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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Questions about null geodesic [closed]

Show for the null geodesic in 3D flat spacetime using polar coordinates so the line element is $ds^2=-dt^2+dr^2+r^2d\phi^2$. Do light rays move on straight lines? My question is that I only learned ...
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What is really sought when we purpose Einstein's postulates in Special Relativity?

Special Relativity can be motivated by looking at Maxwell's Electrodynamics and noticing that there is some kind of inconsistency between it and Newtonian Mechanics. Indeed, as Einstein pointed out on ...
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How to motivate the importance of the spacetime interval

The spacetime interval is a rather important thing in Special Relativity. It allows us to define the separation between any two events as spacelike, timelike or lightlike and more importantly, the ...
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What is the inconsistency between Maxwell's electrodynamics and newtonian mechanics?

As far as I understand, when a modification of a theory is made it is because some observation required this modifcation. Quantum Mechanics is a nice example of that: observations of microscopic ...
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Does contracted spring weigh more than stretched one?

(One of examples that potential energy contributes to mass.) Does hot object weigh more than cold one? (One of examples that kinetic energy contributes to mass.) If these are true and justified by ...
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66 views

Limits used to find non-rel limit of the Klein-Gordon equation

I just have a question regarding assessing the non-relativistic limit of the Klein-Gordon equation. In the book I'm following (Quantum Mechanics by Bransden & Joachain) they use the limits (Chpt. ...
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Classical Klein-Gordon theory is a free relativistic theory

The classical Klein-Gordon theory for a real scalar field is called a relativistic free theory. It is called a free theory because the dynamics of the degrees of freedom in the momentum space of the ...
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The derivation of the Mass-Energy(including mechanical energy) equivalence principle [duplicate]

(Not duplication! I couldn't find the answer for the general case, instead of the special case that I've already seen in Youtube I hyperlinked.) I will fully satisfy with not only a mathematically ...
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30 views

Livestreaming at near lightspeed [duplicate]

Please forgive me if this is a stupid question as I have a very rudimentary understanding of physics. I was reading about how the large hadron collider speeds up subatomic particles to near ...
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The mass-energy equivalence is a principle which can not be derived from anything? [duplicate]

Not duplication) I couldn't find the answer for the general case, instead of the special case that I already seen in Youtube I hyperlinked. I will fully satisfy with not only a mathematically ...
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83 views

Simulation of relativistic probe passing through an external solar system

I recently read about the Breakthrough Initiative to launch "StarShot", a nano-probe that is designed to travel to Alpha Centauri at $0.2c$. One of the challenges to be solved involves the precise ...
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Electron in a Magnetic Field: Force parallel to velocity?

According to the four-force given in this question, Force is parallel to velocity. But the Lorentz Force is perpendicular to velocity in a constant magnetic field. Is this a contradiction? [a ...
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Why do we not apply length contraction when finding out the time taken for objects moving at relativistic speeds?

I was going over a question on my own, then I took a brief look at the solution...it's basically about A rocket has a proper length of 250 m and travels at a speed v = 0.950c relative to the Earth. ...
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Twin paradox in special relativity: length contraction

Can the concept of twin paradox be applied to length contraction as well? meaning that the twin which is in spaceship will have its meter rod "actually" contracted while he will see his brother's ...
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20 views

Time Dilation for a photon [duplicate]

Does a photon experience any time. Since a photon is massless and hence travels at (c) then it should suffer infinite time dilation, and hence shouldn't experience no time?
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How to calculate the maximum speed of an object?

There is a spaceship, whose mass is $100 \, \mathrm{kg}$. The thrust of its rocket is $300 \, \mathrm{N}$. How is it possible to calculate the maximal speed that the spaceship can reach, and the time ...
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23 views

Lorentz invariance & Noether theorem of classical ED

I want to check invariance of the action under Lorentz boosts for classical electrodynamics. The action is $$S = \int \mbox{d}^4x F_{\alpha \beta} F^{\alpha \beta} $$ I assumed that the fields ...
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The Energy Equation

I've been studying the energy equation in relativistic motion $E= \frac{mc^2}{\sqrt{1-v^2/c^2}}$, which can be expanded as $$E = mc^2 + \frac{1}{2} mv^2\text{ + some other terms.}$$ I'm curious ...
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Which reference frame decides the relative velocity of two reference frames?

The following thought experiment is often used to introduce Special Relativity: The thought experiment fails to specify which reference frame establishes $\vec{v}$--the observer on earth or the ...
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Relative velocity of light beams

Assume two light beams moving in the same direction i want to use the relativistic velocity transformation equation to find the relative velocity with each other, Note : i let $C$=1 ...
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What's the connection between the pole contours of propagators and their causality?

Wikipedia distinguishes between three kinds of propagators for a scalar field: The Retarded propagator's contours have $\mathrm{Im}(k^0)>0$ on both poles, so its limit is completely in the first ...
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The motion-independent definition of force

I think we must be able to accomodate a definition of a force on some particle which is independent of the motion of the particle, for all kinds of forces, to surely verify the statement like 'force ...
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Determining Proper Time and Distance in Relativistic Systems

I'm having a heck of a time understand how to account for time dilation and space contraction in the following problem: A mothership traveling at 0.620 c toward the Earth launches a landing craft. ...
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Funny Time Dilation Relation

Today I was curiously calculating/comparing the times of moving observers and the time recorded by a corresponding stationary observer using Einstein's time dilation equation as detailed in Special ...
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If the universe is closed, does the twin paradox really matter? [duplicate]

By closed universe, I mean just something like 3-D analog of a closed ring or a sphere. I think it can be one of arguments that the universe must not be closed. Is that right? The paradox is just the ...
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How far does a photon move in the 4th dimension when it travels one light second? [closed]

In one second a photon moves 3x10^8 meters through the three spatial dimensions. Light's velocity is 3x10^8 m/s. If the photon moved at all in the fourth dimension, it's velocity would no longer be ...
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Simple length contraction question

The question I'm doing states that the nearest star to earth is 4 light years away, as measured on earth and a spaceship can get there in 5 years, as measured by an observer on earth. It asks how long ...
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Coulomb Gauge under Lorentz Boost

In the Coulomb gauge for the Maxwell potential we have $$ A^0 = 0 \\ \partial_i A^i = 0 $$ Under an infinitesimal Lorentz Transformation with parameter $\epsilon$, we have $$ A^\mu(x) \rightarrow ...
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Integrating elements of a Lie group with respect to parameters of the corresponding Lie algebra

I am working with an operator $\textbf{M}$ that is represented by the Lie group SO(1,3), thus it can be written as, $$ \textbf{M} = \exp{\textbf{L}} $$ where, $$ \textbf{L} = \begin{bmatrix} ...
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Could we find relativistic energy in a simple way?

I asked a couple of questions on mass(-energy) increasing with speed, but there is still a very simple aspect I cannot understand, I hope you can give a simple and direct answer: The formula to find ...
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51 views

Centripetal effect or curved space time

I think I understand both the centrepedal effect and Einsteins curved space time. However I am confused about which best describes the motion of a planet ( or other orbiting body ). Simply put, does ...
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68 views

Why don't people use Hamilton's equations for a relativistic free charged particle?

A charged relativistic free particle has the Hamiltonian in general: $$ \mathcal{H} = \sqrt{p^2c^2+m^2c^4}.$$ I read somewhere that says, it is possible to go further and say that the EoM are ...
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Do mechanical waves also carry momentum as well as energy? [closed]

I have read that electromagnetic waves carry momentum because they carry energy, while energy is equivalent to mass. So they carry momentum. But this explanation is in the context of special ...
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Why is a theory Lorentz invariant if the Lagrangian is Lorentz invariant?

For if I started by trying to make the Hamiltonian Lorentz invariant, I would have failed. Indeed, the Hamiltonian is part of a covariant tensor. But how do I know that the Lagrangian is not a part of ...
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Twin Paradox when both twins are moving [duplicate]

Let's say twin scientists A and B start on Earth. Twin A moves east at speed v comparable to light, and Twin B moves west at speed v comparable to light. After some time, they reverse directions and ...
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At what speeds does time dilations start to occur?

My question is, is it possible for time dilation to occur at a speed less than that of speed of light?
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What happens to a ball spinning with peripheral speed near to the speed of light?

I can't imagine such phenomenon. Would it becomes an ellipsoid, or maybe a straight line?
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How is time dilation consistent between both observer?

There is a special variant of time dilation paradox bugs me. Imagine there are 2 small spaceships moving toward each other in constant speed. Each ship has an observer on-board. According to both ...
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Stanford: “Objects in spacetime all move at constant speed $c$.” Are they right? [duplicate]

In this Stanford University lecture on Relativity, it is stated: Likewise, objects in spacetime all move at constant speed c in spacetime but if you change its direction, say by moving at speed v in ...
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Error in deriving constant acceleration relativistic distance

Bob accelerates away from Carol at proper acceleration $a$ (in light seconds per second), and Carol wants to know how far Bob has traveled when $t$ seconds pass in Bob's frame. Using ...
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Do Einstein's postulates of relativity emerge from the Minkowski spacetime metric?

Does the constancy of the speed of light for all observers naturally emerge from the Minkowski spacetime metric? Do Einstein's two postulates of relativity emerge from the Minkowski spacetime metric? ...
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Is the rate of light emissions actually the frequency of the light?

I am confusing with the concept of frequency in the context of Doppler effect studying SR. The Schutz says, if the source emits pulses more frequently, then the observer would see the lights not only ...
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Can $E=mc^2$ be derived from the Minkowski spacetime metric? $s^2=x^2+y^2+z^2-(ct)^2$?

Can $E=mc^2$ be derived from the Minkowski spacetime metric? $s^2=x^2+y^2+z^2-(ct)^2$? If so, how? Can the equivalence of mass and energy be derived from the Minkowski spacetime metric? Has someone ...
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What is the Lorentz group representation for a general spin?

Setup, as I understand things so far: One way to think about where the spin of a quantum field comes from is that it is a consequence of the ways that different types of fields transform under ...
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Synchronization of clocks

I have read the book "Introduction to special relativity " by Robert Resnick In the book I have found that "If the distance between the clocks is L, one observer will see the other clock lag his by ...
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Plane Wave Solutions of the Dirac Equation

I'm trying to understand the plane wave solutions of the Dirac Equation. But I'm still a newbie on indices notation and contravariant and covariant objects. What I don't understand is how to get: ...
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134 views

Meaning and logic of Einstein's train thought experiment

This seems to be a recurrent topic but I wasn't able to find any satisfactory discussion about this tought experiment. I will quote the original story from Einstein's and put my doubts inside: Up ...
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Force, Mass, Motion? $E = mc^2$

Does any object needs force to move? If 'yes', does the matter needs mass to form a force? These questions arises from me because $E = mc^2$ and $F = ma$ does not relate and one does not agrees with ...
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Radiative equilibrium of a relativistic black body

A black body in empty space in the CMB rest frame should (discounting starlight) come to an equilibrium temperature of around 2.7 K. However, if the body is moving relative to the CMB frame, one side ...
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Why is the speed of light being invariant and finite in all inertial reference frames?

I understand the basics of Lorentz transformation and Riemann Geometry but I still cannot understand why the speed of light is the same in all inertial references. Has anyone ever researched about ...