What is Lorents transformations: Definition and 12 Discussions

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  1. J

    Lorentz transformation of infinitesimal boost and rotation?

    1. Show that the infinitesimal boost by ##v^j## along the ##x^j##-axis is given by the Lorentz transformation $$\Lambda_{\nu}^{\mu} = \begin{pmatrix} 1 & v^1 & v^2 & v^3 \\ v^1 & 1 & 0 & 0 \\ v^2 & 0 & 1 & 0 \\ v^3 & 0 & 0 & 1 \\ \end{pmatrix}$$ Attempted solution I know that for x-axis...
  2. S

    I Need to resort to spherical wavefront to derive the LTs?

    I have been reading Wikipedia’s derivations of the Lorentz Transformations. Many of them start with the equation of a spherical wavefront and this reasoning: - We are asked to imagine two events: light is emitted at 1 and absorbed somewhere else at 2. For a given reference frame, the distance...
  3. S

    I Time Dilation Paradoxes Near C: Exploring the Twin Paradox of Special Relativity

    I'm struggling to wrap my head around the twin paradox in special relativity especially when dealing with multiple vectors. In my thought experiment say I have a set of twins. Both set out in opposite directions and intend to sling shot around two different black holes(luckily equidistant from...
  4. Samama Fahim

    I Deriving Lorentz Transformations: Hyperbolic Functions

    While deriving Lorentz transformation equations, my professor assumes the following: As ##\beta \rightarrow 1,## $$-c^2t^2 + x^2 = k$$ approaches 0. That is, ##-c^2t^2 + x^2 = 0.## But the equation of the hyperbola is preserved in all inertial frames of reference. Why would ##-c^2t^2 + x^2##...
  5. R3ap3r42

    Special relativity and Lorentz Transformation Exercise

    Summary:: Special relativity and Lorentz Transformations - I got this problem from a first-semester course at university. I have been struggling for a few days and decided to get some help. A rocket sets out from x = x' = 0 at t = t' = 0 and moves with speed u in the negative x'-direction, as...
  6. bq1892

    Describe the length of an electron's journey in its own frame of reference

    Lv = Lo / γ 1/γ =√(1-v^2/c^2) = √(1-0.8^2) = 0.6 Therefore Lv = Lo x 0.6 = 150 x 0.6 = 90m Therefore electron travels 90m in its own frame of reference (answer key solution) However, shouldn't the electron be assigned rest length, Lo, as its frame of reference is at rest with itself instead...
  7. F

    Lorentz transformations for electric and magnetic fields

    Good evening, I'm trying to solve this exercise that apparently seems trivial, but I wouldn't want to make mistakes, just trivial. Proceeding with the first point I wonder if my approach can be correct in describing this situation. From the assumptions, the two fields are in this...
  8. R

    I Derive Lorentz Transformation by Visualizing Space-Time Coordinates

    This approach is seeming intuitive to me as I can visualize what's going on at each step and there's not much complex math. But I'm not sure if I'm on the right track or if I'm making some mistakes. Here it is: ##A## has set up a space-time co-ordinate system with some arbitrary event along his...
  9. M

    I Spin matrices and Field transformations

    Let us for a moment look a field transformations of the type $$\phi(x)\longmapsto \exp\left(\frac{1}{2}\omega_{\mu\nu}S^{\mu\nu}\right)\phi(x),$$ where ##\omega## is anti-symmetric and ##S^{\mu\nu}## satisfy the commutation relations of the Lorentz group, namely $$\left[S_{\mu \nu}, S_{\rho...
  10. M

    Prove that these terms are Lorentz invariant

    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) -...
  11. J

    B Learning Lorentz Derivation: Solving x=vt+γx' vs. x=vt+x'/γ

    From a previous thread, Nugatory: "If the answers already supplied are not enough for the original poster to work out for themself why x=vt+x'/γ, and not x=vt+γx′, is the correct expression, we can have another thread devoted to only that question." Here it is. Either Wiki is wrong or I am. In...
  12. C

    Unitary operator + Lorents transformations (question from Peskin)

    Hi. I am trying to understand a statement from Peskin and Schroeder at page 59 they write; "The one particle states |\vec p ,s \rangle \equiv \sqrt{2E_{\vec p}}a_{\vec p}^{s \dagger} |0\rangle are defined so that their inner product \langle \vec p, r| \vec q,s\rangle = 2 \vec E_\vec{p}...