Questions tagged [galilean-relativity]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
0answers
53 views

Is time an invariant of Galilean transformation?

Is time an invariant of Galilean transformation? By saying that I mean if there is a quantity analogous to spacetime interval in Lorentz transformation. What is the geometry of "Galilean spacetime"?
0
votes
0answers
36 views

Most general form of Lagrangian only with respect to Galilean invariance

Let us assume we are doing classical one point particle mechanics. Assume that the least action principle holds. Also, assume that Lagrangian $L$ is a function only of coordinate $x$, its derivative $\...
7
votes
1answer
368 views

Why isn't scaling space and time considered the 11th dimension of the Galilean group?

Galilean transformations are said to have 10 degrees of freedom. Four for translation in space and time, three for rotation, and three for direction of the uniform motion. If I scale space axis by $\...
0
votes
0answers
28 views

Question about relative motion by Galilean Transformation?

You are piloting a small airplane in which you want to reach a destination that is 750 km due north of your starting location. Once you are airborne, you find that (due to strong but steady wind) to ...
0
votes
0answers
21 views

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 ...
2
votes
2answers
71 views

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 ...
0
votes
1answer
35 views

Frame uniformly moving to an inertial frame in Landau & Lifshitz mechanics

How to prove frame moving uniformly in straight line to an inertial frame is an inertial frame? (Assuming I do not know Galileo's relativity principle and Galileo's transformations and also taking an ...
0
votes
1answer
32 views

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 ...
0
votes
1answer
69 views

Reference request for Lie algebras

My future adviser just published a beautiful paper, https://arxiv.org/abs/1904.08304, and I am looking for some references/textbooks to look into the following concepts: Lie algebra (central) ...
2
votes
1answer
89 views

Is Lorentz and Galilean invariance mutually exclusive?

I know that the classical mechanics stays valid under Galilean transformation. The same argument applies to relativistic equations and Lorentz transformation. My question is, can a set of equations ...
3
votes
0answers
55 views

In Einstein's 1905 paper on electrodynamics, what he meant by energy of electromotive force?

In his 1905 paper, Einstein says that when the magnet is in motion and conductor stationary, changing magnetic field in space develops electric field "of certain definite energy", and this starts ...
1
vote
3answers
39 views

Defining what it means for a reference frame to move with a velocity $\mathbf{u}$ with respect to another

In describing a Galilean transformation, for example, one might say that if a reference frame $S'$ is moving at a velocity $\mathbf{u}$ with respect to $S$, then an object traveling at a velocity $\...
1
vote
1answer
67 views

Galilei Invariance and Newton Third Law

Let's say we have a system of two point particles that can interact with each other by forces that are position and velocity dependent. The forces might or might not be derivable from a generalized ...
9
votes
4answers
2k views

Are cause and effect the same as in our Universe in a non-relativistic, Newtonian Universe in which the speed of light is infinite? [closed]

Suppose the Universe was non-relativistic so time and space would be independent of each other. In other words, both of them separately would be absolute and independent of an observer's motion (...
0
votes
2answers
54 views

The transformations of Lorentz as a general case of the transformations of Galileo

Starting from the transformations of Lorentz, $$ \left\{\begin{aligned} x&=\gamma (x'+\beta ct)\\ y&=y'\\ z&=z\\ ct&=\gamma (ct'+\beta x')\\ \end{aligned}\right. \quad \tag{*}$$ I ...
1
vote
1answer
33 views

Galilean transformation and differentiation

Given $x=x’-vt$ and $t=t’$, why is $\frac{\partial t}{\partial x’}=0$ instead of $1/v$? $t$ seems to depend on $x’$ because if $t$ changes, $x’$ changes. Also, in this problem, $dx=dx’$ as well, but I ...
1
vote
1answer
31 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 $x'=x-vt$ ...
0
votes
1answer
76 views

What was Newton's idea of absolute space and time?

When one says that Newton believed in the concept of "absolute space" and "absolute time" does it simply mean that the length interval between two points in space and time interval between two events ...
0
votes
1answer
34 views

Question on force invariance under the Galilean Transformations (GT)

By the Galilean transformations, one can easily derive that two different inertial observers 1,2 always measure the same forces. That is: $$ \vec{F_1} \ \left(\vec{r_1}, \frac{d\vec{r_1}}{dt_1},t_1\...
2
votes
1answer
461 views

Newton's theory of gravity is covariant under Galilean transformations

We know from classical mechanics that the gravitational field equation for the scalar potential takes the form $$\nabla^2\phi=4\pi \rho,$$ where $\rho$ is mass density (which, can depend on time and ...
0
votes
1answer
132 views

How length is an invariant in Euclidean space?

The special theory of relativity shows that intervals are invariant under Lorentz transform in the Minkowski space -time. But how can we prove (any postulates or theory) that the length is an ...
2
votes
2answers
130 views

Unlike rotation, why a $3\times 3$ translation matrix cannot be written in 3D? or can it be?

The effect of rotation in 3d on a vector, $\vec{r}=x\hat{x}=y\hat{y}+z\hat{z}$ is given in the form a matrix product:$$\vec{r}\to O\vec{r}$$ where $O$ is a $3\times3$ proper orthogonal matrix. Can we ...
1
vote
1answer
104 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 ...
2
votes
2answers
113 views

Why the Lagrangian of a free particle cannot depend on the position or time, explicitly?

On p. 5 in $\S$3 pf the book of Mechanics by Landau & Lifshitz, it is claimed that [...] for a free particle, the homogeneity of space and time implies that Lagrangian cannot depend on ...
1
vote
1answer
45 views

How does Kinetic Energy transform from one frame of reference to another?

Let's say I observe a charge q floating in the middle of space. I set up another charge Q a distance d away from charge q was causes a force F to act on charge q. As charge q moves away from charge ...
9
votes
3answers
297 views

Should non-relativistic Navier Stokes Equations be modified so that they become pseudo-Lorentz invariant?

Choking mass flow seems to reflect the fact that fluid momentum density has a maximum value (in stationary conditions) equal to $\rho_* c_*$ where $\rho_*$ is the critical mass density and $c_*$ is ...
8
votes
1answer
182 views

How would General Relativity be different if we assumed Galilean instead of Lorentz transformations?

If we assume a universe where Galilean transformations are the correct transformations between inertial reference frames, would GR be any different ? Gravitational and inertial mass would still be ...
1
vote
1answer
69 views

The absoluteness of time intervals in Newtonian mechanics: how is this input used?

One of the assumptions of Newtonian mechanics is that "time is absolute". Absolute, as I understand, implies that it is the same for all observers. But it's not quite true because if Tom's watch is ...
0
votes
1answer
46 views

Relationship between the Galilei Group and the Phase Space

This question is kind of a follow up question to my last question on the need for canonical commutation relations and conjugate observables. A comment from Valter Moretti suggested that, given a ...
0
votes
1answer
90 views

Can we really not tell if we are moving?

It has been a while since I've thought about physics, however, I remember something about how if you are on a train with no windows that is going perfectly straight and is perfectly smooth, there is ...
2
votes
2answers
153 views

Galilean transformations of velocity

If I perform a Galilean boost $$x' = x - vt \\ t'=t$$ between two frames $S$ and $S'$, observers in each frame would disagree on the velocity of a particle because $$ \frac{dx'}{dt'} = \frac{dx}{dt} -...
0
votes
2answers
182 views

Understanding Galilean Structure

I’m a student with a pure math background starting to work through Arnold’s “Mathematical Methods...” and I’m struggling right of the bat with Section 1.2 on Galilean Structure. (pg 4 - 6) So we have ...
0
votes
2answers
84 views

Can we deduce the principle of relativity from some more basic principles?

I was reading "Relativity" by Albert Einstein. In chapter 5 page 14, it is written that If K is a Galilean co-ordinate system, then every other co-ordinate system K' is a Galileian one, when, in ...
1
vote
1answer
66 views

Question about Galilean time invariance

I've been reading Arnold's book on Classical Mechanics. I understand that most "classical" forces such as gravity, spring are supposed to be Galilean invariant. But what if I start a rocket, and ...
2
votes
1answer
70 views

Definition of Galilean structure in Arnold's book?

I am reading Arnold's Mathematical Methods of Classical Mechanics. He quickly introduces the notion of Galilean structure. The universe is defined as the affine space $A^4$ and time is defined as a ...
1
vote
2answers
321 views

About the Galilean non-invariance of the wave equation

So I have this long standing problem. I know that the wave equation (with or without source term) changes form when one makes a Galilean transformation of coordinates. My question is about the ...
2
votes
1answer
296 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 ...
2
votes
2answers
198 views

Are there Galilean scalars?

In special relativity there are scalar quantities which are invariant under any Lorentz transformation, called Lorentz scalars. For example, the magnitude of the four-velocity is a Lorentz scalar. If ...
1
vote
1answer
313 views

Is there an “invariant” quantity for the classical Lagrangian?

$$ L = \sum _ { i = 1 } ^ { N } \frac { 1 } { 2 } m _ { i } \left| \dot { \vec { x } _ { i } } \right| ^ { 2 } - \sum _ { i < j } V \left( \vec { x } _ { i } - \vec { x } _ { j } \right) $$ This ...
2
votes
4answers
560 views

Velocity of light in Galilean transformation

What is the velocity of light in Galilean transformation? Is it infinity?
1
vote
1answer
149 views

Kinetic energy when observer is moving and object is stationary [duplicate]

I know kinetic energy is due to motion of an object. But what if, I, the observer of an object is moving and that object appears to be moving for me, then which one has kinetic energy. is it me or ...
0
votes
1answer
160 views

Galilean Transformation

The transformation between inertial systems are given by affine transformations of $\mathbb{R}^{1+3}$. These are given by $t'=\lambda t+\vec{c}^\top \vec{x} +a$ and $\vec{x}'=\vec{v}t+M\vec{x}+\vec{b}$...
1
vote
1answer
155 views

Transformation of the operators $\mathbf\nabla$ and $\partial/\partial t$ under Galilean transformation

I'm want to know how are the transformations of the operators $\mathbf\nabla$ and $\partial/\partial and $\partial/\partial t$ when the transformation of the Galilean relativity is applied. This is ...
2
votes
1answer
187 views

Does $[P_j,B_k]=i(Mc^2)\delta_{jk}$ imply particle number conservation?

From reading Weinberg's Quantum Theory of Fields, Vol. 1, I learnt that for the Galilean group $[P_j,B_k]=i(Mc^2)\delta_{jk}$, and for the Poincare group $[P_j,B_k]=iH\delta_{jk}$ where $P_j$ and $B_k$...
15
votes
1answer
2k views

What does a Galilean transformation of Maxwell's equations look like?

In the 1860's Maxwell formulated what are now called Maxwell's equation, and he found that they lead to a remarkable conclusion: the existence of electromagnetic waves that propagate at a speed $c$, ...
18
votes
1answer
1k views

How do we know that the laws of physics are invariant in all inertial frames?

Einstein's Special Relativity theory is based on the assumption that the laws of physics are invariant in all inertial frames, and from there - according to Maxwell's equations - it derives that the ...
0
votes
0answers
29 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 ...
1
vote
1answer
131 views

How can I interpret or mathematically formalize Maxwellian, Leibnizian, and Machian space-times?

I've been reading the book, World Enough and Space-Time, and I came across a rough list of classical space-times with varying structural significance. Here is the same list, minus Machian Space-time,...
2
votes
2answers
194 views

Doppler Effect and Relativity

The equation for the Doppler effect is given by $$f_L = \frac{v+v_L}{v+v_S}f_S$$ where the velocities of both the source and the listener matter. My question is, how does this fit into Galilean ...
2
votes
2answers
295 views

Galilean Relativity and Electrodynamics

Consider the following: On the one hand, the principle of relativity, by Galileo, (totally applied to the Newtonian mechanics) says: There is no mechanical experiment that you could perform to ...