What is Lorentz: Definition and 1000 Discussions

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 Particles of mass ##m## and charge ##q## are initially traveling in a beam along the ##z## direction with speed ##v## when they enter a long magnetic quadrupole lens, where there is no E-field and the magnetic flux density is ##B = Ay\hat{i} + Ax\hat{j}##, and where A is a...

Hello! I read that for a boost, for which we have a matrix ##\Lambda## we must satisfy ##\Lambda_\alpha^\mu g_{\mu \nu} \Lambda_\eta^\nu = g_{\alpha \beta}##. I am not sure I understand this. If we have a boost along the x-axis the ##\Lambda_0^0## component is ##\gamma##, but ##\gamma^2 \neq 1 =...

Hello! Can someone recommend me some good reading about Lorentz and Poincare groups. I would like something that starts from introductory notions but treats the matter both from math (proofs and all that) and physics point of view. Thank you

can lorentz contraction be measured via quantum entanglement with one of the entangled particles moving near the speed of light? would the particle in motion be affected by lorentz contraction? if so, would the particle at rest follow suit and appear affected?

A current loop has a wire starting at its center. The wire terminates at the inside of the loop. The loop and wire have 150 and 15 ohms of resistance respectively. Both have 4 volts of potential across them. Looking at this I understand the the wire will experience a lorentz force because the...

Hi I was looking at the Lorentz transformation and I see that it moves in the x-axis if vt is positive. How can I re-arrange the lorentz transformations in a way that will cause the moving frame of reference to get closer to me. I was trying with x'=gamma(x-vt) but I don't know what x is equal...

As far as I understand it, the Lorentz factor ##\gamma(\mathbf{v})## is constant when one transforms between two inertial reference frames, since the relative velocity ##\mathbf{v}## between them is constant. However, I'm slightly confused when one considers four acceleration. What is the...

Hi folks, This is the Lorentz transformation in 1D, x axis: I want to get the second term of the time t equation, I mean vx/c2, in two dimensions, I mean for a point in the XY plane. I know this term arises because if we want to syncronize a point B with the origin what we do is sending a...

The Lorentz transformation matrix may be written in index form as Λμ ν. The transpose may be written (ΛT)μ ν=Λν μ. I want to apply this to convert the defining relation for a Lorentz transformation η=ΛTηΛ into index form. We have ηρσ=(ΛT)ρ μημνΛν σ The next step to obtain the correct...

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...

I've been working my way through Peskin and Schroeder and am currently on the sub-section about how spinors transform under Lorentz transformation. As I understand it, under a Lorentz transformation, a spinor ##\psi## transforms as $$\psi\rightarrow S(\Lambda)\psi$$ where...

Let ##\Lambda## be a Lorentz transformation. The matrix representing the Lorentz transformation is written as ##\Lambda^\mu{}_\nu##, the first index referring to the rows and the second index referring to columns. The defining relation (necessary and sufficient) for Lorentz transforms is...

Homework Statement 2. The attempt at a solution 3. Relevant equations In the first problems of that book i was using the Galilean transformations where V1 = V2 + V But if i use that then V1 = 0.945 - 0.6 V1 = 0.345 Is not the same result, so I am confused. In this new problems we are...

Hi I will write physics terms but actually this is a math problem. Consider a particle which moves in accordance with the following equation $$m\boldsymbol{\ddot r}=\boldsymbol B\times\dot{\boldsymbol r}-\frac{\gamma}{r^3}\boldsymbol r,\quad r=|\boldsymbol r|\qquad (*)$$ and...

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...

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}##...

Is there a way to explain Lorentz contraction on space-time diagrams ? I cannot find a way by myself. Your teaching will be appreciated.

Hello everyone, here I come with a question about inertial frames as defined in General Relativity, and how to prove that the general definition is consistent with the particular case of Special Relativity. So to contextualize, I have found that one can define inertial frames in General...

Homework Statement Reference frame S' moves at speed v=0.94c in the +x direction with respect to reference frame S. The origins of S and S' overlap at t=t′=0. An object is stationary in S' at position x′ = 140 m . Part B What is the position of the object in S when the clock in S reads 1.3 μs...

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)

Compare this with the definition of the inverse transformation Λ-1: Λ-1Λ = I or (Λ−1)ανΛνβ = δαβ,...(1.33) where I is the 4×4 indentity matrix. The indexes of Λ−1 are superscript for the first and subscript for the second as before, and the matrix product is formed as usual by summing over...

Let's say I have a charge q which is viewed from its rest frame. So it's velocity v is 0. So the so-called magnetic component of its Lorentz force, which is q v x B, is 0. But I can have a magnet moving in this frame of reference. Let's say the velocity of this magnet according to the charge's...

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

Homework Statement Show how one can obtain the Doppler transformation for the frequency of a receding source just using the Lorentz transformations for the energy (where E=h). Homework Equations Relativistic transformations for momentum and energy: E = γ(E' + vp'x) pc/E = v/c = β The Attempt...

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...

Hi all - hope I'm not beating a dead horse here, but I'm following up on at least two other threads (made sense to consolidate): There are theories of quantum gravity (or the Standard Model Extension) that allow for local Lorentz violation. So, my first question: is there any reason why there...

Hi forum, I followed through Feynamn's derivation to show the different times taken for light by the parallel and perpendicular paths of the Michelson Morley apparatus. He showed that it took longer for light to go to the far mirror and back if it were parallel to the direction the whole...

I was reading my textbook for my elementary modern class and the author said that a pulse of light from a light bulb would be spherical and could be expressed as x2 + y2 + z2 = c2t2 and x'2 + y'2 + z'2 = c2t'2. Then the author goes on to say that this cannot happen for both reference frames in a...

Posting as this was buried in another thread - If Lorentz invariance is broken in, e.g., whatever theory of quantum gravity turns out to be correct, what effect would this have (if one can speculate) on the physical vacuum? That is, for two observers, let's say, moving at different, constant...

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...

Hi all, Some recent comments from the forums here led me to do a bit of reading on the holographic principle, and to a posting on "The Reference Frame" by Lubos Moti about the (likely lack of) 'holographic noise' in the experiment by Craig Hogan at Fermilab...

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...

In my simulation of the twin paradox, i used the Lorentz transformation formulas to map events from one inertial reference frame into another IRF. Reading through various threads here, i read that spacetime is curved and that space can be considered flat only for small distances. So my...

Homework Statement Hi all I am having trouble working part b of a question that I am currently doing. I have attached the question below in a pdf file. I am really not sure where to start, I have looked in several book and can only think of relating to the light clock thought experiment. But...

Hi, I'm a (hobby) mathematician and only an amateur physicist, so maybe below there are only trivia questions. Thank you in advance for conversation and clarification. All mathematical proofs of "time dilation" I have looked at so far were based on the Pythagorean theorem. In all such proofs...

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

The Lorentz transformation operator acting on an undotted, i.e. right-handed, spinor can be expressed as $$e^{-\frac{1}{2} \sigma \cdot \mathbf{\phi} + i\frac{1}{2} \sigma \cdot \mathbf{\theta}}.$$ There is a very cool, almost childlike, derivation of this expression in Landau Vol. 4 S. 18 I've...

The left-handed Weyl operator is defined by the ##2\times 2## matrix $$p_{\mu}\bar{\sigma}_{\dot{\beta}\alpha}^{\mu} = \begin{pmatrix} p^0 +p^3 & p^1 - i p^2\\ p^1 + ip^2 & p^0 - p^3 \end{pmatrix},$$ where ##\bar{\sigma}^{\mu}=(1,-\vec{\sigma})## are sigma matrices.One can use the sigma...

I am not looking for a solution, just a "starting point"/guidance for calculating the expression: [M^{\mu \nu} , \phi_a] with M^{\mu \nu} being the angular-momentum operators and \phi_a being the field's component, which happens to transform under Lorentz Transformations: x'^\mu = x^\mu + \delta...

I am trying to derive from the Lorentz force equation the time derivative of the total energy. This involves using the equation for the jth electron in an electron beam traveling through an undulator. I have done it in such a way using the work done relation however I have been told that it is...

Homework Statement (a) Let p(t) be a smooth curve in the hyperboloid S = {(x, y, z) ∈ R3 |z^2 − x^2 − y^2 = 1, z > 0}. Prove that p(t) .L p'(t) = 0, where .L is the Lorentz product. (b) Prove that any non-zero tangent vector to S has positive (Lorentz)length. (Hint: Use the Cauchy-Schwarz...

Hello people, I am trying to model a motor in maxwell that has an array of magnets in it , the thing is that I get the non zero forces for the magnets even when there are no excitations if I choose virtual forces , I am selecting the whole array of magnets so the computation should be for the...

From Chris' perspective Bob is traveling with 1.5*108 m/s in direction a. Angelica is also traveling with 2.4*108 m/s in direction a. From Bob's perspective Chris is traveling with 1.5*108 m/s in direction b (The opposite of x). Angelica is traveling with 1.5*108 m/s in direction a. They all...

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...

By y I mean any perpendicular axis to the axis in which there is movement.

Homework Statement [/B] Two particles of rest mass m0 approach each other with equal and opposite velocity v, in a laboratory frame. What is the total energy of one particle as measured in the rest frame of the other? But the question gives a clue which reads "if (v/c)^2 = .5, then E =...

In the representation theory of Lorentz transformations, the words Clifford algebra and Dirac algebra are used interchangeably. However, there is a distinction between the two. Indeed, the Dirac algebra is the particular Clifford algebra ##Cl_{4}({\bf{C}})\equiv Cl_{1,3}({\bf{C}})## with a basis...

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...