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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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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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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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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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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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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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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89 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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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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67 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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24 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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2answers
86 views

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. ...
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42 views

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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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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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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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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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
109 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
161 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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39 views

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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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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142 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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49 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 ...
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Time dilation and symmetry in special relativity

Trying to grasp special relativity concepts, I thought in the following experiment. Imagine Alice took a trip in a spaceship to another star. Now, she is returning close to light speed. When she ...
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58 views

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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At relativistic speeds, how is an object's increased mass created and distributed?

This question says that, at relativistic speeds, an object's increased mass will result in increased weight or gravitational force. But if we have increased mass and corresponding gravitational ...
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Does time dilation affect the speed of a moving object?

Imagine you are traveling at 99% of the speed of light. Will the speed of the moving object slow down for both objects and for the resting observer or either one?
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Confusion about reading of clock as seen from different inertial systems

Suppose a clock, located at point $x'$ in the inertial frame $S'$, registers two events $t_1'$ and $t_2'$. Let $\Delta t'=t_2'-t_1'$. The same two events will be registered by two different ...
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Objective velocity (Relativity theory) [closed]

Suppose that I have a velocity of (approximately) $c$. Then I decelerate with $c$ per hour for exactly one hour. Then I would know that I would be standing still in the end, because the decelleration ...
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Does the speed of light differ for two frames moving at different speeds relative to an non moving observer?

Wikipedia says that: The speed of light in a vacuum is the same for all observers regardless of the motion of the light source. How can this be true and and returning to my question, if there is ...
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Poincare group representation and complete set

In Weinberg's book of Qft, chapter 2 of volume 1, he uses the eigenstates of the four-momentum to construct the unitary irreducible representations of the Poincare group. My question is, since ...
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1answer
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Is this argument valid as to why we can (not can't) reach the speed of light?Please do explain [closed]

I have already asked this question on quora, with difficulty but I have not yet obtained a "works for me" answer. Please discuss with me about this.:) Q:Why can we not touch the speed of light? ...
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Stripped twin paradox [closed]

Consider an empty space, except for Alice and Bob. Suppose Alice sees Bob move away and then come back again. Suppose Bob sees Alice move away and then come back again. Suppose either of them will ...
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Can the single object accelerate? (Relativity theory) [closed]

Suppose space is empty except for one single object. According to relativity theory it doesn't matter whether we assign a constant velocity to it or not; in both scenarios the same is predicted. The ...
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Generation of back emf with relativistic approach to EM Waves

I learnt that Magnetic force around a current carrying conductor is nothing but relativistic electrostatic force observed by a charge particle from its frame of reference. But I am not able to ...
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Covariant and contravariant 4-vector in special relativity

I've just learned about contra- and covariant vector in the context of special relativity (in electrodynamic) and I'm struggling with some concept. From what I found, an intuitive definition of ...
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Is all of a black hole's mass situated arbitrarily close to the event horizon?

Forgive me if I'm thinking about black holes in completely the wrong way, but since time dilation increases to arbitrarily large amounts the closer you get to the event horizon of a black hole, ...
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Does hotter radioactive substance have longer half life?

Sorry to have a newbie question! But I want to ask, if it is possible to change the half life of radioactive substance by heating it, my hypothesis is: When substance becomes hotter, the kinetic ...
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1answer
86 views

Why is $|\Lambda^0_0| \ge 1$ for a Lorentz transformation?

I'm taking a course of QFT and in the notes that the professor gave us he says that for a Lorentz transformation $\Lambda^\mu_\nu$ we have $|\Lambda^0_0| \ge 1$. He doesn't give further information ...
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Minkowski space-time

Suppose we have the vector space $\mathbb{R}^4$ and the Lorentz's transformation $f:\mathbb{R}^4\to\mathbb{R}^4$. Consider a inner product $g$ given by: $$g(x,y)=x^1y^1+x^2y^2+x^3y^3-c^2t^1t^2$$ for ...
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Killing field in Minkowski space-time

If we look at the killing equation for a vector field $X$ in $\mathbb{R}^{(p,q)}$ (or on an open subset thereof) in coordinates with constant diagonal pseudo-metric we get: ...
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Can an event occur before or after the other one depending on what frame of reference we are in?

Two buses moving relative to each other with 30% the speed of light (4 light-min apart). Now by some mysterious way bus 1 comes to the knowledge that after 3 min-bus 2 time bus 2 is going to explode. ...
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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 ...