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.

View More On Wikipedia.org
1. I Lorentz invariant phase space and cross section

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.
2. I Equation which is related with the Lorentz invariant quantities

Hi every one.How can i prove the below equation? And then that it's Lorentz invariant quantitude ? Thanks for your help
3. B Is Bell's inequality Lorentz invariant?

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 ?
4. A Showing Delta^3(p-q) is Not 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})) =...

17. Unraveling the Metric Found in Special Relativity

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...
18. Phonon Lorentz Invariance in Superfluids - Papers?

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..
19. Proof than an equation is Lorentz invariant

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...
20. Lorentz invariant integral measure

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...
21. Proving Maxwell's Equations are Lorentz Invariant

I want to know how can i prove that Maxwell's equations for the propagation of electromagnetic wave are Lorentz invariant.
22. Would magnetic charge be Lorentz invariant?

Would magnetic charge be Lorentz invariant (the way electric charge is) if magnetic charge existed?
23. LQG is not proved to be locally lorentz invariant. (Bee)

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...
24. Showing that the real Klein-gordon lagrangian is Lorentz invariant

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...
25. Particle number lorentz invariant?

Hi folks -- does anyone know of a proof that particle (quanta) number in QFT is / is not Lorentz invariant? I'd be happy to hear of it -- so thanks!
26. Proving the dor product of 4-vectors is Lorentz invariant

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
27. Are the following 2 equations lorentz invariant?

\partialμ\phi\partialμ\phi and \partialμ\partialμ\phi with \phi(x) a scalar field
28. When is something Lorentz invariant.

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...
29. Is power Lorentz invariant

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...
30. Lorentz invariant theory, irreducible representations

"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...
31. Mini black hole not Lorentz invariant?

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...
32. Gamma5 x d^2 Lorentz invariant?

is \overline{\Psi} γ5 \partial2 \Psi Lorentz Invariant? How does this term transform under Lorentz transformations? Here \Psi is a Dirac field. Thanks
33. Lorentz Invariant Volume Element

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...
34. Simple proof that the zero-point energy spectrum is Lorentz Invariant?

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...
35. Planck constant is Lorentz invariant?

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...
36. Derivation of Lorentz invariant

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...
37. Lorentz invariant lagrangian density

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...
38. Lorentz Invariant Vectors and Grammatical Errors

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...
39. Is quantum field theory really lorentz invariant?

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...
40. Why is energy-momentum tensor Lorentz invariant?

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?
41. Lorentz Invariant Majorana Neutrinos

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...
42. Physical interpretation of Lorentz invariant fermion field product?

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
43. Lorentz invariant measure

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)...
44. Why should the action be Lorentz invariant?

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.
45. Lqg is still local lorentz invariant?

How i can see the right lorentz invariance in lqg?
46. Lorentz invariant mass of electromagnetic field?

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...
47. Is the vacuum stress energy tensor Lorentz invariant ?

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...
48. E.H is a Lorentz invariant, when is it different from 0 ?

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...
49. Lorentz Invariant: What & When?

What makes an equation lorentz-covariant? When is an equation lorentz-invariant?
50. Difference between lorentz invariant and lorentz covariant

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...