# Questions tagged [coordinate-systems]

A set of numbers used to quantify location in space.

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8answers
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### Interval preserving transformations are linear in special relativity

In almost all proofs I've seen of the Lorentz transformations one starts on the assumption that the required transformations are linear. I'm wondering if there is a way to prove the linearity: Prove ...
8answers
9k views

### How can time dilation be symmetric?

Suppose we have two twins travelling away from each other, each twin moving at some speed $v$: Twin $A$ observes twin $B$’s time to be dilated so his clock runs faster than twin $B$’s clock. But twin ...
1answer
1k views

### Which transformations are canonical?

Which transformations are canonical? Why do canonical transformations preserve the measure of integration in phase space?
2answers
278 views

### How do frames of reference work in general relativity, and are they described by coordinate systems?

In both Newtonian gravity and special relativity, every frame of reference can be described by a coordinate system covering all of time and space. How does this work in general relativity? When an ...
5answers
10k views

### Conformal transformation/ Weyl scaling are they two different things? Confused!

I see that the weyl transformation is $g_{ab} \to \Omega(x)g_{ab}$ under which Ricci scalar is not invariant. I am a bit puzzled when conformal transformation is defined as those coordinate ...
6answers
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### Minkowski Metric Signature

When I learned about the Minkowski Space and it's coordinates, it was explained such that the metric turns out to be $$ds^{2} = -(c^{2}dx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2}$$ ...
3answers
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3answers
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### What is the physical meaning of the Eddington-Finkelstein coordinates?

What is the physical meaning of the Eddington-Finkelstein coordinates? I want to see a some physical process (experimental) that could explain the many transformations of coordinates into this ...
2answers
210 views

2answers
688 views

### Kerr Metric in Orthogonal form

I've seen the Kerr metric usually presented in the Boyer-Lindquist coordinates where there is a cross term in the $d\phi$ and $dt$ term. I've done a good bit of searching and cannot find any ...
1answer
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1answer
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### For an infinitesimal transformation in phase space, what functions are allowed for this to be a canonical transformation?

Consider an infinitesimal transformation: $$(q_{i},p_{j}) \quad\longrightarrow \quad(Q_{i},P_{j}) ~=~ \left(q_{i} + \alpha F_{i}(q,p),~p_{j} + \alpha E_{j}(q,p)\right)$$ where $α$ is considered to ...
5answers
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### What is really curved, spacetime, or simply the coordinate lines?

It is often said that, according to general relativity, spacetime is curved by the presence of matter/energy. But isn't it simply the coordinate lines of the coordinate system that are curved?
4answers
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5answers
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### Does coordinate time have physical meaning?

I have always been a little confused by the meaning of the "$t$" which appears in spacetime intervals or metrics in general relativity. I concluded that $t$ was just a mathematical thing which allow ...
4answers
2k views

### Does spacetime position not form a four-vector?

When one starts learning about physics, vectors are presented as mathematical quantities in space which have a direction and a magnitude. This geometric point of view has encoded in it the idea that ...
18answers
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### What is an event in Special Relativity?

Lorentz transformations help us transform coordinates of one frame to that of another. For example, let the coordinates of an event in an inertial frame $S$ be $(x, t)$, then the coordinates in frame ...
3answers
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### Is there a quick way of finding the kinetic energy on spherical coordinates?

Assume a particle in 3D euclidean space. Its kinetic energy: $$T = \frac{1}{2}m\left(\dot x^2 + \dot y^2 + \dot z^2\right)$$ I need to change to spherical coordinates and find its kinetic energy: ...