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. H

    A In What Space Does Quantum Spin Take Place

    Quantum spin is orientable so it takes place in a space with an even number of dimensions. What is that space? If the space had an odd number of dimensions, then spin in that space wouldn't be orientable. But quantum spin is orientable. We could say that it is Minkowski space, but that space...
  2. PainterGuy

    I Why is the observed local region of space flat?

    Hi, Also, I read this article, What Do You Mean, The Universe Is Flat? (Part I), on Scientific American; URL: https://blogs.scientificamerican.com/degrees-of-freedom/httpblogsscientificamericancomdegrees-of-freedom20110725what-do-you-mean-the-universe-is-flat-part-i/ I have few questions about...
  3. H

    Vector space of functions defined by a condition

    ##f : [0,2] \to R##. ##f## is continuous and is defined as follows: $$ f = ax^2 + bx ~~~~\text{ if x belongs to [0,1]}$$ $$ f(x)= Ax^3 + Bx^2 + Cx +D ~~~~\text{if x belongs to [1,2]}$$ ##V = \text{space of all such f}## What would the basis for V? Well, for ##x \in [0,1]## the basis for ##V##...
  4. J

    I Dimensions of quantum cell automata's state space

    In the paper C. S. Lent and P. D. Tougaw, "A device architecture for computing with quantum dots," in Proceedings of the IEEE, vol. 85, no. 4, pp. 541-557, April 1997, doi: 10.1109/5.573 about quantum dots, it is stated that the basis vectors in the space of quantum states for a single cell...
  5. JandeWandelaar

    A What does the metric of a 6D space with 3 compactified dimensions look like?

    I'm interested in describing a 6-dimensional space of which three are compactified to small circles. Globally this space looks 3-dimensional, like a 2-dimensional cylinder looks 1-dimensional globally. Kaluza and Klein did a similar thing in the context of 4-dimensional spacetime. They extended...
  6. PainterGuy

    I The curvature of space and curvature of spacetime

    Hi, The quote below has been taken from this article, https://math.ucr.edu/home/baez/einstein/node2.html, which I came across. The quote doesn't make any sense to me, especially the part in boldface. Could you please help me with it?
  7. Diracobama2181

    A Off-Forward quark-quark amplitude in momentum space

    I am having difficulty writing out ##\bra{p',\lambda}\psi^{\dagger}(-\frac{z^-}{2})\gamma^0\gamma^+\psi\frac{z^-}{2})\ket{p,\lambda}## in momentum space. Here, I am working in light-cone coordinates, where I am defining ##z^-=z^0-z^3##, ##r'=r=(0,z^{-},z^1,z^2)##. My attempt at this would be...
  8. D

    B Can an Object with N Dimensions Exist in N-1 Dimensions?

    I am concerned that this question may instead be a philosophical one although if it it mathematical, any insights would be very appreciated. The question is this; could an object of N dimensions exist entirely in N-1 dimensions? In other words, could an infinitely flat object have 3 degrees of...
  9. A

    B Space, Reflection: See Earth's Past in Mirror?

    can you theoretically put a mirror in space, take a photo of earth/dirts reflection and see it in the past?
  10. M

    I Expansion of Space: Questions on How the Universe Works

    I first apologize if this has been posted more than once; sorry. There is a lack of clarity at my end as to whether I am logged on here? Say we have two galaxies, the Milky Way (MW) and galaxy A separated along a straight line 20 x the radius of the Universe visible to us. If I understand...
  11. M

    I Expansion of Space: Exploring the Rate Between Galaxies

    Hi, may I ask a question, please? Say we have two galaxies, the Milky Way (MW) and galaxy A separated along a straight line 20 x the radius of the Universe visible to us. If I understand correctly then the rate of the physical expansion of space between MW and A could be at the rate of say...
  12. Spockishere

    I Infinite Frequencies & Extraterrestrial Signals: What Are We Missing?

    And if there are an infinite amount of frequencies, doesn't that mean that an extraterrestrial civilization could be reaching out without us being able to receive their signals. And even if we did receive their signals, how would we understand their form of communication? What if they...
  13. Spockishere

    B Travel 7 Light Years at 50000km/s - How Long?

    let's say i would like to drop by one of my pals on a certain planet, 7ly away. I got to 42 years but it doesn't really sound correct.
  14. Strato Incendus

    How Can a Ship Safely Brake in Space Without Crushing Its Inhabitants?

    The two most unscientific words in Star Trek are probably "full stop". :wink: The Impulse Drive is described in the Voyager Technical Manual as 0.25 c (25% of the speed of light). Whatever g forces are required to "immediately" come to a halt from that speed - it's certainly way beyond what the...
  15. DhruvSorathiya

    I Could the Sun burn an image sensor of a star tracker in space?

    Hello, I have a question. If a star tracker in space faces the sun directly then could it be possible that the sun completely burns the image sensor? To be specific we are a student satellite team (Student satellite program IIT Bombay) developing a star tracker and we don't have an exact idea...
  16. G

    I The best ways to display a map of non-Euclidean 3-D space?

    You might have seen such a 3-D map of the stars before: And I was wondering about a 3-D map if space was non-Euclidean, what would be the best ways to display it. To keep it simple, if you're considering elliptic space, you can consider the entire "global" map. Just like we have world maps of...
  17. S

    I Are there types of spacetime where no symmetries are valid?

    We derive the most basic laws of physics from several fundamental symmetries (those from Noether's theorems, gauge symmetries, Lorentz symmetry...). But are there any types of spacetime where no symmetries, no matter how fundamental, would be valid? Any special metric, geometry or shape?
  18. A

    I Does electron beam in empty space generate magnetic fields?

    Does electron beam in empty space generate magnetic fields around them just as with current in conductor. If yes, then is it experimentally proven that two parallel electron beam would attract each other.
  19. Melbourne Guy

    Our space ship has lost power, what happens now....

    I'm about 25,000 words into my latest novel and the story arc is coming together nicely, but one aspect I need thoughts on please is what would happen inside a spaceship that has been grievously damaged in battle to the point that it has been abandoned by the fleet as a 500m long wreck...
  20. P

    B Does this thought experiment show that Space must be curved?

    I'm hoping this is basic and obvious, but assume it's not to the general public. Ignore quantum mechanics and diffraction and assume a gun that can fire photons that each hit the center of a remote target. Place one of these and a conventional gun that shoots bullets at 1000 m/sec inside of a...
  21. A

    I Conservation of angular momentum -- spinning a bicycle wheel in space

    Suppose we have a rotating body like a bicycle wheel in space away from gravity. This body stops after a while due to friction between the wheel and wheel axles. Is not the conservation of angular momentum violated?
  22. egoodchild

    I Calculating distance (from magnet) to an arbitrary point in 3D space

    So I'm looking for some advice on a problem that I am trying to solve for a project. I'm an engineer but my background in vector mathematics is very minimal so I'm looking for some assistance. Lets assume we have a permanent magnet. We know the characteristics of this magnet, such as it's...
  23. BigyanAdhikari

    I Acceleration at 1g in space -- Does it create a gravitational field?

    Does a body accelerating at 1g in outer space create a gravitational field around it ?
  24. M

    State space controllers - find equations from differentials

    Summary:: This is similar to the examples of electrical circuit state space analysis, I have been trying to find the state space equations from the following non linear first order differentials but I keep getting stuck. Any help? A) Started off from non linear equations: $$y' =...
  25. M

    Engineering First order non linear to state space equations

    How to represent this system in state space form? where: $$ x' = Ax + Bu \text{ and }y = Cx + Du$$ I am trying to create a state space model based on these equations on simulink, need to find A, B, C and D but like I mentioned, i cannot find the solution when the differentials are not of...
  26. Rzbs

    I Space Group Symmetry: What is F d3m Spinel Structure?

    What does mean spinel structure has F d3m space group? I know F is for face centred cubic, 3 is 3-fold symmetry and m is mirror, but I don't know what means "d"?
  27. K

    A How Does Quantum Theory Provide a Measure for Microstates in Phase Space?

    *Pathria, Statistical mechanics*"The microstate of a given classical system, at any time, may be defined by specifying the instantaneous positions and momenta of all the particles constituting the system. Thus. If ##N## is the number of particles in the system, the definition of a microstate...
  28. A

    I Video of radiation on space ice

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  29. A

    A An ab initio Hilbert space formulation of Lagrangian mechanics

    I want to share my recent results on the foundation of classical mechanics. Te abstract readWe construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered...
  30. S

    A Does Spacetime Absorb Energy in General Relativity?

    Some physicists prefer to explain the problem of conservation of energy in General Relativity by considering the gravitational potential energy of the universe that would cancel all the other energies and therefore the energy in the universe would be conserved this way. However, many other...
  31. A

    Space Qualified Level Shifter Solutions for 1.5V I/O to 1.8V I/O?

    Hello everyone, I am trying to find level shifter/voltage translation solutions that are space-qualified (ideally radiation hardened, etc.) that can logic level translate from FPGA I/O at 1.5V to and ADC at 1.8V while supporting uni- or bi-directional I/O and OE capabilities . This is for high...
  32. DaveC426913

    B Swimming pool in a rotating space station

    The Exodus thread got me thinking about swimming pools in a rotating space station. Assume two scenarios: two toroidal pools that circumscribe the station, one is continuous and one is divided into segments by barriers. (Sorry, typing on my phone is very arduous for these old thumbs, so I...
  33. Isopod

    B Could anything heat back up the core of Mars?

    My understanding of why Mars lost its atmosphere was because it cooled down too much internally and that when this happened, the planet lost its magnetic field that helped protect it from solar winds (which then ended up stripping away the planets atmosphere). Is there anything that people could...
  34. N

    I Curved space and gravitational waves

    Are gravitational waves purely temporal? An object with no spatial velocity experiences gravity due to temporal velocity?
  35. J

    I Question on the space shuttle Challenger experimentation, in 1985

    I have some questions linked to the following experimentation: In 1985, the space shuttle Challenger took on board a cesium atomic clock. The duration of the mission, around our Earth, was seven days and the parameters of the trajectory were as follows: speed equal to 7700 m/s and altitude h...
  36. dirb

    Calculating Angle & Speed to Reach Planet's Moon from Station Orbit

    A station is orbiting a planet at a distance R1, a moon is orbiting the planet at distance R2 with the period T. The planet itself has a radius rp and a mass mp. We know that when an object adds its velocity at a point in the orbit, the height of the opposite orbit will increase. Determine the...
  37. PainterGuy

    B The configuration of galaxies in space

    Hi, In the picture below, M is Milky Way Galaxy in red, both A's are Andromeda Galaxy in positions P1 and P2 , and W is some random galaxy. Milky Way Galaxy lie in one plane just like all the planets in solar system. In what configuration Andromeda Galaxy lies? Does it lie almost at the same...
  38. WMDhamnekar

    MHB Sample space and bridge game

    Bridge : For k= 1,2,3 ,4 let $N_k$ be the event that North has at least k aces. Let $S_k, E_k, W_k$ be be the analogous events for South, East, West. Discuss the number x of aces in West's possession in the events a)$W_1', $ b) $N_2S_2,$ c) $N_1'S_1'E_1'$ d) $W_2- W_3$ e)$N_1S_1E_1W_1$ f)...
  39. S

    B Light Speed in Vacuum: Does It Reach Cosmic Limit?

    As we all know, light itself is the fastest thing in the universe, and the cosmic speed limit, basically. That said, it is said to go at 299,792,458 meters per second in a vacuum. That is pretty fast. However, I have a question I want to ask... Does light really go that fast in a vacuum? I ask...
  40. I

    B Time and Space Distortions of Photons: What Am I Misunderstanding?

    As I understand it, photons are subject to the same time and space distortions under SR as anything else, which is why they don't perceive time or space, since they travel at the speed of light. To an outside observer, then, they should appear stationary, immobile at their moment of creation...
  41. chwala

    Understanding of the Metric Space axioms - (axiom 2 only)

    Am refreshing on Metric spaces been a while... Consider the axioms below; 1. ##d(x,y)≥0## ∀ ##x, y ∈ X## - distance between two points 2. ## d(x,y) =0## iff ##x=y##, ∀ ##x,y ∈ X## 3.##d(x,y)=d(y,x)## ∀##x, y ∈ X## - symmetry 3. ##d(x,y)≤d(x,z)+d(z,y)## ∀##x, y,z ∈ X## - triangle inequality...
  42. C

    I In Euclidian space, closed ball is equal to closure of open ball

    Problem: Let ## (X,d) ## be a metric space, denote as ## B(c,r) = \{ x \in X : d(c,x) < r \} ## the open ball at radius ## r>0 ## around ## c \in X ##, denote as ## \bar{B}(c, r) = \{ x \in X : d(c,x) \leq r \} ## the closed ball and for all ## A \subset X ## we'll denote as ## cl(A) ## the...
  43. Viopia

    B How Can We Prove That Space is Expanding?

    Hi. I have watched some YouTube videos which suggest space (itself) is expanding. This sounds the same as the distance (itself) between moving objects is increasing. What's the difference? How can this even be proven in a laboratory? It doesn't sound as though it can be measured with a tape...
  44. B

    B Why is the Webb Space Telescope placed at L2?

    Why is the Webb placed at L2 (Lagrange point 2)? I read some articles that said it would be perpetually shaded being on the opposite side of the sun and moon, but that makes no sense when the Webb orbit is so huge? So why is it at L2?
  45. A

    I Portable telescopes inside the International space station (ISS)

    I would like to know what will be the visibility from the portable telescope aboard the International Space Station. What could they potentially view, and what are (at least some of) the things they are known to have looked at? Presumably they use it *inside* the ISS and not outside, and are...
  46. D

    Net force and position of objects in space

    Q1a) - My current wrong answer is <-5.9e7, -3.3e8, -2.17e8> I used the Fnet = Gm1m2 / d^2 <unit vector> But i keep getting a dif answer each time Q2a) - I thought i could find net force and then divide it by the mass, and multiply it by the time interval. However I got the answer <-4.5, 4.5...
  47. H

    Prove that the linear space is infinite dimensional

    A space is infinite dimensional when its basis is infinite. But how can I ensure that the basis of the space of all sequences whose limit is zero is infinite? (After solving that, I would like to have a hint on this very similar problem which says: let V be a Linear space of all continuous...
  48. HailSagan

    B What Space Does the Universe Occupy?

    Greetings, all. Please forgive my ignorance, but this is a question which has been on my mind for many years: What space does the universe occupy? To clarify what I mean: I'm in a building which is in the city of Hillsboro, which is the county of Washington, which is in the state of Oregon...
  49. P

    A About the rigged Hilbert space in QM

    In Quantum Mechanics, how can you justify the use of distributions like the delta functional without introducing a rigged Hilbert space? I see that some texts do not make any reference to this subject.
  50. B

    B How hot is the Sun in space? (James Webb related)

    I'm reading about the engineering of the James Webb and it surprised me that the temperature difference will be about 318 degrees from one side of the telescope compared to the other (85 C on one side and -233 on the other). I didn't expect space to be that hot about a million miles further...
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