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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Relativistic correction to Hydrogen atom - Perturbation theory

Given the relativistic correction $$ H_1' = - \frac{p^4}{8m^3 c^2} $$ to the Hamiltonian (i.e. a perturbation), what does it mean when $[H_1', \mathbf{L}] = 0$? The book I'm reading says this implies ...
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2answers
105 views

Is acceleration relative in relativity?

Suppose a box A is moving relative to a Box B, then by time dilation equation if I take 1 sec passed for an observer in A then for an observer in B will be little longer. Now if I suppose that the box ...
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38 views

Galileo's ship experiment with a laser pen instead of a rock

Ship's mast experiment with the boat moving at speed v: If a rock is dropped from the mast, then for an observer inside the boat they will see this: For an observer outside the boat and on the ...
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1answer
29 views

Momentum equation of a beam hitting a stationary target to create antiprotons

I'm struggling with the solution of a physics exercise which is to calculate the minimum energy needed to create antiprotons when a proton beam scatters on a stationary proton target: $$p + p ...
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50 views

Meaning of constant $c$ [on hold]

I have a puzzlement over Einstein's expression $E = mc^2$. The constant expressed as $c$ is the measured speed at which Light crosses a vacuuum. BUT it is also used to denote the maximum possible ...
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47 views

Speed of light interpretation [on hold]

I was wondering if any theory interprets the speed of light such that light needs to stay and visit some small open set for each tick of time? Then it could be renamed law of the good guest or ...
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2answers
69 views

Definition of the Lorentz transformations [on hold]

Until very recently I believed that the Lorentz transformations were defined as "the transformations that carry one inertial reference frame into another". In Wikipedia's page we find something along ...
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5answers
309 views
+200

Can you deduce absolute motion through magnetism?

Trying to understand magnetism I stumble into this example: Suppose there are two electrons travelling side by side in deep space (say, between Mars and Jupiter) at 1 cm distance at .99 c. In this ...
3
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1answer
61 views

Homogeneity and isotropy and derivation of the Lorentz transformations

In deriving the Lorentz transformations I have found (from reading a few different sets lecture notes) that it is argued that they must be linear and thus there general form must be $$x'=Ax+Bt,\quad ...
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0answers
52 views

Zeroth component of 4-momentum and relativistic energy-momentum relation

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under ...
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0answers
37 views

Speed of the Coulomb Field Measured To Be “Infinite”

The paper "Measuring Propagation Speed of Coulomb Fields" by R. de Sangro et al points out that: ...the Lienard-Weichert retarded potential leads to the same formula as the one obtained assuming ...
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25 views

Inertial coordinate systems [duplicate]

In Newtonian mechanics, by the following two assumptions: (i) The time is absolute. (ii) The length is absolute. it is easy find the relations betweem two coordinate systems with uniform motion ...
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58 views

Path integral (sum over paths where $v>c$) [on hold]

The path integral formalism is used to get for example the propagator of particles. In this formalism we integrate over all mathematically possible paths (and weight them with the non-relativistic ...
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2answers
45 views

How do we determine if a certain physical quantity is a vector?

For instance in Newtonian physics we treat position of objects, displacements, velocities, forces, momenta, angular velocities etc all as vector quantities (little arrows in space which have a certain ...
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3answers
30 views

Frames of reference, relativity, and a ball thrown in the air

Ever since my high school physics days I found relativity fascinating but I don't think I have great insight even into special relativity. For example, in almost every lesson or video they give an ...
2
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1answer
79 views

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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Formation of nucleus [on hold]

Is it even remotely possible for a nucleus to be formed in the following way? Consider two nucleons approaching each other at extreme speeds. Could the relativistic increase in mass be so high to ...
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3answers
4k views

Deriving the speed of the propagation of a change in the Electromagnetic Field from Maxwell's Equations

I've been told that, from Maxwell's equations, one can find that the propagation of change in the Electromagnetic Field travels at a speed $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ (the values of which can ...
3
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2answers
843 views

Exact definition of momentarily comoving reference frame (MCRF)

Consider a particle $P$ in the framework of special relativity with position $r(t)=(ct,x(t),y(t),z(t))$ respect to an inertial reference frame $\Sigma=(ct,x,y,z;O)$. I need to know if the following ...
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1answer
52 views

Questions about null geodesic [on hold]

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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1answer
74 views

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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0answers
31 views

Difference in time for clock in attic vs clock in cellar [on hold]

This question is regarding relativity: Two clocks are stationed in a house, one in the cellar and one it the attic. Which one of the following statements is true? A : The clocks tick at the ...
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3answers
668 views

What if a faster-than-light particle is found?

What will be the consequence (severe ones) on laws of physics if a particle that travels faster than light is discovered? I am looking for a more general answer so that a high school student would be ...
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123 views

Model special relativity is built. Question: rod length is reduced by the fact, or it seems to us? [closed]

Model of special relativity is a system of two observers and two rods (Figure 1a). Here $AB$ and $A\,'B\,'$ - rods with a length $l_{\,0}$. At points $D$ and $D\,'$ are observers. $R$ - permanent ...
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2answers
180 views

Relativity gedanken experiment

Lets consider the following thought experiment: A spaceship is in circular orbit around Earth traveling at 99% of $c$ (the orbital distance is chosen in such a way that inside the ship there are no ...
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1answer
65 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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1answer
231 views

Lorentz invariance, energy-momentum conservation & the locality of interactions

I have been reading these notes ("Minkowski Spacetime: A Hundred Years Later", by Vesselin Petkov) 1, in which the author states (in the middle of the text on page 137) that "The only Lorentz ...
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64 views

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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2answers
99 views

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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2answers
502 views

Why doesn't the existence of proper-time $\tau$ imply a preferred reference frame?

A proper time interval $\Delta\tau$ for a given observer is a relativistic invariant. However, the calculation of $\Delta\tau$ requires reference to some arbitrary coordinate time t: $$\Delta\tau = ...
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2answers
281 views

Question/Doubt about Time Dilation Symmetry in Special Relativity

Apologies if this has been asked and answered before, as I am still having doubts reconciling the symmetrical effects of time dilation (i.e each frame sees clocks of other frame slowing down), and I ...
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2answers
119 views

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
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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
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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
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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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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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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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35 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
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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 ...
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
77 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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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
63 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. ...
3
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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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51 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
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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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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 ...