To be used for questions on geometry closely pertaining to physics. Includes differential geometry and euclidean geometry.

learn more… | top users | synonyms

3
votes
2answers
71 views

How much of Minkowski spacetime structure can be recovered from its causal structure?

A beginner's question: I have always understood that (four-dimensional) Minkowski spacetime can be recovered up to a constant factor—i.e. 'up to a dilation' or 'up to global scale'—from its causal ...
3
votes
0answers
41 views

Rigid rectangle in Schwarzschild

Say I build a perfect rectangle. Side lengths $l_1$ and $l_2$ and perfect right angles. I am on earth and the metric is given by the Schwarzschild metric. Setting $dt=0$ leads to the spatial ...
4
votes
2answers
97 views

What is the notion of a spatial angle in general relativity?

Is there a notion of spatial angles in general relativity? Example: The world line of a photon is given by $x^{\mu}(\lambda)$. Suppose it flies into my lab where I have a mirror. I align the mirror ...
0
votes
1answer
48 views

How to calculate spatial distance in space-time?

Pinning two test particles at two different points in space, how can I calculate their spatial distance, when the geometry is given by the Schwarzschild metric? Let's say particle 1 is pinned at ...
1
vote
1answer
55 views

In Minkowski space, why does the hyperboloid appear to each observer as a circle whose radius is increasing faster than the speed of light?

I read the assumption in the above question in the paper Hyperbolic geometry on a Hyperboloid by William F. Reynolds (see here, page 444), but it was not clarified further (the discussion was rather ...
3
votes
2answers
76 views

Scattering geometry question

While reading up on light scattering I came across this slide: My vector maths is a bit rusty and I am having trouble understanding the last term (scattering geometry). What is the significance of ...
2
votes
0answers
90 views

Geodesic distance in de Sitter space

Consider $N$ dimensional de Sitter space embedded in $N+1$ dimensional Minkowski space: $$\eta_{\mu\nu}X^\mu X^\nu=1, \hspace{1cm}\eta_{\mu\nu}=\text{diag}(-1,1,\dots,1)$$ where I set $H=1$ for ...
2
votes
2answers
113 views

Are signal fronts in a beam not at rest to each other?

I'd like to investigate how the notion of "mutual rest" might be applied consistently, but distinctively, in the following thought experiment: Consider a light source ("$A$") which directs a beam ...
0
votes
1answer
46 views

Physics of Skiing: Ideal Carving Equation

I am conducting a research paper on the physics of skiing, specifically how ski parameters affect the ski's ideal carve. I have come across this paper (abstract link to arXiv paper), which is ...
0
votes
0answers
36 views

Transforming the angular momentum operator (from spherical to Euler and the internal valence angle) for a reduced 3-body problem

Let me introduce the problem: In a two electron fixed nucleus problem the "body" is the atom, whose electrons are located relative to the nucleus by the coordinates $r_1$ and $r_2$, and the angle ...
0
votes
0answers
12 views

Did a racer on a “restless” course race at some particular average velocity? (2: Starting gate and finish line being rigid to each other)

Consider two participants, a starting gate ($A$) and a finish line ($B$), in a (sufficiently) flat region, both undergoing uniformly accelerated motion, such that $A$ finds constant ping duration ...
0
votes
1answer
125 views

When to use Cosine or Sine? [closed]

Three blocks of masses $M_A=15.0 \; \text{kg}$, $M_B=12.0 \; \text{kg}$, and $M_C=8.0 \; \text{kg}$ sit next to each other on a frictionless surface. A force $F=54.0 \; \text{N}$ acts on Block $A$ ...
0
votes
0answers
20 views

Did a racer on a “restless” course race at some particular average velocity? (1: Starting blocks, finish line moving uniformly wrt. each o.)

Consider two participants, $A$ and $B$ moving uniformly wrt. each other; first having approached each other, then having met and passed each other, and eventually having separated from each other such ...
0
votes
4answers
108 views

How to determine “timelike”-ness without using a coordinate system?

It has been stated here that: we can say, without introducing a coordinate system, that the interval associated with two events is timelike, lightlike, or spacelike. This assertion appears at ...
0
votes
0answers
47 views

Electric Potential of a Cube Made of Point Charges

I'm trying to find the potential energy of multiple geometric shapes made entirely out of point charges. This particular shape is a cube made out of two different point charges, A and B, each ...
1
vote
2answers
101 views

How far would I have to go to see a fully rounded Earth?

How far would I have to go to see a fully rounded Earth? Recently, I saw a video on Youtube in which a sky diver called Felix Baumgartner ascends to $120,000$ feet (= $39$ miles) in a stratospheric ...
0
votes
1answer
58 views

find distance using a light line

Let's suppose we have a particular light frequency emitter and relative sensor array, and that there is no external source of this light. This emitter has a know angle respect the receiver, and emit ...
2
votes
0answers
35 views

Can a value of “length, in meters” be attributed to a pair of ends which are rigid (but not at rest) to each other? [duplicate]

The definition of the SI base unit "metre" [1] doesn't seem to rule out explicitly that a certain value of "length, in meters" could be attributed to a pair of ends which are rigid to each other, but ...
3
votes
2answers
147 views

Differentials in Spherical Shell - Maxwell Distribution

In explaining the Maxwell distribution of molecular speeds, my pchem textbook uses the following figure: We are basically trying to find the probability of having a particle with a speed $u$ between ...
2
votes
0answers
61 views

If two ends were a certain “length” apart were they therefore at rest (or at least rigid) to each other? [closed]

Considering the definition of the SI unit of "length" [1] and [2 (" method a.")] I'm missing any requirements about the two "ends" of the required "path travelled by light" being "at rest to each ...
5
votes
3answers
201 views

What's the dimensionality of a solid angle?

I haven't seen this explained clearly anywhere. Solid angles are described usually as a fraction of the surface area of a unit sphere, similar to how angles are the fraction of the circumference of a ...
4
votes
3answers
256 views

Calculating the Center of Mass

We have a homogeneous body that looks like this: I have tried dividing the body into different parts using the following definition: R g * A = R 1 * A 1 + ... R n * A n I was thinking I could ...
5
votes
1answer
91 views

Can a very small portion of an ellipse be a parabola?

We consider that when a body is projected from any height from the earth surface with a speed lesser than the orbital speed ( tangentially to the earth surface at that point.) it follows an elliptical ...
1
vote
2answers
128 views

Is the triangle stronger?

I have a friend who cedes that a framework that is a triangle would be stronger than a square framework. But he maintains that a square solid would not be stronger than a triangle solid. Ie a set of ...
2
votes
0answers
70 views

Can we derive the relation between proper time and the spacetime interval?

In GR, it's usually taken for granted - or as a definition - that the time measured by an observer's clock is related to the geometry in a very simple way, $d\tau^2 = |ds^2|$. This is easy enough to ...
0
votes
0answers
20 views

How to express “curvature scalars” in terms of "discrete curvature values $\kappa_n$?

We know from MTW [1] and Synge [2] how, for participants who were (pairwise) rigid to each other, it may be determined whether or not they were straight to each other, plane to each other, or ...
4
votes
2answers
164 views

Textbook on the Geometry of Special Relativity

I am looking for a textbook that treats the subject of Special Relativity from a geometric point of view, i.e. a textbook that introduces the theory right from the start in terms of 4-vectors and ...
3
votes
0answers
68 views

Sound - for purposes of vibration

What is the best way to distribute noise from more than one source (I'm envisioning a system with many), within a dome, with the ground as its primary target, at optimal frequencies and volumes to ...
7
votes
1answer
146 views

Understanding Calculus Notation in Physics

I have just started a first-year calculus-based physics course about electromagnetism and waves. I am having trouble understanding what calculus notation means in the context of physics. Here is a ...
0
votes
2answers
69 views

Spherical coordinate system

I do not understand how is $r^2 = x^2+y^2+z^2$ in spherical coordinate system. Can anybody give a simple derivation? I need to understand this in order to understand the lorentz transformation.
0
votes
0answers
135 views

Tensor of inertia

The tensor of inertia of a solid sphere is $I_{ii}=\frac{2}{5}MR^2$ about an axis passing through its CM. Why would the tensor of inertia of each hemisphere about that axis be ...
2
votes
2answers
106 views

Zwiebach quick calculation 2.5

I am working through Zwiebach's a first course in string theory. It's been a while since I did any math (or physics!), and I am stuck on the following problem (quick calculation 2.5 in the book): ...
0
votes
1answer
85 views

Making a cut trough a center of mass, can the masses of the pieces be equal?

Let's say point $P$ is the center of mass of an irregularly shaped object. If I make a straight cut trough point $P$ and split the object in two, is it possible for the two pieces to have the same ...
0
votes
0answers
24 views

Geometric Interpretation of Rotated basis of Hamiltonian and collective Dicke states

Suppose I start with a basis of states for a two spin-1/2 particle system, namely, $\{\left|\uparrow\uparrow\right\rangle, \left|\downarrow\downarrow\right\rangle, ...
2
votes
1answer
125 views

Where is a closed form also exact?

I'm not very familiar with exterior derivatives. I've some trouble following argument (which is a part of a proof that if the Riemann tensor vanishes, $R^{\,\rho}_{\;\,\sigma \mu \nu}=0$, iff there ...
0
votes
1answer
128 views

Area moment of inertia of regular $n$-gons over polygon center $O$

Is it possible to consider the regular polygons ($n$-gons) as deformed circles and use a pseudo-polar coordinate system to calculate their moment of inertia over its center $O$. Inasmuch as I know (I ...
0
votes
1answer
69 views

virtual boxes mirror reflection

The problem statement Find the lightpath with a given starting and ending points via one or more mirrors. In those kind of problems you try image someone pointing a laser with a very narrow beam ...
4
votes
1answer
272 views

Problem in Youngs double slit experiment

This is from Young Double slit experiment. But How to prove the the two $\theta$ are equal, I meant, how $\angle EAD= \angle PEC$? I see from the both triangle have $90^0$ but what about others?
0
votes
1answer
76 views

Structure factor of crystals (X-ray crystallography)

How can one prove that the degree of each node in a distance graph must be at least four in order to obtain a unique solution to an exact distance geometry problem with sparse distance data? The ...
2
votes
1answer
776 views

Analytic solution for angle of minimum deviation?

Consider a simple prism with a prism angle $A$, angle of incidence $\theta_1$, angle of emergence $\theta_4$ and the first and second angle of refraction as $\theta_2,\theta_3$. the refractive index ...
0
votes
2answers
82 views

Density of a material in different dimensions

Hope this isn't something trivially wrong, I am a beginner in classical mechanics. But anyways, say there is a cube, of side length $a \ \text{cm}$. The volume of the cube is $a^3 \ \text{cm}^3$. If ...
7
votes
1answer
177 views

How did Eratosthenes know the suns rays are parallel?

Eratosthenes famously observed that the suns rays were perpendicular to the ground in one location, yet non-perpendicular to the ground at a location some miles to the north. On the assumption that ...
6
votes
1answer
263 views

Two formulas for a particle's acceleration

While on a class my teacher was taking about particle's motion in space. At some point she said the following: Consider that the particle's path is described by a curve in space defined by the ...
1
vote
2answers
92 views

Paralel light conditions after passing from a sphere

Is it possible to get such result that light will be parallel after passing from the sphere? what is the total condition for such result if possible? Thanks for answers
-1
votes
2answers
97 views

Vectors question? [closed]

I am stuck on this vectors question I have for home work. Does anything think they can help point me in the right direction on how to solve this? An explorer is caught in a whiteout (in which the ...
1
vote
2answers
171 views

Angle needed for object A to intercept with object B

Object B is 15 degrees East of North at a distance of 20km/h. Object B is moving at an average speed of 30km/h in the direction 40 degrees East of North. If object A is capable of moving at 100km/h, ...
2
votes
1answer
130 views

Can two parallel lines meet? [closed]

My physics teacher talked about the meeting of 2 parallel lines, and he said that it may occur in the infinity or something. I know that 2 parallel lines can meet in spherical geometry, (thanks to ...
0
votes
1answer
52 views

Parametric equations of a hypersurface

In light-front QFT, in the Minkowski space, we define a hypersurface, $\Sigma_+ : x^3+ x^0 = 0 $. How can I write its parametric equations?
9
votes
1answer
378 views

Can masses move in 2+1 gravity?

I would like to understand basic concepts of the general relativity in 2+1 spacetime. As far as I know, GR predicts that such a spacetime is flat everywhere except for the point masses which create ...
1
vote
1answer
109 views

Characteristic length of a triangle

I am reading a paper on collision detection in cloth simulation, please help me understanding following lines written in the paper : To check if a point x4 is closer than some thickness h to a ...