Questions tagged [galilean-relativity]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0 votes
1 answer
18 views

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 ...
user avatar
  • 1,295
2 votes
1 answer
43 views

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{...
user avatar
0 votes
1 answer
31 views

Galilean Symmetry of Newtonian Mechanics

So for the equations of motion to be symmetric about a transformation from $(t,x)$ to $(\tau, y)$, the following must be true (for Newtonian mechanics): $$m \frac{d^2 x}{dt^2} = f \left( x, \frac{dx}{...
user avatar
7 votes
2 answers
285 views

Are there two different versions of non-relativistic quantum mechanics?

The first version is the usual one we're taught. But there's this other version too : A quantum non-relativistic field theory. Take a non-relativistic classical field, like the non-relativistic limit ...
user avatar
  • 2,953
4 votes
1 answer
347 views

Aristotelian vs Galilean relativity in terms of bundles

In page-385 of Roger Penrose's Road to Reality, the following is written: In our Aristotelian scheme, it is appropriate to think of spacetime as simply the product: $$ \mathbb{A}= \mathbb{E}^1 \times ...
user avatar
6 votes
1 answer
737 views

How could any frame of reference be inertial?

The image below shows that a bystander watching the merry-go-round is in an inertial frame of reference. However, to nitpick, wouldn't the observer still be accelerating because it's on Earth?
user avatar
2 votes
2 answers
100 views

How do we justify that potential energy in a spring is Galilean invariant (to the extent that Newtonian mechanics holds)?

A spring can store elastic potential energy by elastically deforming and moving its atoms out of their minima potentials. The atoms themselves can be modeled as balls connected by Hooke-like springs ...
user avatar
2 votes
2 answers
108 views

Is angular momentum conservation Galilean invariant?

Suppose I have a system of particles with constant total angular momentum $\mathbf{L} = \sum_a m_a \mathbf{r_a \times v_a}$ in frame K. If frame K' moves with velocity $V$ with respect to K and their ...
user avatar
5 votes
1 answer
310 views

Is Galilean boost actually a gauge transformation?

In elementary physics, it is well-known that the Newton's law $$\vec{F}=m\vec{a}$$ is invariant under Galilean transformations. However, Galilean relativity is not introduced in details in ordinary ...
user avatar
0 votes
0 answers
29 views

In non-relativistic QM are coordinate systems $(\vec{r_1},t)$, and $(\vec{r_2},t)$ indistinguishable if $\vec{r_2}=\vec{r_1}+\vec{u}t$?

As I understand it non QM reduces to classical physics when planks constant is negligible compared to the relevant action, and in non relativistic classical physics coordinate systems $(\vec{r_1},t)$, ...
user avatar
2 votes
2 answers
68 views

Phase invariant under Galilean transformation?

I just watched this video from MIT explaining Galilean transformation of ordinary waves. https://www.youtube.com/watch?v=YdtHAIh-kas Early on, the professor goes on to say that the phase is exactly ...
user avatar
  • 307
1 vote
0 answers
32 views

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 ...
user avatar
  • 1,270
0 votes
1 answer
49 views

Galilean to Lorentz Transformation

I happened to come across a derivation of the Lorentz Transformation stemming from the Galilean Transformation. In two frames $S$ and $S'$ where the position and time coordinates for the frames are $(...
user avatar
1 vote
2 answers
175 views

Kinetic energy seen from two frames of reference

The kinetic energy of two particles (moving in free space) depends on the frame in which you look at the particles. So does total momentum. If I'm standing in the center of mass of the two particles, ...
user avatar
2 votes
2 answers
75 views

Why is vector notation not used in the velocity formula (Galilean Transformations)?

First of all, I'm not that good at physics. This question has to do with a physics course I'm taking at a maths school. With that said, I am currently learning about the Galilean transformations and I'...
user avatar
  • 149
0 votes
0 answers
20 views

Given a path of a particle, how to calculate the path of the particle in a different (moving/rotating) reference frame?

I would like to understand that given a path of a certain particle, how to find the find the curve of that particle in a given reference frame. This is considering classical mechanics. The reference ...
user avatar
  • 1,124
0 votes
1 answer
44 views

Vector calculus of a potential energy formula under Galileo transformation

I'm currently studying MIT OCW 8.20 Introduction to Special Relativity. In pset 1, the following question is being asked: Suppose you have a potential of the form U($\vec{r_1}, \vec{r_2}$) = U(|$\vec{...
user avatar
  • 3
6 votes
6 answers
2k views

Is kinetic energy relative or absolute? [duplicate]

I only can think of kinetic energy as absolute. I know velocity is relative but I can't see kinetic energy as being relative because that would violate energy conservation. For example, if in some ...
user avatar
0 votes
2 answers
72 views

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 ...
user avatar
4 votes
1 answer
125 views

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 ...
user avatar
  • 293
0 votes
0 answers
45 views

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
user avatar
  • 1
20 votes
9 answers
3k views

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 ...
user avatar
-3 votes
1 answer
159 views

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 ...
user avatar
  • 1
0 votes
0 answers
68 views

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 ...
user avatar
  • 332
4 votes
2 answers
368 views

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 ...
user avatar
0 votes
2 answers
39 views

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 ...
user avatar
12 votes
4 answers
1k views

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, ...
user avatar
2 votes
1 answer
139 views

Newtonian quantum gravity

Can someone give me reference about Newtonian (non-relativistic) quantum gravity like unifying Newtonian gravity with quantum mechanics?
0 votes
1 answer
43 views

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,...
user avatar
1 vote
0 answers
22 views

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 ...
user avatar
  • 4,708
2 votes
5 answers
74 views

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 ...
user avatar
1 vote
0 answers
32 views

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 ...
user avatar
5 votes
1 answer
535 views

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 ...
user avatar
1 vote
0 answers
51 views

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 &...
user avatar
  • 2,825
0 votes
1 answer
67 views

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-...
user avatar
  • 841
0 votes
0 answers
29 views

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 ...
user avatar
  • 332
1 vote
1 answer
121 views

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 ...
user avatar
9 votes
0 answers
119 views

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 ...
user avatar
  • 381
0 votes
1 answer
50 views

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 ...
user avatar
  • 129
1 vote
2 answers
94 views

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 ...
user avatar
  • 3,043
2 votes
1 answer
103 views

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 ...
user avatar
  • 332
0 votes
2 answers
67 views

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 ...
user avatar
  • 101
18 votes
4 answers
4k views

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 ...
user avatar
11 votes
2 answers
1k views

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'...
user avatar
  • 332
2 votes
1 answer
369 views

What is the Schrödinger equation in position velocity space?

One way I've seen the Schrödinger equation expressed for the position wave function is $$\frac{i\hbar\partial\Psi\left(\vec{r},t\right)}{\partial{t}}=-\frac{\hbar^2}{2m}\nabla^2\Psi\left(\vec{r},t\...
user avatar
2 votes
3 answers
420 views

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, ...
user avatar
  • 416
3 votes
0 answers
117 views

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, ...
user avatar
0 votes
2 answers
52 views

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 ...
user avatar
1 vote
1 answer
131 views

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 ...
user avatar
2 votes
4 answers
87 views

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 ...
user avatar
  • 77

1
2 3 4 5
7