing a point 13.82b ly away, 1b years ago

I understand that we can observe far away galaxies to get an idea how the universe looked like in the past. Assuming the universe is 13.82b years old, would it be correct to say that if we looked at ...
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Field of view from travelling at (almost) the speed of light?

As we go faster, our field of view increases, but would happen if we travelled at (almost) the speed of light? My questions: Can we see a 360 degree view while travelling at (almost) the speed of ...
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65 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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59 views

Finding the velocity of a particle [duplicate]

How to find the velocity of a particle which has mass $m$ and energy $E$ considering the non-relativistic and the extreme relativistic limits?
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1answer
50 views

Lorentz contraction of object in circular motion

Apparently a bunch of people totally misunderstood my previous question and choose to ignore the clarifying comments. Let me change the conditions to remove all the confusion. A group of particles ...
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47 views

How does flying over synchronize clocks look like?

I have a relatively (pun intended) simple conceptual question that has me going in circles as I begin my course work into Modern Physics. The question is straight forward enough: You are gliding ...
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0answers
82 views

What happens to wheels of a car moving near speed of light? [duplicate]

Let's take a standard ACME Thought Experiment Division car with a max speed of a leisurely, constant 0.75c in a straight line. So, for an external observer, the body of the car behaves like a typical ...
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2answers
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Triplet paradox

The situation is: A stay at a station B,C board the same train that moving away from the station while the train moving away C start moving inside the train in the opposite direction as such A sees ...
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Can absolute speed of object be measured? [closed]

Let's say there are two objects in space - Station and huge non-transparent sphere. Sphere starts to move from station 5000 km/h. Inside the sphere, beam of light is produced in direction the sphere ...
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1answer
61 views

Is $E = p^0$ in non-inertial frames?

In special relativity the energy of a particle is the 0-component of the 4-momentum. However, is this still true in non-inertial frames, and in particular in non-freely-falling frames in general ...
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Performing Wick Rotation to get Euclidean action of scalar field

I'm working with the signature $(+,-,-,-)$ and with a Minkowski space-stime Lagrangian $$ \mathcal{L}_M = \Psi^\dagger\left(i\partial_0 + \frac{\nabla^2}{2m}\right)\Psi $$ The Minkowski action is $$ ...
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View of right-angled-triangle from a constant-velocity relative observer [closed]

Suppose I have a picture of a right angled triangle drawn in the X-Y plane, and a man whose velocity relative to the to picture is $0.4c\hat{x}-0.4c\hat{y}$. Will the angle $\theta$ that the man ...
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2answers
159 views

Does relativity violate uncertainty principle?

Let us say I sit on an electron. According to me the electron is at rest. Also, I will know the position of the electron accurately as I can take the electron as the origin. So, I know both position ...
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4answers
84 views

if mass is dependent on velocity, and velocity is relative, how can we determine rest mass [closed]

If I'm not mistaken, $m=\gamma*m_0$ ($\gamma$ being the lorentz transformation) But $\gamma$ depends on velocity. How do we determine velocity if velocity is relative? If we are currently being flung ...
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How much is the maximum posible information travel speed in medium?

Light has slower speed in medium. Should we consider this when we use special relativity in atmosferic(or any other type of medium) motions? If we should use vacuum light speed, does it mean photons ...
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1answer
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Relationship between locality, causality, and free theories

This text on QFT defines a free theory as that in which dynamics of the field for each degree of freedom evolves independently from all the other. In principle we have an infinite degrees of freedom, ...
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Constancy of speed of light in vacuum? [closed]

Have scientists tried their best to calculate speed of light in vacuum? It seems very absurd to me that light of all frequencies have same velocity in space. Can someone find in future if this speed ...
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Length contraction: Is it permanent? [closed]

Lorentz contraction problem: By Bertrand Boucquillon Components of the problem: - Bob (observer) - 2 identical rods that both measure 1 meter. Let's call them rod X and rod Y - Point A - Point B ...
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Do we know why there is a speed limit in our universe?

This question is about why we have a universal speed limit (the speed of light in vacuum). Is there a more fundamental law that tells us why this is? I'm not asking why the speed limit is equal to ...
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Showing $\frac{d^3\underline{k}}{2\omega_{k}(2\pi)^3}$ is Lorentz invariant [duplicate]

Show $\frac{d^3\underline{k}}{2\omega_{k}(2\pi)^3}$ is Lorentz invariant. Hint: try to evaluate $\int dk_0\delta(k_0^2 - M^2)\theta(k_0)$ where $M^2 = \underline{k} + m^2$ My attempt is as ...
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Available energy in centre of mass system

The problem given is "A proton of total energy 3GeV makes a head-on collision with a 5GeV electron. Calculate the available energy in the centre-of-mass system to create any new additional particles ...
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Requesting explanation for why dark matter evidence is not explained by special relativity [duplicate]

Good afternoon. I'm doing research for a possible hard science fiction project and was looking up information on dark matter. Wikipedia--hardly an authoritative source, I know--mentions that the ...
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2answers
320 views

Lorentz invariance of the Minkowski metric

As far as I understand, one requires that in order for the scalar product between two vectors to be invariant under Lorentz transformations $x^{\mu}\rightarrow ...
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6answers
155 views

Light in mass moving at high velocity

Imagine if you will, a strand of fiber optic cable 186,000 miles long. A pulse of light is sent through the stationary cable: it takes 1 second for light to travel the entire length of the cable. Now ...
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3answers
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acceleration and its effect on the speed of light

One of Einstein's thought experiments involved a rocket and two light sensors inside the rocket, one at the top, and one at the bottom. When the rocket was at rest, a pulse of light from the bottom ...
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1answer
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Does momentum space have a speed limit?

In ordinary $xyz$ space, the maximum velocity of propagation for mass-energy and/or information is $c$. So, my question: Is there also a maximum velocity of propagation in momentum ${p_x}{p_y}{p_z}$ ...
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2answers
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How do the postulates of relativity relate Lorentz transforms to their inverses?

This question is about one of the assumptions involved when one is deriving the Lorentz transformation, for example under "Principle of Relativity" in Wikipedia's page on the derivations. Let me ...
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1answer
48 views

Acceleration of free particle in Minkowski space! [duplicate]

In Minkowski space, the equation of motion is $$a^c=\frac{d^2}{d\tau^2}x^c(\tau)=0.$$ How is this derived?
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Is mass directly or inversely proportional to time? [closed]

From a Newtonian perspective: F = ma F dx = ma dx E = m (dv/dt) dx m = (E dt) / (dv dx) Mass is directly proportional to time, if time slows down then mass goes down or decreases. From a ...
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1answer
52 views

Given a current velocity and a fixed input energy, how much faster will a relativistic particle be?

The relativistic kinetic energy of a particle with mass $m$ and velocity $v_0$ is $$m c^2 (\gamma_0 - 1) \textrm{ where } \gamma_0 = \frac{1}{\sqrt{1 - \frac{v_0^2}{c^2}}}$$ I would like to know how ...
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Is magnetic field due to an electric current a relativistic effect?

I was reading a paper of the same name by Oleg D. Jefimenko; here is the concerned text: [...] relativistic force transformation equations demand the presence of an electric field when the ...
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1answer
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What is the physical significance of taking derivative with respect to proper time?

I would like to know if there is any physical significance associated with the derivative of a quantity with respect to proper time or is it just a mathematical trick. Since proper time is measured in ...
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2answers
115 views

What does diagonalization mean here?

In a gravity theory in spacetime, the metric has signature $− + +· · ·+$. Concretely this means that the metric tensor $g_{μν}$ may be diagonalized by an orthogonal transformation, i.e. ...
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39 views

Is the matrix representation of the Lorentz transform the same for all 4-vectors?

If I have a four vector of the form: $$ \left( \begin{array}{ccc} T\\ \vec{X}\end{array} \right) $$ where $T$ is the analogous time component (i.e. energy, angular frequency, scalar potential, charge ...
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103 views

Does the property of being “virtual” for a particle depend on the observer?

I've read at several places that a static magnetic (and electric for that matter) field can be thought of as made by virtual photons, at least that's what I understood. Now, in Special Relativity we ...
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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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1answer
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Minkowski metric: Why does it look like it does? [duplicate]

I have been searching for why would we even start with Minkowski spacetime metric as being written as: $$ds^2=-dt^2+dx^2+dy^2+dz^2.$$ No really, so why would we have a negative sign for temporal ...
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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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0answers
72 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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1answer
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What's wrong with using the 4-current to find the potential of a moving particle?

According to Feynman (Lectures on Physics, Vol. II, 21–6), the potential of a moving point charge is: $$\phi = \gamma \cdot \frac q {4\pi\epsilon_0} \cdot \frac 1 {\sqrt{ \gamma^2 \left( x-vt ...
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1answer
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Lorentz covariant completeness relation

Let be $$ P^\mu |p> = p^\mu |p> $$ i.e. $|p>$ is the eigen-vector of the 4-momentum operator. Where does the following Lorentz-covariant completeness relation come from? $$ \int d^4p ...
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1answer
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Relativistic Scattering

When we work out the relativistic general two-body scattering in the CM frame (like two elementary particles producing two other P1 +P2 -P3 -P4) , the cross section is proportional to absolute final ...