What is Space: Definition and 1000 Discussions

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. D

    Phase space of a harmonic oscillator and a pendulum

    Hello everybody, new here. Sorry in advance if I didn't follow a specific guideline to ask this. Anyways, I've got as a homework assignment two cannonical transformations (q,p)-->(Q,P). I have to obtain the hamiltonian of a harmonic oscillator, and then the new coordinates and the hamiltonian...
  2. Math Amateur

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

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  3. A

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

    Summary:: I would like to get a career in commercial space technology and business and that is why i started my 2nd bachelors in aeronautics at the age of 30 three years early. I am about to complete my bachelors in aeronautical science from Embry riddles world wide. I don't know what next to...
  4. 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?
  5. 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...
  6. HEXiT

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

    probably a daft question asked before, but. if space is expanding at an accelerating rate would that mean time is accelerating too?. after all Einstein* claims and the maths seems to say that space and time are the same thing, ie space-time. so if space is expanding faster and faster shouldn't...
  7. Math Amateur

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

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  8. 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
  9. Math Amateur

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

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  10. Arman777

    I Affine Space: Understanding the Difference from Ordinary Space

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  11. O

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

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  12. bland

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

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  13. patric44

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

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  14. W

    B Measurement of an unknown velocity vector of a closed space

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  15. V

    Determining whether a set is a vector space

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  16. F

    I Running on the Space Station compared with running on Earth

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  17. Grinkle

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

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  18. S

    MHB Understanding Example from Topics in Banach Space Integration

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  19. D

    Space vector modulation, motor control, implementation question

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  20. G

    I Visualizing the cotangent space to a sphere

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  21. T

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

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  22. ramim

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

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  23. 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...
  24. Math Amateur

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

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  25. Z

    Paging, Virtual Address Space and Physical Memory and Page Frames

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  26. Math Amateur

    I Closed Subsets in a Toplogical space ....

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  27. davenn

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  28. TaurusSteve

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  29. 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
  30. 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...
  31. B

    Exploring the Potential of Space as Propulsion in SciFi

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  32. CrunchBerries

    Physics Employment Prospects of a BSc in Space Science

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  33. 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...
  34. 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?
  35. cookiemnstr510510

    Understanding inner product space and matrix representations of Operat

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  36. Athenian

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

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  37. jk22

    Destiny: space does not exist, only time and a suite of commands?

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  38. mnb96

    I Question on tangent space and jet spaces

    Hello, I am reading some material related to jet spaces, which at first glance seem to be a generalization of the concept of tangent space. I am confused about what is the correct definition of a jet space. In particular, given a map ##f: X \rightarrow Y## between two manifolds, what is the...
  39. Athenian

    [SR] - Test Particle inside the Sun's Gravitational Field - Part 3

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  40. K

    I Questions about the expansion of space on galactic scales

    How would the expansion on a scale of 10 kpc be measured, by a red or blue shift? How can expansion of space be differentiated from the velocity of stars? It seems that the expansion of space weakens the effects of gravity?
  41. Shahi

    Unraveling Landau's Mechanics: Why is Space Isotropic?

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  42. Athenian

    [SR] - Test Particle inside the Sun's Gravitational Field - Part 2

    To begin with, I posted this thread ahead of time simply because I thought it may provide me some insight on how to solve for another problem that I have previously posted here: https://www.physicsforums.com/threads/special-relativity-test-particle-inside-suns-gravitational-field.983171/unread...
  43. Athenian

    [Special Relativity] Test Particle Inside the Sun's Gravitational Field

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  44. G

    B Understanding Dual Space: Mapping Vector Space to Real Numbers

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  45. johnconner

    I Transformation matrix for an expanding space

    Hello. I am confused with this matter that how should we write the transformation matrix for an expanding space. consider a spacetime that is expading with a constant rate of a. now normally we scale the coordinates for expansion which makes the transformation matrix like this: \begin{pmatrix}...
  46. J

    Job Skills Miltary to Space Industry Career Advice Needed

    Everyone, this post is going on multiple forums/subreddits so I can get diverse feedback. Pardon the spam if you see it elsewhere: I am retiring from the military in three years from a non-technical specialty. I have a bachelors in management. I will be 45 when I depart. I will have a security...
  47. B

    Temperature inside an enclosed space

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  48. B

    How Long Would Scifi Space Travel Really Take?

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  49. phinds

    The first British woman to space is a <can't say>

    Sigh ... Best statement "... although aliens may not be made up of carbon and nitrogen like humans "it's possible they're here right now and we simply can't see them". " https://www.bbc.com/news/uk-51003374
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