Space Definition and 1000 Threads

A thought experiment. Two rigid, concentric rings, joined together by a series of lightweight elastic radial spokes. These rings and a heavy mass are approaching each other, such that in the frame of the rings, the mass is traveling along the central, perpendicular axis and will pass through the...

It is obvious that there is a one-to-one relationship between real numbers (defined to include infinity) and their multiplicative inverses (assuming we map the inverse of zero to infinity and vice versa). Thus, one should be able to replace the distance between two points in space with it's...

Hi, I'm not a really mathematician...I've a doubt about the difference between a trivial example of fiber bundle and the cartesian product space. Consider the product space ## B \times F ## : from sources I read it is an example of trivial fiber bundle with ##B## as base space and ##F## the...

What does a helium balloon do on the ISS . most say, its a 0 g environment, but is it really the same as intercosmos travel "0g"? I saw a video of helium ballons on the vomit comet, where during the "0 g phase" the helium balloons went to the floor, while all other things floated. I would...

Hello, Can you please explain the analogy oft quoted to explain the concept of applied motion to objects in space, which goes as follows : 1. You are standing on a skateboard or sitting in a boat floating on the water, holding a bowling ball. 2. You throw the bowling ball towards the back of...

Quantum fields have wave functions that determine a particle position in space. It solves non-locality, double-slit paradox, tunnel effect, etc. What if the wave function is also in time? Won't it solve the breaking of causality at quantum level? (Delayed Choice/Quantum Eraser/Time) Not much...

So we had an exam question which was the following: Assume you have N identical balls and K different contains if there are N pre-Selected boxes and that N < k what is the probablity that none of these pre-selected boxes are empty? I answered it and it was the same as the professor's answer...

Imagine a 400-meter-long pipe with a 1600-meter diameter, floating in inter-planetary space. It is spinning at 0.5 gravity along its major axis and there are no secondary-axes spins. We need to increase rotation to 0.85 g. Its density is a uniform 2.3 kg/m³ and it weighs 49,120,056 kg. Thanks to...

TLDR I have no idea what I am talking about . Read this if you're bored. I now realize I may have the wrong category. Please let me know what category would be best for my question. Thanks. Can energy be stored in space itself? With the equation e = mc^2 if we set the constant to c=1...

So I had a topic which I would like to fact check from an informed scientific source. Basically there is an argument about whether or not an object that naturally exists in a fourth dimensional space, would by default have more than countably infinite times the energy of a 3 dimensional Object...

Would it be possible for photons to form some sort of static structure, like a standing waveform, if space-time was curved enough? It seems like a structure like this exists around black holes. Is there any other distortion or phenomenon that could cause this, such as a neutron star or a galaxy?

First time poster here, and I need some experts to weigh in on a debate that I'm having on the Skeptics Guide to the Universe forum, here (https://sguforums.com/index.php/topic,51110.0/topicseen.html ). In my opinion, a few of the other posters are being pessimistic. Given recent advances in...

Basically how do we know that since it is not possible to see the 4th dimension, is it for simplicity ?

Thanks for being here, this is my first post. Imagine on a dark night a very powerful beam of light was aimed at the sun from earth and switched on, at 23:00. I am observing from side on, in space, at a distance far enough away to get a good view of the beam as it travels out into space on its...

Hi, I am writing a report on uniqueness theorems and I am at the section for non asymptotically flat spacetime. I know that if we request certain restrictions, there are the existence of certain uniqueness theorems, however for the most part there are (so far) not many and they are hard to find...

The best story from space I remember is how NASA spent a huge pile of money trying to get a pen to work in so little to no gravity in space. They worked and worked away and the Soviets found the solution: using a pencil.

According to QFT or Quantum Gravitation Theory space and time are discrete or continuous?

All the white space among words in a text file was lost. Write a C++ program which using dynamic programming to get all of the possible original text files (i.e. with white spaces between words) and rank them in order of likelihood with the best possible runtime. You have a text file of...

Can the low temperatures in Space be employed to cool a Quantum computer installed on an operational Space vessel doing away with the need of a super fridge or whatever they use here on Earth? Thank you.

Homework Statement Problem given to me for an assignment in a math course. Haven't learned about roots of unity at all though. Finding this problem super tricky any help would be appreciated. Screenshot of problem below. [/B] Homework Equations Unsure of relevant equations The Attempt at...

I am reading the book: Multivariable Mathematics by Theodore Shifrin ... and am focused on Chapter 8, Section 2, Differential Forms ... I need some help in order to fully understand the vector space of alternating multilinear functions ... The relevant text from Shifrin reads as follows: In...

I keep hearing in these Science Channel programs that the reason why the Big Bang banged (instead of immediately collapsing into a black hole) is that when it banged it made space to expand faster than the speed of light. I'm always puzzled on how sure and certain the speakers look in these...

When a rocket engine exhausts into Space what happens to the particles or molecules that are thrown out? My interest is firstly where do they go e.g.: orbit the Earth or other planetary body if from a shuttle, orbit the Sun if ejected outside the capturing influence of a planetary body, or just...

Hi everyone. I'd like to verify my thoughts about travellig through space using a space curvature. Imagine you have a spaceship and you want to travel some distance. Your ship launches an object into space that has huge mass and density. It curves space. Now, you enter the curved space and...

Hi PF Given some linear differential operator ##L##, I'm trying to solve the eigenvalue problem ##L(u) = \lambda u##. Given basis functions, call them ##\phi_i##, I use a variational procedure and the Ritz method to approximate ##\lambda## via the associated weak formulation $$\langle...

Hello everyone! I am an undergraduate getting three bachelors in Anthropology/Ecology/Neurosciences (just to show off of course), but sadly no true physics (I don't show off that much, I'm still humble). I am working on a personal project, a tabletop role playing game, where my main struggle is...

Did a quick search of an explosion in a vacuum and got most of what I was looking for, but on CBS Sunday morning they had a segment on restoring and reevaluating all of the immense footage of America's atmospheric nuclear testing program. They showed some amazing footage of the expansion of the...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 12: Multilinear Algebra ... ... I need some help in order to fully understand the proof of Theorem 12.22 on page 276 ... ...The relevant text reads as follows: In the above...

Our 4-D space is ##x^1,x^2,x^3 ,t##. Our sub-manifold is defined by ##(x^1,x^2,x^3)## Therefore for this sub-manifold to be maximally symmetric and for which the tangent vector ##\frac{∂}{∂t}(\hat t)## orthogonal to this sub-manifold The metric becomes...

{Moderator's note: Moved to Cosmology forum.] Dark matter and the fabric of space time, Can someone with a real knowledge base of physics and the current accepted theories, please explain why the fabric of space is not the candidate for the elusive dark matter? Having read extensively about...

Greetings: I watched several videos describing so-called "empty space" as being permeated with fields (electron field, quark field, etc.). Is it possible that it is actually these fields that curve about large masses and that the trajectory of light and matter curve because they follow the...

From the geodesic equation d2xμ/dΓ2+Γμ00(dt/dΓ)2=0,for non-relativistic case ,where Γ is the proper time and vi<<c implying dxi/dΓ<<dt/dΓ. Now if we assume that the metric tensor doesn't evolve with time (e,g gij≠f(t) ) then Γμ00=-1/2gμs∂g00/∂xs. If we here assume that the metric components of...

Homework Statement In the far future, humans have built a space elevator as a cheap means of access to space. However before that could be done, a few basic principles had to be worked out. . . a) What is the minimum initial speed (in an Earth-centered inertial reference frame) needed for an...

Hey, i can't see actual space in tesseract. Like in 3 dimensional cube, you have squares as faces and between them there is a space. But in tesseract where you have 8 cubes as faces, this leaves 0 space for actual space inside, i can see only 8 faces and nothing between them. I first thought it...

Why couldn't the space shuttle slow down in space and eliminate the dangerous temps during reentry?

Just a random thought: IF a strong rare Earth magnet and a superconductor like YBCO can perform meissner effect that holds them both in place, is it possible to make that in a larger scale, like in space? I was thinking that since space's temperature is almost 0K, it can cool down...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 12: Multilinear Algebra and am specifically focused on Section 12.1: Vectors and Tensors ... I need help in fully understanding Corollary 12.4 to Theorem 12.2 ... ... Theorem...

Hey! :o Let $S_{X,3}$ be the vector space of cubic spline functions on $[-1,1]$ in respect to the points $$X=\left \{x_0=-1, x_1=-\frac{1}{2}, x_2=0, x_3=\frac{1}{2}, x_4\right \}$$ I want to check if the function $$f(x)=\left ||x|^3-\left |x+\frac{1}{3}\right |^3\right |$$ is in $S_{X,3}$...

Let $$\left[\begin{array}{rrrrrrr} 1 & 0 & -1 & 0 & 1 & 0 & 3\\ 0 & 1 & 0 & 0 & 1 & 0 & 1\\ 0 & 0 & 0 & 1 & 4 & 0 & 2\\ 0 & 0 & 0 & 0 & 0 & 1 & 3 \end{array}\right]$$ Find a basis for the null space of A, the dimension of the null space of A, and...

I am reading Loring W.Tu's book: "An Introduction to Manifolds" (Second Edition) ... I need help in order to fully understand Tu's section on the dual space ... ... In his section on the dual space, Tu writes the following: In the above text from Tu, just preliminary to Proposition 3.1 Tu...

I am reading the book: Multivariable Mathematics by Theodore Shifrin ... and am focused on Chapter 8, Section 2, Differential Forms ... I need some help in order to fully understand some statements of Shifrin at the start of Chapter 8, Section 2 on the dual space ... The relevant text from...

Hi Physics Forums community. Let me briefly explain my current state of affairs. Next season, if every goes as planned, I will begin my Master's in Physics. I have, what I call, a positive problem; I like lots of branches of Physics (I study Physics because of pure passion and not because I...

I have a question regarding the nature of 2-forms (indeed k-forms ... but I'll focus the question on two forms ... ) ... Defining 2-forms and the space $$ {\bigwedge}^2 ( \mathbb{R}^3 )$$ , Jon Fortney in his book: A Visual Introduction to Differential Forms and Calculus on Manifolds, writes the...

Hi all. I have a question about something Nima Arkani-Hamed said in his lecture on space-time about space contraction near light speed. I included a link to the lecture at the point where he refers to contraction of two space ships with a 'cable' between them, they are accelerating towards the...

this is what is given so by addition $$\begin{bmatrix}x_1\\y_1\\5z_1\end{bmatrix} \oplus \begin{bmatrix} x_2\\y_2\\5z_2 \end{bmatrix} = \begin{bmatrix} x_1+x_2\\y_1+y_2\\5z_1+5z_2 \end{bmatrix} = \begin{bmatrix} X\\Y\\10Z \end{bmatrix}$$ uhmmmm really?

Determine if the set of vectors $\begin{bmatrix} x\\y\\3x+2y \end{bmatrix}$ $\in \Bbb{R}^3$ form a vector space (with the usual addition and scalar multiplication for vectors in $\Bbb{R}^3$).OK first of all this doesn't have z in it. So I don't know if this meets the requirement of...

On the set of vectors $\begin{bmatrix} x_1 \\ y_1 \end{bmatrix}\in \Bbb{R}^2 $ with $x_1 \in \Bbb{R}$, and $y_1$ in $\Bbb{R}^{+}$ (meaning $y_1 >0$) define an addition by $$\begin{bmatrix} x_1 \\ y_1 \end{bmatrix} \oplus \begin{bmatrix} x_2 \\ y_2 \end{bmatrix} = \begin{bmatrix} x_1 + x_2 \\...

I've always wondered how we came to come up with such an idea. Was he one day sitting around and thinking, then made a random assumption and go "ah hah!". Or did his idea come up through his calculations on the nature of how gravity should cause interaction? Is their a literal fabric of space...

Would an astronaut really bale able to make it back to the space station by throwing a wrench in the opposite direction if his cable broke and floated away? I heard this question as it relates to Newton's third law. Wouldn't the astronaut need to throw the wrench faster than he is moving before...

Just read somewhere that we have left some 500,000 pieces of debris orbiting around earth. Some probably are near enough to touch a little atmosphere so it is reasonable to expect they will fall eventually. But what about the ones a little further? Will they never return to earth?