Questions tagged [galilean-relativity]

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6
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2answers
469 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 ...
2
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1answer
874 views

Generator of Velocity Transformations - Galilean Transformations

Under a Galilean transformation, the coordinates and momenta of any system transform as: $$ t \rightarrow t',\\ \vec r\:' = \vec r + \vec vt,\\ \vec p\:' = \vec p + m\vec v $$ where $\vec v$ is ...
5
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2answers
470 views

Does Galileo's Tower of Pisa argument contradict quantum mechanics?

(My questions are at the end, but they may not mean much without explanation below.) Galileo argued that because the mass of a falling object can always be redistributed in ways that asymptotically ...
8
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3answers
8k 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
482 views

Mechanics Landau Galilean Principle

I started reading Landau's Mechanics book and was having some trouble understanding the Galilean Relativity Principle. What does Landau mean by saying space to be homogenous and isotropic and time is ...
0
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2answers
585 views

Is the assumption that the two reference frames be inertial required in the derivation of transformation equations?

In the derivation of Galilean transformations the only assumption is that the two frames are moving with some uniform relative velocity $u$. Suppose with respect to some inertial frame $O$ the two ...
2
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0answers
293 views

Jacobian matrix of Galilean transformation

If we want to transform to another inertial frame of reference using Galilean transformation in 4-dimensional space-time, what is the Jacobian matrix of Galilean transformation?
2
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1answer
146 views

Event horizons in Newtonian mechanics and Galilean relativity

I've been revisiting classical physics (in the sense of Newtonian mechanics and Galilean relativity) and I was thinking why can't we have an event horizon in classical physics? Is it because the ...
6
votes
2answers
5k views

Galilean invariance of a subset of Maxwell equations

I read in Feynman's proof of Maxwell equations the statement that the subset of Maxwell equations comming from the Bianchi identity: $$ \nabla \cdot {\bf B} = 0, \quad \nabla \times {\bf E} + \frac{1}...
3
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1answer
4k views

Newton's second law invariant under law of addition of velocities

I'm currently reading Schutz' first course in general relativity, and on the second page (already) I've encountered a problem: We have the Galilean law of addition of velocities: $ v(t) = v'(t) = v(t)...
2
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2answers
19k views

Lorentz and Galilean transformation

I read about Lorentz and Galilean transformation in a book of modern physics some days back, but couldn't clearly understand the difference between the two? Also it was stated there that maxwell's ...
2
votes
2answers
781 views

Velocity of an object undergoing homogenous acceleration

So I was considering the following problem within the context of Special Relativity: Given an object O, with initial velocity v, undergoing constant acceleration at a rate of a, I want to express the ...
3
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6answers
5k views

Inertial Frames of Reference - Inertial vs. Accelerated Frames

According to Robert Resnick's book "Introduction to Special Relativity", a line states the following as the definition of an inertial frame of reference: "We define an inertial system as a frame of ...
13
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2answers
13k views

Galilean invariance of the Schrodinger equation

Is the Schrodinger equation invariant under Galilean transformations? I am only asking this question so that I can write an answer myself with the content found here: http://en.wikipedia.org/wiki/...
6
votes
1answer
1k views

Faraday's Law and Galilean Invariance

In Jackson's text he says that Faraday law is actually: $$ \oint_{\partial \Sigma} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} = -k\iint_{\Sigma} \frac{\partial \mathbf B}{\partial t} \cdot \mathrm{...
2
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1answer
633 views

Galilean relativity in projectile motion

Consider a reference frame $S^'$ moving in the initial direction of motion of a projectile launched at time, $t=0$. In the frame $S$ the projectile motion is: $$x=u(cos\theta)t$$ $$y=u(sin\theta)t-\...
4
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3answers
3k views

Maxwell equations invariant under Lorentz transformation but not Galilean transformations

Why Maxwell equations are not invariant under Galilean transformations, but invariant under Lorentz transformations? What is the deep physical meaning behind it?
0
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1answer
83 views

Proper notation when working with three Euclidean spatial coordinates in a setting with a time parameter

The How does the Euclidean metric is the symmetry group of Euclidean space. It includes rotations and translations. Say I consider an Euclidean space and a time parameter. How does the Euclidean ...
1
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1answer
196 views

Do observers at different speeds perceive other speeds differently?

I was told that if a plane takes less time to travel from the China to US as opposed to the other direction due to rotation of the earth. I suspect this is incorrect however. From this scenario I ...
2
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2answers
545 views

Confused on Newton's second law being invariant under relativity

I am a math student with some interests in physics. I picked up a book called "A First Course in General Relativity", and I am confused on the second page. I am assuming by notation or convention. ...
0
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2answers
666 views

Inertial and non-inertial frames of references

I've heard from a physics professor that there's no stationary platform to observe and analyze a body in motion. Why did he mention that? Is it because even seemingly stationary objects like a parked ...
18
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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 ...
4
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2answers
8k views

Galilean invariance proof

I'm studying for a physics test, but I think I don't really understand Galilean invariance. In my textbook there is an example in which they prove that if you consider 2 frames S and S' in standard ...
7
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2answers
349 views

Why absoluteness of time implies galilean transformations?

In Landau course, vol.1 Mechanics, one finds the statement: ...the absoluteness of time necessarily implies that the ordinary law of composition of velocities is applicable to all phenomena. I ...