The geometry tag has no wiki summary.
12
votes
2answers
160 views
Generalized Complex Geometry and Theoretical Physics
I have been wondering about some of the different uses of Generalized Complex Geometry (GCG) in Physics. Without going into mathematical detail (see Gualtieri's thesis for reference), a Generalized ...
9
votes
2answers
486 views
The Reeh-Schlieder theorem and quantum geometry
There have been some very nice discussions recently centered around the question of whether gravity and the geometry and topology of the classical world we see about us, could be phenomena which ...
8
votes
6answers
1k views
Experimental evidence of a fourth spatial dimension?
As human beings, we observe the world in which we live in three dimensions. However, it is certainly theoretically possible that more dimensions exist.
Is there any direct or indirect evidence ...
8
votes
3answers
290 views
Question about associative 3-cycles on G2 manifolds
Let $X$ be a manifold with $G_2$ holonomy and $\Phi$ be the fundamental associative 3-form on $X$. Let $*\Phi$ be the dual co-associative 4-form on $X$. Now consider a particular associative 3-cycle ...
7
votes
4answers
533 views
Why is there a search for an exchange particle for gravity?
Here's a question on something I've been wondering about for quite some time. (I am not a physicist.)
If I understand correctly, according to Einstein's General Theory of Relativity, mass results in ...
7
votes
4answers
8k views
Does the rotation of the earth dramatically affect airplane flight time?
Say I'm flying from Sydney, to Los Angeles (S2LA), back to Sydney (LA2S).
During S2LA, travelling with the rotation of the earth, would the flight time be longer than LA2S on account of Los Angeles ...
6
votes
2answers
376 views
Why are conformal transformations so prevalent in physics?
What is it about conformal transformations that make them so widely applicable in physics?
These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, ...
6
votes
1answer
277 views
Why are fractal geometries useful for compact antenna design?
While most of what I've read about fractals has been dubious in nature, over the years, I keep hearing that these sorts of self-similar (or approximately self-similar) geometries are useful in the ...
6
votes
1answer
401 views
Is C60 really the “most spherical” fullerene?
In the late 80's and early 90's, Smalley and others made claims that the C60 fullerene bearing icosahedral symmetry was the most spherical molecule known, and perhaps the most spherical that could ...
6
votes
1answer
302 views
The role of metric in the Wave Equation
The wave equation is often written in the form
$$(\partial^2_t-\Delta)u=0,$$
involving the Laplace-Beltrami operator $\Delta$. However, the Laplace-Beltrami operator $\Delta$ is defined only in the ...
5
votes
1answer
148 views
An astronaut and a vengeful pole
Imagine an astronaut floating in free-space with no significant nearby gravitational influences. The astronaut takes an arbitrarily thin pole of uniform density with length $l$ and mass $m$, orients ...
4
votes
2answers
207 views
Space-time geometry and metric
I am confused in one question in general relativity, why we can always express a space-time geometry only by metric. It means a metric, which is just about distance in tangent space, can tell us all ...
4
votes
2answers
212 views
Can the electroweak/strong forces, and/or quantum mechanics be thought of as geometric?
Can the electroweak and strong forces be written as geometric theories? - Why and why not?
Can quantum mechanics in general?
For example, the Kaluza-Klein theory explains the electromagnetic field ...
4
votes
2answers
149 views
Is a semi-Euclidean space possible?
Does exists a geometry (3d for example) which is Euclidean in 2 dimensions (x and y coordinates) and non-Euclidean when the third dimension (z) is taken into account? In other words a space where it ...
4
votes
2answers
344 views
Prerequisites to start the study of noncommutative geometry in physics
What are prerequisites (in mathematics and physics), that one should know about for getting into use of ideas from noncommutative geometry in physics?
4
votes
1answer
227 views
Relativistic space-time geometry
What subject (suggest book titles, etc.) should I study to get a clear grasping of hypersurfaces, 2-surfaces, and integration on them, mostly in special relativity (I'm not messing with general ...
4
votes
1answer
97 views
Is there an upper bound on the gauge group rank in F-theory compactifications on CY 4-folds?
It is known that in F-theory compactifications on CY 4-folds one can get gauge groups with very large ranks. The largest single factor* gauge group for compact CY 4-folds I found in the literature is ...
4
votes
1answer
128 views
How is the equation of motion on an ellipse derived?
I would like to show that a particle orbiting another will follow the trajectory
\begin{equation}
r = \frac{a(1-e^2)}{1 + e \cos(\theta)}.
\end{equation}
I would like to do this with minimal ...
4
votes
1answer
95 views
Flat space metrics
This question concerns the metric of a flat space:
$$ds^2=dr^2+cr^2\,\,d\theta^2$$ where $c$ is a constant. Why is it necessary to set $c=1$ to avoid singularities and to restrict $r\ge 0$?
Thanks.
3
votes
11answers
749 views
Is it possible for a physical object to have a irrational length?
Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational.
If I were to use this ...
3
votes
2answers
369 views
Where do I start with Non-Euclidean Geometry?
I've been trying to grok General Relativity for a while now, and I've been having some trouble. Many physics textbooks gloss over the subject with an "it's too advanced for this medium", and many ...
3
votes
1answer
107 views
Nanotube chiral angle as a function of $n$ and $m$
I'm looking into nanotubes and I thought I'd assure myself that the basic geometry equations are indeed correct. No problems for the radius, I quickly found the known formula:
$$R = ...
3
votes
1answer
158 views
Is Dyson Sphere a stable construction?
Suppose that a star is encompassed by a Dyson Sphere. Do we need a position control system for the Dyson Sphere to keep its origin always aligned with the center of the star? Will it stay aligned ...
3
votes
4answers
316 views
Gravitation is not force?
Einstein said that gravity can be looked at as curvature in space- time and not as a force that is acting between bodies. (Actually what Einstein said was that gravity was curvature in space-time and ...
3
votes
1answer
164 views
What's a pseudo-rotation?
I'm sorry for this lexical, probably extremely elementary, question. But what is a pseudo-rotation? I just read this term for the first time, in the beginning of the 4th chapter book of CFT by Di ...
3
votes
1answer
49 views
Uniqueness and existence of polygonal orbits through a spherical shell
Say we have a spherical wire mesh raised to a negative voltage. Then let's say we release a proton from near the surface, and away from the surface, at some angle and speed. Also, imagine that the ...
3
votes
1answer
107 views
How would one calculate the amount of water contained in a cloud?
So I was looking out the sky one day and I wondered how I would go about calculating how much water was contained in a cloud. I figured the following simple outline
1) We need to roughly know how big ...
3
votes
4answers
210 views
Formulation of general relativity
EDIT: I think I can pinpoint my confusion a bit better. Here comes my updated question (I'm not sure what the standard way of doing things is - please let me know if I should delete the old version). ...
3
votes
1answer
82 views
How does holographic voxel density scale with holographic film metrics?
I'm trying to understand how one can generate bounds on the effective number of voxels (volumetric pixels) in a hologram, or information density, provided various metrics for the two-dimensional ...
3
votes
2answers
459 views
Why was the truncated icosahedron (i.e. soccer ball) geometry chosen for the implosive lenses in the “Fat Man” atomic bomb?
Quoting from Wolfram Mathworld: " It is the shape used in the construction of soccer balls, and it was also the configuration of the lenses used for focusing the explosive shock waves of the ...
2
votes
2answers
185 views
Shape of electric charges on sphere in equilibrium state
When electric charges of equal magnitude and sign are released on a regular sphere (and assume that they stick to the surface of the sphere, but they are free to move along its surface), what is the ...
2
votes
1answer
180 views
Why is physical space equivalent to $\mathbb{R}^3$?
Why is physical space equivalent to $\mathbb{R}^3$, as opposed to e.g. $\mathbb{Q}^3$?
I am trying to understand what would be the logical reasons behind our assumption that our physical space is ...
2
votes
2answers
219 views
The shape of the earth$\ldots$
....is an oblate spheroid because centrifugal force stretches the tropical regions to a point farther from the center than they would be if the planet did not rotate. So we all learned in childhood, ...
2
votes
1answer
1k views
How to calculate the projected area at different angles/vectors?
Please help me with the following. I want to know if there is an equation/set of equations to find out the projected area of a (3-D) cube when it is oriented at different angles of attack to the fluid ...
2
votes
1answer
218 views
Tiling hexagons on a sphere surface
In attemopt to understand basic principles of non-Euclidean geometry and its relation to physical space, I am reading General Relativity by Ben Crowell. On page 149 there is a discussion of hexagons ...
2
votes
1answer
1k views
Determining the center of mass of a cone
I'm having some trouble with a simple classical mechanics problem, where I need to calculate the center of mass of a cone whose base radius is $a$ and height $h$..!
I know the required equation. But, ...
2
votes
1answer
111 views
No attraction radially in an cylinder of spherical magnets
I have a set of small magnetic spheres the size of ball bearings. When many of them are built into a cylinder such that they are hexagonally packed, there is no magnetic attraction radially (between ...
2
votes
1answer
164 views
Is it possible to mechanically isomerize an sp3 hybridized carbon center?
Imagine I have an sp3 hybridized carbon attached to four separate polyethylene chains. By pulling on the polyethylene chains in some manner, is it possible for me to mechanically isomerize the chiral ...
2
votes
1answer
85 views
Can we project a 4D world using 3D video technology?
Traditional movies, TV, etc, faithfully show our 3-dimensional world using 2 dimensions. So can we have a movie that shows a 4-dimensional world using 3D technology?
2
votes
5answers
127 views
Why is the world sheet of an open string a cylinder?
I went to a lecture a few weeks ago and was told the following:
The world sheet of a closed string is a normal, standing cylinder.
The world sheet of an open string is a cylinder on its side.
This ...
2
votes
1answer
80 views
How far does typical view of clouds/atmosphere extend?
The specific "sub questions" I'm asking are:
When you are looking at clouds just on the horizon, how far away would they be?
How wide (in km) is that total field of vision at roughly cloud height.
...
2
votes
2answers
107 views
Stroboscope-and-telegraph problem
Narrative:
Consider, in a suitably flat region, two straight lines which don't necessarily intersect. Let vector $\mathbf{x}$ point along one line, and vector $\mathbf{y}$ point along the other. Let ...
2
votes
2answers
63 views
Proof that a spherical lens is stigmatic
In geometric optics, we generally allow that, for example in the case of a convex lens, rays coming from a particular point get refracted towards another particular point on the opposite side of the ...
2
votes
0answers
49 views
Dirichlet's work on gravity in non-Euclidean space?
In the book The Norton History of Astronomy and Cosmology by the late John North I have found the following statement (page 514):
"The German mathematician Lejeune Dirichlet studied the law of ...
2
votes
0answers
91 views
Getting the AdS metric from maximally symmetric spaces
I am familiar with the way we derive the form of the FRW metric by just using the fact that we have a maximally symmetric space i.e the universe is homogeneous and isotropic in spatial coordinates. ...
1
vote
1answer
121 views
Are there any clear and expressive plainword sense of metric tensor components?
Can the following groups of components of metric tensor can assigned a clear sense?
https://docs.google.com/drawings/pub?id=1kVqkN1gT-a2fDy2S851l9iQKaMfaatCDo517OSZBHEo&w=467&h=228
I have ...
1
vote
2answers
196 views
Is it necessary to embed a 4D surface in 5D space?
Lets consider the line element:
$$ds^2=dr^2+r^2[d\theta^2+\sin^2\theta d\phi^2]$$
There are three variables r,theta and phi.
If we use a surface constraint like r=constant the number of
independent ...
1
vote
1answer
55 views
Rømer's determination of the speed of light
I am trying to understand Rømer's determination of the speed of light ($c$). The geometry of the situation is shown in the image below. The determination involves measuring apparent fluctuations in ...
1
vote
2answers
319 views
Does a cycle (in Simple Harmonic Motion) have to equal 2π?
So, I search for the definition of cycle and I get this in Wikipedia:
A turn is a unit of angle measurement equal to 360° or 2π radians (or ...). A turn is also referred to as a revolution or ...
1
vote
2answers
418 views
How to deduce this free body diagram?
Can someone provide a trigonometry/geometry insight to deduce the angle of the plane is the same as the angle of the component of the weight?
