All Questions
Tagged with galilean-relativity inertial-frames
184 questions
3
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Galilean boost operator for quantum multi-particle system
If I have a two particle system with with a potential of form $V(x_1,x_2)$, is it possible to apply the galilean boost operator to only a single coordinate? Essentially, is it possible to move only a ...
- 331
0
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0
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33
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Galilean boost and translation in field theory
I am reading some literature which is considering translations and boosts in field theory. The reference is Construction of Lagrangians continuum theories, Markus Scholle, 2004, The Royal Society. I ...
0
votes
3
answers
94
views
Is the surface of Earth a global inertial frame?
I understand that a reference frame attached to an observer standing on the surface of non-rotating Earth is not a locally inertial frame but I wonder it can taken as a globally inertial frame because ...
- 711
1
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3
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217
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Is the definition of inertial reference frame circular?
In elementary physics classes, inertial reference frames are defined as a coordinate system which is in constant rectilinear motion (or at least that is how it was defined by my professor). How then ...
- 29
2
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1
answer
159
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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
5
votes
3
answers
679
views
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'= ...
-1
votes
1
answer
50
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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 ...
2
votes
3
answers
75
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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 ...
- 21
2
votes
1
answer
168
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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 ...
- 457
3
votes
1
answer
89
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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 ...
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1
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3
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151
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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 $c$ ...
- 61
3
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2
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177
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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 ...
- 147
2
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5
answers
195
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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 ...
- 421
1
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0
answers
29
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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 ...
- 63
5
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3
answers
857
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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 ...
- 61
7
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2
answers
344
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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
$$
\hat{H}|\psi_n\rangle = E_n |\psi_n \...
- 1,252
4
votes
4
answers
356
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Equation of Motion Invariance in Galilean Mechanics
Consider a particle moving freely, where $\vec{r}(t)$ is the position of the particle. Suppose I move into a frame with
$$\vec{r}' =\vec{r} + \epsilon \vec{F}(\vec{r}, t)\tag{1},$$ where $\epsilon$ ...
- 283
0
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2
answers
78
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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 ...
- 45
-3
votes
2
answers
163
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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 ...
- 31
3
votes
5
answers
181
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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 &...
2
votes
0
answers
135
views
Principle of relativity and Galileo's group
A doubt has arisen for me about the principle of relativity, and being such a fundamental subject I think it only fair to try and clarify it. The following line of reasoning was presented to me in a ...
- 1,723
1
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1
answer
683
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 ...
- 2,021
4
votes
1
answer
182
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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 ...
- 275
2
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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
1
vote
4
answers
233
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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....
-1
votes
3
answers
107
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 ...
- 99
1
vote
1
answer
42
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 ...
- 193
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vote
1
answer
93
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 ...
- 535
1
vote
1
answer
83
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 ...
- 27
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2
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353
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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}...
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2
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536
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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 ...
- 702
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2
answers
216
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, ...
- 151
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0
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27
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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 ...
- 1,708
1
vote
1
answer
124
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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 ...
- 129
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1
answer
127
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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 ...
- 115
4
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2
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727
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 ...
- 8,040
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2
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79
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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 ...
0
votes
1
answer
86
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 ...
- 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
1
vote
1
answer
205
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Forces that are invariant under Galilean spacetime rescaling $\mathbf x' = \lambda \mathbf x$, $t' = \lambda^2 t$
Consider a force of the form
$$
m \ddot{\mathbf x}(t) = -k\frac{\mathbf x(t) - \mathbf x_0}{|\mathbf x(t) - \mathbf x_0|^d}.
$$
For what values of $d$ is this force invariant under the Galilean ...
- 553
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4
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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
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1
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61
views
Is Newton's laws formulated using laboratory time?
The second Newton's law can be written as (in SI units)
$$
\frac{d}{dt}\vec p = \vec F.
$$
Newton was considered Galilean transformations and the existence of a "absolute" time. Now suppose ...
0
votes
3
answers
80
views
Einsteinian principle of relativity in the limit of infinite propagation velocity
We can transform between inertial frames of reference using either the Lorentz transform in special relativity or the Galilean transform in the classical limit.
The Galilean transform gives: $$ x' = x ...
- 916
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2
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298
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Is there any proof of Galilean Transformation?
Is there any proof of Galilean Transformation? Is it proved from experiment, theory or it simply is an axiom?
- 315
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1
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189
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Why not define tensors under Galilean or Poincare transformations?
I have seen vectors (and tensors, in general) defined under rotations,
$$V^i=R^i_{~j}V^j$$
and under Lorentz transformations,
$$V^{\prime\mu}=\Lambda^\mu_{~~\nu}V^\nu$$
where $R,\Lambda$ are the ...
- 12.3k
1
vote
0
answers
90
views
Galilean invariance of Burgers Equation [closed]
I think the following statement is true: if $u$ solves the burgers equation (ie $u$ solves $$\frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} = 0$$ then so does $$u^c = u(x-ct,t)+c.$$ I'...
- 123
1
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3
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523
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Deriving transformation property of $\vec{E}$ and $\vec{B}$ under Galilean transformation
How can we determine the transformation property of the electric and magnetic field, $\vec{E}$ and $\vec{B}$, under Galilean transformation (without) using (the $v/c\to 0$ limit of) the Lorentz ...
- 12.3k
1
vote
1
answer
65
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Is there a name for linear/homogeneous Galilean transformations?
In Special relativity, the transition charts are Poincaré transformations and linear/homogeneous Poincaré transformations are called Lorentz transformations. (I distinguish between affine ...
- 1,911
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votes
1
answer
52
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Galilei transformation of mass flux
Is it possible to perform a Galilei transformation of a flux without additional information?
Say we consider a flux $q = \rho v$ that can be written as the product of density $\rho$ and a velocity ...
- 3,265
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1
answer
272
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Galilean Symmetry of Newtonian Mechanics
So for the equations of motion to be symmetric about a transformation from $(t,x)$ to $(\tau, y)$, the following must be true (for Newtonian mechanics):
$$m \frac{d^2 x}{dt^2} = f \left( x, \frac{dx}{...
- 21