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39 views

Has this group something to do with the cone of light?

Consider the group $V=(-1,1)$ with addition $+_{rel}:V\times V\to V$ defined as: $$v+_{rel}w=\frac{v+w}{1+vw}$$ This group is analogous to the relativistic velocities where the speed of light equals ...
0
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1answer
62 views

To Be Forever Young [duplicate]

It is clear from the Lorentz Parameters, applied to Einstein's Equations, that as velocity, v approaches speed-of-light, c, the denominator (1 - [v/c]) tends to zero; when v=c, time, t=0: time stops?! ...
1
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3answers
86 views

Still confuse about tensor

In special relativity, a four-vector $\mathbf{x}$ in an inertial frame is related to $\mathbf{\overline{x}}$ through a Lorentz transformation $\mathbf{\Lambda}$: \begin{align} \overline{\mathbf{x}}...
1
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2answers
66 views

Sound wave and Principle of relativity

Principle of Relativity: "An experimenter doing an experiment in an inertial frame of reference can never measure the velocity of its own frame of reference. OR a law of physics is never expressed ...
1
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0answers
72 views

Motivation for the abandonment of inertial frames in general relativity [closed]

Inertial frames are at the core of special relativity. The laws of physics are supposed to be the same among them and free particles follow rectilinear paths in spacetime or simply stay at rest. Just ...
0
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0answers
91 views

Why the velocity $v$ is taken as value and not as definition in special relativity equations?

Why the velocity $v$ is taken as a value and the definition of velocity not applied on a relativistic equations? The equations of time dilation and length contractions as we know are $$L = {L_0}{\...
4
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3answers
287 views

Is it possible writing conservation of relativistic energy in this naive way?

Conservation of charge or rest mass can be written in this way and it is Lorentz invariant $$ \nabla \cdot (\rho \mathbf{u}) + \frac{\partial \rho}{\partial t} = 0 $$ So we could be tempted to naively ...
6
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3answers
264 views

The interference paradox

This is a thought experiment I created myself. Imagine two radio sources fixed at the ends of a rocket and they produce signal of same frequency such that they arrive at the center simultaneously and ...
5
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6answers
291 views

In Special Relativity, is it allowed to ask 'How much time has elapsed in a second inertial frame at a particular moment in the first inertial frame'?

Or is it a meaningless question? For example, A and his friend B are the same age initially. B travels relative to A at a very high speed. A keeps observing B from his frame. At one moment, A ...
1
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1answer
99 views

To prove: the integration measure is Lorentz invariant (Schwartz's problem 2.6b)

I am stuck on Schwartz's ("Quantum Field Theory and the Standard Model") problem 2.6b, and would be grateful for clarification. (I'm aware that this question has been asked and answered elsewhere (...
2
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2answers
78 views

What's incorrect about this reasoning regarding special relativity?

Say two spaceships start at the same point and from the vantage point of your inertial reference frame $S$, Spaceship A travels at $.75c$ and Spaceship B travels at $.25c$, travelling in the same ...
1
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2answers
61 views

Special Relativity - Reference Frames $S$ and $S'$

Consider the standard arrangement in special relativity. Let S' move in the +ve x-axis with a velocity V with respect to S Question: S then moves with a velocity -V with respect to S'. Is this an ...
2
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3answers
444 views

How to prove a 4D vector is a 4-Vector?

This is a fairly open ended question. Given a set of 4 Components, that is, a 4D Vector, what is the process for determining rather or not it is a "4-Vector" as defined in special relativity? I want ...
1
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2answers
48 views

What is the relativistic energy of a bounded static particle?

Premise: The speed of light is set $c = 1$. Let's consider an electron in an external electromagnetic field. Its four-momentum will be $$p^{\mu} = (E, \bar p) = (\gamma m_e, \gamma m_e \bar v),$$ ...
1
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1answer
60 views

Lorentz Factor from Minkowski's Original Paper 'Space and Time'

Consider the following figure: Minkowski, in his paper 'Space and Time', derives the Lorentz factor $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ from considerations of this figure. He ...
0
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1answer
28 views

Choosing the sign for speed in Lorentz transformations

I am studying the Lorentz transformations and while I [believe] I understand the principle of it (you’re sorta “translating” from one frame of reference to the other), I am having a lot of trouble ...
3
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1answer
87 views

Illusion that $v > c$?

I am currently studying length contraction in special relativity (and having the hardest time getting the harder exercises in my book right) and there is the following exercise in my book is driving ...
-1
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2answers
88 views

A beginner's question on time dilation [closed]

I have just started understanding relativity so the question might look absurd. I know that the faster we move through space , the slower we move through time. But I haven't understood it fully. I ...
2
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1answer
242 views

Does Sagnac effect imply anisotropy of speed of light in this inertial frame of reference?

There seems to be a consensus that the one - way speed of light is anisotropic in a rotating frame of reference (Sagnac Effect). According to this article Einstein synchronization "looks this ...
-1
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1answer
55 views

How do u get Eq3 from Eq2&Eq1 [closed]

I keep getting the wrong results by subbing eq1 into eq2 It’s from Kleppner’s an introduction to mechanics 2nd edition
0
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1answer
46 views

Minkowski diagram

I have not well understood the picture of geogebra regarding the angle of time (t') that is inclined compared to (t) of 26.57°angle . In the picture we see that the velocity is setted at 0.5c, for ...
4
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2answers
87 views

Lorentz-transformation

I don't understand how to derive the matrix representing the Lorentz-transformation given two systems S and S': $$x' = \Lambda x$$ these transformations do not leave the differences $\Delta x^\mu$ ...
9
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1answer
455 views

Combining two Lorentz boosts

Is it possible to express two Lorentz boosts $A_x(\beta)$ and $A_y(\beta)$ along the x/y-axis as one boost described by $A(\overrightarrow \delta)$? To answer this, I start by defining $\theta \equiv ...
1
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0answers
47 views

Is it possible to derive $2\times 2$ Lorentz transformation matrix from only eigenvectors?

As a preface, I am somewhat familiar with year 1 linear algebra but not too familiar with how one makes the connection to Lorentz transformation matrices so I apologize if the answer is obvious. One ...
0
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2answers
48 views

Special Relativity; 3 Momentum Conservation

In SR, I understand you can use 4 momentum conservation, but what are the special cases where you can use 3 momentum/energy conservation? An example I have seen is with $$P_1=(M_1, 0) \\ P_2=(M_2,0) \...
1
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2answers
51 views

Factorising a 4D Dirac delta function in a rest frame

I'm working through a QFT problem and at one stage in the solutions we have this step: $$\delta^{(4)}(p - q_1 - q_2) = \delta(E_1 +E_2 - M)\delta^{(3)}(\bf{q_1} - \bf{q_2}).$$ We are working in the ...
0
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1answer
55 views

Necessity to consider the square of Four Momentum

Why do we often need to consider the square of four momentum transfer $Q$ in scattering experiment or particle physics/cosmology instead of just the $Q$ itself?
1
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1answer
118 views

In what sense do photons exist?

In a photon's frame of reference travel is instantaneous, so presumably a photon cannot exist in its own frame of reference. I am not aware that a "beam" of photons interacts via gravity despite ...
8
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6answers
1k views

Lorentz invariance of Maxwell's equations in matter

I know that Maxwell's equations of electromagnetism are Lorentz invariant in a vacuum. But what about in a generalized medium, e.g. a metal, a rubber, a dielectric, a magnet? I have read it comes down ...
1
vote
6answers
234 views

Twin paradox - is acceleration relative? [duplicate]

The usual answer to the twin paradox is that the twin who undergoes acceleration is the one who finds the other has aged more, because the trajectory of the 'travelling twin' does not amount to a ...
0
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1answer
139 views

Why does time slow down ONLY for objects travelling at high speeds?

Today in physics class, we learned about the theory of relativity and how it relates to time dilation. We were given the example of two photon clocks- one stationary relative to the Earth, and the ...
0
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1answer
59 views

Speed of light as the maximum speed and movement course

Assuming we have 3 objects d,e,f moving on the same line while e is stationary, d is moving to the left at 'almost speed of light' and f is moving to the right at 'almost speed of light'. What is the ...
1
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1answer
85 views

Questions about special relativity, index in the Lorentz matrix

I'm studying special relativity I have read this: We have $ x^u = (ct, x^1,x^2,x^3) $. If we apply Lorentz transformation we can write: $x'^u = \Lambda^{u}_{\hspace{0,2 cm}\nu} x^{\nu} $ $x'_u =...
3
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2answers
139 views

Intuitive explanation for the Lorentz transformation for time

I've recently started learning SR, and while the Lorentz transformation for space is pretty obvious, just the Galilean transformation combined with space contraction, I can't figure out the ...
1
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0answers
30 views

What can I put in $x$ of Lorentz transformation? [closed]

Can I put "x = ct" in the red x?
0
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2answers
232 views

A simple proof covariance of Maxwell equations

I read that Maxwell equations are covariant under Lorentz transformations, but I can't find a proof. Or at least a proof understandable by someone that doesn't know higher mathematics (please don't ...
-1
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1answer
74 views

Thought experiment: if an observer can travel at the speed of light [closed]

What would the observer see if he could travel at the speed of light and shot a photon beam at the same time?
0
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1answer
43 views

Speed of light dependent on source velocity in other medium [duplicate]

Does speed of light depends upon the velocity of source in a medium (like water) other than space? if yes, does the speed gets added up when the light source moves in direction of light?
0
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2answers
70 views

Spaceship A and Spaceship B move in opposite directions at half the speed of light, and A fires a laser at B, does the laser light reach Spaceship B? [closed]

This question has been bugging me for a week now! I believe it would, but logically, I feel like I'm missing something. Please give a full explanation.
0
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1answer
88 views

Is this a right approach to show that $\partial_{\mu} \phi \partial^{\mu} \phi $ is Lorentz Invariant?

When trying to convince myself that $\partial_{\mu} \phi \partial^{\mu} \phi $ is Lorentz Invariant, I stumbled upon this approach: The last equation should read - $\partial_{i} \phi \partial^{i} \...
1
vote
2answers
90 views

What exactly is the meaning of length contraction? [duplicate]

Let's say a train of length $L$ (wrt ground) is standing on rails which have markings for every femtometre (or even smaller units). Now if someone takes a photograph and measures the distance between ...
0
votes
1answer
45 views

Rapidity in 4-vector Transformation

In Lorentz transformation we have a concept of rapidity as related to boost. Rapidity is defined as a hyperbolic angle α such that $$\tanh(α)=v/c .$$ This further defines a matrix for Lorentz ...
4
votes
2answers
171 views

Is this relativistic mass?

I have seen in a lot of places in here clearly stating that relativistic mass is outdated, that we can make do just fine with the concept of invariant mass,etc. But I've also seen people saying that a ...
4
votes
1answer
253 views

Special *set* of inertial frames in an EM field?

Just looking for confirmation of my understanding of the Wikipedia article on classification of electromagnetic fields: The article states that in the case where $E\cdot B = 0$ and $E^2-B^2 \not= 0$...
5
votes
2answers
88 views

Spacetime diagrams and their interpretation

Recently started an introductory course of relativity, and started learning about space time diagrams. I couldn’t figure out what are the uses of a spacetime diagram as an alternative to Lorentz ...
1
vote
2answers
156 views

Problem with speed of light

I constructed a thought experiment, can't figure the answer. Two long (say $1\ \rm{km}$ long) railway cars are on parallel east-west tracks in a zero gravity environment. Each car has a light source ...
0
votes
2answers
105 views

Lorentz transformation of a Weyl Spinor?

A left handed Weyl Spinor belongs to the $(\frac{1}{2},0)$ representation of the Lorentz group. So given the Spinor, the unitary representation of the Lorentz transformation should look like $\exp{iA\...
3
votes
0answers
55 views

In Einstein's 1905 paper on electrodynamics, what he meant by energy of electromotive force?

In his 1905 paper, Einstein says that when the magnet is in motion and conductor stationary, changing magnetic field in space develops electric field "of certain definite energy", and this starts ...
0
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3answers
77 views

Inertial frames?

This is from a book. A traing is moving on earth. A ball is sitting at rest (relative to the train) on the floor of the train which is moving at constant velocity relative to a tree. If the ...
0
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0answers
42 views

Velocity addition formula derived from velocity boosts

I understand the derivation for the equation the velocity in a boosted frame by taking the boosts of the differentials such that: $v'^{\mu}= \frac{dx'^{\mu}}{dt'} $ where $x^{\mu} = \Lambda^{\mu}_{\, \...