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2
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1answer
105 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 ...
0
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2answers
63 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
41 views

Matrix Representations of Galilean group

The general group element (in the vector representation) $$ \left [{ \begin{array} {c} \bar x^1 \\ \bar x^2 \\ \bar x^3 \\ \bar t \\ 1 \\ \end{array} } \right] = \left[ ...
0
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1answer
65 views

In space I am moving wrt to what?

Let us suppose I am running on a street. When my eyes are open, I can see many things moving backward, and thus it gives me an idea that I am moving wrt those things. Not even this, even if I close my ...
2
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0answers
25 views

Casimir Invariants of the Galilean group

I had studied a couple of things about Galilean and Poincare group. But in the Galilean group, there is not enough clarity on how to calculate generators for boosts ($B_i$), which if I do it seems I ...
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0answers
49 views

Time inversion for Euler equation

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 ...
1
vote
1answer
50 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 ...
3
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2answers
206 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 ...
6
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3answers
814 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 ...
1
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0answers
77 views

How to show that a general Galilean transformation in three dimensions is a conformal transformation?

Suppose two particles with equal mass move and then collide. We can easily show that the angle of collision is ninety degree if we choose our frame of reference moving with velocity equal to one of ...
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0answers
78 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?
0
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2answers
1k 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 ...
4
votes
1answer
205 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} + ...
3
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1answer
149 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) = ...
6
votes
2answers
241 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 ...
11
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3answers
2k 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 ...
1
vote
2answers
175 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 ...
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6answers
1k 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 ...
3
votes
1answer
216 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 ...
2
votes
1answer
220 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: $$x=u(cos\theta)t$$ ...
0
votes
1answer
64 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
vote
1answer
142 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 ...