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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Relativity of simultaneity: Is my reasoning here correct?

I have a situation similar to that underlying the twin 'paradox' - the observer m1 below remains stationary while the observer m2 goes off on a space-time trajectory, and then returns to m1's ...
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4answers
449 views

Mass in special relativity?

Is the mass of a object at rest defined by $$E=mc^2$$ where $m$ is the rest mass. I.e. does the rest mass include every thing from thermal to gravitational potential energy and every other possible ...
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3answers
282 views

The mass-energy equivalence for rest mass

It is clear that the kinetic energy can be derived as $(m-m_0)c^2$. However, why do we say that $m_0c^2$ is the rest mass energy? It seems that this mass-energy equivalence for rest mass is just a ...
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1answer
308 views

What do I see if I move quickly past a charge surrounded by iron filings?

This might be a straightforward exercise, in which case I apologize. Suppose I surround a charge by iron filings initially oriented in some fixed direction, and I then move past the charge at an ...
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2answers
52 views

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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1answer
90 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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0answers
32 views

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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0answers
36 views

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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2answers
189 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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0answers
23 views

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 ...
1
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1answer
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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1answer
82 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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0answers
63 views

What is the equation of state for a relativistic fluid/gas? [closed]

say we have a relativistic fluid/gas. now let us write: $e$ - energy density in the fluid's rest frame. $P$ - pressure in the fluid's rest frame. $n$ - number density in the fluid's rest frame. ...
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1answer
64 views

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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1answer
170 views

Hidden momentum

I'm trying to learn about hidden momentum. After reading what I could find with a google search, I understand that it is equal to the momentum carried by radiation, calculated with the Poynting ...
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0answers
52 views

Relativity of time in regard to speed of light [closed]

Someone stated that if you go on a train for 1 year going 99.999999999% the speed of light 233 year would have passed to those outside the train due to time dilation. So what speed do we perceive time ...
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2answers
69 views

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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0answers
50 views

Weinberg's QFT I Chapter 1 Problem 1 [closed]

I'm trying to solve the following problem: Suppose that observer $\cal O$ sees a $W$-boson (spin one and mass $m \neq 0$) with momentum $\textbf{p}$ in the $y$-direction and spin $z$-component ...
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1answer
183 views

Plane curve transform to moving inertial system coordinates

As a non-phycisist I hope my question makes sense and is understandable. It deals with special relativity. I suppose there is a e.g. plane curve ( e.g. a circle ) given in the x-y plane of of an ...
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2answers
2k views

What is time, does it flow, and if so what defines its direction?

This is an attempt to gather together the various questions about time that have been asked on this site and provide a single set of hopefully authoritative answers. Specifically we attempt to address ...
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0answers
19 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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2answers
38 views

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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1answer
51 views

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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0answers
21 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 ...
3
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1answer
53 views

Is time a vector in Minkowski space? [duplicate]

I am arguing about this topic with my school teacher in so long time, I want to finish this debate. My teacher's opinion is "Yes, Time is vector" because four-vector has $t$ component, and mine is ...
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3answers
78 views

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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3answers
160 views

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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1answer
49 views

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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0answers
34 views

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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2answers
222 views

Doppler effect of matter waves

We all know that the relativistic mass of a moving object in Special relativity increases for an observer who is measuring it for a moving object. We also know the the concept of particle-wave ...
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1answer
70 views

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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2answers
2k views

Why does time dilation cause you to age slower? And is time considered relative to the observer?

I understand that the higher your velocity the slower light will move. But how does time itself slow down while you are moving faster?
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1answer
100 views

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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1answer
41 views

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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2answers
59 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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5answers
127 views

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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1answer
108 views

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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2answers
369 views

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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1answer
46 views

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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2answers
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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0answers
39 views

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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1answer
42 views

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 ...
4
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1answer
67 views

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 ...
8
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1answer
89 views

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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2answers
81 views

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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1answer
50 views

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 ...
9
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1answer
378 views

How is the Photoelectric Effect affected by Blue-Shifting

I was thinking about the Photoelectric Effect and Blue-Shifting when I came up with a thought experiment that I couldn't think of an answer for. The thought experiment is as follows: A metal plate is ...
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2answers
114 views

(Hyper)Surface of Simultaneity

How can I determine the surfaces of simultaneity if I know the metric? In particular, what are the surfaces of simultaneity for rotating disk with Langevin metric: $$ ...
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1answer
416 views

Derivation of force law in special relativity

I've seen force defined in special relativity as the rate of change of 4-momentum $$ {\bf{F}} = \frac{d {\bf{p}}}{dt} $$ Can anyone comment on the following derivation of that relation? Take one ...
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0answers
34 views

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 ...