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. M

    I Properties of Defective Matrices in Space?

    Let me start by saying that my question will be somewhat vague by mathematical standards. I'm not a mathematician! I'm looking for some intuition about how defective matrices are distributed in the space of all matrices. I understand that they are rare and in some sense discontinuous - matrices...
  2. E

    Stargazing How much brighter is the Sun when viewed from space?

    How much brighter is the sun when seen from space than it is when viewed from Earth?
  3. cookiemnstr510510

    Understanding inner product space and matrix representations of Operat

    (scroll to bottom for problem statement) Hello, I am wondering if someone could break down the problem statement in simpler terms (not so math-y). I am struggling with understanding what is being asked. I will try to break it down to the best of my ability Problem statement:Consider the inner...
  4. Athenian

    [SR] - Test Particle inside the Sun's Gravitational Field - Part 4

    So, here's an attempted solution: With ##r_{min}##, $$r_{min} = \frac{1}{B + \frac{\beta}{\alpha^2}}$$ With ##r_{max}##, I get: $$r_{max} = \frac{1}{B - \frac{\beta}{\alpha^2}}$$ or $$r_{max} = \frac{1}{\frac{\beta}{\alpha^2}}$$ Other than this, I and the team have absolutely no idea on how...
  5. jk22

    Destiny: space does not exist, only time and a suite of commands?

    What if the brain received simply a list of commands to execute, like a processor ? Hence all the visualization were just a creation of an internal geometry. Fatality is then unavoidable since the commands have to be executed and since the datas are one dimensional, there were no way to escape.
  6. mnb96

    I Question on tangent space and jet spaces

    Hello, I am reading some material related to jet spaces, which at first glance seem to be a generalization of the concept of tangent space. I am confused about what is the correct definition of a jet space. In particular, given a map ##f: X \rightarrow Y## between two manifolds, what is the...
  7. Athenian

    [SR] - Test Particle inside the Sun's Gravitational Field - Part 3

    Below, I have already solved - I assume - correctly for question 1. Question 2, I am nearing to what I believe is the solution. Question 3, I simply have no idea where I should begin considering that it is interconnected with question 2. With that said, below is the lengthy and somewhat tedious...
  8. K

    I Questions about the expansion of space on galactic scales

    How would the expansion on a scale of 10 kpc be measured, by a red or blue shift? How can expansion of space be differentiated from the velocity of stars? It seems that the expansion of space weakens the effects of gravity?
  9. Shahi

    Unraveling Landau's Mechanics: Why is Space Isotropic?

    Hi I am reading Landau's mechanics So in the first chapter page 5 It reads : since space is isotropic, the lagrangian must also be independent of the direction of v , and is therefore a function only of it's magnitude ... I can't understand why , I think Landau's book has many fans in this...
  10. Athenian

    [SR] - Test Particle inside the Sun's Gravitational Field - Part 2

    To begin with, I posted this thread ahead of time simply because I thought it may provide me some insight on how to solve for another problem that I have previously posted here: https://www.physicsforums.com/threads/special-relativity-test-particle-inside-suns-gravitational-field.983171/unread...
  11. Athenian

    [Special Relativity] Test Particle Inside the Sun's Gravitational Field

    Below is an attempted solution based off of another user's work on StackExchange: Source: [https://physics.stackexchange.com/questions/525169/special-relativity-test-particle-inside-the-suns-gravitational-field/525212#525212] To begin with, I will be using the following equation mentioned in...
  12. G

    B Understanding Dual Space: Mapping Vector Space to Real Numbers

    I understand that the Dual Space is composed of elements that linearly map the elements of the Vector Space onto Real numbers If my preamble shows that I have understood correctly the basic premise, I have one or two questions that I am trying to work through. So: 1: Is there a one to one...
  13. johnconner

    I Transformation matrix for an expanding space

    Hello. I am confused with this matter that how should we write the transformation matrix for an expanding space. consider a spacetime that is expading with a constant rate of a. now normally we scale the coordinates for expansion which makes the transformation matrix like this: \begin{pmatrix}...
  14. J

    Job Skills Miltary to Space Industry Career Advice Needed

    Everyone, this post is going on multiple forums/subreddits so I can get diverse feedback. Pardon the spam if you see it elsewhere: I am retiring from the military in three years from a non-technical specialty. I have a bachelors in management. I will be 45 when I depart. I will have a security...
  15. B

    Temperature inside an enclosed space

    its summer where i live and the ceiling space gets extremely hot, much hotter than ambient outdoor. under a shade outdoor, the air temp beneath shade will be colder than air temp in sunlight. yet in a space with no air flow, the temp is always hotter from my experience. why is this? this isn't...
  16. B

    How Long Would Scifi Space Travel Really Take?

    The interesting thing about scifi space travel is that it remains hard even with scifi tech, so long you allow propellant and gravity limits to still exist. In a way it is kind of a good thing, only in that it prevents widespread easy RKV starship use. My question is how long would travel take...
  17. phinds

    The first British woman to space is a <can't say>

    Sigh ... Best statement "... although aliens may not be made up of carbon and nitrogen like humans "it's possible they're here right now and we simply can't see them". " https://www.bbc.com/news/uk-51003374
  18. 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...
  19. 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...
  20. 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...
  21. 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...
  22. 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...
  23. 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...
  24. wolram

    B Exploring Interstellar Space: What Voyager 2 Has Taught Us

    With voyager 2 now going to interstella space what have we learned?
  25. 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.
  26. 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,...
  27. 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...
  28. 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.
  29. 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...
  30. 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.
  31. 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...
  32. 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...
  33. 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...
  34. 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...
  35. 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?
  36. 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?
  37. 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
  38. 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...
  39. 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...
  40. 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...
  41. 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...
  42. 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...
  43. 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?
  44. 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...
  45. 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...
  46. 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...
  47. 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?
  48. 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...
  49. 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...
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