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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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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53 views

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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43 views

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
526 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 x^{\mu^{'}}=\Lambda^{\mu^{'}}_{\,\,\...
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6answers
163 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
126 views

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
91 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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2answers
174 views

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
60 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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138 views

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
55 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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135 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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1answer
85 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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2answers
132 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. $$(O^{-1})_{μ}^...
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50 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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2answers
105 views

What happens during mass-energy conversion?

A mass is another form of energy. When a mass ceases to exist as 'matter', it exists as energy - in the forms of energy we generally know (light, heat). But is this so simple? When a mass exists in ...
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1answer
108 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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74 views

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
59 views

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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47 views

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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119 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
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
54 views

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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67 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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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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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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1answer
47 views

Time and velocity

Suppose two cars are traveling at a velocity of $c/2$ ($c$=speed of light) in two straight lines parallel to each other but in opposite direction in vacuum. Then what will a person sitting in one of ...
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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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1answer
93 views

Spin of a gauge field

I was wondering what is the simplest way to understand the reduction of the Wigner's little group from $SO(d-1)$ to $SO(d-2)$ when one considers massive and massless fields respectively (in a $d$ ...
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2answers
103 views

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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2answers
108 views

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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80 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 $B^0$...
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29 views

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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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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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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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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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. $$m(\vec{v})=m_{0}/\sqrt{...
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Special relativity and black hole paradox [duplicate]

Today a friend of mine posed me a paradox involving black-holes, one that I couldn't solve. Suppose we have planet, with a density such that it is almost to the point of turning into a black hole, ...
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92 views

Historical vs modern presentation of special relativity

I have noticed that historical or brief introductions of special relativity will discuss it in terms of inertial frames and postulates: Principle of Relativity - (from Einstein's 1905 paper) "the ...
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1answer
53 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 ...
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2answers
68 views

Is there a most efficient speed to travel in space with reference to time dilation? [closed]

I was thinking hypothetically, a ship traveling to a distant star system with something like food wants to get to the system as fast as possible. The trick is, we want to travel as fast as possible in ...
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2answers
114 views

Particle accelerators reaching light speed [duplicate]

I just have a question in mind that's stuck in my head, and it's why particle accelerators cannot accelerate any particle to the speed of light. I'm assuming it involves Einstien's theory of ...
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3answers
176 views

Do all predictions of special relativity follow from the Lorentz transformations? [closed]

Is there a proof that all observable predictions of special relativity follow from the Lorentz transformations? I have edited my question with concrete examples, so that it can be understood more ...
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Construct fields from from unitary representation of Poincaré group

I am trying to understand how construct fields from unitary representation of Poincaré group and the reasoning that Weinberg give in his book is the cluster decomposition principle and Lorentz ...
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1answer
81 views

How to construct fields from from unitary representation of the Poincaré group?

I want to construct fields from unitary representation of the Poincaré group but I do not know how. In Weinberg book he proposed that the Hamiltonian should be of certain kind and from that he derived ...
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2answers
151 views

Is it possible to go faster than the speed of light in vacuum?

If it is possible for particles to go faster than the speed of light in certain events, would it be possible to create a situation in which the barrier of the speed of light can be crossed?
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51 views

When spinning a pole with uneven mass at relativistic speeds will its center of gravity change?

Scenario: You have a pole that is a meter long and it is balanced when you rest it on your finger at the 10 cm mark due to the uneven weight distribution. (center of gravity at 10 cm mark) You also ...