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.
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Question about relative motion from "A Brief History of Time" [closed]
I read this example in Stephen Hawking's A Brief History of Time:
If one sets aside for a moment the rotation of the Earth and its orbit round the Sun, one could say that the Earth was at rest and ...
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The metric of world lines in Newtonian and Galilean spacetimes
Consider a flat Newtonian or a flat Galilean 2+1 spacetime. So, mainly a flat 2D Euclidean space, evolving over time, where each time-slice is connected with the next one by a world line. Like in this ...
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How can I show that the one-dimensional wave equation (with a constant propagation velocity $c$) is not invariant under Galilean transformation? [duplicate]
The one-dimensional wave equation is given by
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What is the connection between mechanics and electrodynamics that makes it necessary for both of these to obey the same principle of relativity?
Mechanics obeyed Newtonian relativity (faithful to Galilean transformations) before Einstein.
Einstein formulated Special relativity (faithful to Lorentz transformations), and Maxwell's equations ...
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Violation of Einstein equivalence principle and Galileo Relativity
Two pulleys with one motor with the same force in each one. Between them a half strap or a rope which last sides is glued to each pulley. The force of the motors acts on opposite direction. Each motor ...
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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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Is Newton's law really invariant under Galilean transformation (for velocity-dependent Lorentz force)?
Consider the motion of a charged particle of charge $q$ and mass $m$ from two different inertial frames $S$ and $S'$ connected by Galilean transformation equation ${\vec r}'={\vec r}-{\vec V}t$. This ...
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Can distance be relative in Galilean relativity?
In case 1 the A travels the distance D while traveling from X to Y.
In case 2 the velocity of A according to Sam will 'a' and distance travelled by A will be greater than D because the wall Y is also ...
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Is acceleration absolute and if so, how can we measure it?
A person standing on a uniformly moving car can never know (without looking outside, or at the speedometer) whether the car is at rest or in motion at a uniform nonzero velocity w.r.t earth. However, ...
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Newtonian quantum gravity
Can someone give me reference about Newtonian (non-relativistic) quantum gravity like unifying Newtonian gravity with quantum mechanics?
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Dummy variables and Galilean Invariance
I've faced a small doubt, and I was hoping someone could verify this for me.
According to Galilean transformation, consider $2$ frames - $S_1$ and $S_2$ moving relative to each other. $S_1$ is at rest,...
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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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If motion relative to a frame of reference is purely relative, how do we account for the work done to move relative to the frame of reference?
I get the idea that everything is in motion, and there's no absolute reference frame for everything.
But when we consider local events, like a train passing through a town, I have trouble accepting ...
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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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Is moving into a rotating frame a Galilean transformation?
In classical mechanics, we know that laws of physics are invariant in Galilean transformations of the form:
$$ x' = x -vt$$
My question is does shifting to rotating frame also count as a Galilean ...
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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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Deriving "Galilean Electromagnetism"
I'm taking an introductory E&M course, and we're currently covering what our text calls "Galilean Electromagnetism" (i.e. the transformation of electric and magnetic fields between non-...
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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 ...
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What is the relationship between the Galilean group and the Poincaré group?
What is the relationship between the Galilean group and the Poincaré group?
Are they siblings within the Lie group? Or does the Poincaré group contain the Galilean group as a subgroup?
I'm not so much ...
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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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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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Right way to define vectors under Galilean transformations?
This two questions: Vectors under Galilean transformation and Galilean transformations of velocity seem to tackle the issue but one was closed and the latter did not refer to vectors.
To me a vector ...
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Why isn't time reversal a Galilean transformation?
I'm a mathematician learning physics from scratch, starting from Newtonian mechanics. As far as I understand, Galilean transformations are defined as transformations of space-time that transform from ...
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Galilean's principle implies independence of time and dependence on relative distance
Suppose a system of particles $q_1,\ldots,q_N$ of masses $m_1,\ldots,m_N$ that follow the equations of motion
$$m_j\ddot{q}_j=f_j(q_k,\dot{q}_k)$$
in an inertial frame and satisfy the Galilean ...
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How is Newton's first law of motion different from Galileo's law of inertia? If the two are the same, then why is the first law named after Newton?
Galileo's law of inertia (at least what I've learned) is
"A body moving with constant velocity will continue to move in this path in the absence of external forces".
And Newton's first law ...
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Do Newton's laws of motion imply no physical difference between different inertial frames of reference?
I'm a mathematician learning physics from scratch, for my own curiosity and interest. Starting from the basics, I'm trying to get a deep grasp of Newton's laws of motion.
V.I. Arnold describes Galileo'...
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Velocity and kinetic energy, violating galilean relativity
I have a toy car and a battery. The barrery has a screen that shows how much energy it has left. Since kinetic energy is proportional to velocity squared, I need 1J of energy to go from 0m/s=>1m/s, ...
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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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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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Can we write the mass $M$, a Casimir invariant of the Galilean group, as a function of its generators?
According to Wikipedia, the mass $M$ is one of the Casimir invariants of the Galilean group. Casimir invariants of a group are made out of the generators, and they commute with all the generators of ...
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Alternative universes without max speed and with absolute time
I'm not asking of something real but something mathematically possible.
Is it possible to do a math model of an universe (not ours) without max speed and without time dilatations? What would be the ...
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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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Conservation of Energy in Collision
Consider two cars of mass $m$ travelling towards each other at velocity $v$. A bystander (mass $m_b$) on the side of the road would calculate that cars have a total kinetic energy of $mv^2$, while a ...
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Why is absolute time considered an axiom of Newtonian mechanics? What statements are based on this axiom?
I guess absolute time is associated to classical mechanics because people like Newton believed in that concept, but are there actually any statements whose derivation is based on this assumption?
I've ...
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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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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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Is this the correct way to transform a trajectory between Galilean frames?
Consider the general Galilean transformation in one spatial dimension:
$$(x, t) \mapsto (x', t') = (x + vt + a, t + b).\tag{1}$$
I want to use it to transform trajectories $x(t)$ in a frame $S$ to the ...
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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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How should this argument (about the non-validity of Special Relativity) be interpreted? [closed]
I have read the following (here) by Stephen J. Crothers:
Einstein’s Special Theory of Relativity requires systems of clock-synchronised stationary observers and the Lorentz Transformation. Without ...
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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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Why is the phase of a matter wave not Galilean invariant? And what does this say about the Schrödinger equation? [duplicate]
Matter waves are not Galilean Invariant
Consider a non-relativistic freely-propagating matter wave in an inertial frame $\Sigma'$ moving along the $x'$-direction with kinetic energy $E'=1/2m_0v'^2$, ...
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Why is it that a vertically thrown ball will move horizontally if we are travelling in a non-inertial reference frame?
If I throw a ball vertically inside a moving train, there will be horizontal movement if the train accelerates/decelerates (ie is not an IRF) and no horizontal movement if it does not (ie is an IRF).
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What is a time-dependent symmetry in Hamiltonian mechanics?
I've read something from John Baez which I don't understand:
If we consider a single nonrelativistic free particle - in
one-dimensional space, to keep life simple - and describe its state by
its ...
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Interpretation: Galilean Transformation of Force Laws
so my books says
The transformation that allows us to go from one inertial frame $O$
with coordinates $x_i$ to another inertial frame $O'$ with coordinates
$x_i'$ is the Galilean transformation. If ...
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Why the basic laws of physics are covariant under Galilean transformation? [closed]
If we use Galilean transformation, why is that basic laws in physics are covariant?
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Law's of Mechanics are Galilean invariant
In my current physics book one line reads:
"The laws of mechanics are Galilean invariant.",
with corollary:
"No mechanical experiment can be used to tell whether an inertial frame is ...
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Length measurement in Galilean relativity. Problem understanding a paragraph from Resnick's Relativity
The paragraph below is taken from the book An Introduction to Special Relativity by Robert Resnick.
Let A and B be the endpoints of a rod, for example, which is at rest in the S-frame. Then the ...
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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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When is a Hamiltonian Galilean invariant?
The Hamiltonian of a point mass connected to a fixed point by a spring in (1-dimensional) space is
$$H(x,p)=\frac{p^2}{2m}+\frac{1}{2}kx^2\tag{1}\label{eq1}$$
The Hamiltonian equations are
$$\begin{...
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Contradiction between Galilean transformation and conservation of mechanical energy
Consider the system described by the above diagram. The table is frictionless and the string and the pulley are massless. Suppose that at heights $h$ and $\widetilde{h}$ of $m_2$ the corresponding ...
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