Questions tagged [lorentz-transformation]
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23 questions
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Lorentz transformation from the Minkowski metric
Is it possible to derive the matrix:
$$\Lambda=\begin{pmatrix}
\gamma & -\beta\gamma \\
-\beta\gamma & \gamma
\end{pmatrix}$$
From the condition:
$$\Lambda g\Lambda^T=g \ \ \ \ g=\begin{...
- 371
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Lorentz transformation on field theory using coordinate expressions not representations
This is probably a stupid question but, I want to show that a Lagrangian written in field theory is Lorentz invariant WITHOUT using the Lorentz transformation representation / generators. I know we ...
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On the distinction between Lorentz group and proper orthochronous group via Jacobian determinants
The group $O(1,3)$ is defined as the set of matrices which are orthogonal with respect to the Minkowski metric $\eta$, i.e. those matrices $\Lambda$ satisfying
$$\Lambda^T \eta \Lambda = \eta.$$
...
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Lorentz algebra representation
In my QFT lecture the following was derived, but I have no idea how:
We consider a scalar field : $\phi(x^\mu)$.
$\phi(x^\mu)=\phi'(x'^\mu)$
Then:
$\phi'(x'^\mu)=\phi((\Lambda^{-1})^\mu_{\ \ \nu}x'^\...
- 1,624
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Generators and Lorentz transformations (LT)
I have been trying to understand how $SO^+(1,3)$ generators are related to LT elements.
I am confused as I don't know how many types of generators are considered.
If we consider the following ...
- 1,624
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Why do we need to apply Lorentz transformation twice when transforming the electromagnetic field tensor and what does it mean?
I would understand if this was following the defined way of lowering or raising of the indices of a four vector after a Lorentz transformation.
$$F^{'}_{\mu\nu} = \Lambda_{\mu}^{\alpha} \Lambda_{\nu}^{...
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Could someone explain this leap in the Feynman lectures that 'derives' the fourth Lorentz transformation equation
So suppose that two coordinate systems are in uniform relative motion. Then the Lorentz transformation is:
$$x' =\frac{x-ut}{\sqrt{1-u^2/c^2}}$$
$$y' = y$$
$$z' = z$$
$$t' = \frac{t- ux/c^2}{\sqrt{1-u^...
- 75
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The Low Velocity Limit of the Electric and Magnetic Field Transformations
From the covariant formulation of electromagnetism we know that the fields transform as:
$$\vec{E}'=\gamma \vec{E}-\frac{(\gamma-1)}{u^2}(\vec{u}\cdot \vec{E})\vec{u}+\frac{\gamma}{c}[\vec{u}\times\...
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Does Wigner rotation mean that in special relativity it is possible to rotate an object without applying any torque to it?
Does Wigner rotation mean that in special relativity it is possible to rotate an object (change its orientation relative to the three spatial axes) without applying any torque to it?
It is assumed ...
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Why does applying boost to state reduction give an incorrect result?
Suppose we have a state $|\psi \rangle (t)$ in quantum field theory. Till $t=t_0$, the state evolves unitarily using field Hamiltonian $\int d^3x H(x)$. At time $t=t_0$, we perform a measurement and ...
- 6,742
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Is it possible to derive Rindler coordinates using inverse Lorentz transforms?
In page 8 of this notes, the author shows that accelerated observer's spacetime coordinates $(ct', x', y', z')$ is related to inertial observer's spacetime coordinates $(ct, x, y, z)$ by
$$
\begin{...
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Definition of 'proper lorentz transformation' being having positive determinant or preserving the orientation of spatial axes
In the book I am reading, the proper Lorentz transformations are defined as Lorentz transformations (hereinafter LT) with $\det \Lambda =1$. It states that:
The proper Lorentz transformations ...
- 331
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Relativistic time transformation in a rotating reference frame
I'm working to better understand Lorentz transformations, and it was suggested that a good exercise would be to derive the relativistically correct transformation laws from a stationary reference ...
- 1,978
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How can we derive the Lorentz Factor? [closed]
So I've seen a lot of derivation of it on online. Many of them are very easy to understand. But my course teacher taught this following derivation from this book which is a lot more rigourious than ...
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Is it possible to directly measure Lorentz length contraction? [duplicate]
Could one design an accelerator ring, which constructs a packet of charges, in roughly cylindrical shape, then accelerate it around the ring, and measure its length contraction?
That is, we wish to ...
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Four-vector algebra - Notation confusion [duplicate]
I am trying to understand what are the consequences of the ordering (and placement in general) of the subscripts and superscripts for the matrix representation of different elements in four-vector ...
- 1,624
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Confusion about why time coordinate of Lorentz transformation and time dialation don't align? [duplicate]
If there is a stationary observer and one is moving to the right at 1/2 speed of light. And there is a light moving to the right at the speed of light. I tried to calculate the coordinates of light ...
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3
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Why Lorentz transformations instead of general linear transformations?
I am trying to understand why, in physics, we look specifically at Lorentz transformations, instead of the larger group of general linear transformations.
To fix the terminology: let spacetime be ...
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Practical question related to reference frames in general relativity
Sorry if my question requires clarification. I am having trouble conveying exactly what my problem is.
I'm trying to code a ray tracer that works in curved spacetime. In principle, this just entails ...
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Does $d\theta = d\theta' / \gamma$? [closed]
Is anything wrong with this argument?
Let the relativistic frame $K'$ be moving at $v$. Let $\theta'$ be with respect to the direction of motion.
I know $tan(\theta') = y/x$
So in the lab frame $K$, $...
user424559
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Understand the Lorentz transformation in QFT
I am a beginner in QFT,so let me introduce my question by the problem in MIT8.323 (2023 spring,by Hong Liu) pset 1
.
All steps seem clear, the measure is invariant because the Jacobian is 1 and the ...
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Equation of Motion after Boost
In paper of analyticity and positivity constraints, they take example of effective field of Goldstone boson in a linear sigma model,
$$\mathcal{L}_{\text{eff}} = (\partial{\pi})^2 + \frac{c_3}{\Lambda^...
- 938
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Does the Lorentz Transformation preserve the physical integrity of objects?
As is well known, the Lorentz transformation does not only result in a length contraction of objects, but also in different parts of it transformed to different times according to
$$t'=\gamma (t-\frac{...
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