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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 ...
7
votes
3answers
1k 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 ...
6
votes
2answers
251 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 ...
6
votes
0answers
79 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 ...
4
votes
1answer
79 views

Possible mechanics based on the known symmetries in the nature (investigating rumor)

Somewhere I've heard about a relative new mathematical result regarding mechanics. Specifically, there is a list of the known symmetries of mechanics (both Newtonian and relativistic), i.e. different ...
4
votes
2answers
241 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 ...
4
votes
1answer
304 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
votes
1answer
182 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) = ...
3
votes
1answer
261 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
118 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 ...
2
votes
1answer
234 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: $$x=u(cos\theta)t$$ ...
2
votes
0answers
59 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[ ...
2
votes
0answers
37 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 ...
2
votes
0answers
83 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?
1
vote
2answers
188 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 ...
1
vote
1answer
62 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 ...
1
vote
1answer
150 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 ...
1
vote
0answers
10 views

Question about Galilean transformation

I'm just learning about relativity, and every equation I see for a galilean transformation of frame $S'$ (moving with uniform velocity in the $x$-direction with respect to frame $S$) is $x'=x-vt$, ...
1
vote
0answers
58 views

Galilean Transform

I tried to solve a problem using two different ways and I had some trouble, the problem is: We define a symmetry transform of the expected value of $\vec{P}$ like this: $$\langle \psi|\vec{P}|\psi ...
1
vote
0answers
82 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 ...
1
vote
7answers
2k 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 ...
0
votes
3answers
137 views

Is it possible to tell whether the space ship is moving or not?

Consider a space ship which is not under any force. Being inside the space ship, I will make a robotic fly from the platform to crawl inside using my remote. For simplicity assume that space ship will ...
0
votes
2answers
2k 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 ...
0
votes
1answer
77 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 ...
0
votes
2answers
102 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 ...
0
votes
1answer
66 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 ...
0
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0answers
28 views

Galilean group time interval

I have a question that arised by reading A Course in Modern Mathematical Physics by Peter Szekeres. He defines the galilean space $\mathbb{G}^{4}$ to be the space of events with a structure ...