Dear reader,
there is a physics problem where I couldn't understand what the solutions.
It is about the lorentz transformation of a bilinear spinor matrix element thing.
So the blue colored equation signs are the parts which I couldn't figure out how.
There must be some steps in between which...
As we all know, for the reference frame S' and S of relative motion, according to Lorentz transformation, we can get
As we all know, for the reference frame S' and S of relative motion, according to Lorentz transformation, we can get
As we all know, for the reference frame S' and S of relative...
"My" Attempted Solution
To begin, please note that a lot - if not all - of the "solution" is largely based off of @eranreches's solution from the following website: https://physics.stackexchange.com/questions/369352/scalar-invariance-under-lorentz-transformation.
With that said, below is my...
I am trying to understand the last block of equations in the picture (after 3.31). In the first line of that block, he transforms the spinor ##\psi## which I have no problem with. What I have a problem with is the ##\gamma ^{\mu} \partial _{\mu}##. They form a Lorentz scalar, so they should not...
I would like to apply a General Lorentz Boost to some Multi-partite Quantum State.
I have read several papers (like this) on the theory of boosting quantum states, but I have a hard time applying this theory to concrete examples.
Let us take a ##|\Phi^+\rangle## Bell State as an example, and...
Since for the two events of Samir starting the stopwatch, and the stopwatch reaching 10.0s, Samir and his stopwatch are stationary from his own frame of reference, I said it was the proper time and that delta t0 = 10s. Then the speed of the moving frame of reference was 0.6c. I thought placing...
The Lorentz transformations are mathematically simple. I had always imagined they could be easily derived. I however just found out from another PF thread that this is not so. Their originators Lorentz and Poincaré simply stated them without derivation. And the "proofs" I have seen to date have...
Is it possible to derive the Lorentz transformation from time dilation and length contraction?
If so, how should I start?
I know how to derive it while considering 4 scenarios finding values of A, B,D,E in x'=Ax+Bt t'=Dx+Et
and the transformation is:
x'=(x-vt)/sqrt(1-v^2/c^2)...
Suppose I had cylindrically-symmetric rotating magnet surrounded by a plasma.
I rotate it on its axis at a constant angular velocity, and so the electric field E produced is non-solenoidal and can be described as the negative gradient of some potential V(x,y,z).
The electric field is induced...
Homework Statement
For massless particles, we can take as reference the vector ##p^{\mu}_R=(1,0,0,1)## and note that any vector ##p## can be written as ##p^{\mu}=L(p)^{\mu}_{\nu}p^{\nu}_R##, where ##L(p)## is the Lorentz transform of the form
$$L(p)=exp(i\phi J^{(21)})exp(i\theta...
Homework Statement
Special Relativity Question.
Consider objects 1 and 2 moving in the lab frame; they both start at the origin, and #1 moves with a speed u and #2 moves with a speed v. They both move in straight lines, with an angle θ between their trajectories (again in the lab frame). What...
I read the Special Theory of Relativity in Jackson's textbook, Classical Electrodynamics 3rd edition.
Consider the wave front reaches a point ##(x,y,z)## in the frame ##K## at a time t given by the equation,
$$c^{2}t^{2}-(x^{2}+y^{2}+z^{2})=0 --- (1)$$
Similarly, in the frame ##K^{'}## the wave...
This is an IB problem from November 2017. Two rockets are separated by 6E8m (2 sec x c, or two light-seconds), w.r.t. Earth, and are approaching Earth from opposite directions. Rocket A approaches from left at 0.6c. Rocket B approaches form right at 0.4c.
According to Earth, when do they...
Homework Statement
An electric dipole instantaneously at rest at the origin in the frame K' has potentials \Phi'=\mathbf{p}\cdot\mathbf{r}'/r'^3 and \mathbf{A}'=0 (and thus only an electric field). The frame K' moves with uniform velocity \mathbf{v}=\vec{\beta }c in the frame K.
Show that in...
Hi.
I'd like to ask about the calculation of Noether current.
On page16 of David Tong's lecture note(http://www.damtp.cam.ac.uk/user/tong/qft.html), there is a topic about Noether current and Lorentz transformation.
I want to derive ##\delta \mathcal{L}##, but during my calculation, I...
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 travelled by light in one second) behind...
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...
Why does it use t' in that equation and not t? Isn't the equation relative to what an observer in the external frame of reference see? So if it is why not using the time he register?
(The equation is uploades in the photo)
Homework Statement
Suppose that A', B', and C' are at rest in frame S', which moves with respect to S at speed v in the +x direction. Let B' be located exactly midway between A' and C'. At t' = 0, a light flash occurs at B' and expands outward as a spherical wave. (A', B', and C' are all on...
What was the need for Lorentz transformation in pre-relativity period?
Why was it necessary for the velocity of light to be invariant between different inertial frames and hence what was the need for Lorentz transformation when it was believed that velocity of light was constant with respect to...
For quite a long time now I'm having some trouble to bridge the gap between two different approaches to Special Relativity.
The first approach is the traditional one. It is the approach that Einstein presented in his paper and that is taught in most of the basic textbooks. In this approach...
In Einstein’s book Relativity – the special and the general Theory (authorized translation by Robert W. Lawson, University of Sheffield) in chapter XI (the Lorentz Transformation), he gives us these formulas as the transforms:
x’ = (x-vt)/sqr(1-(v^2/c^2))
y’ = y
z’ = z
t’ = t-(v/c^2) ∙x /...
Let's say you have a rod that is 10 meters long. Observer O sees the ends of the rod at (t=0, x=0), and (t=0, x=10). Observer O' moves at speed v = 0.8c relative to O. What is the length of the rod in O's perspective?
Using the length contraction formula L' = γL, we find that O' sees the rod as...
I recently started studying Special Relativity an my book discusses the following:
Say I have synchronized two separated clocks in a reference frame S, if then an observer in another reference frame S' for whom the clocks are moving sees the clocks he would say those clocks are out of...
Are you good with Lorentz' tranformations ?
I tought I was, until I tried to do this exercice (it is really classical):
Two planets, A and B, are at rest with respect to each other, a distance L apart, with synchronized clocks. A spaceship flies at speed v past planet A toward planet B and...
Hi,
I've been studying Dirac's theory of fermions. A classic topic therein is the proof that the equation is covariant. Invariably authors state that the gamma-matrices have to be considered constants: they do not change under a Lorentz-transformation. I am looking for the reason behind this. It...
I'm going through Ray D'Iverno's "Introducing Einstein's Relativity", and there is a step he makes in deriving the Lorentz transformations that doesn't seem necessary to me. So I'm not sure what I'm missing. He derives them from Einsteins postulates of relativity. From the postulate that the...