In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
The laws of physics are invariant (that is, identical) in all inertial frames of reference (that is, frames of reference with no acceleration).
The speed of light in vacuum is the same for all observers, regardless of the motion of the light source or observer.
Given a Weyl Hamiltonian, at rest,
\begin{align}
H = \vec \sigma \cdot \vec{p}
\end{align}
A Lorentz boost in the x-direction returns
\begin{align}
H = \vec\sigma\cdot\vec{p} - \gamma\sigma_0 p_x
\end{align}
The second term gives rise to a tilt in the "light" cone of graphene. My doubts...
I am trying to get this idea of Time dilation understood.
If there exists only two objects in a Universe and one object is stationary and the other object is moving at 99 % the speed of light. Their clocks were both synchronized when both objects were stationary relative to each other. Then the...
Homework Statement
I have noticed that in some calculations they use $$ \vec{\nabla}\cdot\vec{u}=\frac{1}{V}\frac{dV}{d\tau}$$. I would like to derive it.
Homework Equations
##\vec{u}=(\frac{dt}{d\tau},\frac{dx}{d\tau},\frac{dy}{d\tau},\frac{dz}{d\tau})##
##\vec{A}\cdot\vec{B}=A^{\mu}B_{\mu}##...
Problem statement:
A rocket propels itself rectilinearly by giving portions of its mass a constant (backward) velocity ## u ## relative to its instantaneous rest frame. It continues to do so until it attains a velocity ## v ## relative to its initial rest frame. Prove that the ratio of the...
Homework Statement
Special relativity: A rod traveling with the relativistic velocity of 0.866c moving towards a garage. The length of the rod is L, that of the garage is L/2. From the reference frame of the garage, we find the value of Lorentz factor = 2 we say that rod would fit inside garage...
Consider two bodies A &B are moving apart with a velocity V due to the expansion of space. According to an observer in A the body B is moving away and an observer in B feels the body A is moving apart. Can some one answer in which body the time dilates and why?. ( I am specifying once again that...
So, I am a newbie in quantum mechanics, took modern physics last fall for my physics minor.
I know that Schrodinger based his equation based on the equation K + V = E,
by using non-relativistic kinematic energy (P2/2m + V = E)
p becoming the operator p= -iħ∇ for the wave equation eigenfunction...
Homework Statement
A train of length L moves at speed 4c/5 eastward, and a train of length 3L moves at speed 3c/5 westward. How fast must someone run along the ground if he is to coincide with both the fronts-passing-each-other and backs-passingeach-other events?
Homework Equations
Velocity...
Suppose I'm an observer out in space and 30 km from me there's another observer, who is static with respect to me. Let's say my name is A and the other is B. We're both far far away from all the cosmical objects that might have a gravitational influence on us.
We both notice a spaceship flying...
Dear All,
I am doing the Special Relativity course at World Science U, and came across this question which I got wrong:
When 100 nanoseconds have elapsed on traveling Gracie's watch, she immediately stops, turns around, and heads back toward George at the same speed of her outbound journey...
I am trying to understand why the special relativity is not suitable for describing the gravity.
Consider a counterexample assuming it is the suitable and the space-time containing a gravitational mass is flat. Then one could describe the acceleration of a test particle from his inertial frame...
Dear All,
Just wanted to share this excellent free Special Relativity online course I came across by Brian Greene, which I believe is one of the best around. Not sure if it's been shared before here.
Special Relativity — World Science U, by Brian Greene...
Homework Statement
A cone has half angle θ0 and lateral surface area S0 in the frame in which the cone is at rest. If someone moves at relative speed β=v/c along the cones symmetry axis, what surface area will they see for the cone?
Homework Equations
I believe the lateral surface area of a...
Two spaceships with their engines shut off and identical radio receiver-amplifier-reemitting devices are in the empty space, very far from each other and from any celestial body. The lag time from absorbing to reemitting in the device is vary small compared to the return time of the signal (2t)...
Context
The following is from the book "Ideas and methods in supersymmetry and supergravity" by I.L. Buchbinder and S.M Kuzenko, pg 56-60. It is about realizing the irreducible massive representations of the Poincare group as spin tensor fields which transform under certain representations of...
I think special relativity would disallow our universe from having the structure similar to an ant on a sphere. What I mean is that it can't be possible to travel in a constant direction and to come back to your original location.
Suppose there is an observer S on a planet and an observer S'...
This may seem like a stupid question, but i can't get my head around this so please bear with me.
I just looked at the derivation of Dirac equation and my question is:
do the solutions for a free particle obey special relativity? because if yes why? I mean I thought using E2=(mc2)2+(pc)2 would...
I just want to be sure I understand this correctly:
Suppose there's a long spaceship moving in uniform motion relative to me (an inertial frame). Now someone in the front* of the spaceship calls someone (on the phone) in the back of the spaceship.
*(this long length of the ship is oriented...
I was reading about Rest Energy and came across this line:
"In special relativity, however, the energy of a body at rest is determined to be mc2. Thus, each body of rest mass m possesses mc2 of “rest energy,” which potentially is available for conversion to other forms of energy. The...
What is the correct way to expand (p3-p4)2 where p3 and p4 are 4-vectors, with metric gmu nu=diag[1,-1,-1,-1], p = [wp, p], where p is 3-vector, and wp= (p2+m2)(1/2)
Homework Statement
In a particle physics lab, an electron e− and a positron e+ collide, annihilate, and produce a W+ boson and a W− boson. Just before the collision, the electron and positron have a total energy of E = 100 GeV each, with velocities pointing along the +x-axis and -x-axis...
From the reference frame of the earth, the distance between the surface of the Earth and the muon is longer, but the muon survives because time for the muon is slowed down.
From the reference frame of the muon, the time experienced by the muon is not slowed down but the muon survives because...
Homework Statement
A particle of mass m is moving along the positive x direction with momentum p and energy E
It collides with a particle of the same mass at rest to form a new particle of mass M.
Show that
M^2 = 2m/c^2 * (E + mc^2) 2. Homework Equations
E^2= p^2c^2 + m^2c^4 The Attempt...
Homework Statement
i)A police spaceship P is chasing another spaceship A. Both ships have velocities βP = βA = 3c/5 as measured along the x-axis in the Solar System reference frame O. The police ship is a distance L = 1 light-second (i.e. the distance traveled by light in one second) behind...
Hi, I was wondering, as in the Bachelor's degree curriculum there is no SR course, for one who is interested in theoretical physics (as me), would do it alone, perhaps with texts such as Rindler or Synge ...?
Thank you in advance !
In his little book for the layman, Seven Brief Lessons on Physics author Carlo Rovelli states:
What is it about SR which is incompatible with gravity-as-a-force?
Its been a few years since I have done any special relativity so I am a bit rusty, need help with either my working/understanding or if correct, making sense of my answer. This is not CW, just a question from a past exam paper that I am using as preparation.
1. Homework Statement
Street light...
Homework Statement
Hi all, I'm given an electron with momentum 2.0*10-20kgm/s and was asked to convert the momentum into units of Mev/c then calculate the total energy of the electron, the lorentz factor and the speed of the electron, I did this successfully but then the question got confusing...
Two clocks A and B are orbiting a non-rotating planet. Each clock periodically transmits its current time value via a radio signal and the other can receive that value.
Their orbits are in closely-spaced parallel planes and both orbits are the same distance from the planet. The two clocks are...
While studying about some physics things, I came to know a term Relativistic beaming. I looked up in wiki and found a pretty decent article which gives you an equation where the real and apparent luminosity are related by a factor of (Doppler factor)^3-a where a is spectral index.
But where's...
I was reading about the Ehrenfest Paradox and it got me thinking about something (that I think is) similar:
Suppose we take a large, flat, and rigid disk, and we attach to various parts of it a number of clocks (some very close to the center of the disk, some along the edge, others in between)...
I'm reading the book "Quantum Field Theory and the Standard Model" by Matthew Schwartz and I'm finding it quite hard to understand one derivation he does. It is actually short - two pages - so I find it instructive to post the pages here:
The point is that the author is doing this derivation...
Homework Statement
Einstein developed much of his understanding of relativity through the use of gedanken, or thought, experiments. In a gedanken experiment, Einstein would imagine an experiment that could not be performed because of technological limitations, and so he would perform the...
Homework Statement
Consider the process of decay of a muon into one electron, one electron antineutrino and one muon neutrino using the Fermi theory. Assume the matrix element is, ignoring the electron's and the two neturino's masses,
|\mathcal{M}|^2 = 32G_F^2(m^2-2mE)mE
being E the electron...
Homework Statement
Muons of Kinetic energy 'E' are produced in collision with a target in a laboratory. The mass of a muon is ##106MeV/c^2## and its half life in it's rest frame is ## 1.4 * 10^{-6}## in its rest frame. what should be the minimum KE such that more than half of the muons...
I know variations of these have probably been asked numerous times before, but I'm having trouble with this specific scenario.
Imagine the classic Train Paradox, except instead of lighting strikes we have an observer at the centre of the train shooting laser pulses towards the rear (Event E1)...
Hello! I have a small problem with a task professor gave us. I tried many options (you will see below) but I cannot seem to get the right solution. Any advice or guideline how to solve this would be really helpful. In advance I thank you for helping me.
Homework Statement
Our professor of...
1. The problem statement, all variables, and given/known data
A car of proper length 12m is being driven at 0.9c through a garage of proper length 6m. The garage has a front and back door. The garage owner, Joe, says that the car will fit inside the garage with no damage to it, albeit for a tiny...
Homework Statement
Plane A flies with speed 0.6c chasing plane B which speed is 0.4c . Both speed is measured by observer on Earth. Then, plane B fires a small rocket which rest mass is 10 kg towards plane A. Rocket speed is 0.2c relative to plane B where c equals the speed of light in vacuum...
Homework Statement
A spaceship moves away from Earth at 0.9c and fires a probe in the same direction as its motion at 0.7c. What is the probe's velocity relative to Earth?
Homework EquationsThe Attempt at a Solution
The Lorentz velocity transformation is ##v_x' = \frac{v_x -...
Hello,
I read that satellites is effected by the time dilation caused by gravity and also by that one from special relativity. And so there is a need to prepare the onboard clock to ensure that the time is synchronized with a clock on Earth.
But why is this effect not symmetric? The...
As far as I understand it, the Lorentz factor ##\gamma(\mathbf{v})## is constant when one transforms between two inertial reference frames, since the relative velocity ##\mathbf{v}## between them is constant.
However, I'm slightly confused when one considers four acceleration. What is the...
Homework Statement
You approach an enemy ship at a speed of 0.5c measured by you, and the ship fires a missile toward your ship at a speed of 0.7c relative to the enemy ship. What speed of the missile do you measure, and how much time do you have measured by you and the enemy ship before the...
Given a massive particle traveling freely. Also assume that it is in a momentum eigenstate - a pure unmodulated sine wave in position space. In non-relativistic quantum mechanics, the phase velocity for that particle would be greater than the velocity of light.
Does the phase velocity for...
Homework Statement
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The problem is as follows: in a reference frame there is one electron at rest and one incoming positron which annihilates with the electron. The positron energy is E and two gamma rays are produced. Find first the energy of the photons in the center of mass frame as...
Special relativity states that the speed of light is constant for all the references, as long as they are not accelerating. For example, the speed of light would be c for a train moving linearly with a constant speed and would also be c for an observer who's not moving at all (I took the Earth...
Two chunks of rock, each having a mass of 1.00 kg, collide in space. Just before the collision, an observer at rest in the reference frame of a nearby star determines that rock A is moving toward the star at 0.800 c and rock B is moving away from the star at 0.750 c .
If the rocks stick...
The Lorentz transformation matrix may be written in index form as Λμ ν. The transpose may be written (ΛT)μ ν=Λν μ.
I want to apply this to convert the defining relation for a Lorentz transformation η=ΛTηΛ into index form. We have
ηρσ=(ΛT)ρ μημνΛν σ
The next step to obtain the correct...