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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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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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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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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Conservation of 4-momentum in special relativity

I understand that the inner product of two 4-vectors is conserved under the Lorentz transformations, so that the absolute value of the four momentum is the same in any reference frame. This is what I ...
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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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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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1answer
87 views

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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If a spaceship were to be able to travel at light speed, would it pass through objects undamaged? Would it damage/destroy objects?

We know, not just by scientific theory, but by practice (I have seen it with my own eyes), that an increase in velocity increases the mass of the given object proportionally. One day visiting a ...
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125 views

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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4answers
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Fundamental invariants of the electromagnetic field

It is a standard exercise in relativistic electrodynamics to show that the electromagnetic field tensor $F_{\mu\nu}$, whose components equal the electric $E^i=cF^{i0}$ and magnetic ...
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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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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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What would happen in this “close to the speed of light” scenario?

Say you had a really long pole made of a super strong material, and at the you turned it through an angle of (for example) 45 degrees. Turning the pole through a small angle at the bottom would ...
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1answer
71 views

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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1answer
46 views

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
107 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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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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Calculating threshold energy of particle reactions

{..everything that follows is in the domain of relativistic kinematics..} Say a particle A collides with a particle B at rest and produces particles C and D. What exactly is the definition of ...
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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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4answers
542 views

How can we know, today, that there's something from 100 light-years from here?

In my understanding, to take a picture of something that is 100 light-years from here, our "camera" would have to travel 100 years at light speed, take the picture, send to us, and 100 years later we ...
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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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213 views

Is this statement correct or incorrect: Moving objects undergo length contraction because they appear in space-time cross-section

Why or why not? This is closely related to another question I posited here, Does it make sense to say that objects moving at relativistic velocities appear in space-time cross-section? What I mean ...
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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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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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The Ehrenfest Paradox and Euclidian Assumptions [duplicate]

As a result of the Ehrenfest Paradox, the geometry of a rotating disc is non-Euclidean. However, while reaching this conclusion, we assumed that "the radius doesn't undergo Lorentz contraction", ...
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Does the pilot of a rocket ship experience an asymptotic approach to the speed of light?

A question has recently come up that goes beyond my knowledge of special relativity. Suppose a pilot has his foot on the gas pedal of a rocket ship and keeps it applied to achieve a constant ...
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60 views

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 ...
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1answer
166 views

What is the intuitive meaning of $Q^2$?

In particle physics, $-Q^2$ is defined by the four momentum transfer squared: $$Q^2 = -(p_i - p_f)^2 = (\vec{p}_i-\vec{p}_f)^2-(E_i-E_f)^2$$ For elastic scattering, the meaning of $Q^2$ is clear - it ...
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Generators of Poincare Groups

How can I determine the generators of the Poincare Group, $P(1,3)$ explicitly? Here $P(1,3)$ means a matrix Lie group.
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1answer
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Does scale invariance imply massless or continuous mass distribution?

$\newcommand{\ket}[1]{\lvert #1 \rangle}\newcommand{\bra}[1]{\langle #1 \rvert}\newcommand{\scp}[2]{\langle #1 \vert #2 \rangle}$ In his 2008 slides (PDF), Tzu-Chiang Yuan mentions the following on p. ...
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402 views

Finding the total energy in centre of mass frame

I'm working through a problem in a special relativity textbook (Woodhouse) and I'm having some difficulty. I have to show that if I have a particle of rest mass $M$, total energy $E$ colliding with a ...
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Deriving the Electromagnetic Tensor

The electromagnetic tensor is given as: \begin{equation} F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \end{equation} How do you derive this? And how come there is a partial derivative in ...
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Relativistic particle decay in ZMF [closed]

This is a problem that I feel is harder than I am making it but say you have: A particle at rest of mass $M$ decays into two smaller particles of masses $m_1, m_2$ where $m_1 \neq m_2$ and $M > ...
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Why time slows only for moving object and not stationary observer? How the “stationary” & “moving” are decided? [duplicate]

Explanation for the questions in the title: According to the the (special theory of) Relativity, if an observer is stationary and sees a fast moving object then time runs faster for the observer ...
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Momentarily Comoving Reference Frame Question

Consider a reference frame $S'$ moving with constant velocity $\vec{V}$ relative to a second nonrotating reference frame $S$. Also consider a particle moving along a trajectory $\vec{r}$ with perhaps ...
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Frustrated by the light clock special relativity thought experiment [closed]

Here is this age old thought experiment being told by a professor on Sixty Symbols: https://youtu.be/Cxqjyl74iu4 This explaination using the light clock is extremely frustrating. How can one use a ...
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Conservation of linear momentum (classical mechanics and special relativity)

How did Newton deduce the law of conservation of linear momentum? Can it be derived only by Newton's laws, or does it follow from practical experiments? If the law of conservation of linear momentum ...
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A doubt in special relativity

I read in the Feynman Lecs about muons. They are created in the upper atmosphere and hav a lifespan of about 2.2 micro seconds and if there was no relativity, they can travel as much as 600 metres ...
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75 views

Electron positron collision producing mesons

An electron of an energy 9 GeV and a positron of energy E collide to produce a $B^0$ and anti-$B^0$ meson, each with a mass of 5.3 GeV. What is the minimum positron energy required to produce the ...
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1answer
79 views

Tachyons and Lorentz velocity transformation

In general, is it possible to apply the Lorentz velocity transformation to a tachyon? I have tried to do so but the results seemed very illogical. Here's my attempt: suppose an evil spaceship named ...
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4answers
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Does the special theory of relativity form the foundation of modern physics?

Does the Special Theory of Relativity "form" the foundation of Modern Physics? My question is in reference to Geoff Brumfiel's Scientific American article "Particles Found to Travel Faster than Speed ...
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1answer
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Magnetic field felt by an observer “orbiting” a proton

Classically, if one has an electron orbiting a proton, how can the magnetic field felt by an observer with the same instantaneous velocity as the electron be calculated? It seems that I may find the ...
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2answers
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How does one show Maxwell's equations in vector calculus form describe the same motion in all reference frames?

The covariant form of Maxwell's equations is Lorentz invariant. $$\partial_{\alpha}F^{\alpha\beta} = \mu_{0} J^{\beta}$$ $$\partial_{\alpha}F_{\beta\gamma} + \partial_{\beta}F_{\gamma \alpha} + ...
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1answer
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Is there any way to justify or derive the form of the Lorentz force from relativity theory?

Lorentz force is in this form: $$\vec{F}=q[\vec{E}+\vec{u}\times\vec{B}]$$ As we know, it is Lorentz-invariant. Is there any way to justify or derive its form from relativity theory?
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Using wormholes to see out of the visible universe

As is commonly known, using our telescopes, we can only see so much of the universe because of its faster than light expansion. However, although under normal circumstances it is impossible to see ...
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Lorentz group in SUSY

Why do we carry Lorentz group to be included also in supersymmetry? That is after we extend our symmetry to supersymmetry, we carry with us the Lorentz group. Why not other group instead?
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Why can the spin of a relativistic particle not be orthogonal to its momentum?

I have read that the 3-momentum of a relativistic particle cannot be orthogonal to its spin 3-vector. When thinking about how the spin vector transforms when the particle approaches light speed, it ...
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3answers
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Are all conserved scalars proportional to relativistic mass? [closed]

I have read in Rindler's relativity book that all scalars depend only on the magnitude of velocity of a particle and that are conserved are proportional to relativistic mass. ...
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1answer
51 views

What happens when an open string start to stretch in a full Neumann boundary scenario?

I'm only reading about string theory. I'm an undergraduate. I see that for a full Neumann boundary condition the ends of a relativist string travel at the speed of light. If they travel in opposite ...
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4answers
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Special relativity-measuring a lorentz contraction as reference frame changes

Ok so, in the context of special relativity alone, If you were to have a train moving at a speed near the speed of light (say 0.7c), and containing two people, who, with their watches synchronised in ...