Questions tagged [galilean-relativity]

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742 views

What is the Galilean transformation of the EM field?

Consider a reference frame $S$ and which we observe some electric field $\mathbf{E}$ and magnetic field $\mathbf{B}$. Let $S'$ be a reference frame moving at a constant velocity $\mathbf{u}$ with ...
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1answer
313 views

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

$$ L = \sum _ { i = 1 } ^ { N } \frac { 1 } { 2 } m _ { i } \left| \dot { \vec { x } _ { i } } \right| ^ { 2 } - \sum _ { i < j } V \left( \vec { x } _ { i } - \vec { x } _ { j } \right) $$ This ...
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0answers
53 views

Is time an invariant of Galilean transformation?

Is time an invariant of Galilean transformation? By saying that I mean if there is a quantity analogous to spacetime interval in Lorentz transformation. What is the geometry of "Galilean spacetime"?
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36 views

Most general form of Lagrangian only with respect to Galilean invariance

Let us assume we are doing classical one point particle mechanics. Assume that the least action principle holds. Also, assume that Lagrangian $L$ is a function only of coordinate $x$, its derivative $\...
7
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1answer
367 views

Why isn't scaling space and time considered the 11th dimension of the Galilean group?

Galilean transformations are said to have 10 degrees of freedom. Four for translation in space and time, three for rotation, and three for direction of the uniform motion. If I scale space axis by $\...
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27 views

Question about relative motion by Galilean Transformation?

You are piloting a small airplane in which you want to reach a destination that is 750 km due north of your starting location. Once you are airborne, you find that (due to strong but steady wind) to ...
2
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1answer
187 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
54 views

In Einstein's 1905 paper on electrodynamics, what he meant by energy of electromotive force?

In his 1905 paper, Einstein says that when the magnet is in motion and conductor stationary, changing magnetic field in space develops electric field "of certain definite energy", and this starts ...
2
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2answers
71 views

Inertial frames as in Landau & Lifshhitz mechanics 1st chapter

If we see inertial frames from a basic point of view (precisely more basic axiom from which I can at least derive the law of free body as in landau mechanics first chapter) that inertial frames are ...
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0answers
21 views

Inertial frame definition in Rindler Introduction to STR vs Landau' & Lifshitz Mechanics

Juxtaposing Rindler's Introduction to STR (page 7) vs Landau's Mechanics (page 5) inertial frame definition,I get that rindler assumes frame moving uniformly w.r.t inertial frame as an inertial frame ...
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1answer
35 views

Frame uniformly moving to an inertial frame in Landau & Lifshitz mechanics

How to prove frame moving uniformly in straight line to an inertial frame is an inertial frame? (Assuming I do not know Galileo's relativity principle and Galileo's transformations and also taking an ...
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2answers
558 views

The Meaning of Newton's Second Law of Motion Being Invariant Under Certain Transformations

What do we mean when we say that Newton's Second Law of Motion is invariant under Galilean transformations? Does it mean that the value of a force measured in one reference frame is the same when ...
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1answer
131 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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1answer
32 views

Galilei group and Constrained QM

Let's assume spin-0 for simplicity. So far as I understand the issue, the Galilei simmetries constraints the possible hamiltonians of a quantum systems so that the only possible interactions of a ...
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1answer
69 views

Reference request for Lie algebras

My future adviser just published a beautiful paper, https://arxiv.org/abs/1904.08304, and I am looking for some references/textbooks to look into the following concepts: Lie algebra (central) ...
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1answer
89 views

Is Lorentz and Galilean invariance mutually exclusive?

I know that the classical mechanics stays valid under Galilean transformation. The same argument applies to relativistic equations and Lorentz transformation. My question is, can a set of equations ...
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1answer
429 views

Coordinate Transformation in Classical Mechanics

The coordinates in one inertial frame are represented by $(x,t)$. Under coordinate transformation, the coordinates in another inertial frame can be represented by $f(x(t),t)$. It can be shown that the ...
2
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1answer
652 views

Calculating relative velocity in three dimensional space

Given two points $\mathcal{A}$ and $\mathcal{B}$ in $\mathbb{R^3}$ whose position and velocity vectors are, respectively: $$\mathbf{r_A}=\begin{pmatrix}r_{A_{x}}\\r_{A_{y}}\\r_{A_{z}}\end{pmatrix}$$ $$...
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2answers
221 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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3answers
38 views

Defining what it means for a reference frame to move with a velocity $\mathbf{u}$ with respect to another

In describing a Galilean transformation, for example, one might say that if a reference frame $S'$ is moving at a velocity $\mathbf{u}$ with respect to $S$, then an object traveling at a velocity $\...
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1answer
67 views

Galilei Invariance and Newton Third Law

Let's say we have a system of two point particles that can interact with each other by forces that are position and velocity dependent. The forces might or might not be derivable from a generalized ...
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4answers
2k views

Are cause and effect the same as in our Universe in a non-relativistic, Newtonian Universe in which the speed of light is infinite? [closed]

Suppose the Universe was non-relativistic so time and space would be independent of each other. In other words, both of them separately would be absolute and independent of an observer's motion (...
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2answers
54 views

The transformations of Lorentz as a general case of the transformations of Galileo

Starting from the transformations of Lorentz, $$ \left\{\begin{aligned} x&=\gamma (x'+\beta ct)\\ y&=y'\\ z&=z\\ ct&=\gamma (ct'+\beta x')\\ \end{aligned}\right. \quad \tag{*}$$ I ...
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1answer
33 views

Galilean transformation and differentiation

Given $x=x’-vt$ and $t=t’$, why is $\frac{\partial t}{\partial x’}=0$ instead of $1/v$? $t$ seems to depend on $x’$ because if $t$ changes, $x’$ changes. Also, in this problem, $dx=dx’$ as well, but I ...
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1answer
31 views

Issue showing that the phase of a harmonic wave is invariant under a Galilean transform

The phase $Φ$ of wave is defined as $kx-wt$. It should be the case that all observers moving relative to each other in the non relativistic case will agree on this. So given the transforms $x'=x-vt$ ...
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1answer
70 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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1answer
76 views

What was Newton's idea of absolute space and time?

When one says that Newton believed in the concept of "absolute space" and "absolute time" does it simply mean that the length interval between two points in space and time interval between two events ...
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1answer
34 views

Question on force invariance under the Galilean Transformations (GT)

By the Galilean transformations, one can easily derive that two different inertial observers 1,2 always measure the same forces. That is: $$ \vec{F_1} \ \left(\vec{r_1}, \frac{d\vec{r_1}}{dt_1},t_1\...
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2answers
309 views

Question on Galilean transformation

Let $a$ be a scalar, $D$ a rotation matrix and $b$ and $v$ are $1\times 3$-vectors. We had the following Galiean transformation: $(t, x(t)) \to (t + a, Dx + b + v\cdot t)$ But why is it not $(t, x(...
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1answer
182 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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2answers
350 views

Does the density of a galaxy affect time?

Can denser galaxies appear blue shifted? Can galaxies with different densities then our own galaxy appear blue or red shifted from movement when in fact it could be from the time dilation from ...
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1answer
461 views

Newton's theory of gravity is covariant under Galilean transformations

We know from classical mechanics that the gravitational field equation for the scalar potential takes the form $$\nabla^2\phi=4\pi \rho,$$ where $\rho$ is mass density (which, can depend on time and ...
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1answer
131 views

How length is an invariant in Euclidean space?

The special theory of relativity shows that intervals are invariant under Lorentz transform in the Minkowski space -time. But how can we prove (any postulates or theory) that the length is an ...
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3answers
7k views

Why does tossing a coin in a train and on a train differ?

Suppose that I am inside of a moving train. I have a coin in my hand and I am standing still. If I toss this coin straight up, it will fall back into my hand. Now, suppose that I am on that moving ...
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2answers
340 views

How does the Lorentz force work for all velocities

At small velocities, the lorentz force in the boosted frame is approximately $F' = q(E + 2v \times B)$, where the one for the rest frame is $F = q(E + v \times B)$. How is this invariant if the two ...
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2answers
130 views

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
294 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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1answer
104 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 ...
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3answers
296 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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4answers
5k views

Galilean invariance of Lagrangian for non-relativistic free point particle?

In QFT, the Lagrangian density is explicitly constructed to be Lorentz-invariant from the beginning. However the Lagrangian $$L = \frac{1}{2} mv^2$$ for a non-relativistic free point particle is ...
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2answers
111 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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1answer
45 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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2answers
560 views

Does the lorentz force law only consider relative velocity?

A magnet moving through a fixed solenoid will produce a force on the electrons, creating a current. However, the solenoid has 0 velocity, so the Lorentz force law doesn't work. My question is, for ...
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1answer
381 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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2answers
194 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 ...
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1answer
595 views

Relativity and how speed affects passage of time

This is one where it doesn't matter how many books I've read about it, they all seem to evade the elephant in the room - from examples like the mirror on the boat reflecting a single photon up and ...
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1answer
2k views

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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1answer
69 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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2answers
446 views

Time inversion for Euler equation in fluid dynamics

Consider Euler equation for continuum body: $$\frac{\partial u^i}{\partial t}+\mathbf u\cdot \nabla u^i=- \frac{1}{\rho} \frac{\partial p}{\partial x^i} $$ where $\rho$ is the mass density, $p$ is ...
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1answer
46 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 ...