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

    I Possible webpage title: Is There an Upper Limit to the Size of a Black Hole?

    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...
  2. A

    SpaceX Space X reusable rocket landing

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  3. fascinated

    Stargazing Does anyone know where Earth's gravity stops and space begins?

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

    I What happened to the spatial degrees of freedom for the second particle?

    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...
  5. nomadreid

    I Hyperbolic Geom of Minkowski Space: Chung et al. 2009

    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...
  6. T

    Does Deleting Files in a Shared Dropbox Folder Affect Other Users?

    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...
  7. S

    B Why is "time orthogonal to space" in inertial reference frames?

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  8. F

    Earth's satellite and its first space speed

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  9. nomadreid

    I Quantum logic based on closed Hilbert space subspaces

    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...
  10. pairofstrings

    Mathematical Name of this Space

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  11. Arman777

    I Curvature of Space in the Context of Cosmology

    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...
  12. TheDS1337

    How would you define a mathematical space?

    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...
  13. G

    I Possible illogicalness of a 3-sphere shape of the Universe's space?

    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...
  14. D

    Phase space of a harmonic oscillator and a pendulum

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  15. Math Amateur

    I Interior and Closure in a Topological Space .... .... remark by Willard

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  16. A

    Bachelor of Science for a career in commercial space technology and business

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  17. Z

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

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

    I Proving Convexity of the Set X = {(x, y) E R^2; ax + by <= c} in R^2

    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...
  19. HEXiT

    B Space + time = space time? then....

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  20. Math Amateur

    I Closure in a Topological Space .... Willard, Theorem 3.7 .... ....

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  21. A

    I How to find the canonical form of a straight line equation in space?

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

    MHB Open Sets in a Discrete Metric Space .... ....

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  23. Arman777

    I Affine Space: Understanding the Difference from Ordinary Space

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  24. O

    I How does Jupiter protect the Earth from collision with space rocks?

    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...
  25. bland

    I How Elastic is Space (Spacetime)? | LIGO & Gravitational Waves

    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...
  26. patric44

    Number of k-cells for a 1D lattice in reciprocal space

    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 ?
  27. W

    B Measurement of an unknown velocity vector of a closed space

    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
  28. V

    Determining whether a set is a vector space

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  29. F

    I Running on the Space Station compared with running on Earth

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  30. Grinkle

    B Meaning of Time / Space axes swapping (for Time)

    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...
  31. S

    MHB Understanding Example from Topics in Banach Space Integration

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  32. D

    Space vector modulation, motor control, implementation question

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  33. G

    I Visualizing the cotangent space to a sphere

    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...
  34. T

    A Are Tait and Euler angles a complete parametrization of 3D space?

    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...
  35. ramim

    B Is it possible to see the history of space if it expands faster than light?

    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...
  36. P

    I What are the many null-infinities in Minkowskian space?

    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...
  37. Math Amateur

    I Limit Points & Closure in a Topological Space .... Singh, Theorem 1.3.7

    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...
  38. Z

    Paging, Virtual Address Space and Physical Memory and Page Frames

    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.
  39. Math Amateur

    I Closed Subsets in a Toplogical space ....

    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...
  40. davenn

    I A new space rock to my collection

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  41. TaurusSteve

    Stargazing So If Something Happened In Space, Say 350 Million Years Ago....

    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!
  42. H

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

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

    I Is Zero Curvature Space Equivalent to Flat Space in General Relativity?

    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...
  44. B

    Exploring the Potential of Space as Propulsion in SciFi

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  45. CrunchBerries

    Physics Employment Prospects of a BSc in Space Science

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  46. M

    I Properties of Defective Matrices in Space?

    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...
  47. E

    Stargazing How much brighter is the Sun when viewed from space?

    How much brighter is the sun when seen from space than it is when viewed from Earth?
  48. cookiemnstr510510

    Understanding inner product space and matrix representations of Operat

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  49. Athenian

    [SR] - Test Particle inside the Sun's Gravitational Field - Part 4

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