Lorentz invariance Definition and 101 Threads

If we don't multiply time by the speed of light C, in Lorentz transformation equatins, the invariant tensor of U.U will not be equal to c^2. So it seems the coefficient of C is an obligation for parameter t. I thought it's just for visual convenience in graphs, besides C is not dimensionless.

This is probably a stupid question but, I want to show that a Lagrangian written in field theory is Lorentz invariant WITHOUT using the Lorentz transformation representation / generators. I know we know that a Lorentz scalar is automatically Lorentz invariant, but, I want to show this by...

Hi, starting from a recent thread, I'd like to discuss a point related to the Lorentz transformation of EM Faraday tensor field between inertial reference frame. As explained in this video at minute 11:20, in the Lab inertial frame there is only a magnetic field B in the region surrounding the...

Hi, I was thinking about the following. From a mathematical point of view, SR assumes the following postulate: spacetime is a flat Lorentzian smooth manifold. From the above and a minimal interpretation (i.e. a minimal set of "rules" to define the correspondence between mathematical objects...

I was going through Spacetime Physics by Taylor and Wheeler and came to a point where they showed a proof of Invariance of Spacetime Interval. You can find the proof Here and Here is the second part of that proof. They used an apparatus that flies straight "up" 3 meters to a mirror. There it...

What are the implications that the wavefunction is not Lorentz invariant?

In this popular science article [1], they say that if our universe resulted to be non-uniform (that is highly anisotropic and inhomogeneous) then the fundamental laws of physics could change from place to place in the entire universe. And according to this paper [2] anisotropy in spacetime could...

Are there non-smooth metrics for spacetime (that don't involve singularities)? I found this statement in a discussion about the application of local Lorentz symmetry in spacetime metrics: Lorentz invariance holds locally in GR, but you're right that it no longer applies globally when gravity...

I was reading a discussion where some physicists participated* where the topic of Lorentz invariance violations occurring in cosmology is mentioned. There, they mention that we can imagine a Lorentz-violating solution to the cosmological equations. What do they mean by that? Can anyone specify...

I have heard that some types of inhomogeneties and topological defects (like cosmic strings) in cosmology have been proposed to be able to break fundamental symmetries of nature such as the Poincaré, Lorentz, diffeomorphism CPT, spatial/time translational...etc symmetries... However, I have not...

I was discussing this paper with a couple of physicists colleagues of mine (https://arxiv.org/abs/2011.12970) In the paper, the authors describe "spacetimes without symmetries". When I mentioned that, one of my friends said that no spacetime predicted or included in the theory of relativity...

We derive the most basic laws of physics from several fundamental symmetries (those from Noether's theorems, gauge symmetries, Lorentz symmetry...). But are there any types of spacetime where no symmetries, no matter how fundamental, would be valid? Any special metric, geometry or shape?

Before introducing Special Relativity, a textbook highlights the inconsistency of Maxwell's Electrodynamics and Newtonian Mechanics through the standard discussion about the velocity of light in different frames of reference. A further inconsistency discussed. In some inertial frame of...

I am reading pretty much everywhere that LET (Lorentz Ether Theory, or call it Neo-Lorentzian Relativity, or whatever theory that involves a preferred undetectable frame with some yet unknown properties that make all the moving objects with respect to this frame length contact and time dilate)...

If ##\partial_{\alpha} J^{\alpha}(x) = 0## then ##Q \equiv \displaystyle{\int} d^3 x J^t(x)## is time-invariant. To show that if ##J^{\alpha}(x)## is a four-vector then ##Q## is also Lorentz-invariant, he re-writes it as \begin{align*} Q = \int d^4 x J^{\alpha}(x) \partial_{\alpha} H(n_{\beta}...

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...

I was looking at this video , and I was wondering if a (Riemannian)manifold violates the "lorentz invariance" would it become a discrete manifold?

The Lorentz covariance of Maxwell equations was known before Einstein formulated special relativity. So what exactly special relativity brought new with respect to mere Lorentz covariance? Is special relativity just an interpretation of Lorentz invariance, in a sense in which Copenhagen...

Why is that when there is lorentz invariance. Large 3-momentum corresponds to a large energy. And if there was no lorentz invariance. Large 3-momentum does not necessarily need to correspond to a large energy? What has Lorentz invariance got to do with 3-momentum having large energy or not?

We're trying to reduce the tensor integral ##\int {\frac{{{d^4}k}}{{{{\left( {2\pi } \right)}^4}}}} \frac{{{k^\mu }{k^\nu }}}{{{{\left( {{k^2} - {\Delta ^2}} \right)}^n}}}{\rm{ }}## to a scalar integral (where ##{{\Delta ^2}}## is a scalar). We're told that the tensor integral is proportional...

Homework Statement Prove that $$\begin{align*}\mathfrak{T}_L(x) &= \frac{1}{2}\psi_L^\dagger (x)\sigma^\mu i\partial_\mu\psi_L(x) - \frac{1}{2}i\partial_\mu \psi_L^\dagger (x) \sigma^\mu\psi_L(x) \\ \mathfrak{T}_R(x) &= \frac{1}{2}\psi_R^\dagger (x)\bar{\sigma}^\mu i\partial_\mu\psi_R(x) -...

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 a really naive question that I didn't manage to explain to myself. If I consider SUSY theory without R-parity conservation there exist an operator that mediates proton decay. This operator is $$u^c d^c \tilde d^c $$ where ##\tilde d## is the scalar superpartner of down quark. Now...

Hi there, I just saw some lectures where they claim that the Klein Gordon equation is the lowest order equation which is Lorentz invariant for a scalar field. But I could easily come up with a Lorentz invariant equation that is first order, e.g. $$ (M^\mu\partial_\mu + m^2)\phi=0 $$ where M is...

As I understand it Horava Lifschitz theory breaks lorentz invariance at high energies. Does this mean we should see photons from gamma ray bursts leave a signal of varying speeds of light for different frequencies?

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...

Hi all, Clarification question: I've read that string theory is manifestly Lorentz invariant - however, I'm confused about this being true in 4D spacetime or in the full 10D setting of the theory (well, one version anyway). At some point I'd also read in a paper that 4D Lorentz invariance...

Hello! I started reading stuff on QFT and it seems that one of the main points is for the Lagrangian to be Lorentz invariant, so that the equations of motion remain the same in all inertial reference frames. I am not sure however i understand how do non inertial reference frames come into play...

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...

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...

is spacetime Lorentz invariant like the quantum vacuum? They say the quantum vacuum is Lorentz invariant.. you can't locate it at any place.. but if spacetime manifold is also Lorentz invariant and you can't locate it at any place.. how come the Earth can curve the spacetime around the Earth...

Doesn't the Many Worlds Interpretation violate Lorentz symmetry when the universe splits?

Consider the following Lagrangian: ##YHLN_{1}^{c} + Y^{c}H^{\dagger}L^{c}N_{1} + \text {h.c.},## where ##L=(N_{0}, E')## and ##L^{c} = (E^{'c}, N_{0}^{c})## are a pair of ##SU (2)## doublets and ##N_{1}## and ##N_{1}^{c}## are a pair of neutral Majorana fermions...

One more question before Santa comes. There are a number of different related threads, so hopefully I'm not repeating this - however, I haven't found a crisp answer yet. If one introduces a UV cutoff in the vacuum energy (in an attempt to avoid having infinite vacuum energy), is it possible at...

I read Lucien Hardy's paper whose tittle was "Quantum Mechanics, Local Realistic Theories, and Lorentz Invariant Relativistic Theories". There, he argued that lorentz invariant observables which involved locality assumption contradict quantum mechanics. I tried to follow his argument, but got...

How to find some papers on Lorentz invariant extensioning of standard electromagnetism that include magnetic charges

Homework Statement For a plane, monochromatic wave, define the width of a wavefront to be the distance between two points on a given wavefront at a given instant in time in some reference frame. Show that this width is the same in all frames using 4-vectors and in-variants. Homework...

Homework Statement I'm asked to prove that Et - p⋅r = E't' - p'⋅r' Homework Equations t = γ (t' + ux') x = γ (x' + ut') y = y' z = z' E = γ (E' + up'x) px = γ (p'x + uE') py = p'y pz = p'z The Attempt at a Solution Im still trying to figure out 4 vectors. I get close to the solution but I...

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...

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...

Is it proved experimentally that the Planck constant is invariant in the moving system? If that experiment exists, would you show me that in detail?

I would like to prove the Lorentz invariance of the Klein-Gordon equation by proving the invariance of the action ##\mathcal{S} = \int d^{4}x\ \mathcal{L}_{KG}## under a Lorentz tranformation. I would like to do this by first proving the Lorentz invariance of the ##\mathcal{L}_{KG}## and then...

Homework Statement 1. Show directly that if ##\varphi(x)## satisfies the Klein-Gordon equation, then ##\varphi(\Lambda^{-1}x)## also satisfies this equation for any Lorentz transformation ##\Lambda##. 2. Show that ##\mathcal{L}_{Maxwell}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}## is invariant under...

Consider the Heaviside function ##\Theta(k^{0})##. This function is Lorentz invariant if ##\text{sign}\ (k^{0})## is invariant under a Lorentz transformation. I have been told that only orthochronous Lorentz transformations preserve ##\text{sign}\ (k^{0})## under the condition that ##k## is a...

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...

Hello, I am re-reading a book about quantum physics and general relativity. To introduce representation of the lorentz group, they explain the definition of lorentz group as the group of transformation that let x² + y² ... -t² unchanged. But in cuved space the distance is not the same as in...