# Questions tagged [galilean-relativity]

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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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### Is relativity of simultaneity just a convention?

Lorentz transformations are well known to imply time dilation, length contraction, and relativity of simultaneity. This is prominently featured in any course on Special Relativity (SR), e.g. in ...
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### How do we mathematically know for sure that absolute time is abandoned in relativity?

It is an often mentioned assumption in physics that in going from classical to relativistic spacetime the main difference is that the absolute time postulate holding in the former is "relaxed" or ...
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### Shouldn't work be the same in all coordinates?

We know that the work done by a force $\mathbf{F}$, along a path $\mathbf{x}$, is given by: $$W = \mathbf{F}^T \cdot \mathbf{x}$$ However, suppose that i apply some change ...
222 views

### Does Galilean relativity constitute a dynamical symmetry or an isometry?

There are many papers which derive the form of the Lorentz transform from elementary symmetry principles (usually homogeneity of spacetime, isotropy of space, and the fact that boosts form a group), e....
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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 ...
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### Symmetry properties of time and space in non-inertial frames

Are symmetry properties of time and space true for non-inertial frames? If yes, how? If no, why not? Please, can you explain? We already know that an important feature of inertial frames is the ...
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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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### Silly question about Galilei Group

I have an silly doubt about Galilei Group. From Wikipedia: "The Galilean symmetries can be uniquely written as the composition of a rotation, a translation and a uniform motion of spacetime. Let x ...
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### Are vectors truly independent of coordinate systems?

I have been told to think of vectors as existing independent of a coordinate system. This means that the magnitude of a vector should be independent of any coordinate system we choose. Galilean ...
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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 does a Galilean transformation actually mean?

What does a Galilean transformation actually mean? I'm having trouble defining the equation for displacement shifts $x'=x-vt$. Does it mean that to any event $C$ the displacement in the primed ...
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### Constancy of the speed of light in the hypotenuse of the triangle in the Michelson and Morley experiment [closed]

In Michelson and Morley experiment, Michelson calculated that the total time traveled by light with respect to the stationary observer standing at ether field was $2L/c$. Here, Michelson followed ...
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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 ...