Lorentz Definition and 1000 Threads

How to prove that direct product of two rep of Lorentz group ##(m,n)⊗(a,b)=(m⊗a,n⊗b)## ? Let ##J\in {{J_1,J_2,J_3}}## Then we have : ##[(m,n)⊗(a,b)](J)=(m,n)(J)I_{(a,b)}+I_{(m,n)}⊗(a,b)(J)=## ##=I_m⊗J_n⊗I_a⊗I_b+J_m⊗I_n⊗I_a⊗I_b+I_m⊗I_n⊗J_a⊗I_b+I_m⊗I_n⊗I_a⊗J_b## and...

I am reading Tong's lecture notes and I found an example in which there are several aspects I do not understand. This example is aimed at: - Understanding what is the analogy in field theory to the fact that, in classical mechanics, rotational invariance gives rise to conservation of angular...

Hi! As I outlined in my https://www.physicsforums.com/threads/hello-reality-anyone-familiar-with-the-davisson-germer-experiment.985063/post-6305937, I'm curious to ask if there is anyone with knowledge on the theory of the piezoelectric effect on this forum? I think it's fascinating how a...

How are the Lorentz transforms inverted from x' = gamma(x -vt) and t' =gamma(t - vx/c^2) to the equations x =gamma(x'+vt') and t = gamma(t'+ vx'/c^2) ? The closest explanation I have seen on line is to change the non-primes to primes and reverse the direction of v). But what is the algebra...

I wanted to make a derivation of the Lorentz transformation : $$x'=Ax+Bt\\t'=Dx+Et$$ The conservation of the quadratic form ##c^2t'^2-x'^2## yields the equations: $$A^2-B^2/c^2=1\\D^2-E^2/c^2=-1/c^2\\AD=BE/c^2$$ Hence ##B=c\sqrt{E^2-1}##,##D=\sqrt{E^2-1}/c##,##A=\pm E##. The speed of the...

I bought the book "The principle of Relativity" by Einstein et al. and was really surprised by the (low) level of explanation by Lorentz regarding the compression of rods on the experiment carried out by Michelson & Morley. I reproduce part of it below: Well, he gave absolutely no arguments to...

What is the difference between special relativity and the Lorentz transformation? Aren't they basically the same thing? Also, I was wondering what about matter makes spacetime curve?

As object separate with a receding velocity proportional to the distance, it would seem appropriate to think that objects and space itself, which are located at a distance sufficiently far away (and beyond) to were recession velocities are large enough that Lorentz length contraction effects...

If we have motion of system ##S'## relative to system ##S## in direction of ##x,x'## axes, Lorentz transformation suppose that observers in the two system measure different times ##t## and ##t'##. x'=\gamma(x-ut) x=\gamma(x'+ut') Why we need to use the same ##\gamma## in both relations? Why not...

Could it be that the transformations keeping the wave equation invariant have other solutions than the usual Lorentz ones ?

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 ?

I have a question which I've found very difficult to Google. The easiest way to frame it I can think of is this: Given a cylinder moving lengthwise by an observer at some significant fraction of C, with the forward half of the cylinder (relative to the direction of motion) painted red, and the...

Li=1/2*∈ijkJjk, Ki=J0i,where J satisfy the Lorentz commutation relation. [Li,Lj]=i/4*∈iab∈jcd(gbcJad-gacJbd-gbdJac+gadJbc) How can I obtain [Li,Lj]=i∈ijkLk from it?

This is my first thread. I hope I do it right. I just started reading the book Special Relativity by W.Rindler. And as I was reading it, I stumbled upon a pickle. So in Lorentz theory, it says, supposedly we could measure the original to-and-fro time T2 directly with a clock, and suppose we...

Homework Statement: This seemed at first glance very easy. But there appeared some confusion. A is moving to the right with velocity v with respect to B. The proper time for A is ##t_a=t_b\sqrt{1-v^2/c^2}##. And B is moving to the right with velocity u with respect to C. Proper time for B...

of course y and z terms are invariant but for the x and t terms I am getting an additional factor of 1/1-v^2/c^2

[BEGINNGING NOTICE] Before I begin showing my attempted solution, I would just like to quickly mention that this is a "repost" of the same question I had around a week ago. While I would usually use the "reply" function on the same thread, I believe that thread is getting pretty messy (sometimes...

Summary: The problem is to generalize the Lorentz transformation to two dimensions. Relevant Equations Lorentz Transformation along the positive x-axis: $$ \begin{pmatrix} \bar{x^0} \\ \bar{x^1} \\ \bar{x^2} \\ \bar{x^3} \\ \end{pmatrix} = \begin{pmatrix} \gamma & -\gamma \beta & 0 & 0 \\...

with distance between planets as 4x10^8m measured by you on the ship My attempt: t' = γ(t - ux/c^2) γ = 5/3 u = 0.8c t = 0.9s x = 4x10^8m answer is: -0.278 Therefore not possible My question is what if we traveled rightwards, from p2 to p1, would the answer change? Should my above information...

Unfortunately, I am not entirely confident of the above equations being able to do the trick and ultimately solve for the question. However, my guess is that using the equation written above for "boost", I could perhaps use ##v## and insert it into the ##x##-direction part of the matrix...

a) I know the invariants are $\mu = \frac{0.5*m*v_{perp}^2{B} $ and $J = v_{parallel} x b) I used the invariance of $\mu$ to get the following equation: $$ v_{perp}^2 = v_{perp,0}^2(1+\alpha(t)^2 z^2) $$ I am thinking of using the Lorentz force to get $v_z$, but I'm not so clear on how to go...

To find the Lorentz transformation, should it start with the invariance of the wave-equation ? If so, then it gives 5 equations, 2 of them being wave-equations again. If however the invariance of the space-time interval is demanded only 3 quadratic equations come out. Which way should be...

I have been getting back to studying physics after a long break and decided to go through the problems in Rindler. But there is something I don't quite understand in this problem. To first answer the second part, Exercise II(12), I wrote $$\frac{du_2}{dt} = \frac{du_2}{du_2^\prime}...

I am trying to push the boundaries of special relativity with a self-imposed challenge problem. A common derivation of relativistic kinetic energy involves an object to which a constant force is applied. I want to consider a similar scenario, but instead of a point object we now have a uniform...

In his book, Landau derives the Lorentz transformations using the invariance of the interval, and I have some questions about it that I would like to clarify 1. What is a parallel displacement of a coordinate system? Does it refer to moving along any axis? I don't see how any arbitrary...

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...

I want to know why an else solution can not get the right answer. And want to know the way to correct this solution.Supposed that a frame S'' is moving in the lab frame at ##\beta_x## in the x-direction, ##\beta_y## in the y-direction, now I want to find out the Lorentz transformation between...

1) Likely an Einstein summation confusion. Consider Lorentz transformation's defined in the following matter: Please see image [2] below. I aim to consider the product L^0{}_0(\Lambda_1\Lambda_2). Consider the following notation L^\mu{}_\nu(\Lambda_i) = L_i{}^\mu{}_\nu. How then, does...

1) How do we determine a Lie group's global properties when the manifold that it represents is not immediately obvious? Allow me to give the definitions I am working with. A Lie group G is connected iff \forall g_1, g_2 \in G there exists a continuous curve connecting the two, i.e. there...

Hey y'all Can anyone just tell me every detail about Lorentz forces ? I have a pretty good idea, but i want to surprise everyone in the presentation that i am about to give, so please just tell me whatever detail you know . Every single detail might be helpful . Also , if anyone knows how to...

Two charges are moving mutually perpendicular to each other in space with constant velocities. The moment one charge crosses over the line of path of second charge the force on 1st charge (located just behind the 2nd charge moving away from it) appear to be zero (Magnetic field due to 2nd...

A particle is moving in the lab frame ##S'## at ##\beta'_z##. I want to transform coordinates and momenta of the particle to a frame ##S## moving at ##\beta_0##. At time ##t = t' = 0##: $$z = \frac{z'} { \gamma_0 (1 - \beta'_z \beta_0) },\, \gamma\beta_z = \gamma_0 ( \gamma'\beta'_z -...

I'm currently watching lecture videos on QFT by David Tong. He is going over lorentz invariance and classical field theory. In his lecture notes he has, $$(\partial_\mu\phi)(x) \rightarrow (\Lambda^{-1})^\nu_\mu(\partial_\nu \phi)(y)$$, where ##y = \Lambda^{-1}x##. He mentions he uses active...

I would like to apply a General Lorentz Boost to some Multi-partite Quantum State. I have read several papers (like this) on the theory of boosting quantum states, but I have a hard time applying this theory to concrete examples. Let us take a ##|\Phi^+\rangle## Bell State as an example, and...

What about if the speed parameter in a Lorentz boost were in fact related nontrivially to a Galilean speed ? More formally ##L(v_L)=G(v)\circ F## where L is a Lorentz boost with Lorentz speed ##v_L##, G is a Galileo transformation with speed ##v## and ##F## is still an unknown linear...

In physics, a symmetry of the physical system is always associated with some conserved quantity. That physical laws are invariant under the observer’s displacement in position leads to conservation of momentum. Invariance under rotation leads to conservation of angular momentum, and under...

Two frames measure the position of a particle as a function of time: S in terms of x and t and S', moving at constant speed v, in terms of x' and t'. The acceleration as measured in frame S is $$ \frac{d^{2}x}{dt^{2}} $$ and that measured in frame S' is $$ \frac{d^{2}x'}{dt'^{2}} $$My question...

There are several ways to show that the Lorentz transformations must be linear. What's the best/more intuitive argument in your opinion?

Why representation of Lorentz group of shape (A,A) corespond to totally symmetric traceless tensor of rank 2A? For example (5,5)=9+7+5+3+1 (where + is dirrect sum), but 1+5+3+9+7<>(5,5) implies that (5,5) isn't symmetric ? See Weinberg QFT Book Vol.1 page 231.

I read the Lorentz transformation can be obtained by solving the requirement of invariance of the wave equation. If one considers linear transformations this the same as the spacetime interval squared to be invariant. What are the other nonlinear transformations keeping the wave equation...

I am working on derivation of Lorentz force. (I know that Lorentz force is in some sense definition of fields, but still there is nontrivial dependence on velocity). I want to derive that the force is linear in components of velocity, so for example $$F_x=q(E+Av_x + Bv_y + Cv_z ),$$where ##A...

Problem Statement: Consider three frames Σ (x, y, z, t), Σ' (x', y', z', t'), and Σ'' (x'', y'', z'', t'') whose x, y, and z axes are parallel at each point in time stay. Σ' moves relative to Σ with velocity v1 along the x-axis. The system Σ'' moves relative to Σ' with the velocity v2 along the...

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})) =...

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?

Can someone tell me why the proper time between αβ is not t2+x2 but rather t2-x2? Background:

It seems that there is a considerable number of ways of deriving the Lorentz transformations. Does anyone know how many ways are there?

Hi guys, I'm reading a book 'the theoretical minimum: special relativity and classical field theory'. In chapter 1.3, author explains the general Lorentz transformation. He said "Suppose you have two frames in relative motion along some oblique direction, not along any of the coordinate axes...

In the Earth’s reference frame, a tree is at x=0km and a pole is at x=20km. A person stands at x=0 (stationary relative to the Earth), and at t=10 microseconds, this person witnesses two simultaneous lightning strikes. One of these strikes hits the tree he is standing under, and the other hits...

As homework, I shall show that the retarded scalar potential satisfîes the Lorentz gauge condition as well as the inhomogenous wave equation. We saw in class how to do it. But I was thinking about this, and it seems to me that it's redundant to prove both of those things. For, if the scalar...

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...