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Questions tagged [galilean-relativity]

This tag is for questions related to the Newtonian Era idea that space and time are the same for everyone while speed adds up in the straightforward direction (if you are going 50 mph and throw something 20 mph it is going 70 mph) DO NOT use this tag for questions related solely to General Relativity.

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Galilean invariance of the wave equation

Given the wave equation for a material wave: $$\frac{\partial^2 \phi}{\partial x^2} = \frac{1}{c^2} \frac{\partial^2 \phi}{\partial t^2},$$ we can apply the Galilean transformation $x'=x-Vt$ and $t'= ...
Hubert van Luytelaar's user avatar
1 vote
1 answer
88 views

Could we deduce energy, momentum and angular momentum conservation laws from only Galilean relativity?

In Newtonian physics we could deduce conservation of energy, momentum and angular momentum from Newton's three laws. But by Noether's theorem, conservation laws could be deduced from symmetries. Could ...
moshtaba's user avatar
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-1 votes
1 answer
62 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 ...
poisson's user avatar
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-1 votes
1 answer
33 views

Invariance of Acceleration vs Invariance of Magnitude of Acceleration and help with proof

This question is a half-rant, half-question, as I am genuinely curious as to what the standard physics view is on this question. As someone who has studied math extensively (but not physics), please ...
atonaltensor's user avatar
-6 votes
1 answer
93 views

It seems as if Special Relativity breaks Galileo's principle of Relativity [closed]

simultaneity is redefined in special relativity because of the discovery that the speed of light is always constant. However, I think this violates Galileo's relativity, which states that you cannot ...
I am Einstein's user avatar
2 votes
3 answers
65 views

If an observer was trapped in a closed box with no way to interact with the external surroundings how will he know if he is moving or at rest [duplicate]

I am a high-school student. Recently we learned the concepts of relative motion and velocity. The idea that anything in motion can subsequently be at rest depending on the frame of reference ...
AMAL's user avatar
  • 21
2 votes
1 answer
140 views

Transformation of wavefunction

While learning QM, I was wondering how would the wavefunction of a particle, suppose charged particle, look for different observers moving with respect to each other. To begin with, let the electric ...
Users's user avatar
  • 426
3 votes
1 answer
85 views

The principle of relativity and why Inertial frames attribute the same velocity to one another

In introductory texts introducing relativity, it is always assumed that frames measure the same velocity for each other. For example if frame S' moves at velocity v with respect to respect, then S ...
Talha Ashraf's user avatar
6 votes
4 answers
124 views

How do we interpret measurements of Mercury's position?

When scientists measured the position of Mercury in the 18th century, they interpreted the results assuming a Euclidean background, because they did not know general relativity. So they measured $r$ ...
Giovanni's user avatar
0 votes
0 answers
43 views

Galilean transformation vs boost matrices

I'm confused about the difference between a Galilean transformation and boost with reference to their matrices. I was given four statements (listed below) but I'm not sure what I should be looking for ...
rose's user avatar
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2 votes
3 answers
127 views

Is a Lorentz transformation allowing an infinite value $c$ still a proper Lorentz transformation?

Is it correct to say that inertial systems are related by Lorentz transformations even if we do not know if the "invariant speed" is finite or infinite? To me, this is incorrect because $c$ ...
Real Pattern's user avatar
2 votes
1 answer
46 views

Are projective representiations of a Lie group a representation of the semi-direct product of the group with $U(1)$ if the norm is preserved?

Let's say we have a function $f(x_{\mu},t)$ that transforms under the action of an $N$-parameter group $G(a_{\nu})$. Then a projective representation of $G(a_\nu)$ in the $f(x_\mu,t)$ basis would ...
Ilya Iakoub's user avatar
4 votes
0 answers
68 views

Using Galilean covariance to find conditions on physical observables

Let's suppose that coordinates have to transform accoring to the Inhomogenous Galilean Group. Then $$ x' = x + a + v(t+b) $$ $$ t' = t + b $$ Let's use a funtion $\psi(x,t)$ of $x$ and $t$ as the ...
Ilya Iakoub's user avatar
3 votes
2 answers
169 views

Schutz description of Galilean invariance of interval

In B. Schutz's textbook "A First Course in General Relativity", there is a sentence on page 172 discussing Galilean relativity and how the distance between events is invariant in coordinate ...
nickodel's user avatar
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2 votes
5 answers
137 views

Violation of Newton's second law if the mass if changing?

I learned some thing called Galilean principle of relativity which says that two inertial frames are equivalent and the laws of physics are the same in both inertial frames. However here comes the ...
Bruce M's user avatar
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1 vote
0 answers
54 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 ...
qqq qqq's user avatar
  • 39
1 vote
0 answers
28 views

Generalizing the Galilean law of addition of velocities using the Lorentz transformation [closed]

I am reading about how to generalize the Galilean law of addition of velocities using the Lorentz transformation, but I am confused about one step. Here, I have the following equations for Lorentz ...
Gene's user avatar
  • 63
5 votes
3 answers
721 views

What is the exact meaning of Galileo's principle of relativity?

Galileo's principle of relativity states that the laws of mechanics are invariant in every inertial frame of reference. This is well illustrated by Galileo’s ship. What is meant here by "laws of ...
Phys23's user avatar
  • 61
6 votes
2 answers
261 views

Energy levels of a translating quantum harmonic oscillator

It is well known that the energy levels $$ E_n = \hbar \omega\left(n+\frac{1}{2}\right) $$ of the quantum harmonic oscillator verify the eigenvalue problem $$ \hat{H}|\psi_n\rangle = E_n |\psi_n \...
AndreaPaco's user avatar
  • 1,232
2 votes
0 answers
35 views

Is there a general methodology for causal nets of observables regardless of kinematics?

The typical definition of a causal net of observables in quantum theory is to consider, for the case of a (globally hyperbolic) spacetime $M$, the category of open sets $O(M)$ ordered by inclusion, in ...
Slereah's user avatar
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4 votes
4 answers
326 views

Equation of Motion Invariance in Galilean Mechanics

Consider a particle moving freely, where $\vec{r}(t)$ is the position of the particle. Suppose I move into a frame with $$\vec{r}' =\vec{r} + \epsilon \vec{F}(\vec{r}, t)\tag{1},$$ where $\epsilon$ ...
CosminA's user avatar
  • 283
0 votes
2 answers
71 views

Why is force independent of frame of reference (inertial)

This question has been bugging me for quite some time, I have seen some explanations which are mathematical and don't make sense to me, most of them talk about Galilean relativity, but I am looking ...
bobby76's user avatar
  • 45
-3 votes
2 answers
157 views

Is the principle of relativity correct? [closed]

Imagine two platforms side by side. The only difference is one of them is moving while the other is at rest. If a person wants to transition from the moving one to the stationary one he has to jump ...
Hazim Ahmed's user avatar
1 vote
5 answers
157 views

Why isn't the idea of an inertial frame relative? [closed]

I truly apologise if this has been asked to death somewhere, I imagine it has, but I'm yet to find an answer that completely satisfies me. In short, I don't see why our chosen inertial frames are &...
TheInquisitiveOne's user avatar
1 vote
1 answer
84 views

How Feynman proves momentum is conserved in this example?

Here is what Feynman says in section I.10-3: "Suppose we have two equal masses, one moving with velocity $v$ and the other standing still, and they collide and stick; what is going to happen? ...
Plague's user avatar
  • 121
1 vote
1 answer
674 views

Differential Equation that combines QM with Galilean relativity

In Galilean Relativity if there are two objects, the initial positions of the objects, their masses, and the forces acting on the objects is not enough to uniquely determine where the objects will be ...
Anders Gustafson's user avatar
4 votes
1 answer
145 views

Understand the definition of frame and inertial frame in Arnold's Galilean spacetime definition

In Arnold's Mathematical Methods of Classical Mechanics, we define the physical space time as a four dimensional affine space with associated Galilean structure. I understand this part. Now what I'm ...
Rui Liu's user avatar
  • 275
2 votes
1 answer
147 views

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\...
Silas's user avatar
  • 425
-2 votes
4 answers
206 views

Why is it "forbidden" to use EM waves as a way of detecting motion in two different inertial frames?

Constant motion can not be detected by neither particles (because of inertia) nor mechanical waves ( because they need a medium ). However when you consider light for example and assume it does not ...
michaeloppenheimer's user avatar
5 votes
1 answer
191 views

Relationship between symmetries and additive integrals of motion

I'm currently reading Landau and Lifshitz's Statistical Physics. In it, they attempt to justify that the density function only depends on the energy by arguing that the logarithm of this function is ...
Lourenco Entrudo's user avatar
1 vote
4 answers
220 views

Reference frame doubts about isotropy

Landau & Lifshitz on p.5 in their "Mechanics" book states the following: ...a frame of reference can always be chosen in which space is homogeneous and isotropic and time is homogeneous....
Giorgi Lagidze's user avatar
5 votes
2 answers
312 views

The limit of GR with infinite speed of light $c$

Just answer what you can. I don't mean the zero curvature flat space time version. I know that the Einstein Field equations use $c$ as a constant, but what would the universe be like if gravity was ...
Lina Jane's user avatar
1 vote
0 answers
103 views

Why does the ball in Galileo's double inclined plane experiment reach the same height?

Why does the ball in Galileo's double inclined plane experiment reach the same height? I know how to show it by energy conservation law but am unable to prove it by the equations of motion. Can anyone ...
Mathologist's user avatar
-1 votes
3 answers
104 views

Why doesn't Galilean relativity lead to a contradiction in SR?

Two identical spaceships commanded by Alice and Bob are at rest next to each other in outer space. The clocks of the spaceships are synchronised; and when they are close by Alice can see Bob's clock ...
John Nygate's user avatar
1 vote
1 answer
75 views

Principle of Relativity and the invariance of Newton's law in IRFs

Newton's law are form invariant under the coordinate substitutions: $$ \tilde{x^{i}}=x^{i}+a^{i} $$ This means that Newtons' equation of motion, $$ F^{i}=m \frac{d^{2} x^{i}}{d t^{2}} $$ (where $i=1,2,...
HRTninja's user avatar
1 vote
1 answer
41 views

Coordinate Transformation using a Matrix

Consider two inertial and resting frames $K$ and $G$. The only difference between the two frames is that the axes of $G$ has been rotated with $\theta$ with respect to $K$. $G$ is not constantly ...
gluon's user avatar
  • 193
1 vote
1 answer
87 views

Galilean relativity in terms of homogenity for car example

I have a question related to Landau & Lifshitz's book. In that, he says: If we were to choose an arbitrary frame of reference, space would be inhomogeneous and anisotropic. This means that, even ...
Giorgi's user avatar
  • 525
0 votes
0 answers
31 views

How can I solve this problem about energy conservation according to different frames of reference?

We have two frames of reference: the Earth (E) and a train (T) uniformely moving at velocity u relative to the Earth. We also have a particle that is initially stationary relative to the train, and is ...
Fede's user avatar
  • 435
0 votes
1 answer
59 views

Inertial coordinate systems being invariant under time translation in Newton's Principle of Detrimancy

I have the same question posted as Newton's equation under time translation except I am not seeking the physical justification of the first claim but rather the mathematical justification of the ...
Chordx's user avatar
  • 17
0 votes
0 answers
45 views

D Alembert Wave Equation is not Gallean Invariant but Why y=Asin(wt-kx) is Gallean Invariant? [duplicate]

I just watched this video from MIT 8.04 Quantum Physics I by Barton Zwiebach, explaining Galilean transformation of y=Asin(wt-kx). I have a confusion, are ordinary waves Galilean invariant or not? ...
Dibyajit Bhattacharyya's user avatar
0 votes
2 answers
294 views

Why are the transformations from the Galilean transformations affine?

In Arnold's Mathematical Methods of Classical Mechanics, he says on page 6 the following are Galilean transformations on the Galilean coordinate space $\mathbb{R} \times \mathbb{R}^3$ where $\mathbb{R}...
Chordx's user avatar
  • 17
6 votes
2 answers
431 views

Confusion regarding bundle structure of Galilean spacetime in Penrose's The Road to Reality

I am reading Roger Penrose's The Road to Reality. In section 17.3, I encounter the following passage. To give a context, Penrose was explaining that even though an Aristotelian spacetime can be ...
Faber Bosch's user avatar
0 votes
1 answer
51 views

Center of Mass and Systems of Particles in Galilean relativity

Consider a reference frame in which two particles move with constant velocities $\vec{v}_1 = v_1 \hat{i}$ and $\vec{v}_2 = -v_2 \hat{i}$. Their center of mass would be the vector $\vec{R} = \frac{(...
EM_1's user avatar
  • 860
0 votes
2 answers
190 views

What is metric (invariant) in Newton mechanics (equivalent to spacetime interval of Minkowski space)?

The answer might be obvious for those with much experience, but I could not get it via web search. https://en.wikipedia.org/wiki/Minkowski_space From the second postulate of special relativity, ...
Alex Martian's user avatar
0 votes
0 answers
27 views

Extending the Galilean transformation to the case of a possibly spacetime-dependent velocity field?

In all literature I have searched, the Galilean transform between two coordinates $(\overrightarrow{x},t)$ and $(\overrightarrow{x'},t')$ have been considered for a "constant velocity". That ...
Keith's user avatar
  • 1,669
1 vote
1 answer
85 views

Galilean Transformation of the EM fields

I was going through the proof that Maxwell's equations are not invariant under Galilean Transformations. If we consider two inertial frames (S and S' moving with velocity $\vec u$ with respect to the ...
JS30's user avatar
  • 129
0 votes
1 answer
105 views

Invariance of continuity equation for Galilei transformations

I want to prove that the continuity equation for fluids, $$\dfrac {\partial \rho}{\partial t} + \nabla \cdot (\rho \textbf{u}) = 0$$ is invariant by Galilei transformations. My attempt: Using index ...
RicardoMM's user avatar
  • 115
4 votes
2 answers
724 views

How can we talk about motion when space at different times can't be compared? (Explanation of Galilean Spacetime by Penrose)

In Galilean dynamics, we do not have just one Euclidean 3-space $E_3$, as an arena for the actions of the physical world evolving with time, we have a different $E_3$ for each moment in time, with no ...
Cathartic Encephalopathy's user avatar
0 votes
2 answers
76 views

In galilean relativity, is an observer assumed to be at rest only to simplify calculations, or is there a physical reason for this assumption?

I am a beginner in Physics and my teacher taught us "Relative Motion" yesterday. He said that the "Observer is assumed at rest." Is the observer assumed to be at rest only to ...
Anmol verma's user avatar
0 votes
1 answer
76 views

Velocity addition as a special case of change of reference frame

In this question, I want to restrict the discussion to classical mechanics as understood before 1900; that is, to exclude any discussion of relativity (however, if there is a neat generalization I ...
EE18's user avatar
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