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47 votes
Accepted

Why are spherical shapes so common in the universe?

Spherical shapes in the universe are common because the dominant long range forces like gravity and electromagnetism are central (in that they only depend on the distance between objects). Our planet, ...
CStarAlgebra's user avatar
  • 2,687
17 votes

Why are spherical shapes so common in the universe?

On a astronomical scale spherical shape is due to gravity and the more massive the body the bigger gravity. Let's start with the stars: Stars form by collapsing cloud of gas in so called "pre-...
Graphenjoyer's user avatar
12 votes

Why are spherical shapes so common in the universe?

A planetary body would always want to achieve hydrostatic equilibrium: In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at ...
Nilay Ghosh's user avatar
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10 votes

Why are spherical shapes so common in the universe?

A classical philosopher like Aristotle would say this is because "sphere is a perfect solid and the heavens are a region of perfection". A more modern version of the essentially same answer ...
John's user avatar
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6 votes

Why are spherical shapes so common in the universe?

Equilibrium states in time-varying processes are local minima of exergy which preserve conserved quantities. Those things are (or can be reliably predicted to be) roughly sphere-like for which ...
g s's user avatar
  • 13.9k
4 votes

Why are spherical shapes so common in the universe?

The surface to volume ratio is the least for a spherical object. This means that a sphere for attractive forces will have the highest binding energy. All objects tend to a state of lowest potential ...
SAKhan's user avatar
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2 votes
Accepted

Why the unit of quantum information for anyons systems should be the qubit?

A classic source of anyon theories is the family $SU(2)_{k}$ where $k\geq1$. Such a theory has particle types $\{j/2\}_{j=0}^{k}$ and fusion rules \begin{equation} j_{1}\times j_{2} = \sum_{j=|j_1 - ...
Sachin Valera's user avatar
2 votes
Accepted

Topological behavior (or asymptotics at infinity) of gauge fields assumed in Fujikawa method

Indeed, from a mathematical standpoint, all the physics that has to do with the global topological terms of gauge theory "on $\mathbb{R}^4$" really happens on $S^4$. So how is it possible ...
ACuriousMind's user avatar
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2 votes
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Visualization of a gauge field with non-null winding number

The proper answer is that fully visualizing this winding would involve imagining the winding on a 3-sphere. Just in case someone reading this doesn't know why that is, it's because the boundary ...
11zaq's user avatar
  • 861
2 votes

Why are spherical shapes so common in the universe?

I kept reading and reading and couldn't believe I wasn't finding anything about hydrostatic equilibrium.... Until I did. In space, when an object has enough mass, it will ALWAYS take the shape of a ...
JP Anthony's user avatar
2 votes

Why are spherical shapes so common in the universe?

Although Torus/Donut Shapes are among the most common shapes in the transparent, invisible universe, like the Magnetospheres of various planets and galaxies, what humans can easily discern are dense ...
Tristian's user avatar
  • 121
2 votes
Accepted

Are $i^\pm$ and $i^0$ codimension 1 surfaces?

Penrose diagrams are a diagrammatic representation of the conformal compactification of a manifold, not of the manifold itself. The compactification part is required so we can draw the manifold on a ...
Prahar's user avatar
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1 vote

Why are spherical shapes so common in the universe?

In a wider sense: The sphere is the smallest surface that encloses a given volume. The sphere is the solution to one of the most general optimization problems in three-dimensional geometry. This makes ...
Peter - Reinstate Monica's user avatar
1 vote
Accepted

How does one prove that the electric field is conservative when it is not defined on simply-connected regions?

Definition of a potential field. A conservative field is a field so that the line integral $$\int_{\gamma} \mathbf{F} \cdot \mathbf{\hat{t}} \ ,$$ is independent on the path but only depends on its ...
basics's user avatar
  • 9,521
1 vote

How does one prove that the electric field is conservative when it is not defined on simply-connected regions?

I don't know about proving it mathematically, but intuitively, you can always imagine that there are no real point charges or infinitely thin rods. You can assume they are super small, but the charge ...
Wolphram jonny's user avatar
1 vote

What's the relations between Quantum spin liquid and Quantum magnetism?

Depends on what you mean by the "prospects". "Prospects" could mean what technological advancements might it lead to, what problems would it solve, how will it deepen our ...
mike1994's user avatar
  • 683
1 vote

What objects are solutions to the Einstein Field Equations?

There are basically two general ways of solving the Einstein field equations (EFE). The EFE gives the relationship between the distribution of matter and the geometry of the spacetime. Specifically ...
Dale's user avatar
  • 102k

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