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

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6
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1answer
237 views

Null Coordinates

I have a very basic question: what are the advantages of writing a metric in the null coordinates? Which extra insight do they provide? I've looked in Caroll's "Spacetime and Geometry" and Wald's ...
3
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1answer
63 views

When is a circle not a circle?

Imagine a 2D uniform circular motion of constant magnitude but changing direction in an area of zero g. The forces will be equal all the way round - it will be a perfect circle. Now imagine the same ...
2
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1answer
50 views

Satellite and gravitational acceleration

According to $0.5gt^2$ object will fall 5m in first second. Earth curve is 5m for 8km So if we can project object at 8000 m/s speed object will never fall into ground. Above scenario is correct ...
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1answer
16 views

How to express in terms of spacetime intervals whether two participants in a flat region were at rest to each other

Given a flat region of spacetime as set $\mathcal S$ of events together with values of spacetime intervals (up to a common non-zero constant) for each pair of events, $s^2 : \mathcal S \times \mathcal ...
9
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0answers
214 views

The dual of a surface element in 4-space

In reading the classic text, "The Classical Theory of Fields", Third Edition, by Landau and Lifschitz, I found an "obvious" statement not so obvious to me. It is on p.19, the statement of the ...
6
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59 views

Motivating Irreducibility of Hilbert Space for Quantization Axioms

In the context of geometric quantization, we usually look for a map from the Poisson algebra of classical observables to the algebra of quantum observables (or rather, a sub-algebra of the classical ...
3
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0answers
42 views

Derived Geometry and Deformation Quantization

Can anyone please explain to me in layman' terms what derived geometry deals with and what deformation Quantization is? I have only a good understanding of Relativity,Classical Mechanics.
3
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0answers
39 views

Snyder's Lorentz invariant discrete space-time

Can theories which say space-time is fundamentally discrete be compatible with Lorentz invariance? And if the answer is yes, in what sense is space-time no longer continuous? I'm sure this has been ...
3
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0answers
70 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 ...
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394 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 ...
3
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0answers
116 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 ...
2
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0answers
52 views

Terminology - optical (visual) properties of a structure

I am trying to understand few terminological problems that I encounter. Without knowing keywords it is hard to perform search for literature or publications in the area. The area relates to the ...
2
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0answers
126 views

Circumference measurement using a capacitive sensor

I have a question which I hope someone in here can help me answer. Background: I’m building a device where I intend to use a stretchable capacitive sensor to define the radius change of an object. ...
2
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0answers
65 views

Is there a theory that physically explains the origin equivalence principle / explains gravity via acceleration?

I've been thinking about how gravity could arise from a 4th dimensional spinning cylinder with space-time that has pliability like rubber (which I think is a generally accepted analogy). The ...
2
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0answers
54 views

T duality for lower codimension branes or ALF spaces

These are purely mathematical questions in some sense but I believe this is relevant in string theory as the title says. I wonder if it is possible to perform T-duality of Taub-NUT space not along ...
2
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0answers
152 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 ...
2
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0answers
81 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
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0answers
175 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. ...
2
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0answers
109 views

Does the measure of proximity of two theories in “theory space” run?

From reading this article, I have learned that two effective QFTs can be very close together in the "theory space" appropriate to describe for example physics at the LHC scale, whereas the ...
2
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0answers
97 views

Self-organizing maps

I'm currently interested in this subject but all I can see is about neural networks and I'm more interested on the Theoretical point of view: "how can a system (Lagrangian/Hamiltonian) alter it's ...
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0answers
14 views

What determines the sign of phase dislocations?

I am studying the nonlinear Schrodinger equation $$A_t+iA_{xx}+i|A|^2A=0$$ for $A=ae^{i\theta}$ a complex valued function, with $a,\theta$ real. I am trying to figure out what sets the signs of the ...
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0answers
51 views

Does Earth eclipse the Sun at the L2 Lagrange point?

Is Earth's diameter large enough to eclipse the sun at the L2 Lagrange point? Or does the sun shine around the edges of the earth? I understand the useful area of the L2 Lagrange point is somewhat ...
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0answers
46 views

Defining a room that is equally lit at every point

Imagine you were in a room designed such that no matter where in the room you stand, a sphere of volume 1 liter held at 2 meters above the ground would be exposed to the same amount of light. How ...
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0answers
41 views

Given a dimension of a known object in the image, how can we calculate the dimension of other objects in the same image ?

The question considers a very specific scenario in which we have an image with let us say, two rectangle objects. We know width and height of one object. How can we calculate the dimensions of the ...
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0answers
56 views

Alternative ways of calculating the principal moment of inertia

Let's say I am given 2x2 masses ($m$ and $m'$ have the same mass, just different coordinates): $m_1: (-a,b,0)$ $m_1':(a,-b,0)$ $m_2: (a,b,0)$ $m_2': (-a,-b,0)$ Due to symmetry the center of mass ...
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0answers
184 views

Can the universe be round but still infinite?

Can the universe still be infinite in space if its curvature is > 1? Is a manifold of positive curvature necessarily compact? Does the Tarski paradox have any bearing on the finite or infinite ...
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0answers
85 views

Justifying the use of real numbers for measuring length

I am not sure if this is the most appropriate place to post this but here goes nothing: Assume we were trying to come up with system of numbers $S$ to model our intuition of length. We want $S$ to ...
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0answers
41 views

Increasing the volume of a object in a photograph

I have two images which look like this --- These images are two views of a calibration object --- the white die that you see hanging in the middle. The problem is that, the die is too small and ...
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0answers
65 views

Bending of a pipe filled with sand

There is this industrial pipe made out of steel that is 1 meter in diameter and 6 meters long (and volume 4,71 cubic meters). The thickness of the pipe "wall" is 4 centimeter. The pipe is filled ...
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0answers
155 views

Could a fourth dimension be “spatially simulated” one point at a time by using movements?

I wonder if time and movement can be translated into a simulation of an extra spatial dimension. At least in one point at a time. I'll try to explain. Imagine a fixed probe which measures the ...
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0answers
136 views

How far is the horizon, if a 2m tall man watches to the sea?

How far is the horizon, if a $r=2 m$ tall man watches to the sea? I have calculated that it would be even just about 6 km. if R = radius of earth( $6370 \cdot10^3$ m ). By pythagorean theorem we ...
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0answers
7 views

Coordinate Equation of a curve which bends all the parallel incoming rays from infinity towards a single point

How should i proceed on to find the coordinate equation of a curve such that it bends all the parallel rays coming from infinity towards a single point. Yes I know that it would be a 2nd degree ...
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0answers
39 views

Is there a 3D analogue of angle?

A one-dimensional angle is a wedge, almost like a slice of pizza. A two-dimensional angle is an angle squared, like the cone of light produced by a flashlight. This is called a solid angle. Is ...
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29 views

View factor of two parallel coaxial *rectangular* plates

I've found a lot of tables and resources that list view factors (VF) for various geometrical configurations, but I couldn't find a single one that has the VF for two parallel coaxial rectangular ...
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0answers
23 views

How to calculate apex angle of sun shining on the Earth

I'm trying to compare the brightness of various LEDs to the average brightness of natural daylight. LEDs are rated in terms of candelas whereas the Sun is measured in terms of lumens, so I need to ...
0
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0answers
21 views

Angular current in torus

I'm trying to find the magnetic field due to a torus anywhere in space. I'm approximating it as a circular current loop. What I'm having a hard time with is the current in the theta direction, that ...
0
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0answers
39 views

Simple Stern-Gerlach Apparatus Orientation

I have been reading Townsend(2012)A Modern Approach to Quantum Mechanics. In the first chapter, he introduces the idea of intrinsic spin angular momentum, and some of its strange quantum properties ...
0
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0answers
34 views

Will a string always be tangent to a pulley at 45 degrees above the horizontal?

I just spent about an hour trying to figure out which part of my calculation was giving me the incorrect answer, and now I've finally got it. At first, it made sense,but now it doesn't again. There ...
0
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0answers
41 views

What is the scale factor of a hyperbolic universe?

I wanted to derive the solution to this question from the Friedmann equations myself but I ran into some trouble. I was working in natural units where $c=G=1$, then, for brevity, I defined ...
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0answers
91 views

Are Landau levels always degenerate?

Solving the Landau problem, namely the quantum mechanical problem of a particle in a magnetic field leads to degenerate energy states, the famous Landau levels. My question consists of two parts. ...
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0answers
54 views

Compute distance travelled based on a yaw-rate

Assume that a rigid body is traveling with constant velocity $v$, and (this rigid body) is rotating with a constant yaw rate of $\dot{\theta}$. Find the distance travelled in one time step, $\Delta ...
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0answers
22 views

How is the inertia tensor (just diagonal elements) of a quarter disk related to the full disk one?

Let be a disk of radius $R$ and mass $M$ with an uniform distribution of mass $\sigma$, centered in the origin O, laying in the $OXY$ plane. If I know that $$I_x=I_y=\frac{1}{4}MR^2, \qquad ...
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0answers
39 views

Radian Zeno-version paradox: Can a particle moving in the circular path reach the angular position of non-terminating decimal form radian value?

Consider a particle P moving in a circle of radius r as shown in the figure. Premise 1: Position of the particle can be described by the angle $\theta$. Premise 2: Particle reaches the position ...
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0answers
37 views

Is the total length of the inner sheet of a two ply roll of toilet paper shorter than the outer sheet?

If you look at any individual square of two plies, each ply looks the same. But musn't the inner ply be shorter? Wouldn't the inner ply develop kinks if it was the same length as the outer ply? Or ...
0
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0answers
54 views

What's wrong with this calculation of the center of mass of a triangle?

Find the center of mass $(x_G,y_G)$ of a homogeneous triangle of mass $m$. Divide it into infinitesimal rectangles of width $dy$, length $x$, mass $dm$ and area $dA$. We have $d A = x dy $ ...
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0answers
214 views

Gaze tracking with the pupil-glint response how does the geometry work?

I am struggling to understand the geometry behind the pupil glint response (see above) (With only one light source). I understand that you use the glint to find the corneal centre (Centre of corneal ...
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0answers
297 views

Close-packing of equal spheres - one sphere in a pyramid with a square base and four equilateral trianglular faces

I'm trying to determine the "packing efficiency" of fitting on sphere into a square based pyramidal container with four equilateral triangular faces. In other words, how much space within the pyramid ...
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0answers
21 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
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0answers
86 views

Water Stream from a Horizontal Surface

If water was projected from a flat surface where gravity was equal all over the surface. What would happen when the water fell in on itself? The water is in a continuous stream and is perfectly ...
0
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0answers
255 views

Extrinsic curvature versus Intrinsic curvature (Euclidean versus Riemannian)

Do we believe the universe has any extrinsic curvature at all? As far as I'm aware extrinsic curvature is only used in geometry/math to model the intrinsic curvature, correct? From the answers to ...