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. R

    B What is Absolute Time and Space?

    In physics, the concept of absolute time and absolute space are hypothetical concepts closely tied to the thought of Newton. Absolute, true and mathematical time of itself, and from its own nature flows equally without regard to anything external. There is another term duration measures...
  2. anorlunda

    Boeing Starliner launches to space (but not ISS) (reached ISS in 2022)

    The Boeing Starliner just launched into a pre-sunrise cloudless sky. It was fun to see the black smoke trail change to white as it lifted into the sunlight (pic 1). It was not as spectacular as the post-sunset launch from California a few months ago. The trajectory became more horizontal...
  3. A

    I Expansion of space & expansion of matter within space

    Space evidently is expanding, so we say that the very fabric of space time is expanding uniformly in all directions, so two questions 1)originally this expansion was driven by the energy content within the universe aka the dense hot matter , versus nowdays the acceleration is picking up speed...
  4. chasrob

    How Fast Could a Saturn 5 Rocket Travel in Outer Space with FTL Mechanics?

    I'm writing an SF novel with FTL travel. In my story, there are different motion regimes, including superluminal, based on this https://www.researchgate.net/publication/333614143_A_GENERAL_LOCAL_CAUSALITY_PRINCIPLE_OF_SPACE-TIME_A_PREPRINT I found. My story: in our (c1) regime, whatever...
  5. shintashi

    B 100sqft wormhole from sea level to outer space?

    Hypothetical scenario and I'm trying to understand the velocity of the air as it tries to equalize with a large vacuum. I presume this model isn't very much different from an initial loss of 1 atmosphere pressure in space via some puncture. I'm mainly concerned with the immediate wind speeds and...
  6. B

    Expensive Quality VS Cheap Quantity Space Battles

    Which do you think is superior, given similar tech for both opponents? If one opponent nation went all in for mass produced cheap space vehicles, would that not beat one that produced a limited number of heavily armed spacecraft ? Scenario is a space battle only, from deep interplanetary...
  7. wolram

    B Exploring Interstellar Space: What Voyager 2 Has Taught Us

    With voyager 2 now going to interstella space what have we learned?
  8. N

    I What does it mean to say space and time are fundamental in physics?

    What feature of the equations of classical physics show that space and time are fundamental and how would the equations differ if space and time were not fundamental but emergent? I heard all of this from a previous talk and I would appreciate any help and any further reading recommendations.
  9. TTT

    I Rigged Hilbert Space X: Eq (1) and (2)

    X=e+or-kx (1) <X(x)|Φ(x)>=∫-∞∞X*(x)Φ(x)dx (2) where Φ(x) satisfies the following. ∫-∞∞|Φ(x)|2(1+|x|)ndx is finte if n=0, 1, 2,...
  10. G

    I How do we know space is expanding?

    I understand that there are many forums and topics written on the fact that space is expanding. But I've looked and looked, and couldn't find an answer to my specific question. How do we know space is expanding, rather than galaxies just regularly moving apart? How do we know galaxies are...
  11. TTT

    Nuclear Space in QM: Exploring & Integrating Finite Solutions

    If I understand this question correctly, I am supposed to prove an integrate from negative infinity to infinity ∫x|∅(x)|2(1+|x|)ndx is finite. Sorry, but I have no idea.
  12. davenn

    A SPACE ROCKS: Latest meteorite into my collection

    I have a bit of a love affair with rocks that come from outer space. To hold a piece of rock that has zoomed through space for zillions of years before finally crashing to Earth still gives me that WOW factor. I have around 55 samples in my collection from many different falls around the world...
  13. C

    Phase space volume with a potential (microcanonical ensemble)

    I don't know how to solve that integral, and to calculate the number of microstates first, then aply convolution and then integrate to find the volume of the phase space seems to be more complicated. Any clue on how to solve this? Thank you very much.
  14. K

    A Exploring Rocket Exhaust Plume Molecules in the Upper Atmosphere

    I'm pondering the behavior and persistence of rocket exhaust plume molecules far above the atmosphere. For example, the plume from an apogee circularization thrust from GTO (Geosynchronous Transfer Orbit) to GEO (Geosynchronous orbit). CO₂ and H₂O are among the molecular species emitted by a...
  15. Moara

    Spherical gas distributed symmetricaly over space

    . We have that energy in a infinitesimal Spherical layer with number of mols dn is: dU=Cv.T.dn (1) But by the ideal gas law: PV=nRT (2) Differentiation gives: PdV+VdP=RTdn (3) (3) in (1) and using CV=3R/2 (monoatomic) gives: dU=3/2.(PdV+VdP) (4) Integration of (4) over the whole gas will...
  16. C

    I Question regarding a Free particle and Hilbert space (QM)

    In quantum mechanics, the Eigenfunction resulting from the Hamiltonian of a free particle in 1D system is $$ \phi = \frac{e^{ikx} }{\sqrt{2\pi} } $$ We know that a function $$ f(x) $$ belongs to Hilbert space if it satisfies $$ \int_{-\infty}^{+\infty} |f(x)|^2 dx < \infty $$ But since the...
  17. TheQuestionGuy14

    B Do quantum fluctuations actually occur in De Sitter space?

    A little while back I asked a question about quantum fluctuations, and I got some great answers. Just recently, I stumbled upon a paper by Sean Carroll, which states that there isn't quantum fluctuations after all, in a De Sitter space in a vacuum state. He used this to argue against Boltzmann...
  18. S

    Periodic images of dipole line charge followed by a vacuum space

    Can I sum up the potential due to all positive line charges and all negative line charges separately, with the boundary condition being at the edge of my unit cell, the potential should be the same and inside the metal there is a contant potential?
  19. TOMMiB

    The Pressure in Interstellar Space.

    n = 11000 because n = N/V and V = 1m^3. Using P = nRT/V I get that P = 7.32x10^6 Pa. considering that the gas is in a high vacuum, this value seems far too high to be true. Please help?
  20. A

    Torque and inertia of a space object

    I= 524kg * 6m^2 = 18.86E3kg*m^2 KE=(1/2) (18.86E3kg*m^2) (0.16 rad/s )^2= 241.5 J torque= 0.25* 57N* (6m)=85.5 N*m
  21. JEB33

    Two-Parter: Stationary Bodies in Space and Orbits

    Summary: (1) Would it be possible (relatively speaking) for a spaceship to "sit" stationary in space, i.e., not in orbit around a planet; and (2) if possible, how long would it take a planet, viewable from the spaceship's window (humor me) to pass through your field of vision? Part One I'm...
  22. M

    Global Positioning System / Clocks in Space

    I'm a bit lost at how to exactly start this exercise... As far as I understand we need to first determine ##d\tau_E## and ##d\tau_S##. First question: Since we can neglect the Earth's movement, can I also neglect the movement of the satellite with respect to the far away observer? If so, I...
  23. X

    Project Orion-Like Space Vehicle

    Nations prohibit the detonation of nukes in space, but I don’t know there is a better way to use these weapons of mass destruction, than propelling a probe on a interstellar travel at relativistic speeds in the near future. Also, the origin Orion, where all the nukes are carried onboard, will...
  24. X

    Was KSP a somewhat accurate space flight simulator?

    KSP was one of the most famous science games as it simulates a complete space program, as well as physics such as aerodynamics and orbital mechanics. Such science focused games are rare, and something favourable amongst nerds. To make it even better, it is easy to modify the game and add almost...
  25. M

    NASA Which of these methods is the best bet for space propulsion?

    1.) Ion drive 2.) Black hole starship 3.) Fusion Rocket 4.) Fission sail https://en.m.wikipedia.org/wiki/Fission_... 5.) Halo drive https://arxiv.org/abs/1903.03423 6.) Horizon drive https://www.tsijournals.com/articles/pro... 7.) Pitch drive, Diametric drive, Disjunction drive...
  26. D

    I The Shape of Space: How Does It Move?

    Mass causes space to change shape, and that's what we see as gravity. But does space move when it changes shape? If yes, relative to what?
  27. M

    Vector space - polynomials vs. functions

    As per source # 1 ( link below), when treating polynomials as vectors, we use their coefficients as vector elements, similar to what we do when we create matrices to represent simultaneous equations. However, what I noticed in Source #2 was that, when functions are represented as vectors, the...
  28. ohwilleke

    I QFT of Gravitons in Minkowski Space vs GR

    A central feature of classical GR that it is background independent and operates via a curvature in space-time. As I understand it, this is not true of the other Standard Model forces which are consistent with special relativity and operate in Minkowski space, in which forces are transmitted via...
  29. Suppaman

    B Expanding Space in the Lab: Investigating the Possibilities

    When I ask Google how to expand space, I get suggestions on removing junk or questions on what it is expanding in to. I am going to try asking here and I know I must phrase the issue properly. It is agreed that many scientists claim that space expanded around the time the universe began. I...
  30. M

    Why do we try to find if a subset is a subspace of a vector space?

    I am assuming the set ##V## will have elements like the ones shown below. ## v_{1} = (200, 700, 2) ## ## v_{2} = (250, 800, 3) ## ... 1. What will be the vector space in this situation? 2. Would a subspace mean a subset of V with three or more bathrooms?
  31. dRic2

    I Are electron bands symmetric in the reciprocal space?

    Hi, in the lecture notes my professor gave us, it is stated that, due to Kramers theorem, the energy in a band must satisfy this condition: $$E(-k) = E(k)$$ But, judging from actual pictures of band structures I don't find this condition to be true. Here's a (random) picture I guess it looks...
  32. Bofors

    Rotating planet moving through space

    Its velocity, Vp, is towards some other part of the universe, It rotates in the same plane as its direction of travel. The linear velocity of an object on the surface of the planet relative to the centre is Vr. That means the object's total linear velocity is Vp+Vr when it's at one point in its...
  33. bland

    B Relative Dead Stop in Deep Space

    So there's two spaceships in deep space. at rest with respect to each other. Then one of them shoots off at some huge speed and everyone feels it. Then they shut the engines off suddenly. No one is going to suddenly lurch forward, they will at the instant the engines are shut off effectively be...
  34. skyshrimp

    Possible to build a space tower?

    Is it possible to build a skyscraper that's so tall that it enters the ozone layer? I was imagining such a tower where customers could go to the top in elevators and view the Milky Way in bed with a glass roof in their luxury apartments :) Obviously not just a tower without supports. Maybe with...
  35. S

    I Showing direct sum of subspaces equals vector space

    If one shows that ##U\cap V=\{\textbf{0}\}##, which is easily shown, would that also imply ##\mathbf{R}^3=U \bigoplus V##? Or does one need to show that ##\mathbf{R}^3=U+V##? If yes, how? By defining say ##x_1'=x_1+t,x_2'=x_2+t,x_3'=x_3+2t## and hence any ##\textbf{x}=(x_1',x_2',x_3') \in...
  36. Meruem

    Force Needed to Push Bodies in Space: 100kg vs 1kg Mass

    Do we need more force to push a body with 100kg mass than of 1kg mass in space(in vacuum)?
  37. P

    A Connection between Reciprocal Space and Cotangent Space

    [Moderator's note: Link to reference protected by copyright removed.]
  38. Eclair_de_XII

    I How do you define unboundedness in Euclidean space?

    I read in my textbook Calculus on Manifolds by Spivak that a set ##A\subset \mathbb{R}^n## is bounded iff there is a closed n-rectangle ##D## such that ##A\subset D##. It should be plain that if I wanted to define unboundedness, I should just say something along the lines of: "A set ##A\subset...
  39. dRic2

    Hamiltonian Mechanics: why paths in state space never cross each other

    I'm reading a book about analytical mechanics and in particular, in a chapter on hamiltonian Mechanics it says: "In the state space (...) the complete solutionbof the canonical equations is pictured as an infinite manifold of curves which fill (2n+1)-dimensional space. These curves never cross...
  40. Z0dCHiY8

    Why Is Space Travel More Complex Than It Seems?

    Most sources of pop culture & even engineering ones have failed to provide the key problems of space traveling. For example, dv ain't that hard as aerodynamics of Space. For 1st glance, it looks ridiculous == Space is Vacuum. Mostly, yes.. but Space has a lot of dust & gaseous clouds. Just one...
  41. GeolPhysics

    I Schrodinger equation for a free particle in 3d space

    I've got the solution to the question but I just need more detail. I can't work out the first step of the solution to the second step. That should read, I don't know what they multiplied ih-bar by to make it (i/h-bar)^2?
  42. P

    I "Adding" a Vector Space and its Dual

    Given that the Set of 1-Forms is a Vector Space distinct from, but complimentary to, the Linear Vector Space of Vectors. And given that there is an Isomorphism between the linear space of vectors and the dual vector space of 1-forms, does it make mathematical sense to combine a vector space and...
  43. jk22

    B How to know if a Euclidean space is not a 3-sphere?

    If we suppose the following 8-dimensional manifold given by $$a_1=cos(x)cos(y)cos(z)$$ $$a_2=cos(x)cos(y)sin(z)$$ $$a_3=cos(x)sin(y)cos(z)$$ $$a_4=cos(x)sin(y)sin(z)$$ $$a_5=sin(x)cos(y)cos(z)$$ $$a_6=sin(x)cos(y)sin(z)$$ $$a_7=sin(x)sin(y)cos(z)$$ $$a_8=sin(x)sin(y)sin(z)$$ Then obviously...
  44. Eclair_de_XII

    If V is a vector space why is T^2(V) = T(V) iff ker(T^2) = ker(T)?

    --##ker(T^2)=ker(T)## if ##T(V)=T^2(V)##-- Suppose that ##T^2(V)=T(V)##. So ##T:T(V)\mapsto T^2(V)=T(V)##. Hence, ##T## is one-to-one and so ##ker(T)=\{0\}##. Suppose that ##T^2(w)=0## for some ##w\in ker(T^2)##. Then ##T^2(w)=T(T(w))=0## which implies that ##T(w)\in ker(T)## and so ##T(w)=0##...
  45. asca

    B How Does LIGO Detect Gravitational Waves Despite Changes in Spacetime?

    Sorry if the question has been already answered, but I didn't manage to find it. Let's go back to ligo detection of gravitational waves, my question is the following: if space time changes its texture due to a gravitational effect, all the rulers (and clocks) in that spot will be affected, so...
  46. amare

    Troubleshooting Corrupted Audio Files When the C Drive is Low on Space

    When the C drive gets limited in space, I take some space from the D drive and the audio files in D drive corrupted and can not open. How do I open these files?
  47. davenn

    I What is the new source of space radiation discovered near Earth?

    Interesting article ...NEW SOURCE OF SPACE RADIATION: Astronauts are surrounded by danger: hard vacuum, solar flares, cosmic rays. Researchers from UCLA have just added a new item to the list. Earth itself.“A natural particle accelerator only 40,000 miles above Earth’s surface is producing...
  48. H

    I Preferred orientation of a nitrogen molecule in space?

    Consider an ##N_2## molecule. Chemists say that the triple bond is due to one ##p_x - p_x## overlap, one ##p_y - p_y## overlap and one ##p_z - p_z## overlap. The x-axis (the label is not important; I’m sure you know what I mean) is clear because it’s the longitudinal axis of the molecule. But...
  49. dedocta

    I Deflect Asteroid w/ Collisions: Calculating Theta & MJ Interractions

    In short, I was trying to look into feasibility of deflecting an asteroid with a collision of ~32MJ of direct energy. I wanted to know how many collisions are necessary to deflect at a given time out (distance away.) I found this link, where the collision is perpendicular to the motion of the...
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