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. R

    Space Travel with balloon assist

    Near space travels with balloons. http://edition.cnn.com/2015/03/05/tech/balloons-fly-edge-of-space/index.html look at above link. balloons goes just 36 km above Earth surface. but Earth orbit is 100 km away. so my thinking is if we pump oxygen outside near helium balloon artificially when u...
  2. ISamson

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  3. Drakkith

    Does the Null Space of a 2x3 Matrix Determine its Column Space?

    Homework Statement Let ##A## be a 2x3 matrix. If Nul(##A##) is a line through the origin in ℝ3, then Col(##A##) = ℝ2. Explain why. Hint: Think about the number of pivots in ##A##. Homework EquationsThe Attempt at a Solution So, Nul(##A##) is the set of all solutions to the equation ##Ax=0##...
  4. S

    I Generating a Hilbert space representation of a wavefunction

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  5. Poetria

    Tension Ratio in a Uniformly Distributed Rope System

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  6. R

    B 2 clocks -- Using orthogonal light path detectors in a space ship

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  7. S

    What is 'phase space in chaos theory and nonlinear dynamics?

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  8. S

    No sublimation for human body in vacuum? [Thermodynamics]

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  9. S

    I What is the difference between phase space and state-space?

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  10. weezy

    I Explore Homogeneity of Space: Effects on Relativity Theory

    This is a basic assumption that's made during the derivation of results of special theory of relativity is that space is homogeneous i.e. space intervals shouldn't be given preference based on our choice of origin. However I want to understand more about this assumption and its importance...
  11. R

    Resultant Force and Acceleration of Space craft

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  12. nmsurobert

    I Nuclear batteries on space probes

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  13. B

    Closure of Connected Space is Connected

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  14. Andrea Vironda

    Exploring the Homogeneity of Space & Time in Lagrangian Mechanics

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  15. R

    B Understanding the Expansion of Space: Galaxies Moving Away and Proving Expansion

    How does knowing that galaxies are all moving away from each other and the farthest ones are moving more quickly prove that space is itself expanding and not just that the galaxies are moving through it?
  16. M

    MHB Calculate the volume of the space D

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  17. H

    I Moving through space vs sitting in an expanding space

    Suppose an object is moving away from you. Is there a way to determine, experimentally or otherwise, whether it is moving through space or whether it is sitting still but appears moving because the space between you and the object is expanding? Galaxies that are sufficiently far away from us...
  18. H

    A Calculating Ricci tensor in AdS space

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  19. B

    Metric of a globally negatively curved space

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  20. R

    I First Chinese space station about to de-orbit soon

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  21. Y

    MHB What Is Required to Prove a Subset is a Vector Space?

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  22. T

    I Shape of Vacuum Space: Constant Spatial Volume with Time

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  23. M

    MHB How Can I Calculate a Double Integral Using a Change of Variable?

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  24. FallenApple

    I Need to know the Topology on the Space of all Theories?

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  25. M

    Problem Set Involving Inertia and Balloons

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  26. P

    I Understanding Coulomb's Force Equation in Free Space: Exploring Permittivity

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  27. PsychonautQQ

    I Proof that retract of Hausdorff space is closed

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  28. PsychonautQQ

    I Retract of a connected space is connected

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  29. D

    Free Space Loss at Low Frequencies: Is It Really Zero?

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  30. S

    I Definition of tangent space: why germs?

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  31. L

    A Integration along a loop in the base space of U(1) bundles

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  32. Julio1

    MHB Convergence in topological space

    Let $(X,\tau)$ an topological space. Show that $x_n\to_{n\to \infty} x$ if and only if $d(x_n,x)\to_{n\to \infty} 0.$ Hello, any idea for begin? Thanks.
  33. A

    A How can I plot a 3D phase space for a system of differential equations?

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  34. D

    What does object space and image space mean in optics?

    What does object space and image space mean in optics?
  35. tomwilliam2

    Studying What can I study for Space Science & Technology MSc

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  36. menniandscience

    B Is Einstein's explanation of gravity just a geometrical replacement?

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  37. karush

    MHB 12.4.9 - Area of a triangle given points in 3D space

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  38. C

    A Symplectic geometry of phase space

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  39. FallenApple

    I Is Euclidean Space Inherently Geometric or Just a Vector Space?

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  40. C

    Variable Space Vacuum Tank - Pump question help

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  41. U

    B Brainstorm: Is absolute zero relative

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  42. C

    Spring in Space: 3 Questions Answered

    I would like to ask some questions. I am in a spacecraft (I have grip on the floor) and at one end a spring is attached to the wall. I hold the spring and begin to walk backwards, extending the spring. 1) What will happen to the spacecraft as I walk backwards? 2) What will happen to the...
  43. Y

    Could Microbial Life Survive in the Harsh Conditions of Space?

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  44. P

    I Hilbert space in Everettian QM

    Is it assumed that Hilbert space is an infinite manifold that the non-collapsing wave function occupies in Everettian QM? Thank you.
  45. F

    A Space is "Entangled", says Leonard Susskind

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  46. UsableThought

    Stargazing Yet another Wall Street Journal article about space debris

    The Wall Street Journal is definitely interested in space debris - dead satellites, boosters, etc. - as they've run a number of stories on this topic over the past few years. E.g. Wikipedia has a link to a story from 2009 as one of the footnotes to their article on space debris, plus a web...
  47. T

    I Can We Mathematically Define Everyday Objects Like Smartphones?

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  48. D

    To find the energy eigenvalues in the 3D Hilbert space

    A fictitious system having three degenerate angular momentum states with ##\ell=1## is described by the Hamiltonian \hat H=\alpha (\hat L^2_++\hat L^2_-) where ##\alpha## is some positive constant. How to find the energy eigenvalues of ##\hat H##?
  49. T

    I Meaning of permeability in free space

    Permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. And the inductance of an electric circuit is one henry (H) when an electric current that is changing at one ampere per second results in an electromotive force of one volt across...
  50. S

    B Exploring the Theory of Space: Understanding the Nature and Changes in Space

    Is there any theory law explaining the nature of space and describing what is space and what happens to space when some event take place in space.
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