What is Lorentz invariant: Definition and 50 Discussions
In relativistic physics, Lorentz symmetry, named after Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame. It has also been described as "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space".Lorentz covariance, a related concept, is a property of the underlying spacetime manifold. Lorentz covariance has two distinct, but closely related meanings:
A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group. According to the representation theory of the Lorentz group, these quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a Lorentz covariant scalar (e.g., the space-time interval) remains the same under Lorentz transformations and is said to be a Lorentz invariant (i.e., they transform under the trivial representation).
An equation is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities (confusingly, some use the term invariant here). The key property of such equations is that if they hold in one inertial frame, then they hold in any inertial frame; this follows from the result that if all the components of a tensor vanish in one frame, they vanish in every frame. This condition is a requirement according to the principle of relativity; i.e., all non-gravitational laws must make the same predictions for identical experiments taking place at the same spacetime event in two different inertial frames of reference.On manifolds, the words covariant and contravariant refer to how objects transform under general coordinate transformations. Both covariant and contravariant four-vectors can be Lorentz covariant quantities.
Local Lorentz covariance, which follows from general relativity, refers to Lorentz covariance applying only locally in an infinitesimal region of spacetime at every point. There is a generalization of this concept to cover Poincaré covariance and Poincaré invariance.
Can someone please explain to me how can we obtain this integral in eq. 5.27 from eq. 5.26? I quite do not understand how is it possible to make this adjustment and why the (p_(f))^2 appeared there in the numerator and also why a solid angle appeared there suddenly.
I browsed the net and found :
https://arxiv.org/abs/quant-ph/0408127
It is said the value of Bell's operator depends on the speed, so how can it be Lorentz invariant ?
From page 22 of P&S we want to show that ##\delta^{3}(\vec{p}-\vec{q})## is not Lorentz invariant. Boosting in the 3-direction gives ##p_{3}' = \gamma(p_{3}+\beta E)## and ##E' = \gamma(E+\beta p_{3})##. Using the delta function identity ##\delta(f(x)-f(x_{0})) =...
Last night I was pleasantly surprised to discover that, given a particle trajectory
x^2 - c^2t^2 = a^2
when viewed through a Lorentz transformation
x' = \gamma (x-vt)
t' = \gamma (t - vx/c^2)
produces exactly the same shape
x'^2 - c^2t'^2 = a^2
.
I suppose this is equivalent to the...
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...
Modal interpretations are a class of realist non local hidden variable theories. However, they cannot be made fundamentally lorentz invariant. However, neither can bohmian mechanics but BH is still emprically lorentz invariant. So are modal interpretation empirically lorentz invariant as well?
We've just been introduced to Langrangians, and my lecturer has told us that the Lagrangian density ##\mathcal{L} = \frac{1}{2} (\partial ^{\mu}) (\partial_{\mu}) -\frac{1}{2} m^2\phi^2## is obviously Lorentz invariant. Why? Yes it's a scalar, but I can't see why it obviously has to be a Lorentz...
Homework Statement
Show that ##d^4k## is Lorentz Invariant
Homework Equations
[/B]
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...
Let ##j^{\mu}(x)## be a Lorentz 4-vector field in Minkowski spacetime and let ##\Sigma## be a 3-dimensional spacelike hypersurface with constant time of some Lorentz frame. From those I can construct the quantity
$$Q=\int_{\Sigma} dS_{\mu}j^{\mu}$$
where
$$dS_{\mu}=d^3x n_{\mu}$$
and ##n_{\mu}##...
Homework Statement
Professor C. Rank claims that a charge at (r_1, t_1) will contribute to the air pressure
at (r_2, t_2) by an amount B \sin[C(|r_2 − r_1|^2− c^2|t_2 − t_1|^2)] , where B and C are constants.
(A) Is this effect Galilean invariant?
(B) Is this effect Lorentz invariant...
Hi. This question most probably shows my lack of understanding on the topic: why are scalar fields Lorentz invariant?
Imagine a field T(x) [x is a vector; I just don't know how to write it, sorry] that tells us the temperature in each point of a room. We make a rotation in the room and now...
As I understand it, since space-time is modeled 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...
Hi.
I read that the Lorentz invariance Minkowski norm of the four-momentum
$$E^2-c^2\cdot \mathbf{p}^2=m^2\cdot c^4$$
has no analogue in Newtonian physics. But what about
$$E-\frac{\mathbf{p}^2}{2m}=0\quad ?$$
It might look trivial by the definition of kinetic energy, but it's still a relation...
In special relativity, we can prove that the metric is -+++ for all observers and that is by making use out of lorentz invariance. Some on this forum say that it comes as a result of constancy of light and others say that Minkowski predated einstein in making that metric, which was confusing...
It is said phonon(not photon) in superfluid experiments could also produce similar upper-limit speed effect which I'm not sure if that's also Lorentz invariant.
Another problem is that I can't dig out those paper that demonstrates this kind of effect. Anyone ever seen any of this paper? Thanks..
In Peskin and Schroeder page 37, it is written that
Using vector and tensor fields, we can write a variety of Lorentz-invariant equations.
Criteria for Lorentz invariance: In general, any equation in which each term has the same set of uncontracted Lorentz indices will naturally be invariant...
Hi
I'm studying electron-muon scattering
and now considering the Lorentz invariant integration measure.
The textbook introduced it, which use dirac delta function to show that d3p/E is a Lorentz scalar.
I understood it but I wanted to find other way and tried like this:
I need a hint on the...
Sabine Hossenfelder said...
Arun: This has never been proved. These deformations are problematic for other reasons, but they don't suffer from the density problem that I alluded to here, if that is what you mean, yes. LQG itself isn't actually based on a space-time network so the argument...
Homework Statement
Hey guys!
So this question should be simple apparently but I got no idea how to do it. Basically I have the following Lagrangian density
\mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)(\partial^{\mu}\phi)-\frac{m}{2}\phi^{2}
which should be invariant under Lorentz...
Homework Statement
Let A and B be 4-vectors. Show that the dot product of A and B is Lorentz invariant.
The Attempt at a Solution
Should I be trying to show that A.B=\gamma(A.B)?
Thanks
Hello there,
I'm having a real problem understanding when a certain 'something' (for example Eddington-Finkelstein coordinates) is Lorentz invariant or how you can 'calculate' it.
Heck, I'm not even sure if a coordinate system must be lorentz invariant, or if the metric in the equations...
Power, defined as P = dE/dt is Lorentz invariant according to
http://farside.ph.utexas.edu/teaching/em/lectures/node130.html, Eq. 1645
But, considering another equation for the power, P = q E v, where E and v are electric field and velocity vectors, respectively; this is obviously not the...
"In a Lorentz invariant theory in d dimensions a state forms an irreducible representation under the subgroups of SO(1,d-1) that leaves its momentum invariant."
I want to understand that statement. I don't see how I should interpret a state as representation of a group. I have learned that...
Let's say that we have a particle flying through space, at a collision course with a planet. As seen from an observer on this planet, the particle has an enormous energy, and its wavelength is just slightly bigger than the Planck length. As the particle falls down the gravitational well of the...
So, the upper light cone has a Lorentz invariant volume measure
dk =\frac{dk_{1}\wedge dk_{2} \wedge dk_{3}}{k_{0}}
according to several sources which I have been reading. However, I've never seen this derived, and I was wondering if anyone knew how it was done, or could point me towards...
In his article on the Zero-point Energy:
http://www.calphysics.org/zpe.html
Bernard Haisch says:
That the spectrum of zero-point radiation has a frequency-cubed dependence is of great significance. That is the only kind of spectrum that has the property of being Lorentz invariant. The...
It is widely recognized in physics textbooks that Planck constant is a "universal constant". But I nerver see a proof. As we know, in the special theory of relativity, c is a universal constant, namely a Lorentz invariant, which is Einstein's hypothesis. But How do we know the Plack constant h...
Some time ago, I came across a nice justification (by Einstein IIRC) for the formula x'^2 + y'^2 + z'^2 - c^2t'^2 = x^2 + y^2 + z^2 - c^2t^2.
The argument went something like this:
(1) x'^2 + y'^2 + z'^2 - c^2t'^2 = x^2 + y^2 + z^2 - c^2t^2 = 0 for light.
(2) *reasoning I forget*, therefore...
Hi,
Would someone know where I can find a derivation of the lorentz-invariant lagrangian density?
This lagrangian often pops-up in books and papers and they take it for granted, but I was actually wondering if there's a "simple" derivation somewhere... Or does it take a whole theory and...
A vector in special relativity is the quantity:
V = V^\mu \hat{e_\mu}
On a change of coordinates, the basis vectors co-vary with the coordinate derivatives:
\hat{e_\mu'} = \frac{\partial x_\mu'}{\partial x_\mu} \hat{e_\mu}
The vector elements are the opposite. They are said to be...
Hi guys,
Before responding to my post, please note that I am only familiar with the mathematics of nonrelativistic quantum mechanics, and don't know any quantum field theory. All I have is this vague idea that quantum field theory is the union of special relativity and quantum mechanics...
I'm studying General Relativity and facing several problems. We know that energy-momentum must be Lorentz invariant in locally inertial coordinates. I am not sure I understand this point clearly. What is the physics behind?
I have a two component Weyl spinor transforming as \psi \rightarrow M \psi where M is an SL(2) matrix which represents a Lorentz transformation. Suppose another spinor \chi also transforms the same way \chi \rightarrow M \chi. I can write a Lorentz invariant term \psi^T (-i\sigma^2) \chi where...
Hey all!
Just a very short question: May I interpret the Lorenz invariant quantity
\bar\psi\psi
as being the probability density of a fermion field? Thanks!
Blue2script
Hi
I have a question about Lorentz invariant measures,
consider an integral of the form:
\int d\mu(p) f(\Lambda^{-1}p)
where d\mu(p) = d^3{\bf p}/(2\pi)^3(2p_0)^3 is the Lorentz invariant measure.
Now to simplify this I can make a change of coordinates
\int d\mu(\Lambda q) f(q)...
Why should the action be Lorentz invariant? Every time I come across this it is assumed by the author without qualification. As too obvious to explain maybe? Ain't obvious to me.
An photon has mass zero by virtue of its momentum canceling its energy in
m^2c^4 = E^2-p^2c^2
But in electromagnetism a field configution only has momentum when both a magnetic field and an electric field are present, e.g. in an electromagnetic wave. Now when there is only an electric or...
In many textbooks on relativity, one finds at some point a statement that the vacuum stress energy tensor should be Lorentz invariant, from which it then follows that the vacuum pressure is minus the vacuum energy density.
However, the vacuum energy density (or stress tensor) is not an...
From the Lorentz-invariant Faraday tensor F(H,E) two scalar invariants can be constructed:
Inv1 = H²-E²
and
Inv2 = E.H
Thinking at waves, electrostatic fields, magnetostatic fields, I see examples where Inv2 = 0.
It is however easy to arrange an electrostatic field...
title says it all. I've heard these two phrases.
Lorentz invariant: Equation (Lagrangian, or ...?) takes same form under lorentz transforms.
Lorentz covariant: Equation is in covariant form.
I'm don't think I know what I mean when I say the latter. Can someone elucidate the...