Questions tagged [galilean-relativity]
This tag is for questions related to the Newtonian Era idea that space and time are the same for everyone while speed adds up in the straightforward direction (if you are going 50 mph and throw something 20 mph it is going 70 mph) DO NOT use this tag for questions related solely to General Relativity.
60 questions with no upvoted or accepted answers
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What are Galileons good for?
Lately I've seen many papers (for example "The galileon as a local modification of gravity"; 292 total hits on the arXiv) on types of field theories known as Galileons, and I'm wondering ...
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What is the symmetry group of Mach's spacetime?
Newtonian spacetime can be modeled as a geometric object $M$ (affine space or manifold with connection with an absolute time function etc. etc.) that is symmetric under the action of the Galilean ...
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What would Maxwell's equations look like in a universe which followed Galilean transformations?
I was wondering how the electromagnetic force would behave in a Gallilean transformation universe. Would the magnetic force be non-existent?
We know that Gallilean transformations are Lorentz ...
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Using Galilean covariance to find conditions on physical observables
Let's suppose that coordinates have to transform accoring to the Inhomogenous Galilean Group. Then
$$ x' = x + a + v(t+b) $$
$$ t' = t + b $$
Let's use a funtion $\psi(x,t)$ of $x$ and $t$ as the ...
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Why do Galilean transformations change both states and operators?
When a Galilean transformation on a quantum system is performed, the states and the operators change:
$$|\phi\rangle \rightarrow |\phi\rangle'$$
$$\hat A \rightarrow \hat A'$$
I don't understand the ...
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3
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32
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Galilean boost operator for quantum multi-particle system
If I have a two particle system with with a potential of form $V(x_1,x_2)$, is it possible to apply the galilean boost operator to only a single coordinate? Essentially, is it possible to move only a ...
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Goldstone Modes, Galilean Symmetry, and Negative Excitations in Fermi Gas
Considering the centrality of Goldstone quasiparticles in condensed matter theories, I was wondering if the converse of the theorem might also be true: Does the existence of a gapless excitation imply ...
- 1,370
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Is there a general methodology for causal nets of observables regardless of kinematics?
The typical definition of a causal net of observables in quantum theory is to consider, for the case of a (globally hyperbolic) spacetime $M$, the category of open sets $O(M)$ ordered by inclusion, in ...
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Principle of relativity and Galileo's group
A doubt has arisen for me about the principle of relativity, and being such a fundamental subject I think it only fair to try and clarify it. The following line of reasoning was presented to me in a ...
- 1,723
2
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1
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Implications of Galilei-Invariance on a time-independent potential
I'm trying to compute a result shown in my classical mechanics lecture on my own. Namely, consider that a system composed of $n$ particles follows a law of force
$m_k\ddot{\vec{x_k}} = \vec{F_k}(\vec{...
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What do these Casimir invariants of the Galilean group physically represent?
There exist Casimir invariants of the Galilean group which commute with all the generators of the group. They are, of course, Galilean scalars (i.e., scalars under space and time translations, ...
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About the definition of world-line in Arnold's book
I am reading Arnold's Mathematical Methods of Classical Mechanics. I have some questions about the definition of world-line. The book says:
A curve in Galilean space which appears in some (and ...
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1
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Why must the logarithm of the distribution function depend only upon additive integrals of motion (Landau & Lifshitz)?
Denote by $\rho(p,q)$ (the $p$ and $q$ are being used as shorthand for several degrees of freedom), the phase space probability distribution function, (so $\rho\,\text{d}p\text{d}q$ is the probability ...
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Why should the potential of a non-relativistic isolated system be velocity independent?
The lagrangian function of an non-relativistic isolated system of point masses is
$$L=\sum_i\frac{m_i}{2}\dot{\vec r}_i^2-V,$$
where the potential function $V$ represents all interactions.
If we ...
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Why did Feynman tell "we cannot locate earth's angular position, but we can tell that it is changing"?
I was reading "Symmetry in physics" by Feynman, where he wrote:
If we perform sufficiently delicate experiments, we can tell that the earth is rotating, but not that it had rotated. In other words, ...
user36790
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Question about Origins in Galilean transformation
I'm just learning about relativity, and every equation I see for a galilean transformation of frame $S'$ (moving with uniform velocity in the $x$-direction with respect to frame $S$) is $x'=x-vt$, $y'=...
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Jacobian matrix of Galilean transformation
If we want to transform to another inertial frame of reference using Galilean transformation in 4-dimensional space-time, what is the Jacobian matrix of Galilean transformation?
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1
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Could we deduce energy, momentum and angular momentum conservation laws from only Galilean relativity?
In Newtonian physics we could deduce conservation of energy, momentum and angular momentum from Newton's three laws.
But by Noether's theorem, conservation laws could be deduced from symmetries.
Could ...
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0
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Independence of Lagrange function from time and position
In Landau & Lifshitz "Mechanics", it is said that from the time/space homogeneity Lagrange function is independent from time/position. I always thought that homogeneity means that motion ...
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Why does the ball in Galileo's double inclined plane experiment reach the same height?
Why does the ball in Galileo's double inclined plane experiment reach the same height? I know how to show it by energy conservation law but am unable to prove it by the equations of motion. Can anyone ...
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1
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Principle of Relativity and the invariance of Newton's law in IRFs
Newton's law are form invariant under the coordinate substitutions:
$$
\tilde{x^{i}}=x^{i}+a^{i}
$$
This means that Newtons' equation of motion,
$$
F^{i}=m \frac{d^{2} x^{i}}{d t^{2}}
$$
(where $i=1,2,...
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1
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Bernoilli effect on either side of a plate is not Gallilean invariant
Consider the airflow above and below a horizontal plate:
Particle density either side of the plate is the same. Ignoring thermal motion, the particles above the plate move with velocity $v$ and the ...
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Why does it not matter that the material wave equation is not invariant under the Galilean transformation?
I have a doubt, when the Galileo transformations are applied to the electromagnetic wave equation, more terms appear and to solve it the Lorentz transforms are used, however, what does not comply with ...
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Affine space in classical mechanics and it's applicability in general relativity
In the first chapter of Arnold book of Classical Mechanics while giving Galilean structure of spacetime we're introduced to affine space. As already mentioned in answers to this question this is done &...
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1
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Why does the derivation for the Michelson & Morley time difference assume Earth moves in only one direction relative to the Aether?
In the Michelson and Morley experiment, we predict with Galilean relativity and the assumption of the existence of a luminiferous aether that there should be a time difference between the two beams of ...
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Assumptions in Galilean and Relativistic Frame Transformation
While deriving the frame transformation equations, either the Galilean Transformation or Lorentz transformation. I have seen almost all authors mentioning/assuming that if an inertial frame $\textbf{S}...
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Is Galilean Conformal Algebra (GCA) isomorphic to any other algebra in $d$ dimension?
I was recently studying stuffs related to Conformal Field theory and its Galilean version. It's known that CFT algebra in $d$ dimension is isomorphic to $SO(d+1,1)$ algebra. We also know that Galilean ...
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Lattice Gas Automata and Galilean Invariance
I have been studying Lattice Gas Automata methods (also this), and every time I read up on their drawbacks, I see that they are not Galilean invariant and that the simulations have statistical noise. ...
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Galilean boost on transverse momentum in infinite momentum frame
In the infinite momentum frame in $11$ dimensions, if we do a large boost along the $x^{11}$ direction, the total mass shell energy $E$ can be shown in a non relativistic approximation to be $ E - p_{...
- 1,105
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Transformation law of momentum under Galilean transformation
I'm reading the article On the Galilean Covariance of Classical Mechanics (pdf link here), in which the authors want to establish the transformation rule for momentum, assuming only that $\vec{F}=d\...
- 1,071
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How does Galilean invariance lead to equality of "mass" flux and momentum density?
Let us consider a fluid, with spacetime translation symmetry, and one internal $U(1)$ symmetry. Corresponding to the spatial translation symmetry, we can write down a momentum conservation equation ...
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The absoluteness of time intervals in Newtonian mechanics: how is this input used?
One of the assumptions of Newtonian mechanics is that "time is absolute". Absolute, as I understand, implies that it is the same for all observers. But it's not quite true because if Tom's watch is ...
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Mass, Spin, Internal Energy and 1-Particle States in Galilean Quantum Mechanics
I have been reading an article discussing the unitary representation of Galilean group and non-relativistic quantum mechanics. The link to the article is given below.
http://arxiv.org/abs/1107.2442
...
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Galilean Transform
I tried to solve a problem using two different ways and I had some trouble, the problem is:
We define a symmetry transform of the expected value of $\vec{P}$ like this:
$$\langle \psi|\vec{P}|\psi \...
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Galilean boost and translation in field theory
I am reading some literature which is considering translations and boosts in field theory. The reference is Construction of Lagrangians continuum theories, Markus Scholle, 2004, The Royal Society. I ...
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The Low Velocity Limit of the Electric and Magnetic Field Transformations
From the covariant formulation of electromagnetism we know that the fields transform as:
$$\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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2
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$E=mc^2$ derivation using waves other than light
Can $E=mc^2$ be derived using waves other than light?
Einstein's derivation of his famous equation $E=mc^2$ relies on light waves (or photons). He considered a scenario with a light-emitting material ...
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Galilean transformation vs boost matrices
I'm confused about the difference between a Galilean transformation and boost with reference to their matrices. I was given four statements (listed below) but I'm not sure what I should be looking for ...
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How can I solve this problem about energy conservation according to different frames of reference?
We have two frames of reference: the Earth (E) and a train (T) uniformely moving at velocity u relative to the Earth.
We also have a particle that is initially stationary relative to the train, and is ...
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Extending the Galilean transformation to the case of a possibly spacetime-dependent velocity field?
In all literature I have searched, the Galilean transform between two coordinates $(\overrightarrow{x},t)$ and $(\overrightarrow{x'},t')$ have been considered for a "constant velocity".
That ...
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In galilean relativity, is an observer assumed to be at rest only to simplify calculations, or is there a physical reason for this assumption?
I am a beginner in Physics and my teacher taught us "Relative Motion" yesterday. He said that the "Observer is assumed at rest." Is the observer assumed to be at rest only to ...
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Galilei transformation of mass flux
Is it possible to perform a Galilei transformation of a flux without additional information?
Say we consider a flux $q = \rho v$ that can be written as the product of density $\rho$ and a velocity ...
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Formulating Conservation of Energy in Galilean Spacetime
Some background to my question (Galilean spacetime).
The notion of Galilean spacetime is defined at the beginning of Arnold's book on Classical Mechanics. It is a mathematical structure that captures ...
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Interaction forces always depend on positions only through the distance, therefore conservative?
Suppose that two point masses $A_1,A_2$ are in interaction with each other, resulting in forces $F_1$ (acted upon $A_1$) and $F_2$ (acted upon $A_2$). Let $\bf{x}_1$,$\bf{x}_2$ be their respective ...
- 404
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How are energy conserved and momentum both conserved in this system?
In space, a photon with momentum $P$ is reflected off a previously at rest mirror, imparting momentum to the mirror. Even if the wavelength of the reflected photon is much longer than the that of the ...
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Galilean transformation of magnetic and electric field with magnetic monopole
Starting from the lorentz force in presence of a magnetic charge:
$$\vec{F} = q_e(\vec E+\vec v\times \vec B)+q_m(\vec B - \vec v\times\vec E)\tag 1$$
by galilean invariance, we should have $\vec F =...
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Conceptual questions about Galilean relativity
I want to see if Galilean relativity is as mind-blowing as a think it is.
I'm imagining two individuals each on their own planets. Ignore gravity for now, they are attached to the planets, and there ...
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The mathematical model of the Galilean transformation in Hamiltonian mechanics
In my previous question, I asked about the Galilean invariance of the Hamiltonian. I've got already two answers, probably good but I have difficulties interpreting them. Both answers write the ...
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What is the closest anyone got to a proper description of a Galilean universe?
So assuming Einsteinian relativity is a bust, did any physicist thought through properly how a Galilean/Newtonian universe would work? Of course there are infinite ways of how it could, but one is ...
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Lagrangian invariance under Galilean transform and conservation law of linear momentum
I'm currently taking a course of analytical mechanics. We've learned about the invariance of the Lagrangian under change of coordinates, and showed that we get the same Lagrangian for free particle ...
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