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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Potential energy in $E_f^2=(mc^2)^2+(pc)^2$?

Let's consider $$E_f^2=(mc^2)^2+(pc)^2$$ where the $mc^2$ is the rest energy due to the rest mass -- in Finnish "lepomassa". $$ \sqrt{(mc^2)^2+(pc)^2} - mc^2~=~(\gamma-1)mc^2$$ is the kinetic ...
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Matrix manipulation for Dirac matrices

From the Dirac equation in gamma matrices, we know that $$\gamma^i=\begin{pmatrix} 0 & \sigma^i \\ -\sigma^i & 0 \end{pmatrix}$$ and $$\gamma^0=\begin{pmatrix} I & 0 \\ 0 & -I ...
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If airplanes' highest speed depends directly on the air it is moving through and not the ground,

If airplanes' highest speed depends directly on the air it is moving through and not the ground, does it mean we can build a time machine if only the air moves near the speed of light?
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Extended Rigid Bodies in Special Relativity

I was reading Landau & Lifshitz's Classical Theory of Fields and I noticed that they mention that an extended rigid body isn't "relativistically correct". For example, if you consider a rigid ...
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Charge conjugation in Dirac equation

According to Dirac equation we can write, \begin{equation} \left(i\gamma^\mu( \partial_\mu +ie A_\mu)- m \right)\psi(x,t) = 0 \end{equation} We seek an equation where $e\rightarrow -e $ and which ...
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Why geometrically four acceleration is a curvature vector of a world line? And what is proper acceleration?

Why geometrically four acceleration is a curvature vector of a world line? Geometrically, four-acceleration is a curvature vector of a world line. Therefore, the magnitude of the ...
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Is the “How to break the speed of light” minute physics video wrong?

I am referring to this video, on YouTube, by minutephysics, which has quite a lot of views. In the video it states that if you flick your wrist while pointing a laser that reaches the moon, that the ...
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1answer
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Intervals as infinitesimals of same order (Landau & Lifshitz)

I don't understand the following statement in Landau & Lifshitz, Classical Theory of Fields, p.5: $ds$ and $ds'$ are infinitesimals of same order. [...] It follows that $ds^2$ and $ds'^2$ must ...
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2answers
220 views

Can time dilation be explained by limitations on computing power?

Are there any ideas of explaining the time dilatation as limits in "computing power"? What I mean is basically that the greater is a concentrated mass, the harder is to "compute" what happens in such ...
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0answers
233 views

I need to understand the Lorentz transformation [closed]

Two observers A and B, in different initial system describe the same physical event with their particular, different space time coordinates . Let the coordinate of the event be $x^\mu$ for observer A ...
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2answers
390 views

Matrix operation in dirac matrices

If we define $\alpha_i$ and $\beta$ as Dirac matrices which satisfy all of the conditions of spin 1/2 particles , p defines the momentum of the particle, then how can we get the matrix form ? ...
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3answers
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How is quantum mechanics compatible with the speed of light limit?

Consider a free electron in space. Let us suppose we measure its position to be at point A with a high degree of accuracy at time 0. If I recall my QM correctly, as time passes the wave function ...
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1answer
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Empirical meaning of relativity in the context of QM

In special relativity an event E is mapped to coordinates (x,t) in one inertial frame, and to coordinates (x',t') in another, and SR provides the relation between (x,t) and (x',t'). What is the ...
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The definition of an inertial reference frame in Einstein's relativity

I'm reading Sean Carroll's book on general relativity, and I have a question about the definition of an inertial reference frame. In the first chapter that's dedicated to special relativity, the ...
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2answers
227 views

Photons and Relativity

Consider a Photon from Sun and travels with a velocity $c$. Now think we are that photon. For us, it looks like Sun is moving away from us with a velocity $c$. So, why don't we get attracted back ...
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What do massive photons have to do with superconductivity?

I keep reading that the idea of massive photons leads to an explanation of the Meissner effect but I fail to see how photons are involved with the repulsion of fields inside a superconductor. How ...
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1answer
177 views

Scattering Amplitudes in Centre of Mass Frame

I'm reviewing page 59 of the QFT notes here and am a little confused by a reference frame argument. You can compute the second order probability amplitude term for nucleon-nucleon scattering to be ...
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1answer
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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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Lorentz invariance of the integration measure

This is regards to the lorentz invariance of a classical scalar field theory. We assume that the action which is $S= \int d^4 x \mathcal{L}$, is invariant under a Lorentz transformation. How do you ...
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Why do many people say vector fields describe spin-1 particle but omit the spin-0 part?

We know a vector field is a $(\frac{1}{2},\frac{1}{2})$ representation of Lorentz group, which should describe both spin-1 and spin-0 particles. However many of the articles(mostly lecture notes) I've ...
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Why do Maxwell's equations contain each of a scalar, vector, pseudovector and pseudoscalar equation?

Maxwell's equations, in differential form, are $$\left\{\begin{align} \vec\nabla\cdot\vec{E}&=~\rho/\epsilon_0,\\ \vec\nabla\times\vec B~&=~\mu_0\vec J+\epsilon_0\mu_0\frac{\partial\vec ...
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1answer
323 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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Does Bernoulli's principle hold in moving reference frames? [duplicate]

Possible Duplicate: Bernoulli’s equation and reference frames Sometimes in train, when setting behind opening window, I can feel strong gale blowing in. The closer to the window the ...
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2answers
156 views

Mass-Energy Equivalency

We call $E=mc^2$ the Mass-Energy Equivalency because it equates mass and energy together. But, by that same logic, shouldn't we call $E=\frac{1}{2}(mv^2)$, the equation of kinetic energy in Newtonian ...
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Limitations on how far one can travel in the universe

Someone once incorrectly told me that, given the speed of light is the speed limit of the universe, aliens would have to live for hundreds of years if they are to travel distances of hundreds of light ...
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What does a sphere moving close to the speed of light look like?

What shape does the viewer in a reference frame with $v=0$ perceive? I suppose that since the sphere moves in one direction only (oX only, not oY) its section would change into an ellipse, where the ...
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1answer
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Classical vs. Quantum use of the spin 4-vector

I have a few basic questions about the Pauli-Lubanski spin 4-vector S. I've used it in quantum mechanical calculations as an operator, that is to say each of the components of S is a matrix operator ...
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1answer
256 views

Proper times of two observers in a three-torus

Consider two observer in a tree-torus space of size $L$. Observer $A$ is at rest, while observer $B$ moves in the $x$-direction with constant velocity $v$. $A$ and $B$ began at the same event, and ...
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How much does a proton weigh when it is going around the LHC at CERN?

Considering that speed increases weight and the proton is going at almost the speed of light, I would like to know how much a speeding proton would weigh in the LHC.
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Minimal voltage in linear accelerators to achieve relativity?

Could anyone tell me what is the minimal voltage between anode and cathode in a linear accelerators to achieve speeds where relativity starts to show? Let me ask in a different way: "What is the ...
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2answers
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Is there a way to formulate relativistic dynamics in a way that “hides” the finite speed of light?

I'm not referring to the dimensional choice that makes $c=1$; rather I'm imagining something more about replacing all references that apparently involve velocities with the appropriate $\gamma$ ...
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1answer
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Connecting 4-velocity to equation for adding velocities

Is there a way to connect 4-velocity to equations for adding speeds? I know 4-velocity $U^\mu$ is derived like this: \begin{equation} \begin{split} P^\mu &= m U^\mu \Longrightarrow U^\mu = ...
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2answers
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Terminology for opposite null lines

Is there a name for two null lines that lie on the opposite sides of the null cone? Each line can be obtained from the other by reflection in the axis of the null cone (the time-axis). In terms of ...
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The Four-Clock Special Relativity Conundrum

Two open-car trains approach each other at fixed velocities. Each has a radar to see how quickly the other train is approaching, but apart from that the trains have no a priori knowledge of each ...
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1answer
168 views

Why is energy-momentum 4-vector so much easier to explore/observe than spacetime 4-vector

I have read that spacetime 4-vector is quite difficult to observe/explore and that energy-momentum 4-vector is much more appropriate for CERN etc. Why is that? Could anyone give me a brief ...
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2answers
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Two photons of different frequencies collide to create electron and positron

A photon of frequency f, and another of frequency f' (take f' as given) collide to create an electron-positron pair. The frequency f is such that when the collision is head on, there is exactly enough ...
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1answer
263 views

Temporal part of Quantum Wavefunction

I was hoping that someone could give me the more fundamental reason that we take as the temporal part of a quantum wavefunction the function $e^{-i\omega t}$ and not $e^{+i\omega t}$? Clearly ...
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2answers
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What's the difference between space and time?

I'm having a hard time understanding how changing space means changing time. In books I've read people are saying "space and time" or "space-time" but never explain what the difference is between the ...
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346 views

Does General Relativity encompass Special Relativity?

Can all of the predictions made in Special Relativity (SR) also be made in General Relativity (GR)?
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4-momentum and an $y$ component of momentum

I have 2 coordinate systems which move along $x,x'$ axis. I have derived a Lorentz transformation for an $x$ component of momentum, which is one part of an 4-momentum vector $p_\mu$. This is my ...
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How to express $ds$?(when we know expression for $ds^{2}$) [closed]

We know that $$ds^2 = g_{\mu\nu}dx^{\mu}dx^{\nu},$$ Can you say how to calculate $ds$?
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1answer
190 views

Accelerating expansion of universe - entire universe a non-inertial frame of reference?

If the expansion of the universe is accelerating, doesn't that mean that the entire universe is a non-inertial frame of reference? And if so, what implications does this have (if any)?
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Lorentz Transformations and Aberration

Why does the azimuthal angle, $\phi$, remain unchanged between reference frames in special relativity? Edit: Here is a link from "Radiative Processes in Astrophysics": ...
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Help identifying an expression for the action

I found the following expression for the action of a (free, I think) relativistic particle in my notes but I can't remember from what it came from: $$ S = \int_{0}^{N} \left [ ...
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2answers
208 views

Acceleration and relativity

Usually in physics books this equation used $a=\frac {dv}{dt}$ to calculate the relativistic acceleration. It is true that speed $v=\beta c$ don't have relativistic (Lorentz) factor, But time have a ...
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2answers
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If acceleration causes relative time dilation does the eventual deceleration reverse it?

If acceleration causes relative time dilation does the eventual deceleration reverse it? For example: traveling to Alpha Centauri Based on me reading this site: ...
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deriving a Lorentz transfomation for velocity vector components

If $S'$ and $S$ are two different inertial reference frames and $S$ moves along the $x$ axis of $S$ in a standard configuration, then the Lorentz transformation will be: $$x'=\gamma(v)[x-\beta ct]$$ ...
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3answers
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Why does an object with higher speed gain more (relativistic) mass? [duplicate]

Today, in my high school physics class, we had an introductory class on electromagnetism. My teacher explained at some point that an object with a very high speed (he said it started to get somewhat ...
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Special Relativity [closed]

Could someone explain to me how special relativity works? I know there are thousands of sources and databases of knowledge out there, but I find it difficult to understand, even after reading up on ...
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1answer
210 views

Vector transformation in special relativity

Please note that I am very new on this website so have some difficulties in writings as required here but trying really hard to learn quickly. La-Tex is the main problem but please understand me that ...