Space Definition and 1000 Threads

Presume we look at a two-dimensional view of space time, with no local masses, and we draw a grid of equidistance spaced lines. The intent is to look at space but not time. As we begin, we look in all directions and the grid lines are evenly spaced. Begin adding mass to the center of the grid...

Since they started this I have been somewhat amazed by the ability to not only launch but also peacefully get back a rocket intact and landing on it's vertical axis. I'll admit I haven't read a ton of material with regards to this so pardon if this has been asked already. To me it seems that...

HI all! Clearly a noob here. The title says it all. I can't seem to find anything. Thanks for any help, folks.

In Henley and Garcia's Subatomic Physics, they introduce phase space in chapter 10 by considering all the possible locations a particle can occupy in a plot of ##p_x \ vs. x##, ##p_x## being the momentum of the particle in the x direction. They next consider an area pL on this plot, and state...

In "The Geometry of Minkowski Space in Terms of Hyperbolic Angles" by Chung, L'yi, & Chung in the Journal of the Korean Physical Society, Vol. 55, No. 6, December 2009, pp. 2323-2327 , the authors define an angle ϑ between the respective inertial planes of two observers in Minkowski space with...

I'm often involved in projects where Dropbox is used to share documents, and members are invited in order to gain access to a folder established by one of the members (not me). I recently got a message that my Dropbox quota (2 GB) is us up. I don't sync anything locally, I only use the documents...

I'm reading about the geometry of spacetime in special relativity (ref. Core Principles of Special and General Relativity by Luscombe). Here's the relevant section: ----- Minkowski space is a four-dimensional vector space (with points in one-to-one correspondence with those of ##\mathbb{R}^4##)...

Hello All :) I am a student of mathematics, but I have only one semester of physics in college. I can't solve one with homework. Will there be anyone wise who can solve this? The task is as follows: Calculate: at what height the artificial satellite must move (orbit height): geostationary...

One proposal that I have read (but cannot re-find the source, sorry) was to identify a truth value for a proposition (event) with the collection of closed subspaces in which the event had a probability of 1. But as I understand it, a Hilbert space is a framework which, unless trivial, keeps...

I am surrounded by Space and so I am curious to know what the name of this Space is. Is this Space given any name by a Mathematician? I suspect that this Space may be called Euclidean Space because Euclidean Space knows how to present point in three-dimensions. Euclidean Space talks about...

Recently I asked a question about the curvature of the universe. https://www.physicsforums.com/threads/constant-curvature-and-about-its-meaning.977841/ In that context I want to ask something else. Is this curvature (##\kappa##) different than the Gaussian Curvature ? Like it seems that we...

So, I'm a little confused and I thought I might get some help here. I have just started learning about manifolds and its super confusing because I've always worked with Euclidean spaces, too much that I didn't even realize it's euclidean and that it has different properties from others. So my...

Metaphorical depictions of the universe in the shape of a 2-sphere are very common. Now, let's consider mapping the three dimensions of space onto the "surface" of a 3-sphere. Like Non-Euclidean de Sitter geometry. The surface of a sphere is positionally symmetrical. However, the positional...

Hello everybody, new here. Sorry in advance if I didn't follow a specific guideline to ask this. Anyways, I've got as a homework assignment two cannonical transformations (q,p)-->(Q,P). I have to obtain the hamiltonian of a harmonic oscillator, and then the new coordinates and the hamiltonian...

I am reading Stephen Willard: General Topology ... ... and am currently focused on Chapter 2: Topological Spaces and am currently focused on Section 3: Fundamental Concepts ... ... I need help in order to fully understand a result or formula given by Willard concerning a link between...

Summary:: I would like to get a career in commercial space technology and business and that is why i started my 2nd bachelors in aeronautics at the age of 30 three years early. I am about to complete my bachelors in aeronautical science from Embry riddles world wide. I don't know what next to...

Are there any elements found in space but not on Earth?

This exercise is located in the vector space chapter of my book that's why I am posting it here. Recently started with this kind of exercise, proof like exercises and I am a little bit lost Proof that given a, b, c real numbers, the set X = {(x, y) E R^2; ax + by <= c} ´is convex at R^2 the...

probably a daft question asked before, but. if space is expanding at an accelerating rate would that mean time is accelerating too?. after all Einstein* claims and the maths seems to say that space and time are the same thing, ie space-time. so if space is expanding faster and faster shouldn't...

I am reading Stephen Willard: General Topology ... ... and am currently reading Chapter 2: Topological Spaces and am currently focused on Section 1: Fundamental Concepts ... ... I need help in order to fully understand an aspect of the proof of Theorem 3.7 ... ..Theorem 3.7 and its proof...

Hi friends How exactly do we change the general equation of a line in space( given two intersecting planes) into the canonical form Thanks

In a discrete metric space open balls are either singleton sets or the whole space ... Is the situation the same for open sets or can there be sets of two, three ... elements ... ? If there can be two, three ... elements ... how would we prove that they exist ... ? Essentially, given the...

I am reading this book and in there the spacetime defined as a manifold such that an affine space of dimension 4. I am having trouble to understand the affine space. I made some reasearch but I couldn't grasp the idea of it. In the books its also stated that " We are familiar with the structure...

I read (in "The View From The Center") that Jupiter protects the Earth from collision with large space rocks, asteroids, etc. What I can't get out of my mind is that could it also cause collisions. A large rock (initially not heading for Earth) could be put on a different path by Jupiter's...

Now that gravitational waves are more famous because of LIGO, it got me to thinking about what we (lay people) are usually told would happen, which is that the Earth will continue in a straight line at a tangent to its orbit at that moment that information arrives eight minutes later. Which is...

hi guys our solid state professor sent us a work sheet that included this example : i solved it not sure its correct tho : is it that simple , or this is not the right approach for it ?

Hi I found this paper on the measurement of unknown velocity vector of a closed space. Does it mean that it is possible to measure the unknown velocity vector of a closed space ? Can someone explain it to me

Summary:: the set of arrays of real numbers (a11, a21, a12, a22), addition and scalar multiplication defined by ; determine whether the set is a vector space; associative law Question: determine whether the set is a vector space. The answer in the solution books I found online says that...

The ISS includes a very fancy running machine which astronauts use to maintain fitness. Several astronauts have run Marathons at the same time as the earthly race (London, Boston etc) and, while there have been many press reports of these runs, none has given any indication as to how hard it is...

I am including a link to a B level discussion of this I found on-line to try and anchor my question, not because I think the below article is good or poor - I am not able to assess that. https://www.einstein-online.info/en/spotlight/changing_places/#The_analogy In particular I am asking about...

Hey Could you give me a hint how to explain this example? Need help to prove statement in red frame. Example from book (Topics In Banach Space Integration) by Ye Guoju‏، Schwabik StefanThank you

Hello, I am after some help to try and understand SVM implementation is a micro that controls a motor. As I understand it one of the advantages of using space vector modulation over sinusoidal PWM modulation in motor control is that it can control the phase voltages such that the line-to-line...

Is it correct to say that: the cotangent is given by the gradients (*) to all the curves passing through a point and it actually spans the same tangent space to a point of a sphere? If you visualize them as geometric planes (**), the cotangent and the tangent spaces are more than isomorphic...

Hi With displacements, I KNOW that three orthogonal axes cover all of 3D Space. What about rotations? How do I KNOW that the Tait or Euler angles cover all orientations? For Tait, I would almost "expect" it. The object rotates about the local body axes in order of: one axis, then a second...

I was wondering if it would be possible to see the history of space if one was to stand at the edge of the universe as it expanded faster than the speed of light. If the universe was to be expanding faster than the speed of light right now, and I was able to somehow go there and keep up with it...

From Tong gravity notes pdf page 32 : We see from the picture that there are more ways to “go to infinity” in a null direction than in a timelike or spacelike direction. This is one of the characteristic features of Minkowski space. I read that also elsewhere. Why are there many null-like...

I am reading Tej Bahadur Singh: Elements of Topology, CRC Press, 2013 ... ... and am currently focused on Chapter 1, Section 1.2: Topological Spaces ... I need help in order to fully understand Singh's proof of Theorem 1.3.7 ... (using only the definitions and results Singh has established to...

Hi, The following is not a homework question. My question is: My answer is: Total pages required = 2^32/2^7 = 2^25 pages Thus page table has 2^25 entries PM = 2^16 Total page frames in PM = 2^16/2^ 7= 9 page frames Somebody please guide me what is the correct solution for the above. Zulfi.

I am reading Sasho Kalajdzievski's book: "An Illustrated Introduction to Topology and Homotopy" and am currently focused on Chapter 3: Topological Spaces: Definitions and Examples ... ... I need some help in order to fully understand Kalajdzievski's definition of a closed set in a...

I just love space rocks :biggrin: The latest addition to my meteorite collection NAME (LOCALITY): Huckitta, Huckitta cattle station, NT, Australia FALL DATE: Unknown, found 1924 (TKW 2300kg) CLASS: Pallasite, PMG-an WEIGHT g: 220.1g METEORITICAL BULLETIN: Never published in the...

If something happened 350 million years ago in space, are we just seeing it/ receiving the light now? From SpacePlace "The nearest large galaxy to us, Andromeda, is 2.5 million light-years away. So, we see Andromeda as it was 2.5 million years in the past." Wow!

If space is transparent how can we not view light from a black hole

In relativity, a flat space is always regraded to be endowed with an invariant metric field ##g_{\mu\nu}(x)= \eta_{\mu\nu}##, So in a flat space the corresponding connection ##\Gamma_{\mu\nu}^\rho(x)=0## It means that if we parallel transport a vector ##v^\nu(x_0)## in the space. Then it...

Space is space with the virtual absence of mass, with the presence of radiation and whatever stray particles that pass over it. From a scifi perspective space can be used for a type or even types of scifi propulsion.Since space is volume and the virtual absence of mass, any scifi drive that was...

Is a BSc in space science regarded as a valid/competitive degree? It looks like a relatively newer degree. I am currently in Space Science, which is a major in Pnysics with a focus on orbital mechanics and space mission management. Basically I am just looking for an industry outlook/opinion on...

Let me start by saying that my question will be somewhat vague by mathematical standards. I'm not a mathematician! I'm looking for some intuition about how defective matrices are distributed in the space of all matrices. I understand that they are rare and in some sense discontinuous - matrices...

How much brighter is the sun when seen from space than it is when viewed from Earth?

(scroll to bottom for problem statement) Hello, I am wondering if someone could break down the problem statement in simpler terms (not so math-y). I am struggling with understanding what is being asked. I will try to break it down to the best of my ability Problem statement:Consider the inner...

So, here's an attempted solution: With ##r_{min}##, $$r_{min} = \frac{1}{B + \frac{\beta}{\alpha^2}}$$ With ##r_{max}##, I get: $$r_{max} = \frac{1}{B - \frac{\beta}{\alpha^2}}$$ or $$r_{max} = \frac{1}{\frac{\beta}{\alpha^2}}$$ Other than this, I and the team have absolutely no idea on how...