Hi,
I've read a number of posts here on PF about Einstein's clock synchronization convention.
In the context of SR we know the transformation law between inertial frame's coordinates is actually the Lorentz one. The invariant speed for Lorentz transformation is c (actually it coincides with...
Homework Statement
I have an assignment to prove that specific intensity over frequency cubed is Lorentz invariant. One of the main tasks there is to prove the invariance of phase space d^3q \ d^3p and I am trying to prove it with symplectic geometry. I am following Jorge V. Jose and Eugene J...
I have an assignment to show that specific intensity over frequency cubed \frac{I}{\nu^3}, is Lorentz invariant and one of the main topics there is to show that the phase space is Lorentz invariant. I did it by following J. Goodman paper, but my professor wants me to show this in another way...
I am working through Lessons in Particle Physics by Luis Anchordoqui and Francis Halzen; the link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 11, equation 1.3.20. The authors have defined an operator ##L_{\mu\nu} = i( x_\mu \partial \nu - x_\nu \partial \mu)##...
I've commonly heard it said that Lorentz invariance is equivalent to saying that special relativity is obeyed, although I also recall discussions arguing that this is not precisely and technically correct, although the two concepts heavily overlap.
I also understand that Lorentz invariance has...
Homework Statement
Show that ##d^4k## is Lorentz Invariant
Homework Equations
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Under a lorentz transformation the vector ##k^u## transforms as ##k'^u=\Lambda^u_v k^v##
where ##\Lambda^u_v## satisfies ##\eta_{uv}\Lambda^{u}_{p}\Lambda^v_{o}=\eta_{po}## , ##\eta_{uv}## (2) the Minkowski...
Homework Statement
[/B]
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...
Why is it that introducing a hard cut-off ##p^{2}=\Lambda^{2}## breaks Lorentz invariance? Is it simply that it introduces an energy scale and energy is not a Lorentz invariant quantity?
Sorry if this is a trivial question, but I just want to make sure I understand the reasoning as I've...
As I understand it, since space-time is modelled as a four dimensional manifold it is natural to consider 4 vectors to describe physical quantities that have a direction associated with them, since we require that physics should be independent of inertial frame and so we should describe it in...
Homework Statement
I am meant to show that the following equation is manifestly Lorentz invariant:
$$\frac{dp^{\mu}}{d\tau}=\frac{q}{mc}F^{\mu\nu}p_{\nu}$$
Homework Equations
I am given that ##F^{\mu\nu}## is a tensor of rank two.
The Attempt at a Solution
I was thinking about doing a Lorents...
I recently had someone ask me why we use 4-vectors in special relativity and what is the motivation for introducing them in the first place. This is the response I gave:
From Einstein's postulates( i.e. 1. the principle of relativity - the laws of physics are identical (invariant) in all...
I understand that in order to preserve the inner product of two four vectors under a change of coordinates x^{\mu}\rightarrow x^{\mu^{'}}=\Lambda^{\mu^{'}}_{\,\, \nu}x^{\nu} the Minkowski metric must transform as \eta_{\mu^{'}\nu^{'}}=\Lambda^{\alpha}_{\,\...
A well known math theorem says that - if the spatial dimension is odd - D'Alembert equation gives rise to a solution containing a term which is completely supported on the light cone.
A mathematical wrap up could be the following:
"in dimension 3 (and in fact, for all odd dimensions), the...
Hi all,
Just doing some hobby physics while I put off working on my research. In one dimension, the function
\begin{equation}
f(a,b)=[1-\exp(-(a-b)^2)]
\end{equation}
vanishes when a=b. In Minkowski spacetime though, such a function is not so easy to find (if you require Lorentz invariance). If...