Questions tagged [galilean-relativity]
The galilean-relativity tag has no usage guidance.
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Galilean invariance of the potential [closed]
The first problem on my exercise sheet is about the galilean invariance and im stuck there. So the Problem is:
We consider a system of n particles, described by the following galilean invariant law ...
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What's wrong with this argument that time and length measurements change outside of special relativity? [closed]
Let us go back to the time of Galileo, let us forget about Einstein and the Michelson-Morley experiment: 1905 never happened.
Now, as the following thought experiment will highlight, I think it should ...
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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 ...
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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 ...
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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 ...
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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,...
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Coordinate Transformation using a Matrix
Consider two inertial and resting frames $K$ and $G$. The only difference between the two frames is that the axes of $G$ has been rotated with $\theta$ with respect to $K$. $G$ is not constantly ...
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Galilean relativity in terms of homogenity for car example
I have a question related to Landau & Lifshitz's book. In that, he says:
If we were to choose an arbitrary frame of reference, space would be
inhomogeneous and anisotropic. This means that, even ...
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How can I solve this problem about energy conservation according to different frames of reference?
We have two frames of reference: the Earth (E) and a train (T) uniformely moving at velocity u relative to the Earth.
We also have a particle that is initially stationary relative to the train, and is ...
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Inertial coordinate systems being invariant under time translation in Newton's Principle of Detrimancy
I have the same question posted as Newton's equation under time translation except I am not seeking the physical justification of the first claim but rather the mathematical justification of the ...
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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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Why are the transformations from the Galilean transformations affine?
In Arnold's Mathematical Methods of Classical Mechanics, he says on page 6 the following are Galilean transformations on the Galilean coordinate space $\mathbb{R} \times \mathbb{R}^3$ where $\mathbb{R}...
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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 ...
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Why do Galilean boosts change the Lagrangian whereas translations don’t? [duplicate]
In Landaus mechanics he claims the homogeneity of space/time allows us to drop the $q$/$t$ dependence of the lagrangian for free space. Even though I don’t see a way to “prove” this I guess we can ...
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Center of Mass and Systems of Particles in Galilean relativity
Consider a reference frame in which two particles move with constant velocities $\vec{v}_1 = v_1 \hat{i}$ and $\vec{v}_2 = -v_2 \hat{i}$. Their center of mass would be the vector $\vec{R} = \frac{(...
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Orbital motion described from an external frame of reference
I am working on proyect where I have to simulate a rocket mission to Mars, and I am having some trouble with it so I wanted to check if my math is ok.
The frame of reference I am using to describe the ...
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What is metric (invariant) in Newton mechanics (equivalent to spacetime interval of Minkowski space)?
The answer might be obvious for those with much experience, but I could not get it via web search.
https://en.wikipedia.org/wiki/Minkowski_space
From the second postulate of special relativity, ...
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Extending the Galilean transformation to the case of a possibly spacetime-dependent velocity field?
In all literature I have searched, the Galilean transform between two coordinates $(\overrightarrow{x},t)$ and $(\overrightarrow{x'},t')$ have been considered for a "constant velocity".
That ...
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Galilean Transformation of the EM fields
I was going through the proof that Maxwell's equations are not invariant under Galilean Transformations. If we consider two inertial frames (S and S' moving with velocity $\vec u$ with respect to the ...
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Invariance of continuity equation for Galilei transformations
I want to prove that the continuity equation for fluids, $$\dfrac {\partial \rho}{\partial t} + \nabla \cdot (\rho \textbf{u}) = 0$$ is invariant by Galilei transformations. My attempt:
Using index ...
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How can we talk about motion when space at different times can't be compared? (Explanation of Galilean Spacetime by Penrose)
In Galilean dynamics, we do not have just one Euclidean 3-space $E_3$, as an arena for the actions of the physical world evolving with time, we have a different $E_3$ for each moment in time, with no ...
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In galilean relativity, is an observer assumed to be at rest only to simplify calculations, or is there a physical reason for this assumption?
I am a beginner in Physics and my teacher taught us "Relative Motion" yesterday. He said that the "Observer is assumed at rest." Is the observer assumed to be at rest only to ...
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Velocity addition as a special case of change of reference frame
In this question, I want to restrict the discussion to classical mechanics as understood before 1900; that is, to exclude any discussion of relativity (however, if there is a neat generalization I ...
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What is the symmetry group of a particle interacting with external fields?
I am following along with Ballentine's (in his Quantum Mechanics: A Modern Development) construction/identification of symmetry generators as operators representing the standard observables (...
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"Deriving" Newton's laws of motion from symmetry assumptions
It is often discussed how certain symmetries and conservation laws can be derived from Newton's laws of motion. My question is: can we go the other way? Can Newton's laws of motion be derived only ...
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How to show the velocity of free motion is constant in Galileo's relativity principle?
Picture below is from Landau & Lifshitz's Mechanics. How to get the red line from green line?
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Forces that are invariant under Galilean spacetime rescaling $\mathbf x' = \lambda \mathbf x$, $t' = \lambda^2 t$
Consider a force of the form
$$
m \ddot{\mathbf x}(t) = -k\frac{\mathbf x(t) - \mathbf x_0}{|\mathbf x(t) - \mathbf x_0|^d}.
$$
For what values of $d$ is this force invariant under the Galilean ...
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Galilean covariance of the Schrödinger equation without choosing a representation
The most general form of Schrödinger equation is
$$i \hbar \frac{d}{d t}\Psi(t) = H\Psi(t) \tag 1,$$
where $\psi(t)$ is an element of a Hilbert space $\mathcal H$ (not necessarily $L^2$), and $H$ is a ...
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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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Is Newton's laws formulated using laboratory time?
The second Newton's law can be written as (in SI units)
$$
\frac{d}{dt}\vec p = \vec F.
$$
Newton was considered Galilean transformations and the existence of a "absolute" time. Now suppose ...
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Einsteinian principle of relativity in the limit of infinite propagation velocity
We can transform between inertial frames of reference using either the Lorentz transform in special relativity or the Galilean transform in the classical limit.
The Galilean transform gives: $$ x' = x ...
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Invariance over Galilean transformation [closed]
I want to prove that the Wave Equation is not invariant under Galilean Transformation. I'm having a little trouble with it but this is my attempt.
1. First of all, what does it mean by "not ...
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Is there any proof of Galilean Transformation?
Is there any proof of Galilean Transformation? Is it proved from experiment, theory or it simply is an axiom?
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Is clause "distance doesn't depend on frame of reference" an axiom in Newtonian Mechanics?
Consider 2 object is 1 and 2, at time t1: 1 has position is C and 2 has position is A.
In frame of reference 1 (1 is stand still), from time t1 to time t2, 2 moves from A to B
In frame of reference 2 ...
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Why not define tensors under Galilean or Poincare transformations?
I have seen vectors (and tensors, in general) defined under rotations,
$$V^i=R^i_{~j}V^j$$
and under Lorentz transformations,
$$V^{\prime\mu}=\Lambda^\mu_{~~\nu}V^\nu$$
where $R,\Lambda$ are the ...
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Compatibility of the existence of ether and Galilean relativity [closed]
Why does the idea of ether contradict Galilean relativity? Consider for example what Coiller wrote in his book, A Most Incomprehensible Thing - Notes Towards a Very Gentle Introduction to the ...
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Galilean invariance of Burgers Equation [closed]
I think the following statement is true: if $u$ solves the burgers equation (ie $u$ solves $$\frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} = 0$$ then so does $$u^c = u(x-ct,t)+c.$$ I'...
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Invariance of potential implies conservation of momentum
I'm a mathematician and I don't know how to read this notation used in classical mechanics to show the that net resulting force $F$ vanishes
Where $V(x_1,\ldots,x_n)$ denotes the potential dependent ...
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Isn't a rotation just a sum of many translations?
If the world is (really or hypothetically) made of elementary, point-particles, then it's there such a thing as rotation?
Point particles by definition can't rotate around themselves. The only ...
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Deriving transformation property of $\vec{E}$ and $\vec{B}$ under Galilean transformation
How can we determine the transformation property of the electric and magnetic field, $\vec{E}$ and $\vec{B}$, under Galilean transformation (without) using (the $v/c\to 0$ limit of) the Lorentz ...
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Is there a name for linear/homogeneous Galilean transformations?
In Special relativity, the transition charts are Poincaré transformations and linear/homogeneous Poincaré transformations are called Lorentz transformations. (I distinguish between affine ...
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Reference request - book on Euclidean space and rigid body kinematics
Ideally, I'd like a comprehensive book that encompasses both subjects: it builds the notion of "space" as related to our physical world (no relativity, though) from the ground up, giving it ...
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Inonu-Wigner contraction in Weinberg Volume I
In volume I of Weinberg quantum theory of fields, on page 61, Weinberg derived the commutation relations of the generators $H,P_i, J_i,K_i$ of the Poincare algebra, then he tried to take the ...
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Galilei transformation of mass flux
Is it possible to perform a Galilei transformation of a flux without additional information?
Say we consider a flux $q = \rho v$ that can be written as the product of density $\rho$ and a velocity ...
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Implications of Galilei-Invariance on a time-independent potential
I'm trying to compute a result shown in my classical mechanics lecture on my own. Namely, consider that a system composed of $n$ particles follows a law of force
$m_k\ddot{\vec{x_k}} = \vec{F_k}(\vec{...
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Galilean Symmetry of Newtonian Mechanics
So for the equations of motion to be symmetric about a transformation from $(t,x)$ to $(\tau, y)$, the following must be true (for Newtonian mechanics):
$$m \frac{d^2 x}{dt^2} = f \left( x, \frac{dx}{...
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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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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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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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How do we justify that potential energy in a spring is Galilean invariant (to the extent that Newtonian mechanics holds)?
A spring can store elastic potential energy by elastically deforming and moving its atoms out of their minima potentials. The atoms themselves can be modeled as balls connected by Hooke-like springs ...
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