66
votes
Why don't we put satellites into an orbit where there is (almost) no time dilation/contraction compared to Earth's surface?
The higher the satellite's orbit, the more of the Earth it can see (and hence the fewer satellites you need to ensure complete coverage of the Earth). The particular orbits chosen for navigation ...
- 7,670
46
votes
Why don't we put satellites into an orbit where there is (almost) no time dilation/contraction compared to Earth's surface?
You have to differentiate between corrections that are sources of error and corrections that are well understood and can be accounted for.
Time dilation is a well understood effect, and if you wanted ...
- 6,083
43
votes
Accepted
What exactly makes a black hole STAY a black hole?
After writing this answer, I noticed there are a couple alternative explanations that might be interesting to mention, so I'll add them as well.
Explanation 1
What makes something into a black hole ...
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41
votes
Accepted
If gravity is not a force, then how come gravitational assists work?
Well, gravity is a force and it isn't. What is a force anyway? It's what makes you accelerate, which is already a statement about a second-order derivative of one variable with respect to another, and ...
- 24.6k
38
votes
Is an atomic nucleus dense enough to cause significant bending of the spacetime?
The density of nuclear matter is on the order of $2 \times 10^{17}\, {\rm kg/m^3}$, while the Planck density--the density at which quantum gravity is "interesting"--is:
$$\rho_P = \frac{m_P}{...
- 30.7k
34
votes
In general relativity, why is Earth able to accelerate?
This is quite a common confusion for students new to general relativity, and it's because in GR the term acceleration means something slightly different from its everyday usage.
In everyday usage we ...
- 349k
33
votes
Accepted
Why is Spacetime described as flat even though we live in 3 dimensions of space?
"Flat space" means that on large scales, Euclidean geometry holds. All the angles in any triangle drawn in space add up to 180°; the total distance between points separated by $\Delta x$, $\...
- 8,105
31
votes
Accepted
Why/When can we separate spacetime into space and time?
The notion that a spacetime can be decomposed into a spacelike and timelike part is generally called a spacelike foliation, where your spacetime manifold can be decomposed into purely spatial ...
- 15.7k
31
votes
Where does the curvature of space happen?
I can't understand the curvature of space because curvature of something happen in space while curvature of space need space itself to happen
What you are describing here is called extrinsic ...
- 91.9k
30
votes
Why is a graviton formulated as an exchange between masses, rather than between mass and spacetime?
One could equally well ask "why is QED formulated as $\text{charge} \to \text{photon} \to \text{charge}$, and not $\text{charge} \to \text{photon} \to \text{EM field}$?" The answer is that ...
- 46.3k
29
votes
What is the cause of the constancy of the speed of light in vacuum?
The invariance of the speed of light follows from the principle of relativity. This says there is no experiment that can distinguish between inertial reference frames: physical laws are the same in ...
- 1,257
29
votes
How can a grain of sand be "spaghettified" when nearing a black hole?
Spagghetification occurs when the gravitational potential energy on the side of the grain of sand closer to the center of the black hole is much larger than the potential energy on the other side. The ...
- 45.1k
29
votes
Is an atomic nucleus dense enough to cause significant bending of the spacetime?
Gravity isn't dependent solely on density, but on both density and size. A very dense object that is very, very small - like an atomic nucleus - may not have a lot of gravity.
To see this, note that ...
- 19.6k
27
votes
Accepted
Does a double star system have more mass than its constituents?
A double star has less energy than if the two stars were separated.
It is fairly easy to see why this is. If you have two stars orbiting each other you would need to add energy to separate them. That ...
- 349k
23
votes
Accepted
Interpreting Christoffel Symbols as Fictitious Forces - General Relativity
It's actually very simple. Newton's second law in General Relativity may be written as $$\ddot{x}^{\mu}+\Gamma_{\nu \lambda}^{\mu}\dot{x}^{\nu}\dot{x}^{\lambda}=K^{\mu},$$
where $K^{\mu}$ is the four-...
- 1,027
20
votes
Where does the curvature of space happen?
I think maybe it is the terminology that causes the difficulty. You don't have to use the word "curvature". You can start from the following observations.
Observation 1. Define a straight ...
- 55.7k
19
votes
Why don't two accelerated clocks behave like two clocks in a gravitational field?
Acceleration in special relativity works a bit differently from the Newtonian version. It takes a while to build up a new set of intuitions.
A uniformly accelerating particle moves along a hyperbola ...
- 191
19
votes
What is the relevance of the Lorentz factor in general relativity?
$γ$ is a geometrical factor that would appear in Euclidean geometry also if it were taught in a slightly different way. A transformation between two Cartesian coordinate systems with a common origin ...
- 24.2k
19
votes
Accepted
How do we know the assumptions of the Schwarzschild solution are valid?
This is a very long-winded answer, so let me state the punchline up front: the boundary condition you pointed out really is physically suspect, and probably not realized in Nature -- however using it ...
- 45.1k
19
votes
Accepted
Is energy "equal" to the curvature of spacetime?
It is common see Einstein's equations described as "curvature equals energy", but that is not a complete description. The full description is complicated, which is exactly why we express it ...
- 6,637
18
votes
What is the cause of the constancy of the speed of light in vacuum?
The constancy of $c$ is an experimental result, verified to great precision. When we make mathematical models that assume the constancy of $c$, we get predictions that match other experimental results ...
- 17.7k
18
votes
Torus shaped event horizon
There is a result in four-dimensional General Relativity that forbids such situations. Namely, the Hawking's Theorem on the Topology of Black Holes. It is given, e.g., on the classic book by Hawking ...
- 16.1k
17
votes
How can a grain of sand be "spaghettified" when nearing a black hole?
The difference in gravity between the "front" and the "rear" of a grain of sand sent towards a black hole should/must be negligible, considering how weak gravity as a force is, ...
17
votes
Is spacetime isomorphic to a metric space?
Yes it is, but the found structure has no physical meaning in general.
As a matter of fact, as a general result on differentiable (paracompact) manifolds, every smooth manifold $M$ (without a ...
- 67.8k
16
votes
Why does acceleration in special relativity give rise to general relativity (and thus gravity)?
If we include accelerated motion in special relativity, the result is general relativity.
This is simply not true. Special relativity can easily handle accelerated motion on its own. The result of ...
- 91.9k
16
votes
Accepted
Why the ant on rubber rope paradox does not work in our universe or de Sitter universe?
In the ant-on-rope problem as stated in the Wikipedia article, the rope's expansion is linear. That means the ant's speed as a fraction of the rope length per unit time goes like $t^{-1}$, so the ...
- 24.2k
16
votes
Schwarzschild metric with negative mass
Yes, the Schwarzschild solution with $M<0$ is still a vacuum solution to the Einstein equations. Bondi explored some ideas about negative mass in GR in this paper, in which he says
As long as ...
- 66k
15
votes
Accepted
Test for inertial frame of reference
The falling elevator's frame is inertial! Congratulations, you've found Einstein's equivalence principle.
In relativity, we have to consider the proper acceleration, which is a 4-vector. Gravitational ...
- 1,708
15
votes
Accepted
What does it mean that a falling mass in space doesn't sense any force?
If you've ever been in an airplane taking off or a car taking a corner fast you'll know that you can feel the acceleration. This is commonly referred to as the g-force.
In general relativity this ...
- 349k
15
votes
Is the gravitational force a phenomenon or a theoretical invention?
how is it possible for a phenomenon to be replaced by a theory?
Theories don’t replace phenomena, they explain them. Newton’s law of gravitation and general relativity both explain the same phenomena....
- 91.9k
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