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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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 ...
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What is the inconsistency between Maxwell's electrodynamics and Newtonian mechanics?
As far as I understand, when a modification of a theory is made it is because some observation required this modifcation. Quantum Mechanics is a nice example of that: observations of microscopic ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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\...
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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 ...
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Deriving the Lagrangian for a free particle
I'm a newbie in physics. Sorry, if the following questions are dumb. I began reading "Mechanics" by Landau and Lifshitz recently and hit a few roadblocks right away.
Proving that a free ...
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Bernoilli effect on either side of a plate is not Gallilean invariant
Consider the airflow above and below a horizontal plate:
Particle density either side of the plate is the same. Ignoring thermal motion, the particles above the plate move with velocity $v$ and the ...
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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 ...
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$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 ...
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What is an inertial frame? [duplicate]
Throughout my life I've been told that an inertial frame is one that is not accelerating and I was satisfied with that. Well up to this day, until I asked: accelerating with respect to what ? Now this ...
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What determines which frames are inertial frames?
I understand that you can (in principle) measure whether "free particles" (no forces) experience accelerations in order to tell whether a frame is inertial. But fundamentally, what determines which ...
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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 ...
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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 ...
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Transformation law of momentum under Galilean transformation
I'm reading the article On the Galilean Covariance of Classical Mechanics (pdf link here), in which the authors want to establish the transformation rule for momentum, assuming only that $\vec{F}=d\...
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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 ...
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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 ...
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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$$
for a non-relativistic free point particle is ...
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Simple Galilean relativity implications
I’m not a physicist but I want to test my understanding of Galileo’s ship thought experiment.
Out space with some light, but no light sources nor features to give away the actual motion(s) there is an ...
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Transformation of force under different types Galilean transformations
Under simple boosts (one ref. frame $S'$ moving at a constant velocity $\mathbf{v}$ w.r.t. another frame $S$), why do we assume that the force vector doesn't change at all, i.e. $\mathbf{F}=\mathbf{F'}...
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Galilean invariance of the wave equation
Given the wave equation for a material wave:
$$\frac{\partial^2 \phi}{\partial x^2} = \frac{1}{c^2} \frac{\partial^2 \phi}{\partial t^2},$$
we can apply the Galilean transformation $x'=x-Vt$ and $t'= ...
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Could we deduce energy, momentum and angular momentum conservation laws from only Galilean relativity?
In Newtonian physics we could deduce conservation of energy, momentum and angular momentum from Newton's three laws.
But by Noether's theorem, conservation laws could be deduced from symmetries.
Could ...
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Aristotelian vs Galilean relativity in terms of bundles
In page-385 of Roger Penrose's Road to Reality, the following is written:
In our Aristotelian scheme, it is appropriate to think of spacetime as simply the product:
$$ \mathbb{A}= \mathbb{E}^1 \times ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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What are Galileons good for?
Lately I've seen many papers (for example "The galileon as a local modification of gravity"; 292 total hits on the arXiv) on types of field theories known as Galileons, and I'm wondering ...
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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 $r$ ...
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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 ...
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Kinetic energy in different reference frames
I've got a strange little paradox I thought of that I just can't figure out. Imagine that you are building a machine that lets a ball fall vertically from a height $h$, and converts the gravitational ...
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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 $c$ ...
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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 ...
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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 ...
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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 ...
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Velocity of light in Galilean transformation
What is the velocity of light in Galilean transformation? Is it infinity?
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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 ...
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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 ...
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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 ...
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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
$$
\hat{H}|\psi_n\rangle = E_n |\psi_n \...
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Generalizing the Galilean law of addition of velocities using the Lorentz transformation [closed]
I am reading about how to generalize the Galilean law of addition of velocities using the Lorentz transformation, but I am confused about one step.
Here, I have the following equations for Lorentz ...
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What is the exact meaning of Galileo's principle of relativity?
Galileo's principle of relativity states that the laws of mechanics are invariant in every inertial frame of reference.
This is well illustrated by Galileo’s ship. What is meant here by "laws of ...
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Equation of Motion Invariance in Galilean Mechanics
Consider a particle moving freely, where $\vec{r}(t)$ is the position of the particle. Suppose I move into a frame with
$$\vec{r}' =\vec{r} + \epsilon \vec{F}(\vec{r}, t)\tag{1},$$ where $\epsilon$ ...
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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 ...
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