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Questions tagged [galilean-relativity]

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Unlike rotation, why a $3\times 3$ translation matrix cannot be written in 3D? or can it be?

The effect of rotation in 3d on a vector, $\vec{r}=x\hat{x}=y\hat{y}+z\hat{z}$ is given in the form a matrix product:$$\vec{r}\to O\vec{r}$$ where $O$ is a $3\times3$ proper orthogonal matrix. Can we ...
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1answer
88 views

Lagrangian of free particle - classical case

I have a question, more related to a mathematical aspect of physics, which seems I am not understanding very well. So, by applying Galilean transformation between two reference frames, which move at ...
2
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2answers
76 views

Why the Lagrangian of a free particle cannot depend on the position or time, explicitly?

On p. 5 in $\S$3 pf the book of Mechanics by Landau & Lifshitz, it is claimed that [...] for a free particle, the homogeneity of space and time implies that Lagrangian cannot depend on ...
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0answers
34 views

Is there ever such thing as pure rotation or translation? [duplicate]

My thoughts... Let us consider that in a given reference frame, we perceive a body moving rectilinearly (i.e. in a straight line). I suppose we can define this "pure translation", since all the ...
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1answer
34 views

How does Kinetic Energy transform from one frame of reference to another?

Let's say I observe a charge q floating in the middle of space. I set up another charge Q a distance d away from charge q was causes a force F to act on charge q. As charge q moves away from charge ...
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3answers
249 views

Should non-relativistic Navier Stokes Equations be modified so that they become pseudo-Lorentz invariant?

Choking mass flow seems to reflect the fact that fluid momentum density has a maximum value (in stationary conditions) equal to $\rho_* c_*$ where $\rho_*$ is the critical mass density and $c_*$ is ...
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0answers
42 views

Galilean transform wave equation differentials

We have the wave equation \begin{equation} -c^2 dt^2 + dx^2 = 0 \end{equation} With typical Galilean transform: \begin{equation} \left\lbrace \bar{x} = x - v t \atop \bar{t} = t \right. \end{...
6
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1answer
133 views

How would General Relativity be different if we assumed Galilean instead of Lorentz transformations?

If we assume a universe where Galilean transformations are the correct transformations between inertial reference frames, would GR be any different ? Gravitational and inertial mass would still be ...
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1answer
66 views

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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1answer
36 views

Relationship between the Galilei Group and the Phase Space

This question is kind of a follow up question to my last question on the need for canonical commutation relations and conjugate observables. A comment from Valter Moretti suggested that, given a ...
0
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1answer
83 views

Can we really not tell if we are moving?

It has been a while since I've thought about physics, however, I remember something about how if you are on a train with no windows that is going perfectly straight and is perfectly smooth, there is ...
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2answers
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Galilean transformations of velocity

If I perform a Galilean boost $$x' = x - vt \\ t'=t$$ between two frames $S$ and $S'$, observers in each frame would disagree on the velocity of a particle because $$ \frac{dx'}{dt'} = \frac{dx}{dt} -...
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2answers
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Understanding Galilean Structure

I’m a student with a pure math background starting to work through Arnold’s “Mathematical Methods...” and I’m struggling right of the bat with Section 1.2 on Galilean Structure. (pg 4 - 6) So we have ...
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2answers
79 views

Can we deduce the principle of relativity from some more basic principles?

I was reading "Relativity" by Albert Einstein. In chapter 5 page 14, it is written that If K is a Galilean co-ordinate system, then every other co-ordinate system K' is a Galileian one, when, in ...
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1answer
43 views

Question about Galilean time invariance

I've been reading Arnold's book on Classical Mechanics. I understand that most "classical" forces such as gravity, spring are supposed to be Galilean invariant. But what if I start a rocket, and ...
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0answers
36 views

Definition of Galilean structure in Arnold's book?

I am reading Arnold's Mathematical Methods of Classical Mechanics. He quickly introduces the notion of Galilean structure. The universe is defined as the affine space $A^4$ and time is defined as a ...
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2answers
150 views

About the Galilean non-invariance of the wave equation

So I have this long standing problem. I know that the wave equation (with or without source term) changes form when one makes a Galilean transformation of coordinates. My question is about the ...
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0answers
103 views

Navier-Stokes Galilean invariance in curvilinear coordinates sytem

I can show that Navier-Stokes is Galilean invariant in Cartesian coordinates system as follows: \begin{eqnarray} \rho'(\mathbf{x'}) &=& \rho(\mathbf{x}), \nonumber \\ \mathbf{w'}(\mathbf{...
2
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1answer
210 views

The Lagrangian of a free particle in Landau & Lifshitz

In Landau & Lifshitz's derivation of the Lagrangian of a free particle in a galilean frame of reference one finds the following argument: the equations of motion in two galilean frames must be ...
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2answers
139 views

Are there Galilean scalars?

In special relativity there are scalar quantities which are invariant under any Lorentz transformation, called Lorentz scalars. For example, the magnitude of the four-velocity is a Lorentz scalar. If ...
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1answer
181 views

Is there an “invariant” quantity for the classical Lagrangian?

This is just a typical classical Lagrangian for $N$ particles. Since the Lagrangian does not explicitly depend on time, the energy must be conserved. Also, the linear and angular momentum seem to be ...
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4answers
367 views

Velocity of light in Galilean transformation

What is the velocity of light in Galilean transformation? Is it infinity?
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1answer
81 views

Kinetic energy when observer is moving and object is stationary [duplicate]

I know kinetic energy is due to motion of an object. But what if, I, the observer of an object is moving and that object appears to be moving for me, then which one has kinetic energy. is it me or ...
0
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1answer
120 views

Galilean Transformation

The transformation between inertial systems are given by affine transformations of $\mathbb{R}^{1+3}$. These are given by $t'=\lambda t+\vec{c}^\top \vec{x} +a$ and $\vec{x}'=\vec{v}t+M\vec{x}+\vec{b}$...
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1answer
91 views

Transformation of the operators $\mathbf\nabla$ and $\partial/\partial t$ under Galilean transformation

I'm want to know how are the transformations of the operators $\mathbf\nabla$ and $\partial/\partial and $\partial/\partial t$ when the transformation of the Galilean relativity is applied. This is ...
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1answer
166 views

Does $[P_j,B_k]=i(Mc^2)\delta_{jk}$ imply particle number conservation?

From reading Weinberg's Quantum Theory of Fields, Vol. 1, I learnt that for the Galilean group $[P_j,B_k]=i(Mc^2)\delta_{jk}$, and for the Poincare group $[P_j,B_k]=iH\delta_{jk}$ where $P_j$ and $B_k$...
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0answers
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Question about frames of reference

I have a general question about (inertial) frames of reference. For the purpose of the question it suffices to consider Galilean relativity. Suppose I is moving with $v$ with respect to to O and I' is ...
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1answer
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What does a Galilean transformation of Maxwell's equations look like?

In the 1860's Maxwell formulated what are now called Maxwell's equation, and he found that they lead to a remarkable conclusion: the existence of electromagnetic waves that propagate at a speed $c$, ...
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0answers
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Question on section 1.2 of Kibble, Berkshire book on classical mechanics

If the two frames are inertial, (which means the moving frame in the following passage from the book is moving with constant velocity), where is the contradiction in the following passage in section 1....
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1answer
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How do we know that the laws of physics are invariant in all inertial frames?

Einstein's Special Relativity theory is based on the assumption that the laws of physics are invariant in all inertial frames, and from there - according to Maxwell's equations - it derives that the ...
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0answers
28 views

Symmetries on a finite Euclidean spacetime and an infinite Euclidean spacetime

Consider the following: The Euclidean plane has $3$ translation symmetries and $3$ rotation symmetries. Any physical quantity $K(x,y)$ on the Euclidean plane, where $x$ and $y$ are two arbitrary ...
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1answer
91 views

How can I interpret or mathematically formalize Maxwellian, Leibnizian, and Machian space-times?

I've been reading the book, World Enough and Space-Time, and I came across a rough list of classical space-times with varying structural significance. Here is the same list, minus Machian Space-time,...
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2answers
150 views

Doppler Effect and Relativity

The equation for the Doppler effect is given by $$f_L = \frac{v+v_L}{v+v_S}f_S$$ where the velocities of both the source and the listener matter. My question is, how does this fit into Galilean ...
2
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2answers
242 views

Galilean Relativity and Electrodynamics

Consider the following: On the one hand, the principle of relativity, by Galileo, (totally applied to the Newtonian mechanics) says: There is no mechanical experiment that you could perform to ...
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2answers
241 views

Galilean spacetime interval?

Does it make sense to refer to a single Galilean Invariant spacetime interval? $$ds^2=dt^2+dr^2$$ Or is the proper approach to describe separate invariant interval for space (3D Euclidean distance) ...
3
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2answers
164 views

Is relativity of simultaneity just a convention?

Lorentz transformations are well known to imply time dilation, length contraction, and relativity of simultaneity. This is prominently featured in any course on Special Relativity (SR), e.g. in ...
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5answers
387 views

How do we mathematically know for sure that absolute time is abandoned in relativity?

It is an often mentioned assumption in physics that in going from classical to relativistic spacetime the main difference is that the absolute time postulate holding in the former is "relaxed" or ...
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1answer
263 views

Galilean Invariance of material derivative

I'm reading some fluid dynamics notes which are talking about a Galilean boost of the form: $$x'=x-vt, \qquad t'=t$$ The notes immediately claim from this that the material derivative $$\frac{D}{Dt}...
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1answer
231 views

Why are Maxwell's equations not Galilean invariant? [closed]

So i am writing an essay on the conflict between galilean invarience and maxwell's electromagnetism. I am struggling to come up with 3 evidences that they conflict because I have a mediocre ...
2
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2answers
234 views

Kinetic Energy in different reference frames

Good morning, I've got a strange little paradox I thought of that I just can't figure out. Imagine that you are building a machine that lets a ball fall in vertical direction from a height h, and ...
0
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1answer
111 views

Angular momentum conservation under Galileo transformation

I was trying to see when angular momentum is independent of choice of origin, but then it seems angular momentum no longer conserved under Galileo transformation to me : Given a point mass is doing ...
2
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1answer
298 views

Derive the Lagrangian that yields the free Schrödinger's equation from Galileian Invariance

The Lagrangian Density $$L(\Psi, \Psi^*)=i \hbar \dot{\Psi} \Psi^* + \frac{\hbar^2}{2m} \Psi \Delta \Psi^*$$ will yield the schroedinger equations for $\Psi$ and $\Psi^*$. Can we derive this ...
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0answers
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Galilean invariance of the free schroedinger equation [duplicate]

My question follows this question: Naive interpretation of Galilean invariance of the TDSE Essentially, I'm not sure how to proceed mathematically. We have the transformations: $$\begin{cases}x'=x-...
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1answer
107 views

Shouldn't work be the same in all coordinates?

We know that the work done by a force $\mathbf{F}$, along a path $\mathbf{x}$, is given by: \begin{equation} W = \mathbf{F}^T \cdot \mathbf{x} \end{equation} However, suppose that i apply some change ...
2
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2answers
165 views

Does Galilean relativity constitute a dynamical symmetry or an isometry?

There are many papers which derive the form of the Lorentz transform from elementary symmetry principles (usually homogeneity of spacetime, isotropy of space, and the fact that boosts form a group), e....
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1answer
553 views

Does force definition depend on frame of reference?

Let’s assume we have 2 different observers. Observer 1 sits in space and observer 2 sits in a space lab which is in a free fall state toward the Earth. We further assume that observer 2 in the space ...
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1answer
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Symmetry properties of time and space in non-inertial frames

Are symmetry properties of time and space true for non-inertial frames? If yes, how? If no, why not? Please, can you explain? We already know that an important feature of inertial frames is the ...
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2answers
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How can Newton's idea of absolute space be reconciled with Galilean relativity?

I wasn't sure if this might be better suited to History of Science and Mathematics SE, but I suppose it is a bit more 'science-y' than historical. Apparently Newton believed in absolute space and ...
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2answers
113 views

Silly question about Galilei Group

I have an silly doubt about Galilei Group. From Wikipedia: "The Galilean symmetries can be uniquely written as the composition of a rotation, a translation and a uniform motion of spacetime. Let x ...
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4answers
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Are vectors truly independent of coordinate systems?

I have been told to think of vectors as existing independent of a coordinate system. This means that the magnitude of a vector should be independent of any coordinate system we choose. Galilean ...