-1
votes
0answers
16 views

Michelson-Morley Experiment, Time Dilation, Length Contraction assignment need help [on hold]

I have Physics assignment about Michelson-Morley Experiment, Time Dilation, Length Contraction need help. The question are in the pictures Thanks
2
votes
0answers
50 views

Show: Lorentz-invariance of solution of Klein-Gordon equation [closed]

Assume $\psi$ is a solution of the Klein-Gordon equation (KGE). Let $\Lambda$ be a Lorentz transformation. Show: $\phi = \psi(\Lambda^{-1} \cdot )$ is also a solution of the KGE. I try to ...
-1
votes
1answer
43 views

How fast must Nadia travel so that she is the same biological age as her twin upon returning to Earth? [closed]

Two twins, Nadia and Aidan, decide to have an adventure when they turn 21. Aidan chooses to travel to a distant star 10 light years away at a speed of 0.8c. Nadia decides to travel to a closer ...
2
votes
2answers
100 views

The variation of the Lagrangian density under an infinitesimal Lorentz transformation

I'm trying to introduce myself to QFT following these lectures by David Tong. I've started with lecture 1 (Classical Field Theory) and I'm trying to prove that under an infinitesimal Lorentz ...
-1
votes
1answer
70 views

Navigating a Time Machine

Notes: The background for this question is working out details of a sci-fi story. Answers to the effect of "time travel isn't possible" or "FTL isn't possible" are therefore not helpful. I'm looking ...
0
votes
1answer
68 views

Time Dilation Problem [closed]

I'm having some trouble using the time dilation formula. Say an astronaut leaves Earth for 10 years, at 0.85c. How much time has passed according to an observer on Earth? I tried using the ...
0
votes
2answers
66 views

Confusion about proper time

A spacecraft flies away from earth with a speed of 4.8 million meter per second relative to the earth, and then returns at the same speed. The spacecraft carries a clock that has been synchronised ...
1
vote
1answer
67 views

Special relativity: circumventing velocity-addition formula

Two spaceships approach an observer from an equal distance and from an opposite direction with an equal speed $v$ in the observer's intertial reference frame $O$. The speed of a spaceship in the ...
1
vote
1answer
35 views

Time difference in clocks of an accelerated frame [closed]

If we have two inertial frames $S$ and $S'$ and $S'$ is moving to the right w.r.t. $S$ with a velocity $v$. Suddenly $S$ undergoes negative acceleration (no longer being inertial) and after some time ...
1
vote
1answer
125 views

GPS Satellite - Special Relativity

I'm going through an old relativity assignment, and I've been asked to calculate the time dilation for a satellite which orbits the earth in 12 hours at 26000km from the surface, and travels at a ...
1
vote
1answer
71 views

Tensors in special relativity [duplicate]

I'm trying to understand tensors, but I've come across the following question: Let $T^{\mu\nu}$ by a $(2,0)$ tensor. Give the definitions of $T_\mu^{\,\nu}$, $T_{\mu\nu}$, and ...
1
vote
0answers
103 views

A question on an exercise from Gravitation by Misner, Thorne and Wheeler

My question is on problem 4.1 of Gravitation. In a generic case of electric field and magnetic field(i.e not $E=0$ or $B=0$ or $E$ and $B$ perpendicular), define the direction $\hat{n}$ unit vector , ...
2
votes
1answer
61 views

Relativity Question Fireworks explosion

A firecracker explodes at the origin of an inertial reference frame. Then, 2.0 microseconds later, a second firecracker explodes 300m away. Astronauts in a passing rocket measure the distance between ...
0
votes
1answer
67 views

Finding the total energy in centre of mass frame

I'm working through a problem in a special relativity textbook (Woodhouse) and I'm having some difficulty. I have to show that if I have a particle of rest mass $M$, total energy $E$ colliding with a ...
0
votes
0answers
49 views

Conditions that the coordinate must satisfy in order to become local inertial

Consider the coordinate transformation $$ \tilde x^a=x^a+\frac{1}{2}\Gamma^a_{bc}x^bx^c $$ I have shown that at the origin $O=(0,0,0,0)$, $$ \frac{\partial\tilde g_{ab}}{\partial\tilde x^c}=0 $$ ...
0
votes
0answers
33 views

(Special Relativity) Points that can be seen by an observer

Let the metric be $$ ds^2=(1+gz)^2dt^2-dx^2-dy^2-dz^2 $$ where $g$ is a positive constant. Let an observer be stationary at $x=y=0$ on the surface $z=0$ and look upwards at an angle $\theta$, how ...
0
votes
1answer
84 views

Bi-vector in Minkowski space

I have a problem, I have a bi-vector that define like: $\omega^{\mu \nu}=a^{\mu}b^{\nu}-a^{\nu}b^{\mu}$ where, $a^{\mu}=(a^0,a^1,a^2,a^3)$ and $b^{\nu}=(b^0,b^1,b^2,b^3)$ I need show that ...
2
votes
2answers
133 views

What is the relative speed of two near-light speed particles headed towards each other?

I understand that nothing can move faster than light due to time dilation. I want to build upon my understanding of Einstein's theory of Special Relativity, so I came up with this hypothetical problem ...
1
vote
1answer
54 views

Proof that 4-potential exists from Gauss-Faraday field equation

This is a problem concerning covariant formulation of electromagnetism. Given $$\partial^{[\alpha} F^{\beta\gamma]}= 0 $$ how does one prove that $F$ can be obtained from a 4-potential $A$ such ...
3
votes
1answer
110 views

4-velocity and 4-acceleration in instantaneous rest frames

I am trying to solve this problem: Consider a rocket moving relative to an inertial frame $\mathcal{F}$ , such that its worldline is given by ...
1
vote
1answer
133 views

Electric field generated by a point charge moving at the speed of light

As you see, this is the electric field generated by a point charge moving at constant speed v. I know that when $v$ -> 0, $E$ is just the Coloumb Law. But how do you interpret $E$ when $v$ -> $c$ ? ...
3
votes
2answers
101 views

Difference between “Lorentz transformation” and “proper orthochronous”

I'm doing an assignment and I've been given a list of $4 \times 4$ matrices and asked: Which of the following are Lorentz transformation matrices? Which are proper and orthochronous? But, as ...
0
votes
2answers
75 views

Special Relativity Problem [closed]

I am having trouble with the following problem: Fry travels in a rocket ship towards Leela, at constant relative speed $v$: Fry is delivering a pizza, which in its rest frame stays hot for ...
0
votes
1answer
75 views

A simple question about special relativity [closed]

Assume that the table moves with the velocity $\vec{v} = v\hat{i}$. For the observer at $x=0$, the event at $(ct',x')=(0,k)$ is observed at $(t,x)=(k\gamma\beta, k\gamma)$ using Lorentz's ...
26
votes
1answer
3k views

How long would it take me to travel to a distant star?

Suppose I wanted to travel to one of the recently discovered potentially Earth-like planets such as Kepler 186f that is 490 light years away. Assuming I had a powerful rocket and enough fuel, how long ...
0
votes
3answers
131 views

Time dilation in special relativity

Suppose a star ship is moving with some velocity. Two light pulses one in direction similar to star ship another opposite to it is shot towards the space ship. Then how time inside space ship adjust ...
1
vote
3answers
106 views

Distance Between Two Photons Calculated in Different Inertial Frames

I am a self-studier. This is a question from a text I am studying: The distance between two photons traveling along the $x$-axis of an inertial frame, $S$, is always $l$. Show that in a second ...
0
votes
0answers
41 views

Angles between axes after Lorentz transformations

Consider frame $K_1, K_2, K_3$ such that $K_1$ moves along the $y$ axis of $K_2$ with speed $v$ and $K_2$ moves along the $x$ axis of $K_3$ with speed $u$. Find the angle between the $x$ axis of $K_1$ ...
1
vote
1answer
64 views

Colliding particles at speeds aproaching c [closed]

(In natural units where $\hbar=c=1$.) Two particles are to be collided. Each of these particles has a rest mass of 0.9 GeV and they will be collided at equal but opposite speeds. What is the minimum ...
0
votes
1answer
37 views

Taking signal travel time into account in Special Relativity

I am having problems taking the time it takes for a light signal from an event to reach an observer into account: For instance, if we have two observers $A$ and $B$ who synchronize their clocks when ...
4
votes
1answer
152 views

Is there a graphical representation of the Lorentz transformation equations?

I always loved theoretical physics as a kid and when I came upon this site while seeking computer advice via superuser I had to stick my silly little head into an oasis of intelligence. I have often ...
0
votes
1answer
48 views

Simple question about the tidal force (Leibniz's notation confuses me)

I started going through Taylor and Wheeler's Spacetime physics (standard textbook on special relativity). This is from exercise 2.8. Basically we're dropping a bearing ball from a 315 m height above ...
1
vote
2answers
56 views

How would an electron bunch/beam look different in the rest and lab frames?

With respect to special relativity, I was wondering how the spatial dimensions would differ between the rest and LAB frame of an electron beam. System: Electron bunch/beam traveling in linear motion. ...
5
votes
1answer
123 views

Relativistic Doppler effect on gamma rays

I'm trying to solve the following problem : An electron-positron pair annihilates, creating two photons. At what speed must an observer move along the line of the photons in order that the ...
2
votes
2answers
157 views

Relativity on a moving train

I've been given the following scenario: Observer $B$ is in the center of a train carriage which is moving at velocity $v$ with respect to an observer $A$. Two light signals are emitted from ...
5
votes
1answer
120 views

$\tau$ pair production question

There's a question on my homework about the process $e^{-} e^{+} \rightarrow \tau^{+} \tau^{-}$. Specifically, it is claimed that the minimum energy required of the colliding positron and electron ...
0
votes
1answer
333 views

Lorentz transformation for electric and magnetic fields

How do derive the following transformation rule (J.D. Jackson third Edition 11.10) for electric and magnetic field? $$\vec E' = \gamma \left( \vec E + \vec \beta \times \vec B\right) - ...
1
vote
2answers
114 views

Time dilation and relativity

We've just started with relativity and I got a question regarding an exercise we got. A spaceship passes by earth on its way to planet X, at the moment it passes by Anna is born on the spaceship. Can ...
3
votes
1answer
178 views

Proper time along path in Minkowski Space

Consider the path $x^\mu(u)$ in Minkowski space; such that: $$t = \frac{a}{c} \sinh(u) , \quad x = a \cosh(u) ,\quad y = 0 ,\quad z = 0 $$ where $a$ is a positive constant and $u$ is a parameter ...
1
vote
0answers
56 views

Questions on 4-vector velocities and invariance [closed]

Unfortunately, I missed a few lectures on four-vectors and I am pretty confused on how to go about solving the below question. I would be extremely grateful for any responses or solutions to enlighten ...
1
vote
1answer
90 views

Problem understanding a step in derivation of Lorentz Transformation

I need to understand a step in the derivation of Lorentz Transformation. I cannot understand how can we equate the equations 1 and 2. I am talking about the relation between ct, x, y, z. Where ...
2
votes
2answers
146 views

Showing the Poincare invariance of a term

I know that this is a simple question! But I would like to know the details. How we can show that the term $$A_\mu(x)\dot{x}^\mu$$ is global and local Poincare invariant? Where $A_\mu(x)$ is ...
2
votes
2answers
200 views

Peskin and Schroeder Equation 3.23

I've been trying (for a while) to prove that $S^{\mu\nu}:=\frac{i}{4}\left[\gamma^\mu,\,\gamma^\nu\right]$ is a representation of the Lorentz Lie algebra, that is, to prove that it satisfies the ...
1
vote
1answer
151 views

Combining relativistic velocities in the same direction using Lorentz transformation matrices

It is known that when combining the Lorentz Transforms of two frames with velocities $v_{1}$ and $v_{2}$ in the same direction it is equivalent of computing a Lorentz Transform of a single frame with ...
6
votes
2answers
620 views

Infinitesimal Lorentz transformation is antisymmetric

The Minkowski metric transforms under Lorentz transformations as \begin{align*}\eta_{\rho\sigma} = \eta_{\mu\nu}\Lambda^\mu_{\ \ \ \rho} \Lambda^\nu_{\ \ \ \sigma} \end{align*} I want to show that ...
1
vote
0answers
57 views

A problem about special relativity [closed]

i can't understand it clearly, so please help me!
0
votes
0answers
70 views

Transformation of a time-dependent acceleration to another frame

How do I transform a time-dependent acceleration between to rest frames? I was given a particular problem and while I found possibilities [1] [2] for acceleration-transformations when the acceleration ...
2
votes
1answer
113 views

Lorentz transformation - need a little clarification

So the question states: A's and B's systems are related by the standard Lorentz transform. B simultaneously fires off two photons from transmitters distance D apart along the x' axis, and in the ...
2
votes
1answer
210 views

twin paradox question

I'm trying to wrap my mind around the twin paradox, but I can't figure out this one problem from my textbook. It uses the relativistic Doppler effect to demonstrate how the paradox works. The first ...
2
votes
1answer
846 views

How do I derive the Lorentz contraction from the invariant interval?

Reviewing some basic special relativity, and I stumbled upon this problem: From the definition of the proper time: $$c^2d\tau^2=c^2dt^2-dx^2$$ I was able to derive the time dilation formula by using ...