Space Definition and 1000 Threads

Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.
Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the Timaeus of Plato, or Socrates in his reflections on what the Greeks called khôra (i.e. "space"), or in the Physics of Aristotle (Book IV, Delta) in the definition of topos (i.e. place), or in the later "geometrical conception of place" as "space qua extension" in the Discourse on Place (Qawl fi al-Makan) of the 11th-century Arab polymath Alhazen. Many of these classical philosophical questions were discussed in the Renaissance and then reformulated in the 17th century, particularly during the early development of classical mechanics. In Isaac Newton's view, space was absolute—in the sense that it existed permanently and independently of whether there was any matter in the space. Other natural philosophers, notably Gottfried Leibniz, thought instead that space was in fact a collection of relations between objects, given by their distance and direction from one another. In the 18th century, the philosopher and theologian George Berkeley attempted to refute the "visibility of spatial depth" in his Essay Towards a New Theory of Vision. Later, the metaphysician Immanuel Kant said that the concepts of space and time are not empirical ones derived from experiences of the outside world—they are elements of an already given systematic framework that humans possess and use to structure all experiences. Kant referred to the experience of "space" in his Critique of Pure Reason as being a subjective "pure a priori form of intuition".
In the 19th and 20th centuries mathematicians began to examine geometries that are non-Euclidean, in which space is conceived as curved, rather than flat. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space.

View More On Wikipedia.org
  1. snypehype46

    I Functor between the category of Hilbert Space and the category of sets

    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...
  2. Tone L

    Satellite Failure: Environmental Causes & Triggers

    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...
  3. docnet

    Poisson's Formula for the half space

    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...
  4. brotherbobby

    I General Relativity: Exploring Space & Time

    (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...
  5. karush

    MHB Matrices.......whose null space consists all linear combinations

    $ 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...
  6. snypehype46

    I Help with a paper on semiclassical strings in anti-desitter space

    Hi, I was given the task to read this paper https://arxiv.org/abs/hep-th/0204051 entitled "A semi-classical limit of the gauge/string correspondence" by Polyakov. On page 7 of this paper it is mentioned that the maximal radial coordinate of the string is p0 and that the string is constrained by...
  7. CallMeDirac

    B Theory about gravitons and space warping

    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.
  8. mfb

    Inspiration4: Raffle for a trip to space (US only)

    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...
  9. I

    Using a minimized nuclear reactor for further space travel

    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...
  10. Pouramat

    Energy-Momentum Tensor for Electromagnetism in curved space

    a) I'd separated the Lagrangian into: $$ \mathcal L = \mathcal L_{Max}+\mathcal L_{int} $$ in which ##\mathcal L_{Max} =\frac{-1}{4}\sqrt{-g} F^{\mu \nu}F_{\mu \nu}## and ##\mathcal L_{int} =\sqrt{-g} A_\mu J^\mu## Thus: $$ T^{\mu \nu}_{Max}= F^{\mu...
  11. F

    A Topology on a space of Lie algebras

    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...
  12. LCSphysicist

    From spinor to ket space: Equivalents eigen equations

    "##\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.
  13. thegroundhog

    I Space - time and the illusion of time

    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...
  14. Eclair_de_XII

    Cartesian sum of subspace and quotient space isomorphic to whole space

    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##...
  15. P

    Stargazing Can distance in space be measured by human systems?

    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...
  16. K

    Ideas for novel I'm writing I would love some insight on a concept

    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...
  17. L

    A Probability and entropy in an exponentially increasing sample space

    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.
  18. Wrichik Basu

    How should I distribute space among different partitions in Ubuntu?

    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...
  19. M

    Engineering Converting a series connected transfer function to the state space model

    Hi, I have a question about a homework problem: I am not sure why I do not seem to get the same answers when using different methods. Question: Given transfer functions G(s) = \frac{s - 1}{s + 4} and C(s) = \frac{1}{s - 1} , find the state space models for those systems. Then find the...
  20. T

    Time dilatation between straight and curved lines in Minkowsi space

    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...
  21. J

    I Constrains on experimental space and parameters

    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...
  22. C

    I Gravity: Compounded Space (Time) Signal?

    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...
  23. sahilmm15

    B Length is the measure of intervals in space?

    What does 'intervals' mean here?
  24. M

    LaTeX How to decrease spacing before single space environment in LaTeX?

    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...
  25. Eumeme

    B Gravitational Wave System and Locations

    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...
  26. R

    How Does Space Travel Affect Natural Aging?

    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?
  27. S

    How Do Vector Spaces of Linear Maps Differ from Standard Vector Spaces?

    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...
  28. J

    B Are subspaces of Hilbert space real?

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

    I Completeness relations in a tensor product Hilbert space

    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...
  30. E

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

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

    How to Make a Vertical Stabilizer for a Model Space Shuttle Discovery

    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,
  32. Martian2020

    B General Relativity and the curvature of space: more space or less than flat?

    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...
  33. kyphysics

    I Does Humidity "Disperse" and "Even Out" in Enclosed Space?

    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...
  34. LCSphysicist

    Is this a curved or flat space?

    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...
  35. archaic

    Finding a matrix from a given null space

    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...
  36. S

    B Question about things moving through outer space

    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...
  37. M

    B Nervous about James Webb Space Telescope?

    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...
  38. LCSphysicist

    Not sure about this statement in vector space and matrix

    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...
  39. S

    Converting State Vectors to Keplerian Orbital Elements for Binary Objects

    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...
  40. F

    Vector space of functions from finite set to real numbers

    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...
  41. LCSphysicist

    Prove a theorem about a vector space and convex sets

    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...
  42. steve1763

    I Parallel transport on flat space

    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?
  43. E

    I Entanglement and Regions of Space in Vacuum

    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...
  44. T

    MHB Proving Zp is a Vector Space for Prime p

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

    I Proving linear independence of two functions in a vector space

    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 ...
  46. D

    A Name for a subset of real space being nowhere a manifold with boundary

    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)...
  47. Py3_3

    I Determining Relative Position of Space Object to Earth

    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...
  48. cestlavie

    How much energy would enter your pupils from an explosion in space?

    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.
  49. BillTre

    The International Space Station as a Human Abode

    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:
  50. L

    A Integrability along a Hilbert space?

    Suppose we have an infinite dimensional Hilbert-like space but that is incomplete, such as if a subspace isomorphic to ##\mathbb{R}## had countably many discontinuities and we extended it to an isomorphism of ##\mathbb{R}^{\infty}##. Is there a measure of integrating along any closed subset of...
Back
Top