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.
403 questions
1
vote
0
answers
37
views
Resources to understand problems posed to Newtonian mechanics by Maxwell equations [closed]
Einstein undertook writing his paper on special relativity in response to the CRISIS that emerged in physics when trying to do mechanics for fast-moving bodies in the light (pun intended) of Maxwell's ...
8
votes
1
answer
119
views
Analogue of Coleman-Mandula theorem for non-relativistic quantum field theory?
For relativistic quantum field theories, the Coleman-Mandula theorem places very strong restrictions on the possible symmetry groups $G$ of the aforementioned quantum field theory, forcing it to be a ...
- 1,857
3
votes
0
answers
32
views
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
1
vote
1
answer
108
views
A problem with unique decomposition of Galilean transformation
It is very well known that any Galilean transformation on $\mathbb{R}^3\times\mathbb{R}$ can be uniquely written as composition of a maps of the following type:
Uniform motion: $(x,t)\to(x+tv,t)\quad ...
- 63
0
votes
0
answers
33
views
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
0
answers
88
views
The Low Velocity Limit of the Electric and Magnetic Field Transformations
From the covariant formulation of electromagnetism we know that the fields transform as:
$$\vec{E}'=\gamma \vec{E}-\frac{(\gamma-1)}{u^2}(\vec{u}\cdot \vec{E})\vec{u}+\frac{\gamma}{c}[\vec{u}\times\...
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
vote
1
answer
47
views
Throwing a clock out of a white hole
If we look at a clock falling into a black hole (Schwarzschild metric), we will see its time slowing down further and further as it approaches the event horizon.
What would we see by looking, from far ...
- 1,231
0
votes
2
answers
105
views
$E=mc^2$ derivation using waves other than light
Can $E=mc^2$ be derived using waves other than light?
Einstein's derivation of his famous equation $E=mc^2$ relies on light waves (or photons). He considered a scenario with a light-emitting material ...
- 2,984
1
vote
3
answers
217
views
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
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
vote
2
answers
87
views
Wave hits beach-example: Does sweeping crest constitute a Frame of Reference?
A long wave rolls in at 1 m/s and hits an almost parallel beach.
It's 900k km long, and hits the beach at .1 micro degrees.
Basic math tells us the crest of the wave rides down the beach at a speed of ...
- 290
0
votes
1
answer
115
views
Analogy between Galilean relativity and thermal physics?
So I was thinking about an analogy, that could potentially be used for an explanation or at least to take a different perspective on thermodynamics as it is. But I don't want to abuse the analogy, so ...
- 2,987
0
votes
1
answer
61
views
Simple Galilean relativity implications
I’m not a physicist but I want to test my understanding of Galileo’s ship thought experiment.
Out space with some light, but no light sources nor features to give away the actual motion(s) there is an ...
- 600
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
vote
1
answer
90
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 ...
- 1,419
-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
votes
1
answer
50
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 ...
-6
votes
1
answer
118
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 ...
2
votes
3
answers
75
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 ...
- 21
2
votes
1
answer
168
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 ...
- 457
3
votes
1
answer
89
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 ...
- 35
6
votes
4
answers
132
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$ ...
- 61
0
votes
0
answers
46
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 ...
- 1
1
vote
3
answers
151
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$ ...
- 61
2
votes
1
answer
57
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 ...
- 372
4
votes
0
answers
77
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 $$
Let's use a funtion $\psi(x,t)$ of $x$ and $t$ as the ...
- 372
3
votes
2
answers
177
views
Schutz description of Galilean invariance of interval
In B. Schutz's textbook "A First Course in General Relativity", there is a sentence on page 172 discussing Galilean relativity and how the distance between events is invariant in coordinate ...
- 147
2
votes
5
answers
195
views
Violation of Newton's second law if the mass if changing?
I learned some thing called Galilean principle of relativity which says that two inertial frames are equivalent and the laws of physics are the same in both inertial frames.
However here comes the ...
- 421
1
vote
0
answers
58
views
Independence of Lagrange function from time and position
In Landau & Lifshitz "Mechanics", it is said that from the time/space homogeneity Lagrange function is independent from time/position. I always thought that homogeneity means that motion ...
- 39
1
vote
0
answers
29
views
Generalizing the Galilean law of addition of velocities using the Lorentz transformation [closed]
I am reading about how to generalize the Galilean law of addition of velocities using the Lorentz transformation, but I am confused about one step.
Here, I have the following equations for Lorentz ...
- 63
5
votes
3
answers
857
views
What is the exact meaning of Galileo's principle of relativity?
Galileo's principle of relativity states that the laws of mechanics are invariant in every inertial frame of reference.
This is well illustrated by Galileo’s ship. What is meant here by "laws of ...
- 61
7
votes
2
answers
344
views
Energy levels of a translating quantum harmonic oscillator
It is well known that the energy levels
$$
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 \...
- 1,252
2
votes
0
answers
41
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 ...
- 16.7k
4
votes
4
answers
356
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 $\epsilon$ ...
- 283
0
votes
2
answers
78
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 ...
- 45
-3
votes
2
answers
163
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 ...
- 31
3
votes
5
answers
181
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 &...
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
vote
1
answer
125
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? ...
- 121
1
vote
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
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 ...
- 275
2
votes
1
answer
247
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\...
- 405
-2
votes
4
answers
277
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 ...
5
votes
1
answer
203
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 ...
- 1,000
1
vote
4
answers
233
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....
6
votes
2
answers
361
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 ...
- 370
1
vote
0
answers
137
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 ...
- 91
-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
77
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,...
- 11