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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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 ...
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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 $c$, ...
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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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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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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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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:...
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Is it possible to stay up while riding a bike on a moving sidewalk without actually moving?
If I ride a bicycle on a moving sidewalk so that I am not in effect moving at all relative to the ground, will I fall over?
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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 ...
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Relativity without constancy of light speed
Using homogeneity of space, isotropy of space and the principle of relativity (without the constancy of light speed), one can derive:
$$x' = \frac{x-vt}{\sqrt{1+\kappa v^2}}$$
$$t' = \frac{t+\kappa vx}...
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How do we know that the laws of physics are invariant in all inertial frames?
Einstein's Special Relativity theory is based on the assumption that the laws of physics are invariant in all inertial frames, and from there - according to Maxwell's equations - it derives that the ...
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How is Newton's first law of motion different from Galileo's law of inertia? If the two are the same, then why is the first law named after Newton?
Galileo's law of inertia (at least what I've learned) is
"A body moving with constant velocity will continue to move in this path in the absence of external forces".
And Newton's first law ...
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How did Maxwell's theory of electrodynamics contradict the Galilean principle of relativity? (Pre-special relativity)
The Galilean principle of relativity:
The laws of classical mechanics apply in all inertial reference systems
OR
No experiment carried out in an inertial frame of reference can determine the ...
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Why are there only $1+3+3=7$ Additive Integrals of Motion?
1. I was reading Landau & Lifschitz's book on Mechanics, and came across this sentence on p.19:
"There are no other additive integrals of the motion. Thus every closed system has seven such ...
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How can Newton's idea of absolute space be reconciled with Galilean relativity?
I wasn't sure if this might be better suited to History of Science and Mathematics SE, but I suppose it is a bit more 'science-y' than historical.
Apparently Newton believed in absolute space and ...
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Why the Galileo transformation are written like this in Quantum Mechanics?
In Quantum Mechanics it is said that the Galileo transformation $$\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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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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Can one derive Galilean transformations from the harmonic oscillator equations of motion and the relativity principle?
I found myself puzzled with some very basic physical concepts and I hope to get enlightened with your help.
Initially my confusion arose in connection with Maxwell's equations and Lorentz ...
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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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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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Do Newton's laws of motion imply no physical difference between different inertial frames of reference?
I'm a mathematician learning physics from scratch, for my own curiosity and interest. Starting from the basics, I'm trying to get a deep grasp of Newton's laws of motion.
V.I. Arnold describes Galileo'...
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About an ambiguity that really prevents me from understanding the principle " the laws of physics are invariant in all inertial frames"
The principle is often stated as self explanatory ....
The sentence " the laws of physics are the same in all inertial frames" could mean 2 very different things ( at least from my point of view).
...
user229097
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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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Why is absolute time considered an axiom of Newtonian mechanics? What statements are based on this axiom?
I guess absolute time is associated to classical mechanics because people like Newton believed in that concept, but are there actually any statements whose derivation is based on this assumption?
I've ...
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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:
$$
\nabla \cdot {\bf B} = 0, \quad \nabla \times {\bf E} + \frac{1}...
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Can Schroedinger equation be derived from the unitary representation of Galilean group?
I have been trying to understand quantum mechanics as a unitary representation of spacetime symmetries.
My first question is: Can Schroedinger equation be derived from the unitary representation of ...
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Why does tossing a coin in a train and on a train differ?
Suppose that I am inside of a moving train. I have a coin in my hand and I am standing still. If I toss this coin straight up, it will fall back into my hand.
Now, suppose that I am on that moving ...
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Can Galilean transformation be derived from length invariance?
Given length invariance in Euclidean 3D space between two inertial frames:$$ds^2=ds'^2$$
Can Galilean transformation be derived like Lorentz transformation derived from space-time interval invariance?
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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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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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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 ...
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Should non-relativistic Navier Stokes Equations be modified so that they become pseudo-Lorentz invariant?
Choking mass flow seems to reflect the fact that fluid momentum density has a maximum value (in stationary conditions) equal to $\rho_* c_*$ where $\rho_*$ is the critical mass density and $c_*$ is ...
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How would General Relativity be different if we assumed Galilean instead of Lorentz transformations?
If we assume a universe where Galilean transformations are the correct transformations between inertial reference frames, would GR be any different ? Gravitational and inertial mass would still be ...
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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 ...
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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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Why isn't scaling space and time considered the 11th dimension of the Galilean group?
Galilean transformations are said to have 10 degrees of freedom. Four for translation in space and time, three for rotation, and three for direction of the uniform motion.
If I scale space axis by $\...
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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 ...
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Are there two different versions of non-relativistic quantum mechanics?
The first version is the usual one we're taught. But there's this other version too : A quantum non-relativistic field theory.
Take a non-relativistic classical field, like the non-relativistic limit ...
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Why are Maxwell's equations correct and not Newton's laws of motion?
In many books, while introducing Special relativity it is shown that Maxwell's equations are not consistent with Galilean transformations. So either Galilean transformations (and consequently Newton'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 transformation in non-relativistic quantum mechanics
I'm reading Weinberg's Lectures on Quantum Mechanics and in chapter 3 he discusses invariance under Galilean transformations in the general context of non-relativistic quantum mechanics. Being a ...
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What is the symmetry group of Mach's spacetime?
Newtonian spacetime can be modeled as a geometric object $M$ (affine space or manifold with connection with an absolute time function etc. etc.) that is symmetric under the action of the Galilean ...
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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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Galilean spacetime interval?
Does it make sense to refer to a single Galilean Invariant spacetime interval?
$$ds^2=dt^2+dr^2$$
Or is the proper approach to describe separate invariant interval for space (3D Euclidean distance) ...
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Energy levels of a translating quantum harmonic oscillator
It is well known that the energy levels
$$
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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Why absoluteness of time implies galilean transformations?
In Landau course, vol.1 Mechanics, one finds the statement:
...the absoluteness of time necessarily implies that the ordinary law of composition of velocities is applicable to all phenomena.
I ...
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Why are forces independent from the frame of reference?
The following question occurred to me while reading a proof of the following statement:
If K is an inertial frame of reference, then a K’ frame of reference,
which is moving with a constant ...
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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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Using the product rule to expand Newton's Second Law?
Newton's second law says that
$$F=\frac{\text{d}p}{\text{d}t},$$
where $F$ is the net force on a body. My question is, why can't the product rule be used to yield
$$F=v\frac{\text{d}m}{\text{d}t}+m\...
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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 ...
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What would Maxwell's equations look like in a universe which followed Galilean transformations?
I was wondering how the electromagnetic force would behave in a Gallilean transformation universe. Would the magnetic force be non-existent?
We know that Gallilean transformations are Lorentz ...
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