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. Addez123

    B Does red-shifted light cause expansion of space?

    Light can get red-shifted due to expansion of space, this leads to a loss of energy. Would it be possible that this energy is what's causing the universe to expand in the first place?
  2. M

    LaTeX How to determine leaving space after \

    Would you explain when the space should be left when backslash, \, is used? For example some codes using backslash. \ \displaystyle a=\frac{dv}{dt} \ : This one works good because there is space between the first two backslashes. But if the space between the first backslash is removed the code...
  3. Lmlodninja

    Vacuum & Sound: What Happens to Energy?

    What happens to sound when it hits a vacuum? Because there is nothing for the sound wave to vibrate against, what happens to the energy?
  4. G

    I The name of the 3+1 metric where time is normal to space?

    I am interested in looking at the metric where time is everywhere normal to space, so gta=0 everywhere, where t is the time coordinate and 'a' is any of the space coordinates. I'm finding it hard to look up in the literature: does it have a name that I can search for? My main interest is in...
  5. STAR GIRL

    B Exploring the Changing Geometry of Space

    Does Geometry of space Changes?
  6. S

    Is 1 in the Closure of (2,3] in the Standard Topology on the Real Numbers?

    Homework Statement Hello All, I am experiencing Adventures in Topology. So far, so good, but I have an issue here. In the topological space (Real #s, U), show that 1 is not an element of Cl((2,3]).Homework Equations The closed subsets of our topological space are the converses of the given...
  7. M

    B Space Dilation Interaction Between Two Masses

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  8. V

    B Exploring the Expansion of Space & Time

    We are told that space is expanding and that the rate of expansion is speeding up. However, as relativity shows that space and time are inextricably linked, does this mean that time is expanding too?
  9. B

    I Humidity when T is not constant in space

    Hi all! How is humidity related to temperature in a system where temperature is constant in time but not in space? As an example: If we have humid air trapped between two parallel walls with T1 and T2 respectively, how does humidity behave along the line from one to the other wall? Is absolute...
  10. J

    B Light & Space: Investigating the Unknown

    how do we know light stays consistent when traveling through the "not nothingness of space"? how do we know the rate at which light degrades as it travels through the medium that has to be there?
  11. S

    A Constraining the parameter space of a function

    Consider the function $$f(x) = - \frac{1}{2}a^{2}x^{2} + \frac{1}{4}bx^{4} + d^{4}\cos(x/c),$$ where ##a##, ##b##, ##c## and ##d## are arbitrary parameters. For some region(s) of the parameter space, there are oscillations in the function. My goal is to identify these regions of the parameter...
  12. P

    A Stress tensor in 3D Anti-De Sitter Space

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  13. Sullivan Stockwell

    B Speed of Light & Space: Exceeding the "Universal Speed Limit

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  14. evinda

    MHB Find Solution to Cauchy Problem & Determine Space in $\mathbb{R}^2$

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  15. B

    Why a E field cannot hold a charge in space?

    From the book, I did not understand, 1. Why does fields coming inwards the sphere contradicts the Gauss law ? 2. I am unable to connect the potential picture and electric field picture. Why does the point P must have lowest or highest potential than neighbouring particles ? 3. I understand...
  16. M

    Express the system in state space form

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  17. Pyrus

    B What is the true meaning of the Big Bang?

    We say that in big bang, a highly dense point like structure exploded and expanded. In what did it expand? If so, universe and space would be different entities. Please elaborate.
  18. Milsomonk

    I Difference between an Algebra and a Vector space

    Hi guys, I am a little confused on the difference between an Algebra and a vector space. I´m guessing there´s a fairly simple distinction. Any guidance would be much appreciated, I accept both hand wavy and hardcore axiom based responses :) Cheers
  19. N

    I Do particles create space over time? Is that expansion?

    If a particle can potentially be transported to any place in space limited only by the speed of light, does that potential amount to an expansion of space? And another question: Does it make sense to define space as any place a particle could go to?
  20. Noisy Rhysling

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  21. tze liu

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  22. binbagsss

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  23. hsdrop

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  24. J

    B Can sound distort the fabric of space?

    Is it possible for Low Frequency to distort the fabric of space? If so, how?
  25. D

    B How Does Space Expand? Understanding Universe Expansion

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  26. I

    I Levi-Civita symbol in Minkowski Space

    I set eyes on the next formulas: \begin{align} E_{\alpha \beta \gamma \delta} E_{\rho \sigma \mu \nu} &\equiv g_{\alpha \zeta} g_{\beta \eta} g_{\gamma \theta} g_{\delta \iota} \delta^{\zeta \eta \theta \iota}_{\rho \sigma \mu \nu} \\ E^{\alpha \beta \gamma \delta} E^{\rho \sigma...
  27. A

    I Time of cooling to equilibrium in space plasma gas

    Hi all, If I have a hot object in space (not a star but say an oven or just a hot gas as would be on Earth < 10,000 degrees Kelvin) glowing at a temperature T and I want to know long it takes to come to equilibrium with the vacuum of space around it, how can I calculate such a time? I could...
  28. D

    MHB Sobolov space boundedness

    If $ r<s<t $ then for any $ ϵ>0 $there exists $ C>0 $ such that $ ∥f∥_{(s)}≤ϵ∥f∥_{(t)}+C∥f∥_{(r)} $for all $f∈H_t $ Can you please tell me how to start thinking of this problem? I really feel stuck and don't know where to start!
  29. G

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  30. A

    Proving Completeness of Continuous Basis Vectors

    Homework Statement Consider the vector space that consists of all possible linear combinations of the following functions: $$1, sin (x), cos (x), (sin (x))^{2}, (cos x)^{2}, sin (2x), cos (2x)$$ What is the dimension of this space? Exhibit a possible set of basis vectors, and demonstrate that...
  31. wolram

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    <Incorrect link deleted. See post below.> For a start the solar cells do not look big enough to power the craft.
  32. DevonZA

    Determine the magnitudes and nature of forces in space truss

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  33. B

    Need help with permeability of free space.

    Homework Statement In a lab that I did in Physics we calculated the magnetic field of a solenoid while constantly increasing the number of time the wire was wrapped around the electromagnet. After I obtained all the values, plotted it in a graph and found the line of best fit, the slope came...
  34. L

    B Can radiation in space be captured and used in an Ion drive?

    Since NASA is currently under way with the deep space Ion drive, they plan on using xenon to power this propulsion system. My question is could they harness the already existing radioactive particles in space to power it? If they could then there would be almost an unlimited supply of fuel for...
  35. M

    I Two orthonormal bases that span the same space

    I just read something that I do not want to misinterpret. If there are two orthonormal basis that span the same space, which I think implies that each basis can be written in terms of the other basis, then measurements made with respect to each basis will not commute? Does this mean that...
  36. Vengo

    Why are astronauts outside a spaceship not pulled by Earth's gravity?

    Another Doubt Guys, I was watching this video on youtube. it is about weightlessness in space. it states that the astronauts inside a spaceship fly in space not due to zero gravity but due to centripetal force with which the satellite is revolving the earth. My question is "then why the...
  37. I

    Can Anyone Help Me Fix My 3D Space Filling Tree Algorithm?

    Hi all, I need an algorithm that fills a 3d lattice from any point, always expanding (no return allowed as in ref. http://msl.cs.illinois.edu/~lavalle/papers/KufLav09.pdf). The cells must be visited just once. My efforts are contained in the attached file. It works ***almost*** correct. Some...
  38. C

    B Space expanding or Time speeding up? Part 2

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  39. M

    I Understanding Abstract Kets & Hilbert Space

    Some posts in another thread lead me to a search which ended when I read the following "kets such as ##|\psi\rangle## are elements of abstract Hilbert Space". That lead me to this paper. http://www.phy.ohiou.edu/~elster/lectures/qm1_1p2.pdf "The abstract Hilbert space ##l^2## is given by a...
  40. S

    B Is it possible to compress the space without gravity?

    Is it possible to compress the space without gravity?
  41. Gean Martins

    I Phase Space and two dimensional Hilbert Space

    I always had this doubt,but i guess i never asked someone. What's the main difference between the Classical phase space, and the two dimensional Hilbert Space ?
  42. D

    I How do we know we are looking back in time in space?

    Sorry new here trying this question. From the perspective of a light particle leaving its star that particle would arrive everywhere in the universe instantly since it is traveling at the speed of light. But we trust our perspective of time and distance in light years to describe what we are...
  43. M

    Decomposing space of 2x2 matrices over the reals

    Homework Statement Consider the subspace $$W:=\Bigl \{ \begin{bmatrix} a & b \\ b & a \end{bmatrix} : a,b \in \mathbb{R}\Bigr \}$$ of $$\mathbb{M}^2(\mathbb{R}). $$ I have a few questions about how this can be decomposed. 1) Is there a subspace $$V$$ of...
  44. Y

    Job Skills Careers in the Space Industry that aren't Aero/Mech

    Are there STEM related careers in the space industry which are different from Aerospace or Mechanical Engineering? If so, what are they?
  45. wasup23

    I Introducing two identical containers with different gasses

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  46. artriant

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  47. Shubham Jaydeokar

    A Space Radio Software: Get Help from Experts Now!

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  48. Dimani4

    I Classical Newtonian Physics: Space & Time Independence

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  49. S

    Would current flow in a vacuum like space

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  50. M

    I How can Spin-up z and spin-down z span the space?

    ##\def \sqx{\frac{1}{\sqrt{2}}}## If Szu represents spin-up in the z-direction and Szd represents spin-down in the z-direction then the vector which represents spin-up in the x-direction is given by the superposition of the z states \begin{equation}|S_{zu}\rangle =\begin{bmatrix}1 \\...
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