Questions tagged [galilean-relativity]

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2answers
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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) ...
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2answers
206 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
426 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
482 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
354 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 ...
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2answers
364 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 ...
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1answer
202 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
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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0answers
109 views

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 ...
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2answers
222 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
806 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
132 views

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
1k views

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 ...
4
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2answers
137 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
4k views

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 ...
4
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1answer
745 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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2answers
460 views

What does a Galilean transformation actually mean?

What does a Galilean transformation actually mean? I'm having trouble defining the equation for displacement shifts $x'=x-vt$. Does it mean that to any event $C$ the displacement in the primed ...
0
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1answer
234 views

Why is the Galilean group not commutative?

As I understand it, the Galilean transformation is a matrix $$ \left[ {\begin{array}{ccccc} R_{11} & R_{12} & R_{13} & v_x & a_x\\ R_{21} & R_{22} & R_{23} & v_y ...
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2answers
774 views

Why the Galileo transformation are written like this in Quantum Mechanics?

In Quantum Mechanics it is said that the Galileo transformation $$\mathbf{r}\mapsto \mathbf{r}-\mathbf{v}t\quad \text{and}\quad \mathbf{p}\mapsto \mathbf{p}-m\mathbf{v}\tag{1}$$ is given by the ...
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0answers
128 views

Observer Watching a Ball Thrown Up on A Train [closed]

Let's suppose I'm on a train, moving with constant speed V1. At a time T1 I throw a ball up in the air, the ball do not accelerate but has constant velocity V2, and, in this hypotetical scenario, no ...
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1answer
97 views

Simultaneity in Newtonian mechanics

How would Newtonian mechanics answer the train and moving light question? The setup is: A train is moving in the positive x_axis with speed c/2. A person stands in the middle of the train. There ...
6
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1answer
224 views

Shouldn't the escape velocity of earth (with respect to earth) be less than $\sqrt{\frac{2GM}{R}}=11.2\,\mathrm{km/s}$

We know that the escape velocity of earth is, $$\sqrt{\frac{2GM}{R}}=11.2\,\mathrm{km/s}$$ Where $G=6.67×10^-11$ $M=\text{mass of earth}$ $R=\text{radius of earth}$ So if throw a object ...
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1answer
61 views

What relative motion tells me about a motorbike shooting out from a bus?

I imagined this situation: Suppose I'm on a motorbike inside a long bus that has a constant velocity v on a street. I start accelerating (in the direction opposite to the motion of the bus) till ...
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2answers
310 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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0answers
47 views

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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1answer
104 views

Galilean group transformations

My problem is the following: I have difficulties in answering questions (c), (d) and (e). For (c) my answer was $\sqrt{x^{2}+t^{2}}$ and yes, the group forms the group of all isometries since the ...
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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
561 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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2answers
138 views

Are laws of physics (mechanics) symmetric under uniform rotation?

I'm just starting to learn about symmetry. I understand that physical laws are symmetric under translation and consequently (is it not a consequence?) under uniform velocity in a straight line. I see ...
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2answers
177 views

Why position and velocity are symmetries and acceleration is not?

Position and velocity are symmetries. The law of physics do not change if the observer changes his position or velocity. But acceleration which is just a derivative of velocity is not a symmetry. In ...
3
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1answer
261 views

Is the Euclidean metric the only one invariant under Galilean Transformations?

Is $$ds^2=dx^2+dy^2+dz^2$$ the only metric that is invariant under Galilean transformations? And if yes how do you prove it?
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2answers
559 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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2answers
149 views

How does the existence of aether allow for the Galilean transformation?

I was reading this and it said that the aether was proposed as a fix to accommodate the Galilean transform because the Laws of Electromagnetism did not remain constant under the Galilean transform. ...
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2answers
3k views

Isn't D'Alembert's wave equation enough to see that Galilean transformations are wrong?

The D'Alembert equation for mechanical waves was written in 1750: $$\frac{\partial^2u}{\partial x^2}=\dfrac{1}{v^2}\dfrac{\partial^2u}{\partial t^2}$$ (in 1D, $v$ being the propagation speed of the ...
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0answers
250 views

Galileo principle (from Landau Lifshitz to derive free particle Lagrangian)

I am reading the Landau & Lifshitz on mechanics to understand how we find the free particle Lagrangian, and there are some things that I don't understand. First, he defines an inertial frame as ...
6
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2answers
481 views

Inonu-Wigner Group Contraction

I am trying to understand how one obtains the Galilean algebra from the Poincare algebra, specifically through the method of central extension. I'm doing this by imposing that the generators of the ...
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1answer
597 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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2answers
494 views

Confusion about momentum in an inertial reference frame?

In my notes, it says that the total change in momentum of an inertial reference frame is zero. Please see the picture below This has confused be because I nnderstand that the inertial reference ...
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1answer
548 views

Do Galilean boosts and Lorentz boosts share the same generators?

Gottfried and Yan's Quantum Mechanics introduces a generator $N$, called the boost, which generates Galileo transformations. I think in other terminology one might say $N$ generates Galilean boosts, ...
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1answer
1k views

Galilean transformation in non-relativistic quantum mechanics

I'm reading Weinberg's Lectures on Quantum Mechanics and in chapter 3 he discusses invariance under Galilean transformations in the general context of non-relativistic quantum mechanics. Being a ...
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1answer
268 views

Question about Galilean relativity [closed]

If a boat is moving at constant speed relative to water, on a trip between two cities, the ride upstream lasts $t_1=6~h$ and the ride downstream lasts $t_2=3~h$. What time ($t'$) will the boat need to ...
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2answers
227 views

Expansion in $\epsilon$ and $v^2$ dependence of the Lagrangian - Landau & Lifshitz's Mechanics [duplicate]

On page 4 of Landau & Lifshitz's Mechanics they say $$L\left({v^\prime}^2\right) = L\left(v^2 + 2\bf{v \cdot} \bf{\epsilon} + \epsilon^2\right).$$ Expanding this expression in powers of $\...
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1answer
790 views

A question concerning the Galilean invariance of Newton's laws

When proving the Galilean invariance of Newton's laws is it tacitly assumed that all equations are covariant, i.e. that they are form invariant? For example, it is fairly trivial to show that the ...
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2answers
292 views

(SR) Lorentz low speed approximations

In Special Relativity, the standard Lorentz transformations are: $t' = \gamma (t - \frac{vx}{c^2}) \\ x' = \gamma (x - vt) \\ y' = y \\ z' = z$ However, if we make a low speed approximation where $v ...
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5answers
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How did Maxwell's theory of electrodynamics contradict the Galilean principle of relativity? (Pre-special relativity)

The Galilean principle of relativity: The laws of classical mechanics apply in all inertial reference systems OR No experiment carried out in an inertial frame of reference can determine the ...
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1answer
187 views

Introduction to Special Relativity Question - Momentum Conservation

I'm currently reading a text for self-study on special relativity, Introduction to Special Relativity by James H. Smith, and I came across a question that I don't see to grasp at the moment. "Figure ...
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1answer
112 views

According to the Galileo Algebra, space translations commute with time translations. Does this mean that $[\vec P,H]=0$?

The Galileo Algebra is discussed in, for example, the wikipedia article Representation theory of the Galilean group. In that article, we can see that, for example, $$ [E,P^i]=0 $$ which means that ...
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1answer
336 views

Constancy of the speed of light in the hypotenuse of the triangle in the Michelson and Morley experiment [closed]

In Michelson and Morley experiment, Michelson calculated that the total time traveled by light with respect to the stationary observer standing at ether field was $2L/c$. Here, Michelson followed ...
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1answer
285 views

Why does galilean invariance imply that particles that start rest stay on the same line?

I'm reading Arnol'd for self study. I'm struggling with this question: "Show that any system of two particles will remain on the same line that connected them at the initial moment, if they started at ...