# Questions tagged [galilean-relativity]

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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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### 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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### 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, ...
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### Galilean relativity & the road to special relativity

Firstly, I just want to make sure that I've understood the notions of relative and absolute quantities correctly. Elementary analysis shows that position and velocity are relative quantities. Indeed, ...
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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 ...
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### Why did Feynman tell “we cannot locate earth's angular position, but we can tell that it is changing”?

I was reading "Symmetry in physics" by Feynman, where he wrote: If we perform sufficiently delicate experiments, we can tell that the earth is rotating, but not that it had rotated. In other words, ...
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### Does Doppler Effect violate Galilean relativity?

Apparent frequency when the source is moving away from the observer the relation between the frequencies is: $$f' = \frac{v}{v+ v_{s} } f$$ Apparent frequency when the observer is moving away from ...
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### Can someone explain intuitively how, for a Galilean universe, $A^4$ is equivalent to $\Bbb{R} \times \Bbb{R}^3$?

I am reading Arnold's book on classical mechanics. Obviously, everyone who's studied basic physics feels comfortable with $\Bbb{R} \times \Bbb{R}^3$. This is just a pair $(t,\mathbf{x})$. There are ...
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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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### Relationship bewtween the principle of Galilean Relativity and absolute time

The principle of Galilean Relativity is: The laws of Mechanics are invariant in every inertial frame of reference. I say "laws of Mechanics" specifically because I'm referring to the principle ...
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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 what the ...
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### How can a Physical law not be invariant?

In Relativity, both the old Galilean theory or Einstein's Special Relativity, one of the most important things is the discussion of whether or not physical laws are invariant. Einstein's theory then ...
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### Importance of the Galilean principle of relativity

The Galilean principle of relativity states that: The laws of mechanics are invariant in all inertial reference frames That means that if we have two inertial frames of reference $S$ and $S'$ then ...
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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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### 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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### 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 ...
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### Galilean group time interval

I have a question that arised by reading A Course in Modern Mathematical Physics by Peter Szekeres. He defines the galilean space $\mathbb{G}^{4}$ to be the space of events with a structure ...
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### In space I am moving wrt to what?

Let us suppose I am running on a street. When my eyes are open, I can see many things moving backward, and thus it gives me an idea that I am moving wrt those things. Not even this, even if I close my ...
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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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### Time inversion for Euler equation in fluid dynamics

Consider Euler equation for continuum body: $$\frac{\partial u^i}{\partial t}+\mathbf u\cdot \nabla u^i=- \frac{1}{\rho} \frac{\partial p}{\partial x^i}$$ where $\rho$ is the mass density, $p$ is ...
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### Generator of Velocity Transformations - Galilean Transformations

Under a Galilean transformation, the coordinates and momenta of any system transform as: $$t \rightarrow t',\\ \vec r\:' = \vec r + \vec vt,\\ \vec p\:' = \vec p + m\vec v$$ where $\vec v$ is ...