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. M

    Medical Memory: Do some people have more “space” or just better retrieval?

    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...
  2. DaveC426913

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  3. nduka-san

    What quirky tradition do astronauts have before launching into space?

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  4. AlfSalte

    B What happens to time as space is expanding?

    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...
  5. snypehype46

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

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  6. Tone L

    Satellite Failure: Environmental Causes & Triggers

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  7. D

    Poisson's Formula for the half space

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  8. brotherbobby

    I General Relativity: Exploring Space & Time

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  9. karush

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

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  10. snypehype46

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

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  11. CallMeDirac

    B Theory about gravitons and space warping

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  12. mfb

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  13. I

    Using a minimized nuclear reactor for further space travel

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  14. Pouramat

    Energy-Momentum Tensor for Electromagnetism in curved space

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  15. F

    A Topology on a space of Lie algebras

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  16. 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.
  17. thegroundhog

    I Space - time and the illusion of time

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  18. Eclair_de_XII

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  19. P

    Stargazing Can distance in space be measured by human systems?

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  20. K

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  21. L

    A Probability and entropy in an exponentially increasing sample space

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  22. 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...
  23. M

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

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  24. T

    Time dilatation between straight and curved lines in Minkowsi space

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  25. J

    I Constrains on experimental space and parameters

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  26. C

    I Gravity: Compounded Space (Time) Signal?

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  27. sahilmm15

    B Length is the measure of intervals in space?

    What does 'intervals' mean here?
  28. 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...
  29. Eumeme

    B Gravitational Wave System and Locations

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  30. 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?
  31. 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...
  32. 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?
  33. 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...
  34. 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.
  35. 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,
  36. Martian2020

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

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  37. 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...
  38. 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...
  39. 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...
  40. S

    B Question about things moving through outer space

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  41. 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...
  42. LCSphysicist

    Not sure about this statement in vector space and matrix

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  43. S

    Converting State Vectors to Keplerian Orbital Elements for Binary Objects

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  44. F

    Vector space of functions from finite set to real numbers

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  45. LCSphysicist

    Prove a theorem about a vector space and convex sets

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  46. 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?
  47. 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...
  48. T

    MHB Proving Zp is a Vector Space for Prime p

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  49. F

    I Proving linear independence of two functions in a vector space

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  50. D

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

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