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
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Invariance of the Schoedinger equation for the Galilean transformation [closed]
Show that the schroedinger e is covariant under the galilean transformation :
$\overrightarrow{r'}=\overrightarrow{r}-\overrightarrow{V}t$
iff the wave fucntion transforms like:
$$\psi^\prime=e^{\left(...
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Is there a Group that covers (classical) relative velocities?
I'm not very well versed in Abstract algebra and group theory, so this question might not make sense to begin with, but I got an idea when reading up on how to rigorously calculate relative velocities....
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Replacing $c$ With Infinity
I am confused about replacing $c$ (the speed of light) with $\infty$. I just do not understand how this recovers the non-relativistic physics, mainly, how would this be demonstrated in the Lorentz ...
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Galilean transformation of the wave equation, derivatives [closed]
So I'm trying to show that when the wave function
$ (-\frac{1}{c^2}\frac{d^2}{dt^2} + \frac{d^2}{dx^2})\phi(t,x) = 0 $
undergoes the Galilean transformation
$ t' = t $
$ x' = x-Vt $
the resulting ...
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How do Galilean transformations give the idea of vector velocity additions or subtractions?
I have been reading an article on Galilean transformation from Wikipedia
and encountered a sentence, quoted- 'In essence, the Galilean transformations embody the intuitive notion of addition and ...
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What is actually meant when it is said Scalar is invariant?
As far as i know a quantity is called invariant if it satisfies some specific transformations.
Now,Suppose a body is moving with velocity $\vec{v}$ as measured from the lab frame.Its non-relativistic ...
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Can’t we explain well the result of the Michelson–Morley experiment only with the Galilean transformation? [closed]
Can’t we explain well the result of the Michelson–Morley experiment only with the Galilean transformation?
In other words, is the speed of light invariant with respect to inertial frame of references ...
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How to properly use Galilean transformation in order to move between inertial frames?
I'm having trouble understanding how to use Galilean transform when moving between coordinates. e.g consider the following problem: a mass attached to a spring inside a moving cart - how can I ...
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Lagrangian invariance under Galilean transform and conservation law of linear momentum
I'm currently taking a course of analytical mechanics. We've learned about the invariance of the Lagrangian under change of coordinates, and showed that we get the same Lagrangian for free particle ...
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Maxwell and Newton [duplicate]
Has anyone tried to modify Maxwell's electromagnetic field theory so that it is invariant under the Galilean transformation?
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What does it mean that two frames are " in a state of constant, rectilinear motion with respect to one another"?
This expression ( applied to reference frames) " being in a state of constant, rectilinear motion with respect to one another "is frequently used as self explanatory . Though I might appear as stupid, ...
user229097
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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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How does one check whether an equation is Lorentz Invariant or Galilean Invariant?
As a physics student, I hear this term a lot that this equation is Lorentz Invariant or galilean Invariant e.g Dirac equation is Lorentz Invariant. Even in a non-linear pde class e.g the KdV equation ...
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Why is acceleration the same in both frames in a Galilean transformation?
I'm confused about this expression showing that the acceleration in a stationary frame is the same as that in a moving frame:
$$a'=\frac{d^2r'}{dt^2}=\frac{d^2}{dt^2}(r-Vt)=\frac{d^2r}{dt^2}+0=a$$
...
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Galilean relativity, flying along the equator: the same amount of fuel in both cases? [closed]
From the book of Jeffrey Bennett (What is relativity). Airplane flying from Nairobi to Quito at 1670 Km/h.The earth rotates in the opposite direction at the same speed.
Seen from the moon, the plane ...
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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 is Newtonian Mechanics contradictory to Special Relativity at a certain parameter? [duplicate]
How is Newtonian Mechanics contradictory to Special Relativity at a certain parameter and what conditions must be met for Newtonian Mechanics to be a suitable model for describing systems?
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Power in different reference frames
I would like to reopen the question asked in this post because I am not quite satisfied with the accepted answer.
Imagine observer A stationary (in world reference frame) and observer B moving with ...
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Do total derivatives have anything to do with central extensions?
I recently got interested in the Galilean group and its central extension and found a paper "Quantization on a Lie group: Higher-order Polarizations" by Aldaya, Guerrero and Marmo.
Before asking my ...
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Differences between the conformal group and the Schrödinger group?
Facts:
The Maxwell (free) equations (4d) are invariant under the 15 dimensional conformal group.
The free Schrödinger equation in 3d is invariant under the 15 dimensional group "called" Schrödinger ...
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Why must the logarithm of the distribution function depend only upon additive integrals of motion (Landau & Lifshitz)?
Denote by $\rho(p,q)$ (the $p$ and $q$ are being used as shorthand for several degrees of freedom), the phase space probability distribution function, (so $\rho\,\text{d}p\text{d}q$ is the probability ...
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time invariance for "Translations" versus "Galilean transformations"
Why would the time coordinate (t) be NOT invariant under translations, but invariant under Galilean transformations? I thought it should be invariant under both
Here is what I'm tying to understand:
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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 is force invariant under a Galilean transformation? [duplicate]
I've had a look around online, but I haven't been able to find something which answers this in a way I understand. Essentially, I'm trying to figure out why force is invariant under a Galilean ...
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Show the Galilean covariance of Schrödinger equation
I'm trying to show the Galilean covariance of the (time-dependent) Schrödinger equation by transforming as follows:
$$
\left\{\begin{eqnarray}\psi(\vec{r},t) &=& \psi(\vec{r}'-\vec{v}t,t),\\ \...
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Is Velocity Really a Vector?
In non-relativistic physics, physical quantities $Q$ are characterized by how they transform under a Galilean transformation $g \in \mathcal{G}$.
$$ Q \rightarrow Q' = D[g]Q$$
where $D[g]$ is the ...
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Is time an invariant of Galilean transformation?
Is time an invariant of Galilean transformation? By saying that I mean if there is a quantity analogous to spacetime interval in Lorentz transformation. What is the geometry of "Galilean spacetime"?
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Most general form of Lagrangian only with respect to Galilean invariance
Let us assume we are doing classical one point particle mechanics.
Assume that the least action principle holds. Also, assume that Lagrangian $L$ is a function only of coordinate $x$, its derivative $\...
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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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Inertial frame definition in Rindler Introduction to STR vs Landau' & Lifshitz Mechanics
Juxtaposing Rindler's Introduction to STR (page 7) vs Landau's Mechanics (page 5) inertial frame definition,I get that rindler assumes frame moving uniformly w.r.t inertial frame as an inertial frame ...
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Inertial frames as in Landau & Lifshhitz mechanics 1st chapter
If we see inertial frames from a basic point of view (precisely more basic axiom from which I can at least derive the law of free body as in landau mechanics first chapter) that inertial frames are ...
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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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Galilei group and Constrained QM
Let's assume spin-0 for simplicity.
So far as I understand the issue, the Galilei simmetries constraints the possible hamiltonians of a quantum systems so that the only possible interactions of a ...
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Reference request for Lie algebras
My future adviser just published a beautiful paper, https://arxiv.org/abs/1904.08304, and I am looking for some references/textbooks to look into the following concepts:
Lie algebra (central) ...
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Is Lorentz and Galilean invariance mutually exclusive?
I know that the classical mechanics stays valid under Galilean transformation. The same argument applies to relativistic equations and Lorentz transformation. My question is, can a set of equations ...
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In Einstein's 1905 paper on electrodynamics, what he meant by energy of electromotive force?
In his 1905 paper, Einstein says that when the magnet is in motion and conductor stationary, changing magnetic field in space develops electric field "of certain definite energy", and this starts ...
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Defining what it means for a reference frame to move with a velocity $\mathbf{u}$ with respect to another
In describing a Galilean transformation, for example, one might say that if a reference frame $S'$ is moving at a velocity $\mathbf{u}$ with respect to $S$, then an object traveling at a velocity $\...
user113773
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Galilei Invariance and Newton Third Law
Let's say we have a system of two point particles that can interact with each other by forces that are position and velocity dependent. The forces might or might not be derivable from a generalized ...
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The transformations of Lorentz as a general case of the transformations of Galileo
Starting from the transformations of Lorentz,
$$
\left\{\begin{aligned}
x&=\gamma (x'+\beta ct)\\
y&=y'\\
z&=z\\
ct&=\gamma (ct'+\beta x')\\
\end{aligned}\right.
\quad \tag{*}$$
I ...
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Galilean transformation and differentiation
Given $x=x’-vt$ and $t=t’$, why is $\frac{\partial t}{\partial x’}=0$ instead of $1/v$? $t$ seems to depend on $x’$ because if $t$ changes, $x’$ changes. Also, in this problem, $dx=dx’$ as well, but I ...
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Issue showing that the phase of a harmonic wave is invariant under a Galilean transform
The phase $Φ$ of wave is defined as $kx-wt$. It should be the case that all observers moving relative to each other in the non relativistic case will agree on this.
So given the transforms $x'=x-vt$ ...
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What was Newton's idea of absolute space and time?
When one says that Newton believed in the concept of "absolute space" and "absolute time" does it simply mean that the length interval between two points in space and time interval between two events ...
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Question on force invariance under the Galilean Transformations (GT)
By the Galilean transformations, one can easily derive that two different inertial observers 1,2 always measure the same forces. That is:
$$ \textbf{F}_1 \ \left(\textbf{r}_1, \dot{\textbf{r}}_1,t_1\...
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Newton's theory of gravity is covariant under Galilean transformations
We know from classical mechanics that the gravitational field equation for the scalar potential takes the form $$\nabla^2\phi=4\pi \rho,$$ where $\rho$ is mass density (which, can depend on time and ...
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How length is an invariant in Euclidean space?
The special theory of relativity shows that intervals are invariant under Lorentz transform in the Minkowski space -time.
But how can we prove (any postulates or theory) that the length is an ...
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Unlike rotation, why a $3\times 3$ translation matrix cannot be written in 3D? or can it be?
The effect of rotation in 3d on a vector, $\vec{r}=x\hat{x}=y\hat{y}+z\hat{z}$ is given in the form a matrix product:$$\vec{r}\to O\vec{r}$$ where $O$ is a $3\times3$ proper orthogonal matrix. Can we ...
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Lagrangian of free particle - classical case
I have a question, more related to a mathematical aspect of physics, which seems I am not understanding very well.
So, by applying Galilean transformation between two reference frames, which move at ...
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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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How does Kinetic Energy transform from one frame of reference to another?
Let's say I observe a charge q floating in the middle of space. I set up another charge Q a distance d away from charge q was causes a force F to act on charge q. As charge q moves away from charge ...
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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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