Lorentz Definition and 1000 Threads

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...

We have that \Lambda^{\mu}_{\nu} = \frac{1}{2}Tr(\overline{\sigma}^{\mu}A\sigma^{\nu}A^{\dagger}) I would like to make sense of the statement that this is a homomorphism because the correspondence above is preserved under multiplication. Can someone clarify how I could see this?

Hello! Got a bit of an issue with thew two above mentioned equations about time. From the Lorentz transformation t' = [t - (vx)/c^2]/lorentz factor, we get that the time read by a moving observer for an event in the stationary observer's frame of reference will always be slower (longer) because...

Homework Statement Show that the isotropy and homogeneity of space-time and equivalence of different inertial frames (first postulate of relativity) require that the most general transformation between the space-time coordinates (x, y, z, t) and (x', y', z', t') is the linear transformation...

<<Moderators note: Discussion split from: https://www.physicsforums.com/threads/motivation-for-the-introduction-of-spacetime.866669/>> You think the violation of Bell's inequality is not a serious challenge? You have to give up realism as well as causality if you want to defend the...

The generators ##\{ L^1, L^2 , L^3 , K^1 , K^2 , K^3 \}## of the Lorentz group satisfy the Lie algebra: \begin{array}{l} [L^i , L^j] = \epsilon^{ij}_{\;\; k} L^k \\ [L^i , K^j] = \epsilon^{ij}_{\;\; k} K^k \\ [K^i , K^j] = \epsilon^{ij}_{\;\; k} L^k \end{array} It has the Casimirs C_1 =...

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...

Homework Statement Greetings So i was trying to solve following prolems: Homework EquationsThe Attempt at a Solution I did manage to solve problem 22 using E = NAB(2pi * f) E = (100)(0.005)(0.9)(2pi)(50) = 141.372 v But I have no idea what to do with problem 21. Mostly because I don't know...

Hey guys, In what circumstance or scenario would you use Lorentz transformations as a opposed to time dilation or length contraction? The reason that I ask this is because in all of the problems that I have worked with, the observer is always stationary relative to the event. For example, if...

You are probably familiar with the following two Lorentz transformations: x' = (x - vt) / sqrt(1 - v2/c2) and t' = [t - (vx/c2)] / sqrt(1 - v2/c2) Well I am having some issues interpreting what each variable refers to. You see, here is how I've been thinking of it: If you have one stationary...

I don't understand why we can write the elements of the lorentransformation in the form ## {\Lambda}^{\mu}\:_{\nu} = [exp(-\frac{i}{2}{\omega}^{\rho\sigma}M_{\rho\sigma})]^{\mu}\:_{\nu} ## I know that we can write it in the form ## {\Lambda} = exp(t\Theta) ## where ## \Theta ## are elements...

Homework Statement Consider the Higgs mechanism lagrangian, $$\mathcal L = (D_{\mu} \phi)^* (D^{\mu} \phi) -\mu^2 (\phi^* \phi) - \lambda (\phi^* \phi)^2 - \frac{1}{4}F_{\mu \nu}F^{\mu \nu},$$ with ##F_{\mu \nu} = \partial_{\mu} A_{\nu} - \partial_{\nu} A_{\mu}## and ##D_{\mu} = \partial_{\mu}...

I am trying to derive the potential based Lorentz gauge, but I am not sure if I am on the right track. Why the second partial derivative of vector potential must be 0? Please correct me where I got this wrong.

I am still a bit puzzled by this video: Does this mean that force exerted on an electrically charged particle facilitated by moving through magnetic field B is due to special relativity, and not virtual photons acting as magnetic force carriers? Thanks

Homework Statement Derive the Lorentz Transformation using light cone coordinates defined by ##x^±=t±x## ##x^+ x^-~## is left invariant if we multiply ##~e^φ~## to ##~x^+~## and ##~e^{-φ}~## to ##~x^-~##, that is ##~x'^+ x'^-=x^+ x^-## Homework Equations ##t'^2 - x'^2 = t^2 - x^2...

Hi Everyone. There is an equation which I have known for a long time but quite never used really. Now I have doubts I really understand it. Consider the unitary operator implementing a Lorentz transformation. Many books show the following equation for vector fields: U(\Lambda)^{-1}A^\mu...

Hi. In the attached proof for Lorentz transformation for momentum http://www.colorado.edu/physics/phys2170/phys2170_sp07/downloads/lorentz_transformation_E_p.pdf, there is this step that I don't understand: 1/√1-u'2/c2 = γ(1-vux/c2)/√1-u2/c2 Can someone explain how they derived this? Thanks! :)

Taking a look at "http://www.space.com/30026-earth-twin-kepler-452b-exoplanet-discovery.html" I observe that planet Kepler-452b (judged to be somewhat Earth-like) is 1400 light years from Earth. If a spaceship leaves Earth at a fifth of the speed of light, traveling toward Kepler-452b, from...

My Quantum Field Theory notes, after explaining the Lorentz condition, say this: I have some questions about this. 1) What exactly does the polarization of a photon mean? 2) Why do the degrees of freedom of the potentials determine the polarizations of the photon? 3) If instead of the Lorentz...

Good day to you all, I could be asking too much here. I’m someone who prefers to understand formulas by deriving them from own made scenarios. In this case I was trying to derive the time dilation Lorentz formula using my own made up example and I wanted to know if I'm on the right track here...

In the system of units where c=1, the Lorentz transformations are as follows: ## x'=\gamma (x-vt) \\ t'=\gamma (t-vx) ## In the limit ## v \ll 1 ##, we have ## \gamma \approx 1+\frac 1 2 v^2 ##, so we have, in this limit: ## x' \approx (1+\frac 1 2 v^2)(x-vt)=x-vt+\frac 1 2 v^2 x-\frac 1 2...

Hey, There are some posts about the reps of SO, but I'm confused about some physical understanding of this. We define types of fields depending on how they transform under a Lorentz transformation, i.e. which representation of SO(3,1) they carry. The scalar carries the trivial rep, and lives...

When ions collide with oppositely charged electrodes, do they experience a Lorentz force as they gain or lose electrons? Is there a force, ignoring the repulsion of the positive electrode, in the direction of the blue arrow depicted here? Only information I find is on ionic fluids.

I'm going through Ray D'Iverno's "Introducing Einstein's Relativity", and there is a step he makes in deriving the Lorentz transformations that doesn't seem necessary to me. So I'm not sure what I'm missing. He derives them from Einsteins postulates of relativity. From the postulate that the...

Homework Statement We now specify the velocity v to be along the positive x1-direction in S and of magnitude v. We also consider a frame \overline{S} which moves at speed u with respect to S in the positive x1-direction. question 1 : Write down the transformation law for p^\mu . question 2...

The thought experiment used to prove Lorentz transform uses a light signal as an assumption. What if there was something other than the light signal then Lorentz transformation would have totally different term in place of 'c'(speed of light).

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..

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}_{\,\...

I was reading this paper: http://dinamico2.unibg.it/recami/erasmo%20docs/SomeOld/RevisitingSLTsLNC1982.pdf It is on superluminal Lorentz transformations and is too advanced for me. :confused: But anyway, take a look at equation(s) (11). For the y' and z' transformations, there is an imaginary...

Why does Lorentz force have that particular direction? Why is it perpendicular to the magnetic intesity and the current? Is it cause of some photons' reactions? Thanks

Lorentz force equation shows us that current is proportional to the force. Is it safe to assume that the force generated by an AC current at 60Hz will always have the same frequency? In other words, as the current increases and deceases (sinusoidal) the force will follow the same pattern at the...

Homework Statement Is the transformation ##Y:(t,x,y,z)\rightarrow (t,x,-y,z)## a Lorentz transformation? If so, why is it not considered with P and T as a discrete Lorentz transformation? If not, why not? Homework Equations The Attempt at a Solution A Lorentz transformation ##\Lambda##...

Homework Statement Derive the transformations ##x \rightarrow \frac{x+vt}{\sqrt{1-v^{2}}}## and ##t \rightarrow \frac{t+vx}{\sqrt{1-v^{2}}}## in perturbation theory. Start with the Galilean transformation ##x \rightarrow x+vt##. Add a transformation ##t \rightarrow t + \delta t## and solve for...

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...

Hello, I do not understand how to compute the infinitesimal variation of the field at fixed coordinates; under lorentz transformation . I am doing something wrong regarding the transformation of the ##x## coordinate. I am looking for: ##\Delta_a=\phi_a'(x)-\phi_a(x)##, variation appearing in...

Hi All; I was trying to understand Lorentz Transformation equation and special theory of relativity, but as I compared the derivation with a thought experiment which I imagined I found the whole Lorentz Transformation Equation fails. The details of the problem is given below. I know I m wrong...

Hi All; I was trying to understand Lorentz Transformation equation and special theory of relativity, but as I compared the derivation with a thought experiment I created I found the whole Lorentz Transformation Equation fails. The details of the problem is given in the pdf file attached. I know...

Why is relative speed taken to be symmetrical i.e. speed of one frame of reference from a second frame is equal to that of the second frame of frame refrence from the first frame

Just for my own entertainment I integrated the Lorentz factor with respect to velocity, using basic trig sub, I got the equation arcsin(v/c)*(mc^2). What does this mean? Is it just useless and irrelevant in the physics world or does it have some sort of hidden meaning?

I'm doing a class on special relativity and when doing some problems, I'm never sure whether I should be using the Lorentz transformations (Eg. x' = γ(x-vt) or t'=γ(t- (v/c^2)x)) or the Time dilation and Length contraction equations to find t or x! Can anyone explain if there's any way of...

Alonso has in fact raised a relevant issue. Given any clock synchronization in the embankment frame, there is a unique pair of points at the embankment with coordinates x=a and x=b, and a unique time t=T, such that at t=T in the embankment frame, these points are next to the back end and the...

Homework Statement Hello I need some advice on how to figure out Part F of the following problem. I was able to find the correct answer but in a very illogical way. I was wondering if I could get some help understanding the lorentz transformations necessary. Here is the full problem, I have...

Homework Statement There are three observers, all non accelerating. Observer B is moving at velocity vBA with respect to observer A. Observer C is moving at velocity vC B with respect to observer B. All three observers and all their relative velocities are directed along the same straight line...

Electric and magnetic parts of Maxwell's equations are kind of similar, so physical effects relating these properties have many 'dual' analogues - with exchanged places. For example in Aharonov-Bohm effect, the phase of charged particle depends on side of magnetic flux tube it comes through...

Sorry, there's going to be a lot of preamble here. I've written a book that involves a lot of space travel, therefore a lot of time dilation (all sub-light travel). I've been calculating the transit times and subjective durations by brute force, i.e. I wrote a program to calculate tau on a...

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, the following is taken from Peskin and Schroeder page 36: ##\partial_{\mu}\phi(x) \rightarrow \partial_{\mu}(\phi(\Lambda^{-1}x)) = (\Lambda^{-1})^{\nu}_{\mu}(\partial_{\nu}\phi)(\Lambda^{-1}x)## It describes the transformation law for a scalar field ##\phi(x)## for an active...

Homework Statement 1. Show that the Lorentz algebra generator ##J^{\mu \nu} = i(x^{\mu}\partial^{\nu}-x^{\nu}\partial^{\mu})## lead to the commutation relation ##[J^{\mu \nu}, J^{\rho \sigma}] = i(g^{\nu \rho}J^{\mu \sigma} - g^{\mu \rho}J^{\nu \sigma}-g^{\nu \sigma}J^{\mu \rho}+g^{\mu...