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. Andrew broome

    B What can be used to propel something in space without fuel?

    To specify, by fuel I mean fossil, nuclear, chemical and pressurized air. Want to build and design a satellite for my daughter with a camera in it (goPro) with an antenna to be able to view anytime she likes. Want to do a hexagonal approach with solar cells only for power. Want to power the...
  2. l0st

    I Gravitational Waves Cause Uniform Space Expansion: Exploring MNRAS Papers

    I am looking at a couple of very interesting papers, published in MNRAS, that deduce, that the accelerated expansion of the Universe we observe can be attributed to gravitational waves, produced by a very distant merger of two or more universe-mass-scale black holes. The last one is on the...
  3. T

    Metric space of continuous & bounded functions is complete?

    Homework Statement The book I'm using provided a proof, however I'd like to try my hand on it and I came up with a different argument. I feel that something might be wrong. Proposition: Let ##<X,d>## be a metric space, ##<Y,D>## a complete metric space. Then ##<C(X,Y), \sup D>## is a complete...
  4. A

    Least cost to get a self-sustaining space infrastructure

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  5. S

    I What's the difference between Euclidean & Cartesian space?

    What's the difference between Euclidean & Cartesian space?
  6. S

    Programs (Space) Industry - Different Paths Towards It

    Hello! I am a returning student, 19YO, and will be starting back in community college in a month retaking classes I failed the first go-around with college. This is hopefully less of a "tell me what to do" thread, and more of a "clarify my misconceptions." Basically, I am very interested in a...
  7. H

    Can we use the momentum of light to propagate spacecrafts in space?

    as we know light has momentum so theoretically we can use it but is it practical? (also this is it that light only exerts force if incident on something?)
  8. I

    I Largest sphere in the space between dense packed spheres

    If I consider a tetrahedron of four densely packed spheres of unit radius, what it the radius of the largest sized sphere that can fit in the space in between?
  9. K

    I Uniqueness of tangent space at a point

    How do you show that there can be only one tangent space at a given point of a manifold? Geometrically it's pretty obvious in 3 dimensions, as one notices that there can be only one tangent plane at a point. But how could we show that using equations?
  10. P

    I Space elevator and Coriolis force

    It seems to me that the concept of a space elevator does not take Coriolis force into account. If the elevator were in built with a space station in geosynchronous orbit and counterweight then there is more to reaching the space station than just climbing the rope. The rope would have to be...
  11. bland

    B Understanding Particle Motion in Deep Intergalactic Space

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  12. BillTre

    Obituary of Constance Adams, Space Habitat Designer

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  13. J

    What is the largest possible Rotating wheel space station?

    What is the largest possible Rotating wheel space station possible to be constructed with current materials? and what would be the population it would support. also formulas used for calculation.would be useful. Could constructing cylindrical space elevators support more population,
  14. K

    B Infinite dimensional Hilbert Space

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  15. J

    Decide if the energy surfaces in phase space are bounded

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  16. R

    Steering rockets in space by shifting CM

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  17. M

    B Light and Reflections in Space

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  18. Mr Davis 97

    I Real function inner product space

    Wolfram says that an example of an inner product space is the vector space of real functions whose domain is an closed interval [a,b] with inner product ##\langle f, g\rangle = \int_a^b f(x) g(x) dx##. But ##1/x## is a real function, and ##\langle 1/x, 1/x\rangle## does not converge... So how is...
  19. V

    B Is space is continuous or discrete?

    I was watching a video where well known physicist Lisa Randall said that we still don't know whether space is continuous or discrete. My question is, how do we find whether space is continuous or discrete?? What type of experiments are possible? Is it being done now?? I am thinking this may be...
  20. M

    What would happen to a blob of mercury in space?

    How long would it take for a blob of mercury (the size of a marble or so) to freeze in space? I'd emagine it would have to boil in some way first, and that would send pieces of it flying around, but the surface tension of mercury is much greater than that of water, or urine (as we'd seen...
  21. M

    A Why Must the Constant in Hilbert Space Function B[f(x)] Be Defined as Shown?

    Hi PF! Given a function ##B## defined as $$B[f(x)]\equiv f''(x) + f(x) + const.$$ Evidently in order for this function to be in the real Hilbert space ##H## we know $$const. = -\frac{1}{x_1-x_0}\int_{x_0}^{x_1} (f''(x) + f(x))\,dx.$$ Can someone please explain why? I can elaborate further if...
  22. WeiShan Ng

    I Momentum/Position space wave function

    These are from Griffith's: My lecture note says that I am having quite a confusion over here...Does the ##\Psi## in the expression ##\langle f_p|\Psi \rangle## equals to ##\Psi(x,t)##? I understand it as ##\Psi(x,t)## being the component of the position basis to form ##\Psi##, so...
  23. J

    I Dynamical Casmir Effect in expanding space?

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  24. vysqn

    Ek vs engine power in cars and space

    Help me please:) (1) An idealized engine with constant torque curve means constant acceleration. So for example if there is no air resistance and no frictions and car is on fixed gear and at 3000Rpm it produces 50Hp so at 6000Rpm will produce 100Hp. So he doubles the speed , doubles power and...
  25. e2m2a

    I Exploring Frame Dragging & Its Impact on Space: Q&A

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  26. S

    How do we know that light that comes from the stars is in past?

    So for some reason, from time to time, i always come back to this question and i can't remember that part of the physics while i was studying and most of the explanation are pretty generic. Basically how do we know that light actually travels and not just oscillate and transfer energy when...
  27. G

    Why is θ Limited to π/2 in Basis Choice for Distinct States?

    Homework Statement Have to read a paper and somewhere along the line it claims that for any distinct ## \ket{\phi_{0}}## and ##\ket{\phi_{1}}## we can choose a basis s.t. ## \ket{\phi_{0}}= \cos\frac{\theta}{2}\ket{0} + \sin\frac{\theta}{2}\ket{1}, \hspace{0.5cm} \ket{\phi_{1}}=...
  28. R

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  29. K

    I Perceived Speed of Objects in Space

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  30. I

    Determining if a subset W is a subspace of vector space V

    Homework Statement Let V = RR be the vector space of the pointwise functions from R to R. Determine whether or not the following subsets W contained in V are subspaces of V. Homework Equations W = {f ∈ V : f(1) = 1} W = {f ∈ V: f(1) = 0} W = {f ∈ V : ∃f ''(0)} W = {f ∈ V: ∃f ''(x) ∀x ∈ R} The...
  31. N

    B Is there a way to measure gravity in a particular area of space

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  32. T

    I How can I go about making a "Space Proof" coating?

    So I am planning on launching a Satellite to promote the Dogecoin cryptocurrency. One of the main points is printing/painting (Or whatever) the logo on the side of a metal panel. How can I make it so it doesn't melt off or turn white from radiation so quickly?
  33. K

    A Vacuum in QFT: Fock space or effective potential?

    There seem to be two ways of defning what a vacuum is in QFT: 1. It is state $|0\rangle$ such that $$a_k|0\rangle = 0$$ for all anihilation operators $$a_k$$, with creation operators $$a_k^{\dagger}$$. Thus, it is defined in Fock space. 2. It is state $$|0\rangle$$ such that derivative...
  34. Zafa Pi

    I Chaos like phenomena on a simple metric space?

    Let M = {p, x1, x2, x3, ...} be a metric space with no isolated points. f: M → M is continuous with f(xn) = xn+1, and f(p) = p. We say f separates if ∃ δ > 0, ∋ for any y and z there is some n with |fn(y) - fn(z)| > δ, where fn+1(y) = f(fn(y)). QUESTION: Does f separate?
  35. M

    A How to determine constant to be in Hilbert space

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  36. R

    I Earth Between 2 Suns: Time & Space Questions

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  37. evinda

    MHB Determining Solution Space for Cauchy Problem ($u_t+xu_x=(x+t)u$)

    Hello! (Wave) I want to find the solution of the following Cauchy problem and determine the space in $\mathbb{R}^2$ where the initial condition defines the solution.$$u_t+xu_x=(x+t)u, u|_{t=0}=\phi(x), x \in [0,1] \cup [2,3].$$ ($\phi(x)$ arbitrary smooth function) I have tried the following...
  38. K

    I Constructing the Tangent Space to the Sphere: A Simple Case Study in Relativity

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  39. tma73

    I Speed of light around a (massive) object in space ...(i.e.sun

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  40. P

    I Free Precession animation - body frame to space frame

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  41. Lunct

    B Did the Big Bang create space and time?

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  42. facenian

    I Problem with countably compact space

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  43. I

    Transform differential equations into state space form

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  44. S

    I Understanding Z2 Graded Vector Spaces: Definition and Examples

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  45. pairofstrings

    Mathematical Structure and Mathematical Space Hierarchies

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  46. G

    B Are the 3 space dimensions "equal"?

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  47. R

    I Do traditional particles occupy space

    For example should a neutron be considered as a point, or does it have volume?
  48. J

    Is free fall NOT the same as floating in space?

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  49. M

    Space Travel & Relativity: Is it Possible?

    I had a bit of a thought experiment the other day, does relativity mean that technically you couldn’t travel faster than the speed of light to the observer. But if you were traveling from Earth to another planet, could you technically be traveling faster than the speed of light relative to the...
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