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"So the idea, is that performing experiments himself, inside the train it is possible to detect the value of the acceleration?" You're spot on. Couldn't write it better myself. BTW in GR we have the same situation, as long as you qualify what you mean. All observers will agree on the reading on an accelerometer fixed in a certain frame, and on the readings ...

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Galilean relativity does not automatically hold in Newtonian mechanics. You are correct that Newton's first two laws appear at first sight to be invariant under galilean transformations, but a galilean transformation only transforms spatial coordinates,they don't actually tell you how forces transform. If your force laws just has forces that depend only on ...

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Unlike light, sound can only travel through a medium - in most situations, air. The velocities in your equations are relative to a fixed reference frame - that of the body of air in which the sound is travelling (which in a typical physics problem is the same as the ground's reference frame). So there really is a tangible difference between the case where ...

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The Galilean spacetime is indeed the affine space $\mathbb{A}^4$. Affine space can be considered as a 'space with no origin', which makes intuitively sense because why would some point (the origin) be special. For example a trivial Galilean space is $\mathbb{E}\times \mathbb{E}^3$ where $\mathbb{E}$ is Euclidean space. The $\mathbb{R}\times \mathbb{R}^3$ ...

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In short, usually I see people saying that Galilean Relativity is bound to one certain structure of spacetime where space is relative and time is absolute. What really is the relation between such structure and the principle stated? Another possibility is that the implication is the other way around: absolute time implies Galilean Relativity. But I also ...

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