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.
83 questions
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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 ...
Joss L
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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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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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4
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Galilean covariance of the Schrodinger equation
Is the Schrodinger equation covariant under Galilean transformations?
I am only asking this question so that I can write an answer myself with the content found here:
http://en.wikipedia.org/wiki/User:...
- 3,802
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answer
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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 ...
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Galilean spacetime interval?
Does it make sense to refer to a single Galilean Invariant spacetime interval?
$$ds^2=dt^2+dr^2$$
Or is the proper approach to describe separate invariant interval for space (3D Euclidean distance) ...
- 75
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Why the Galileo transformation are written like this in Quantum Mechanics?
In Quantum Mechanics it is said that the Galileo transformation $$\hat{\mathbf{r}}\mapsto \hat{\mathbf{r}}-\mathbf{v}t\quad \text{and}\quad \hat{\mathbf{p}}\mapsto \hat{\mathbf{p}}-m\mathbf{v}\tag{1}...
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Why Galilean spacetime is not $\mathbb{E}^4$?
In Newtonian mechanics the physical spacetime is a Galilean spacetime with an affine surjection $\pi : \mathbb{A}^4\to \mathbb{E}^1$ from affine space $\mathbb{A}^4$ to Euclidean space $\mathbb{E}^1$. ...
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How can the Gallilean transformations form a group?
In class my professor said the Galilean transformations form a group of order 10.
$$
x'=x-vt\\
y'=y\\
z'=z\\
t'=t\\
$$
But how do these form a group? I don't see 10 things to interpret as elements. I ...
- 241
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Do Galilean (Euclidean) space transformations implies that time is absolute?
I recently read a paper where it says "if space is universally Euclidean, then time is universal" and I don't understand some key points about the implication.
To put in context, the author ...
- 625
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Isn't D'Alembert's wave equation enough to see that Galilean transformations are wrong?
The D'Alembert equation for mechanical waves was written in 1750:
$$\frac{\partial^2u}{\partial x^2}=\dfrac{1}{v^2}\dfrac{\partial^2u}{\partial t^2}$$
(in 1D, $v$ being the propagation speed of the ...
- 650
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2
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Confusion regarding bundle structure of Galilean spacetime in Penrose's The Road to Reality
I am reading Roger Penrose's The Road to Reality. In section 17.3, I encounter the following passage. To give a context, Penrose was explaining that even though an Aristotelian spacetime can be ...
- 702
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Derive the Lagrangian that yields the free Schrödinger's equation from Galileian Invariance
The Lagrangian Density $$L(\Psi, \Psi^*)=i \hbar \dot{\Psi} \Psi^* + \frac{\hbar^2}{2m} \Psi \Delta \Psi^*$$ will yield the schroedinger equations for $\Psi$ and $\Psi^*$. Can we derive this ...
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How can I interpret or mathematically formalize Maxwellian, Leibnizian, and Machian space-times?
I've been reading the book, World Enough and Space-Time, and I came across a rough list of classical space-times with varying structural significance.
Here is the same list, minus Machian Space-time,...
41
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1
answer
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What does a Galilean transformation of Maxwell's equations look like?
In the 1860's Maxwell formulated what are now called Maxwell's equation, and he found that they lead to a remarkable conclusion: the existence of electromagnetic waves that propagate at a speed $c$, ...
- 2,989
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Why are there only $1+3+3=7$ Additive Integrals of Motion?
1. I was reading Landau & Lifschitz's book on Mechanics, and came across this sentence on p.19:
"There are no other additive integrals of the motion. Thus every closed system has seven such ...
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6
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How did Maxwell's theory of electrodynamics contradict the Galilean principle of relativity? (Pre-special relativity)
The Galilean principle of relativity:
The laws of classical mechanics apply in all inertial reference systems
OR
No experiment carried out in an inertial frame of reference can determine the ...
- 1,039
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2
answers
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Galilean invariance of a subset of Maxwell equations
I read in Feynman's proof of Maxwell equations the statement that the subset of Maxwell equations comming from the Bianchi identity:
$$
\nabla \cdot {\bf B} = 0, \quad \nabla \times {\bf E} + \frac{1}...
- 1,017
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6
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Is kinetic energy relative or absolute? [duplicate]
I only can think of kinetic energy as absolute. I know velocity is relative but I can't see kinetic energy as being relative because that would violate energy conservation. For example, if in some ...
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Special Relativity, 2nd Postulate -- Why? [duplicate]
As a lowly physics undergrad who has been chewing on this 2nd postulate of special relativity for a year or more, I simply can't wrap my head around reasons why it is true or how Einstein might have ...
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Inertial Frames of Reference - Inertial vs. Accelerated Frames
According to Robert Resnick's book "Introduction to Special Relativity", a line states the following as the definition of an inertial frame of reference: "We define an inertial system as a frame of ...
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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 ...
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Representation of the Galileo Group and Central Charges
I've arrived at this question because I've been reading Weinberg's Quantum Theory of Fields Volume I, and I'm in the second chapter about relativistic quantum mechanics. Weinberg discusses the ...
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2
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Casimir Invariants of the Galilean group
I had studied a couple of things about Galilean and Poincare group. But in the Galilean group, there is not enough clarity on how to calculate generators for boosts ($B_i$), which if I do it seems I ...
- 3,134
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3
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Galilean Relativity is already included in Newton's Laws?
Usually I see an inertial reference frame being defined as a reference frame in which Newton's first and second laws holds. That means that if a particle is at rest, it stays at rest unless some ...
- 37.4k
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1
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Can Newtonian gravity be quantized?
Today, nobody knows how GR is truly supposed to be married with QFT. As a result, the standard model as it is typically presented does not include gravity. Could it be modified to include Newtonian ...
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How could any frame of reference be inertial?
The image below shows that a bystander watching the merry-go-round is in an inertial frame of reference. However, to nitpick, wouldn't the observer still be accelerating because it's on Earth?
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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 ...
- 8,040
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Inonu-Wigner Group Contraction
I am trying to understand how one obtains the Galilean algebra from the Poincare algebra, specifically through the method of central extension. I'm doing this by imposing that the generators of the ...
- 1,062
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2
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Is this the reason why acceleration is said absolute?
I've seem sometimes people saying that although uniform motion on a straight line cannot be detected and hence it is not absolute, acceleration is indeed absolute in Classical Mechanics (I don't know ...
- 37.4k
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7
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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 ...
- 37.4k
4
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Additive constants of motion
I've read in a book, that in general case energy $E$, momentum $\textbf{p}$ and angular momentum $\textbf{M}$ of a closed system are the only additive constants of motion, that is, if I have $N$ ...
- 1,642
3
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3
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Doppler shift and Galilean relativity
Doppler shift has different forms if the observer or the source are in motion. I consider Doppler shift in the case of sound.
I tried to find an answer on the non symmetry of Doppler effect, ...
- 2,637
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A question concerning the Galilean invariance of Newton's laws
When proving the Galilean invariance of Newton's laws is it tacitly assumed that all equations are covariant, i.e. that they are form invariant?
For example, it is fairly trivial to show that the ...
- 3,267
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3
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535
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Velocity and kinetic energy, violating galilean relativity
I have a toy car and a battery. The barrery has a screen that shows how much energy it has left. Since kinetic energy is proportional to velocity squared, I need 1J of energy to go from 0m/s=>1m/s, ...
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1
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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 ...
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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? ...
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What is the connection between mechanics and electrodynamics that makes it necessary for both of these to obey the same principle of relativity?
Mechanics obeyed Newtonian relativity (faithful to Galilean transformations) before Einstein.
Einstein formulated Special relativity (faithful to Lorentz transformations), and Maxwell's equations ...
- 1,039
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How can Newton's idea of absolute space be reconciled with Galilean relativity?
I wasn't sure if this might be better suited to History of Science and Mathematics SE, but I suppose it is a bit more 'science-y' than historical.
Apparently Newton believed in absolute space and ...
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Is acceleration absolute and if so, how can we measure it?
A person standing on a uniformly moving car can never know (without looking outside, or at the speedometer) whether the car is at rest or in motion at a uniform nonzero velocity w.r.t earth. However, ...
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Can Schroedinger equation be derived from the unitary representation of Galilean group?
I have been trying to understand quantum mechanics as a unitary representation of spacetime symmetries.
My first question is: Can Schroedinger equation be derived from the unitary representation of ...
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Every Galilean transformation can be written as the composition of rotation, translation, and uniform motion
Having heard many good things about Arnold's Mathematical Methods of Classical Mechanics, I picked it up and started going through it. While I think I understand all of the definitions he makes, the ...
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What is the difference between a translation and a Galilean transformation?
What is the difference between a translation and a Galilean transformation?
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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
7
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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
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What is the Galilean transformation of the EM field?
Consider a reference frame $S$ and which we observe some electric field $\mathbf{E}$ and magnetic field $\mathbf{B}$.
Let $S'$ be a reference frame moving at a constant velocity $\mathbf{u}$ with ...
- 4,666
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Why is the phase of a matter wave not Galilean invariant? And what does this say about the Schrödinger equation? [duplicate]
Matter waves are not Galilean Invariant
Consider a non-relativistic freely-propagating matter wave in an inertial frame $\Sigma'$ moving along the $x'$-direction with kinetic energy $E'=1/2m_0v'^2$, ...
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Most fundamental reason for Newtonian KE loss being invariant in inelastic collisions
This answer to a question about why Newtonian kinetic energy is quadratic in velocity shows that if an inelastic collision's KE loss is invariant under Newtonian boosts it has to quadruple when ...
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Does force definition depend on frame of reference?
Let’s assume we have 2 different observers. Observer 1 sits in space and observer 2 sits in a space lab which is in a free fall state toward the Earth. We further assume that observer 2 in the space ...
- 163
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Maxwell equations invariant under Lorentz transformation but not Galilean transformations
Why Maxwell equations are not invariant under Galilean transformations, but invariant under Lorentz transformations? What is the deep physical meaning behind it?
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