Space Definition and 1000 Threads

I’ve read that the human brain capacity has 2.5 petabytes worth of memory storage. I have an excellent memory for details; even super obscure things that happened decades ago. I only have an average IQ but my recall is very good especially when my memory is jogged or if I had read something...

Finally spotted myself a space traveller, back from a relativistic tour. No one ever suspects the doctor's office is actually paying attention...

it's been 60 years since humanity entered space. What are your favorite things about space or hidden space history tidbits? mine is On the 12 April 1961, the first man in space, Yuri Gagarin asked the bus driver to stop on the route to the launchpad and urinated against the right-hand back tire...

I have one question I hope someone here can answer for me. Relativity theory tells us that space and time are sort of the same thing, as a spacetime. So when space is expanding, what happens to time? I find it hard to believe that time is somehow unaffected by the expansion of space, so while...

I have a question that is related to categories and physics. I was reading this paper by John Baez in which he describes a TQFT as a functor from the category nCob (n-dimensional cobordisms) to Vector spaces. https://arxiv.org/pdf/quant-ph/0404040.pdf. At the beginning of the paper @john baez...

I was thinking this past morning of the challenger explosion due to the stiff and cold failed O-rings in the fuel segments. I was trying to think of satellite failures, I couldn't find too much... Do you all know of satellite (components, instruments, etc) failures that occurred while in...

Hi all, thanks in advance for any constructive feedback. :bow: Definition: If ##x\in R^n\backslash \{0\}## then the map ##\Lambda## takes the point ##x## into ##\bar{x}\in R^n\backslash R^+_3## given by ##\bar{x}=\{x_1,x_2,-x_3\}## We take the reflected point ##\bar{x}## and the fundamental...

(1) I remember reading somewhere that in general relativity, "space" and "time" lose their metrical meanings. Is that true? And yet, we continue talking of space and time in general relativity as spacetime. (2) Moreover, as someone mentioned in this thread, what happens to the speed of light? In...

$ v=\left[\begin{array}{r} -3\\-4\\-5\\4\\-1 \end{array}\right] w=\left[\begin{array}{r} -2\\0 \\1 \\4 \\-1 \end{array}\right] x=\left[\begin{array}{r} 2\\3 \\4 \\-5 \\0 \end{array}\right] y=\left[\begin{array}{r} -2\\1 \\0 \\-2 \\7 \end{array}\right] z=\left[\begin{array}{r} -1\\0 \\2 \\-3...

We know about the Higg's field and boson, so what if gravity is the same. There has long been a dispute as to weather gravity is a field or a particle. Why can't it be like the Higg's boson.

Limited to "U.S. persons" as defined by ITAR. Jared Isaacman, an American businessman, bought a Crew Dragon trip to space: Inspiration4. Currently planned for October 2021 (which would make it the first private flight of Crew Dragon, and the first dedicated private flight to orbit ever), the...

I have been thinking and I thought of a design that may, theoretically result in spacecraft being able to have a self sufficient energy source on board. Here’s my theory, if you have a minimized nuclear reactor (if building something like this is even possible given that the nuclear reaction...

I wonder if anybody has an idea for a topology on the set of Lie algebras of a given finite dimension which is not defined via the structure constants. This condition is crucial, as I want to keep as many algebraic properties as possible, e.g. solvability, center, dimension. In the best case the...

"##\sigma . n X = 1*X##" to "##S. n| S. n; +\rangle = \frac{h}{4\pi}| S .n; +\rangle ##" X is a spinor n is any unitary vector sigma are the pauli matrices ##(\sigma 0, \sigma x,\sigma y,\sigma z)## S is the spin vector. It was claimed that both equations are equivalent, but i couldn't see why.

I have just finished reading The Order of Time by Carlo Rovelli and From Eternity to Here by Sean Carroll. I feel I finally understand that time is simply thermal entropy, but they both also talk about space-time and how time slows under gravity and at high speed. If time is just an illusion as...

Let ##n=\dim X## and ##m=\dim Y##. Define a basis for ##X: y_1,...,y_m,z_{m+1},...,z_n##. The first ##m## terms are a basis for ##Y##. The remaining ##n-m## terms are a basis for its complement w.r.t ##X##. Let's call it ##Z##. ##X## is the direct sum of ##Y## and ##Z##; denote it as ##X=Y+Z##...

I'm past middle age, and it seems I should have fewer questions about life and the universe than ever. I have more now. For some reason this past year or so I've been absolutely consumed with trying to grasp the immensity of the universe and distances. For whatever reason, I'm having more...

Summary:: Ideas for a novel I want to begin writing. Brainstorming ideas and need help with a certain concept. Any help is appreciated! Hello to you all, this is my first post, and I Google searched this astrophysics forum because I thought it might be a good place to begin asking for advice...

Hi, I'm new to PF and not really sure which forum may be the most appropriate to find people with an interest in probability and entropy. But the title of this forum looks promising. If you share an interest in this topic would be delighted to hear from you.

I have had enough with my Windows PC. I have decided to create a dual boot PC with Ubuntu 20.04 LTS. I am doing a dual-boot system because I need Windows for: Amazon prime video app MS office Here is a view of the partitions of the HDD: I have a lot of programs to install: MATLAB Android...

Summary:: Special relativity - 2 astronauts syncronize their clocks and moves in different paths at different velocities, which clocks is left behind? and why? Hi everyone, i have the following problem and I'm not understanding if my strategy to solve it is correct: Two astronauts synchronize...

There is this argument that any new forces of nature or any new interactions would have very small gap of space left in the experimental space or parameter. The argument being that for every force, there is a particle and a field, and virtual particles. And the virtual particles can affect...

Disclaimer - I am not an expert by any means so this might be as much about confirming my understanding as an inquiry from the general public... as such, it might be fairly conversational as I attempt to clearly communicate my thoughts and understanding. Please excuse this. If gravity is the...

What does 'intervals' mean here?

Hi, Question: How can I remove the extra spacing above the single-space equation environment. I have wrapped the equations in a single-space environment as the document has to be double spaced (and I wanted to save as much space as possible) From reading online, I have the following code at...

My hypothesis: A sequence with the gravitational waves detected, sent by modulating radio waves, could be received and used by other intelligent beings to find the corresponding sequence within their records and then compare it to calculate our spacetime position in relation to theirs. As...

Changes in the body that come from space travel resemble growing older, providing opportunities to perform aging studies on astronauts. https://www.nmn.com/news/how-does-space-travel-affect-natural-aging Any validity to this?

Solution 1. Based on my analysis, elements of ##V## is a map from the set of numbers ##\{1, 2, ..., n\}## to some say, real number (assuming ##F = \mathbb{R}##), so that an example element of ##F## is ##x(1)##. An example element of the vector space ##F^n## is ##(x_1, x_2, ..., x_n)##. From...

When orthogonal states of a quantum system is projected into subspaces A and B are A and B real spaces?

Hello, Throughout my undergrad I have gotten maybe too comfortable with using Dirac notation without much second thought, and I am feeling that now in grad school I am seeing some holes in my knowledge. The specific context where I am encountering this issue currently is in scattering theory...

This is a 3D model I made of the Mir space station.

I hope it's appropriate to post a picture of a battery operated model of the Space Shuttle Discovery which flew in the 1960's ; lights and sounds. I came across it at the antique mall. It's missing it's vertical stabilizer, but I can make that,

General relativity. Curvature of spacetime: ok. time dilation: ok. What about space? Curvature is intrinsic and given by complex equations. But could we definitely say is there more space between 2 points along curved space through the star than would be through flat space (no star there) or...

I have a dehumidifier (just one) that is placed indoors in the house in a "central" location (maybe not perfectly center, but close). Obviously, the local humidity around the machine will get sucked out of the air and turn to water. But, would the humidity in a different part of the house be...

I would appreciate if someone check my work: I tried to simplify the answer a lot: I imagined that, if we have this ds between two points different than the distance that should be if the space was flat, so it would be enough to generalize and say that space is not flat. So, using this...

I have solved the exercise, so I'm not giving the vectors explicitly. I just want to know if there is a quicker way than mine. We know that ##A## must have ##4## columns and ##4## lines, and we also know that its nullity is ##2##, thus its rank is ##2##. I took the simplest matrix that can have...

Apparently, if I have this down correctly, even the vacuum of outer space has a density, and thus matter in it. With that, I have a few questions: I think I know what happens when something moves in a vacuum at high speeds, namely around and at light speed. Now, for much slower speeds, I must...

The Hubble Telescope helped us to see how enormous the universe really is. We now know from data built up from that that the universe likely has 2 trillion galaxies in it. Now when James Webb gets out their and starts taking better pictures; I’m afraid the count of galaxies will jump to 10 or...

Be ##T_{1}, T_{2}## upper and lower matrix, respectivelly. Show that we haven't matrix ##M(NxN)## such that ##M(NxN) = T_{1}\bigoplus T_{2}## I am not sure if i get what the statement is talking about, can't we call ##T_{1},T_{2} = 0##? Where 0 is the matrix (NxN) with zeros on all its entries...

Homework Statement:: I'm working on a personal project to convert objects from a simulation using state vectors for position and velocity to Keplerian orbital elements (semimajor axis, eccentricity, argument of periapsis, etc.). However, the equations I am using do not calculate the...

Summary:: Problem interpreting a vector space of functions f such that f: S={1} -> R Hello, Another question related to Jim Hefferon' Linear Algebra free book. Before explaining what I don't understand, here is the problem : I have trouble understanding how the dimension of resulting space...

Summary:: Be the set X of vectors {x1,...,xn} belong to the vector space E. If this set X is convex, prove that all the convex combination of X yet belong to X. Where convex combination are the expression t1*x1 + t2*x2 + ... + tn*xn where t1,...,tn >= 0 and t1 + ... + tn = 1 I tried to suppose...

When parallel transporting a vector along a straight line on flat space, does the connection (when calculating the covariant derivative) always equal zero? Do things change at all when using an arbitrary connection, rather than Christoffel symbols?

Sean Carroll (in a video) claims that regions of empty space (vacuum) that are near each other must be highly entangled. He appears to argue that if they were not, there would be "a lot of energy contained there" which - my conclusion - would not be consistent with these regions being low energy...

How can I prove that Zp is a vector space if and only if p is prime

Hello, I am doing a vector space exercise involving functions using the free linear algebra book from Jim Hefferon (available for free at http://joshua.smcvt.edu/linearalgebra/book.pdf) and I have trouble with the author's solution for problem II.1.24 (a) of page 117, which goes like this ...

I was wondering if anyone knew of a name for such a set, namely a subset S \subseteq \mathbb{R}^n which at every point x \in S there exists no open subset U of \mathbb{R}^n containing x such that S \cap U is homeomorphic to either \mathbb{R}^m or the half-space \mathbb{H}^m = \{(y_1,...,y_m)...

Hello, i'm doing a project where the goal is to get the relative position of a space object to the earth, roughly. Basically, i want to say that this object is currently e.g. above New York. The data for any given space object that i have is (It's sourced from an NASA API). The specific...

The answer is 1.1 J, but I don't know how to get there. The only equation I can think of that might be related to this is Intensity, which I've added above. I could find area, using .0004m as the diameter, and energy using 2.0 E 46 J, but I get stuck on energy.

The NY Times, on the 20th anniversary (on Halloween) of the ISS being continuously occupies, published an article (with lots of pictures and a really cool time line) showing what the inside of the ISS is like. Duct tape on the ISS (didn't see any WD-40): Galley: Science stuff: