All Questions
Tagged with galilean-relativity symmetry
33 questions
2
votes
1
answer
159
views
Proving that the Lagrangian of a free particle depends only on $|\boldsymbol{v}|^2$
The question is NOT answered by
Deriving the Lagrangian for a free particle,
as the answers therein assume the quadratic dependence, which is what
I am trying to prove. Additionally, while one of the ...
- 23
-1
votes
1
answer
77
views
Translational invariance $\neq $ Galilean invariance?
I have the impression that some literature say that Galilean invariance is broken by a uniform lattice. That is, although a uniform lattice like a tight binding model is translationally invariant, it ...
- 2,165
1
vote
0
answers
58
views
Independence of Lagrange function from time and position
In Landau & Lifshitz "Mechanics", it is said that from the time/space homogeneity Lagrange function is independent from time/position. I always thought that homogeneity means that motion ...
- 39
2
votes
1
answer
247
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Action of free particle is invariant under Galilean transformation / Transformation of derivative
I want to show that the action of a free particle is invariant under a Galilean transformation
$$
(t,\vec{x})\rightarrow (t+a,R\vec{x}+\vec{v}t+b)=(t^\prime, \vec{x}^\prime) \quad\text{where}\quad R\...
- 405
2
votes
1
answer
132
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What is the symmetry group of a particle interacting with external fields?
I am following along with Ballentine's (in his Quantum Mechanics: A Modern Development) construction/identification of symmetry generators as operators representing the standard observables (...
- 1,261
5
votes
4
answers
692
views
"Deriving" Newton's laws of motion from symmetry assumptions
It is often discussed how certain symmetries and conservation laws can be derived from Newton's laws of motion. My question is: can we go the other way? Can Newton's laws of motion be derived only ...
- 59
8
votes
4
answers
2k
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Doesn't Newton's equation of motion have a bigger invariance group than the Galilean group?
Newton's equation ${F}^i=m\frac{d^2x^i}{dt^2}$ is unchanged in form, under the Galilean group:
(i) under a translation of the origin of coordinates,
(ii) rotation of coordinates, and
(iii) Galilean ...
- 12.3k
1
vote
2
answers
298
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Is there any proof of Galilean Transformation?
Is there any proof of Galilean Transformation? Is it proved from experiment, theory or it simply is an axiom?
- 315
0
votes
2
answers
310
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Isn't a rotation just a sum of many translations?
If the world is (really or hypothetically) made of elementary, point-particles, then it's there such a thing as rotation?
Point particles by definition can't rotate around themselves. The only ...
- 3,002
0
votes
1
answer
272
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Galilean Symmetry of Newtonian Mechanics
So for the equations of motion to be symmetric about a transformation from $(t,x)$ to $(\tau, y)$, the following must be true (for Newtonian mechanics):
$$m \frac{d^2 x}{dt^2} = f \left( x, \frac{dx}{...
- 21
4
votes
2
answers
727
views
What is a time-dependent symmetry in Hamiltonian mechanics?
I've read something from John Baez which I don't understand:
If we consider a single nonrelativistic free particle - in
one-dimensional space, to keep life simple - and describe its state by
its ...
- 757
1
vote
0
answers
344
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How does Galilean invariance lead to equality of "mass" flux and momentum density?
Let us consider a fluid, with spacetime translation symmetry, and one internal $U(1)$ symmetry. Corresponding to the spatial translation symmetry, we can write down a momentum conservation equation ...
- 760
0
votes
0
answers
54
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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 ...
- 165
2
votes
2
answers
266
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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 ...
- 165
0
votes
1
answer
46
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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 ...
- 458
1
vote
1
answer
316
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 $x'=x-vt$ ...
- 1,545
1
vote
1
answer
182
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 ...
- 19
3
votes
1
answer
2k
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 ...
user115153
0
votes
0
answers
34
views
Symmetries on a finite Euclidean spacetime and an infinite Euclidean spacetime
Consider the following:
The Euclidean plane has $3$ translation symmetries and $3$ rotation symmetries.
Any physical quantity $K(x,y)$ on the Euclidean plane, where $x$ and $y$ are two arbitrary ...
- 3,243
-2
votes
1
answer
173
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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 ...
1
vote
2
answers
891
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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(...
user102683
2
votes
0
answers
56
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 ...
- 18k
3
votes
2
answers
394
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 ...
- 2,786
8
votes
1
answer
4k
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 ...
- 732
4
votes
2
answers
572
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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 ...
- 169
0
votes
1
answer
399
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Galilean relativity in QM
Intro
I've been trying to show that the generator of boosts can be written in operator form as can be seen here, as:
$$ B = \sum_i m_i x_i(t) - t \sum_i p_i $$
As a reminder the transformation ...
- 705
6
votes
2
answers
140
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 ...
- 8,338
1
vote
0
answers
136
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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:
$$\langle \psi|\vec{P}|\psi \...
- 103
9
votes
2
answers
1k
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Casimir Invariants of the Galilean group
I had studied a couple of things about Galilean and Poincare group. But in the Galilean group, there is not enough clarity on how to calculate generators for boosts ($B_i$), which if I do it seems I ...
- 3,134
2
votes
2
answers
855
views
Mechanics Landau Galilean Principle
I started reading Landau's Mechanics book and was having some trouble understanding the Galilean Relativity Principle.
What does Landau mean by saying space to be homogenous and isotropic and time is ...
- 1,586
3
votes
2
answers
24k
views
Lorentz and Galilean transformation
I read about Lorentz and Galilean transformation in a book of modern physics some days back, but couldn't clearly understand the difference between the two?
Also it was stated there that maxwell's ...
- 63
5
votes
4
answers
4k
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Maxwell equations invariant under Lorentz transformation but not Galilean transformations
Why Maxwell equations are not invariant under Galilean transformations, but invariant under Lorentz transformations? What is the deep physical meaning behind it?
- 2,489
30
votes
5
answers
9k
views
Galilean invariance of Lagrangian for non-relativistic free point particle?
In QFT, the Lagrangian density is explicitly constructed to be Lorentz-invariant from the beginning. However the Lagrangian
$$L = \frac{1}{2} mv^2$$
for a non-relativistic free point particle is ...
- 4,156