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.

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  1. B

    Question about the permitivity of free space (from OCR paper)

    the answer is 2.16*10^-11 what i don' t understand about the question is why did they not use the constant Eo 8.85418782 × 10-12 in this case as there is a insulator occupying the area inbetween does that mean then their is no free space ?? Also in this equation the variable A is the area of...
  2. G

    Could Boarding Action in Space be a Reasonable Strategy for Capturing a Ship?

    Yes i know, with realistic space travel it is quite a stunt at best. However i wonder about a situation, when they really want to capture someone alive, and they can take a similar course disguised as a civilan cargo ship. My question is, could it be reasonable, that the attackers need to leave...
  3. T

    I Exploring the Dimension of Space: The Beauty of Cosmology and Unsolved Mysteries

    Motivated by some apparently intractible unsolved problems, I see cosmology as a beautiful mathematical description of a strongly flawed paradigm. This forum wisely does not allow laying out alternate paradigms, so I try to ask questions to guide my immature understanding , in the spirit of...
  4. Greg Bernhardt

    Excited to go to Brian Cox's "ADVENTURES IN SPACE & TIME" tonight

    Tonight I'm taking my wife and parents to Brian Cox's World Tour "ADVENTURES IN SPACE & TIME" with sidekick Robin Ince. All his European stops sold out and so far all of his US stops have been close to selling out. I've been impressed because he's not quite the household name Neil deGrasse Tyson...
  5. L

    I Does Curving Space by an Approaching Mass Do Work?

    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...
  6. J

    B How physics equations transform under inverse of parameters

    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...
  7. cianfa72

    I Product Space vs Fiber Bundle: Understanding the Difference

    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...
  8. Z

    What does a helium balloon do on the ISS vs in open space?

    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...
  9. G

    Understanding forced motion in space

    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...
  10. Silvio Macedo

    I Wave function of particle / quantum field in space, also in time?

    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...
  11. Biker

    Equiprobable sample space: N Identical objects in K different containers

    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...
  12. N

    How would we increase the rotation rate of very large structures in deep space?

    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...
  13. C

    Can Space Itself Store Energy?

    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...
  14. Ryu

    Theoretical Higher spatial dimensions question

    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...
  15. TerranIV

    I Photon Patterns in Space: Could They Exist?

    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?
  16. HammerAndChisel

    Could the kinetic energy of space junk be recycled?

    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...
  17. jk22

    B Why is time orthogonal to space?

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

    Light Beam fired 1 AU into space

    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...
  19. M

    I Uniqueness Theorems in Non-Flat Spacetime

    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...
  20. almostvoid

    Trying to get a pen to work in so little to no gravity in space

    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.
  21. P

    I Space is discrete or continuous?

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

    Dynamic Programming - Restoring white space between words in a file

    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...
  23. H

    B Taking Quantum Computers into Space

    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.
  24. U

    Vector space has dimension less than d

    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...
  25. Math Amateur

    I Vector Space of Alternating Multilinear Functions ....

    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...
  26. F

    B Did anyone actually see the space moving faster than light?

    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...
  27. H

    Rocket debris thrown into Space

    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...
  28. Papo1111

    B Traveling using space curvature

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  29. M

    A Basis functions and spanning a solution space

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  30. H

    Explore a Peculiar Hollow Earth World: Gravity Possibilities

    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...
  31. T

    Nuclear Explosion in Space… How would it work?

    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...
  32. Math Amateur

    I Space of Alternating Tensors of Rank r.... (Browder, 12.22)

    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...
  33. A

    I How Does the Metric of a 4-D Spacetime Define Its Symmetry and Expansion?

    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...
  34. M

    A Dark matter and the fabric of space time,

    {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...
  35. N

    I Space-time curvature and the fabric of space

    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...
  36. A

    I Perturbation to Flat Space Metric: Geodesic Equation

    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...
  37. R

    Space elevator minimum initial speed

    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...
  38. E

    A Where is the actual space inside a tesseract?

    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...
  39. Z

    Why couldn't the space shuttle slow down in space?

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

    I Space docking using the Meissner effect

    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...
  41. Math Amateur

    MHB The Dual Space and Covectors .... Browdwer, Theorem 12.2 and Corollaries ....

    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...
  42. M

    MHB Is f in the vector space of cubic spline functions?

    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 $S_{X,3}$...
  43. karush

    MHB Null Space of A: Find Rank & Dim.

    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...
  44. Math Amateur

    MHB Dual Space .... Loring Tu, Section 3.1, page 19 .... ....

    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...
  45. Math Amateur

    MHB The Dual Space and Differential Forms .... ....

    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...
  46. JD_PM

    Physics Essential skills for applying for Space Agency jobs as a physicist

    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...
  47. Math Amateur

    MHB The Space of 2-Forms .... Fortney, Darling and Weintraub ....

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  48. DarkMattrHole

    I Question about the limits of space contraction near light speed

    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...
  49. karush

    MHB Set of vectors form a vector space

    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?
  50. karush

    MHB Determine vec {{x},{y},{3x+2y}} in R^3 form a vec space

    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...
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