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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Four vector manipulation

I have started doing Relativistic Quantum Mechanics from Greiner. I'm having difficulty understanding the following derivation for commutation relations (page 4): $$[\hat{p}^\mu, x^\nu] = ...
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Energy transfer using quantum entanglement

Can we transfer energy from one place to another separated by arbitrarily large distances without any time lag? For instance, if Alice and Bob are two observers making measurements having a singlet ...
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106 views

S. Weinberg, “The Quantum theory of fields: Foundations” (1995), Eq. 2.4.8

Unfortunately I'm struggling to understand how do we get eq. (2.4.8) from eq. (2.4.7), p. 60; namely how $(\Lambda \omega \Lambda^{-1} a)_\mu P^\mu$ is transformed into ...
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239 views

Minkowski Metric

Hi all I'm a little confused So I have that in special relativity time is included as a coordinate so that in 1 spatial dimension we have 2 space time coordinates. The most basic metric is the ...
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140 views

Do you age at different rate at different speed?

This is probably answered many times, but my confusion is the following. In special relativity it is said that there is no preferred coordinate system. Does that mean that for the people at rest ...
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163 views

Measurements and simultaneity [duplicate]

Picture a situation where we have two observers, $A$ and $B$, and a system in a certain quantum state. If $B$ makes a measurement of some observable, say energy for example, the state will collapse to ...
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240 views

How to add a potential term to the Dirac Equation?

I've read that if you have a Hamiltonian for the Dirac Equation, you can add a potential term to it simply by adjusting the momentum operator so that $p^\mu \rightarrow p^\mu-A^\mu$, where $A^\mu$ is ...
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162 views

Relativistic Lagrangian transformations

I need to study the relativistic lagrangian of a free particle. It's $\ L= - m c^2 \sqrt[2]{1- \frac{|u|^2}{c^2}} $ I need to study the translation, boost and rotation symmetry. I say it doesn't ...
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108 views

Faraday tensor, antisymmetric electromagnetic tensor

I want to write $F^{\mu \nu}F_{\mu \nu}$ in terms of $F_{\mu \nu}F^{\mu \nu}$. How to do it?
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144 views

The Klein–Gordon equation

As we know that the Schrödinger equation presents basis of Quantum Mechanics and analogy with Newton second law in Classical Mechanics, I thought that relativistic interpretation of Schrödinger ...
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93 views

What is movement through time? [duplicate]

In general, when I think of movement through space, I think of this: $$\frac{dx}{dt}$$ But in special relativity, we also have a concept of relative duration, which means that $t$ must have a rate ...
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119 views

The status / acceptance of block time?

What is the current status or acceptance of block time as it relates to Einstein's theory of relativity? Has quantum mechanics ruled it out or is it still the favored view of the world? Perhaps there ...
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196 views

Why does only one twin travel in the twin paradox?

The wikipedia page repeatedly says that the twin travelling in space is the only one which travels, and also is the only one which faces acceleration and deceleration. So it does not age, while the ...
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Special relativity, acceleration and being in two places at once (How to resolve this paradox?):

Imagine I am on Earth I have a clock which measures time $t$. When my Earth clock reads time $t$, then when I look at a moving spacecraft's clock I see the time $t'$. Let us assume time is measured ...
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Calculating the speed of an object moving relative to another moving Object (Frame of reference) [duplicate]

Possible Duplicate: How to deduce the theorem of addition of velocities? Let's say that you are in a rocket speeding at 90% the speed of light away from Earth. Now fire a bullet inside the ...
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270 views

Lorentz Invariant Equation of Motion for Scalar Field

I'm trying to understand why you can't write down a first order equation of motion for a scalar field in special relativity. Suppose $\phi(x)$ a scalar field, $v^{\mu}$ a 4-vector. According to my ...
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A clock devoid of motion

My understanding is that every clock mechanism we have depends on motion of something w.r.t the observer. From atomic transitions to clockwork gears. So, does this property/constraint makes every ...
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328 views

Relativistic Doppler effect

If i have 2 coordinate systems (CS) which are travelling one towards another. CS $xy$ with an observer in its origin and CS $x'y'$ with a source in its origin. Correct me if I am wrong, but i think ...
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593 views

Using Lorentz Invariance of Charge To Calculate Current Density

I'm attempting a problem from Zwiebach: A First Course in String Theory and am completely stuck. Could anyone give me a hint? The problem is as follows. Consider $S$, $S'$ two Lorentz frames with ...
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What are the increasingly sophisticated ways to perform a Lorentz transformation?

Since Einstein first derived the Lorentz transformations, their generalisation and execution has changed over the century. So starting with those first derived by Einstein: What are the main, ...
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Knowing the mass and force acting on a particle, how do we derive the relativistic function for velocity with respect to time?

Use this scenario: An electron gains speed in the Stanford Linear Accelerator (SLA) across 3000 meters, reaching a final velocity of 0.95c due to a constant force pushing on the electron. Given the ...
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The time component is $\gamma m c$, so shouldn't $E=mc$?

Basically, the book is Brian Cox's Why Does $E=mc^2$?: (And Why Should We Care?). I just finished Chapter 5, where we derived the spacetime momentum vector (energy-momentum four vector, as he ...
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140 views

On BE and FD Statistics

Lets consider the Bose-Einstein and Fermi-Dirac statistics: Bose-Einstein statistics: $$\langle n_i\rangle = \frac{1}{\exp{[(\epsilon_i-\mu)/kT]} - 1}$$ Fermi-Dirac statistics: $$\langle ...
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why evaluate at lambda = 0

I am trying to understand Herbert Goldstein's introduction to 4-vectors. He describes a 1-D curve in spacetime $ P_(\lambda) $ then he says a 4 vector is defined as the tangent vector to this curve ...
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478 views

Is there an explicit angular momentum in Maxwell equations?

Electromagnetism implies special relativity and then the universal constant "c". And if we set c=1, the coupling constant has units of angular momentum (so in relativistic quantum mechanics we divide ...
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2k views

Relativistic speed/energy relation. Is this correct?

The relativistic energy-momentum equation is: $$E^2 = (pc)^2 + (mc^2)^2.$$ Also, we have $pc = Ev/c$, so we get: $$E = mc^2/(1-v^2/c^2)^{1/2}.$$ Now, accelerating a proton to near the speed if ...
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Change in line density of electrons

We're proving that electricity and magnetism are essentially two manifestations of the same underlying phenomenon by using the toy example of a positive charge moving parallel to an infinitely long ...
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A confusion regarding absolute motion in SRT

Suppose i am inside a uniformly moving spaceship and I send a light beam perpendicular to the direction of motion towards the opposite wall.Since the spaceship is moving and according to special ...
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43 views

Spaceship Doppler frequency

A spaceship starts falling under gravity with an acceleration $g$ as measured by an observer Barry at rest on Earth. At the instant that the ship starts to fall, an astronaut Harry at the base of the ...
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67 views

Special relativity; rocket moving towards a mirror [closed]

An observer in a rocket moves toward a mirror at speed $v$ relative to the reference frame in which the mirror is stationary - call this frame $S$. A light pulse emitted by the rocket travels ...
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74 views

Do photons change velocity instantaneously?

Any object traveling at c is observed as traveling at c in all reference frames. When a photon travels through a vacuum at c, all reference frames observe it traveling at c. When a photon passes ...
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Relativistic Conservation laws [closed]

Conservation of Relativistic mass and thus energy is easily proven by considering an inelastic collision of two bodies while invoking the conservation of momentum. As such the momentum law appears ...
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74 views

Prove that a derivative with respect to a covariant 4-vector is a contravariant vector operator

In special relativity, I know you can prove that the derivative with respect to a contravariant 4-vector component transforms like a covariant vector operator by using the chain rule, but I can't work ...
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Significance of angle in relativistic mass equation

I was playing with $$M=\frac{m_0}{\sqrt{1-v^2/c^2}}$$ and when I put $v=c\sin\theta$, I got $$M=m_0\sec\theta.$$ And this new equation is appearing so beautiful and attracting to me that I was ...
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176 views

Is time nothing but the speed of light (or the light itself)?

With regard to relativistic effects on time, all the examples and explanations revolve around light and its speed. Especially in explanatory situations that explain this using photon clock, it seems ...
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Universal speed limit [duplicate]

Is there any reason the universe has matter not being able to exceed the speed of light, or why there is a speed limit in the first place? I know why it can't, meaning the basic physics of it. I ...
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How do we know that clocks slow down relative to each other? [duplicate]

For example if a body in motion experiences time dilation, why does it see a body at rest slow down relative to it? wouldn't it make more sense if the body at rest has a faster clock relative to it?
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If the mass of an object or system is a measure of its energy content, multiplied by speed of light squared…?

If the mass of an object or system is a measure of its energy content, multiplied by speed of light squared, does it mean that the total potential energy of the rest mass of object or entire system ...
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Beginner question: timelessness of massless particles [duplicate]

I am not very familiar with the quirkiness of relativity, and I was wondering how to explain this situation. If a beam of light is shining at some object at some distance from the origin of the beam, ...
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50 views

Effective field theory for fermion gas

Reading about fermion gas in a paper they used the following Lagrangian, which describes an effective field theory for nonrelativistic fermions (I neglect the four point interaction term). $$ L = ...
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68 views

Special relativity: circumventing velocity-addition formula

Two spaceships approach an observer from an equal distance and from an opposite direction with an equal speed $v$ in the observer's intertial reference frame $O$. The speed of a spaceship in the ...
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121 views

Is everything moving at c in a c unit circle

I was trying to explain special relativity to a few friends in a simple way and wound up with an analogy using a c unit circle. I was using y as travelling in time, x moving in space; move in space ...
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Quantitative relation between two charges moving in parallel in two frames of reference

The relevant question is here. The accepted answer may have explained my question in a descriptive manner. However, I want to see how things are related quantitatively. Imagine we have two charges ...
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Do the effects of special relativity occur instantaneously?

Imagine a second earth one lightyear away from our earth. Now imagine a bunch of scientists with a plane and some atomic clocks who are living on this second earth and who perform the Hafele-Keating ...
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What is the speed of light from a star moving towards a observer.? [duplicate]

We can say that in vacuum speed of light is constant. But if the star is moving with a certain velocity does it add that velocity to the velocity of photons emitted out of that star?
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Length contraction and simultaneous length measurements

I am just working through an argument from Halliday Resnick to derive the Lorentz contraction (see quote below). Some paragraphs before this, the authors note that: If the rod is moving, ...
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122 views

Can special relativity be extended such that the frame of a photon makes sense?

Suppose I want to know what the universe looks like from the perspective of a frame of reference moving at $c$ relative to my current frame. As discussed at length in various other questions on this ...
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78 views

Arguments for finite speed of physical processes

When beginning a study of the special theory of relativity, one discovers that the theory of special relativity has as an axiom that the laws of physics are invariant with respect to transformations ...
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121 views

Dragon Ball Z: Hyperbolic Time Chamber *(also increased gravity training) [closed]

Firstly, I am sorry if this seems like a joke. It is not. I have always loved the Dragon Ball series, so this question has been on my mind for a while. Can ...
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Complete Energy Equation for Non-Zero Masses

The most simplified version of the energy equation (which is also the most known) is $E=mc^2$ However, I understand that this only applies to objects with non-zero mass and zero velocity. I also read ...