# Tag Info

### I don’t understand Noether’s theorem… there is nothing to prove?

Comments to the post (v3): Noether's theorem is just one method to determine conservation laws. If you have another, that's totally fine. Not all quasi-symmetry transformations (which in principle ...
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### Length contraction of a square moving along the diagonal

The mistake you made was assuming that length contraction is a linear operation. By linear here I mean in the mathematical sense. Length contraction is an operation that takes a position (or length) ...
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### I don’t understand Noether’s theorem… there is nothing to prove?

Invariant Lagrangian and Conservation Laws: You're correct that if the Lagrangian is invariant under a transformation, it leads to a conserved quantity according to Noether's theorem. However, the ...
Accepted

### Is it possible to describe every possible spacetime in Cartesian coordinates?

As the choice of coordinates is arbitrary, can't I just "postulate" to use cartesian coordinates to describe any possible spacetime? If by cartesian coordinates you mean a set of four ...
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### Length contraction of a square moving along the diagonal

My line of thought was that we can resolve v into vx and vy, which have equal magnitude. Because of that, the horizontal and the vertical contractions will be equal and we will get a smaller square. ...
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### Will a distant observer really see an object that has fallen close to a black hole freeze in time?

One reason the Schwarzschild metric is so well known, is because it was the first exact solution found for a gravitational body in General Relativity and even Einstein did not think an exact solution ...
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### Can we define time as a field?

A field is a quantity which typically depends on the location like --- giving a simple example --- a temperature distribution over a piece of metal, on one end of the metal the temperature is low and ...
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### Intuitive explanation of COSMIC TIME?

The cosmic time is defined as the (proper) time experienced by an observer at rest in a co-mobile frame, that is a frame carried by the expansion in an isotropic and homogeneous Universe (As such, it ...
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### Do the Lorentz transformations lead to negative amounts of time?

The word 'event' here is a misnomer, because it carries with it the connotation of time, and the two events are simultaneous in the unprimed frame The word event is correct, not a misnomer. The fact ...
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### Why do we use the Earth inertial frame when solving problems involving non-inertial reference frames?

Why do we use the earth inertial frame when solving problems involving non-inertial reference frames? Because we can. This is the meaning of the general principle of relativity. You can use any ...
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### Length Contraction: is $t'$ or $t = 0$?

David Morin is correct. Length in a given frame is defined as the distance between the two ends of an object at the same time in that given frame. So length is a concept that is intrinsically tied to ...
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### Derivation of the Schwarzschild metric: why are $g_{22}$ and $g_{33}$ the same as for flat spacetime?

I simply do not understand why, there, $g_{22}$ and $g_{33}$ must be those of the flat spacetime. In fact, it is not necessary that $g_{22}$ and $g_{33}$ take on the form of the angular part of the ...
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### Is it possible to describe every possible spacetime in Cartesian coordinates?

Since the question makes no reference to the number of dimensions, you could ask it just as well for a universe that is 2-dimensions of space and 1 of time. If you can't do it even there, then the ...
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### Angular or tangential term in gravitational potential energy change using polar coordinates

The position vector in polar coordinates is $\vec r = r_r\hat r$ in your notation, or simply $\vec r = r\hat r$ without the redundant subscript. There is no component along $\hat \theta$. Consequently ...
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### Will a distant observer really see an object that has fallen close to a black hole freeze in time?

Tristan Diotte wrote: "if we switched to the "Eddington-Finkelstein" coordinate, this singularity would disapear" That doesn't help the far away observer, since the time ...
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### Scalar multiple of inertial frame

Yes. This is still an inertial frame. The transform you have posted is a change of units for the spatial coordinates. The Wikipedia list is not exhaustive.
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### Change of variables from FRW metric to Newtonian gauge

Firstly as you suggested, $$d t_{c} = \frac{\partial t_{c}}{\partial t} d t+\frac{\partial t_{c}}{\partial \vec{x}} d \vec{x}$$ d t_{c} = d t-\frac{1}{2} \dot{H}(t) \vec{x}^{2} d t-H(t) \vec{x} \,d ...
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### Physical Quantities Sign Convention

Other answers have answered the direct questions in the OP. Here, I'd like to expand on the general question a little bit and talk about the fact that negative signs mean different things in ...
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### Physical meaning of each component of the metric tensor in GR

This is like finding the meaning of individual coordinates of a classical position vector. The vertical component has something of a special meaning because gravity is vertical and it matters to just ...
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### Teacher told us we're not allowed to write negative vectors, is this correct or not?

Your teacher is instructing you to define the vectors in terms of their components, \begin{align} \vec F_1 &= \hat x \cdot 20\,\mathrm N \\ \vec F_2 &= \hat x \cdot (-10\,\mathrm N) \end{align}...
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### Connection between pseudometric and Einstein elevator

lalala asked: I do not see how the metric tensor relates to accelerated reference frames. The purpose of the elevator experiment is to showcase that a uniform gravitational field can be switched off ...
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### Resolving an apparent contradiction between Schwarzschild and ingoing Eddington-Finkelstein coordinates

The issue is that in general coordinate induced vector fields depend on all of the coordinates. For example, suppose we have coordinates $x, y, z$, and we change to $u, v, w$. Then even if the ...
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