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. T

    I Can We Mathematically Define Everyday Objects Like Smartphones?

    What are the ways of mathematically defining a space? We usually define a space by stating some common property shared by the points that make up the space in question, that is, a symmetry of that space. For instance, the ordinary 2-sphere is defined as all points ##X## that are at a distance...
  2. D

    To find the energy eigenvalues in the 3D Hilbert space

    A fictitious system having three degenerate angular momentum states with ##\ell=1## is described by the Hamiltonian \hat H=\alpha (\hat L^2_++\hat L^2_-) where ##\alpha## is some positive constant. How to find the energy eigenvalues of ##\hat H##?
  3. T

    I Meaning of permeability in free space

    Permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. And the inductance of an electric circuit is one henry (H) when an electric current that is changing at one ampere per second results in an electromotive force of one volt across...
  4. S

    B Exploring the Theory of Space: Understanding the Nature and Changes in Space

    Is there any theory law explaining the nature of space and describing what is space and what happens to space when some event take place in space.
  5. R

    Short Story Help: Time in a Timeless Space

    Hi, I am currently writing a short story where a character travels to the future. This universe operates much like the George Ellis hypothesis where the future is not defined yet and we are always in the leading edge known as "now". Therefore, by traveling to the future he/she comes to a place...
  6. L

    I GR and its bending of space time

    Hello Maybe my question is dumb but is the bent of space time instant due to gravity? If a mass pops into existence will space time be bent instantly ? Intercations between forces are light speed but gravity is and is not a force depending on pov
  7. L

    I The Expanding Universe: A Scientist's Perspective on Infinite vs Finite Space

    I have read some of the other posts about this topic but am still left unsatisfied. Could just be me. :cool: Did the universe, one minute after the big bang, consist of a finite volume of spacetime? If so, then is it not logically inconsistent that the universe can possibly be infinite now...
  8. G

    I Curvature of space and spacetime

    General relativity suggests that path of light is curved around sun. This curvature is not dependent upon frequency of the photon. What is the physical difference between 'curvature of space' and 'curvature of space-time' ? We can make measurements at two points in space at same time. But there...
  9. Chris Miller

    B Does the Expansion of the Universe Affect Gravity?

    Does the universe’s ongoing expansion mean that some finite amount of space-time is stretching, or that there is simply more and more of the same (space-time) being produced? Given the obvious difference between the dense primordial universe and the present, I’m guessing the former, which, if...
  10. engnrshyckh

    I want to calculate mark space ratio: f=25000Hz,T=4us

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  11. T

    B Why will an object in space continue moving foever?

    Why object in the space will continue moving foever if the object is in dynamic equilibrium?
  12. B

    Is Every Open Neighborhood of a Limit Point in a T_1 Space Infinitely Populated?

    Homework Statement Problem: Let ##A## be an infinite subset of a ##T_1## space, and let ##x## be a limit point of ##A##. Prove that every open neighborhood of ##x## contains infinitely many points of ##A##. Homework EquationsThe Attempt at a Solution First note that if ##\mathcal{O}## is an...
  13. mpolo

    B Does QM state that Space is made of nothing?

    I am trying to understand what space is. Does QM state that Space is made of nothing? In other words it does not exist?
  14. Stavros Kiri

    Stargazing Solar Activity and Space Weather Update thread

    I am picking this up as a continuation and extension of the idea laid out e.g. in @davenn 's thread "The Sun today - 9 July 2017 - nice spot group" https://www.physicsforums.com/threads/the-sun-today-9-july-2017-nice-spot-group.919696/ See also (for continuity purposes)...
  15. Noisy Rhysling

    Wasn't there a thread on making living space out of asteroid

    Because I just got started on John Varley's Dark Lightning, about an asteroid converted to an interstellar vehicle. Nice word pictures there. Any, some possible help for the person asking the question. Original thread is closed.
  16. O

    Stargazing Different Simultaneity for telescopes in space and earth?

    I was just wondering. According to Lorentz transformations, if two events are simultaneous in one reference frame, they will generally not be simultaneous in another. The time difference that I get between the two events in the other reference frame is \Delta t^{`} = \gamma\beta\Delta x...
  17. L

    B Why is resistivity important in solving this problem?

    In free space there are two masses: - Metallic sphere of mass M, radius R and total charge equal to 0. It has also a resistivityρ. - Metallic sphere of mass m, radius r and charge q. The distance between the masses is D. We can assume r <<R<<D and m<<M. The masses start accelerating until they...
  18. C

    I Why centrifuges on Earth and in space would be the same?

    In this forum I read a thread about centrifuge and learned that, ''There is no difference between centrifuges on Earth and centrifuges in space because gravity is in no way related to how a centrifuge works'' Reference https://www.physicsforums.com/threads/how-do-centrifuges-work.148518/ But...
  19. P

    B Can space be curved in relation to an absolute straight space?

    I have always had this question, and I wonder if someone can explain to me if I am wrong about it. In relativity they say space(time) can curve around massive bodies. Let's just consider space for a moment. For example on the surface of a sphere, you tell someone to walk in a straight line...
  20. N

    Information transfer in space - with book research

    I'm not sure if I'm posting in the correct category. Please direct me to the correct one, if I have made a mistake. As I have mentioned in my intro, my knowledge of physics is almost non-existent. I am writing a book series, and I'm trying to base my ideas on science (more or less). This is one...
  21. F

    Space elevator wondering about torque

    Say you have an elevator that reaches space. I have 2 questions : 1) say a space rock hits the top of the elevator... that would create a torque = force * distance on the ground... Wouldn't it instantly snap from any light force or space junk hitting the top of the elevator? Would the station...
  22. T

    B How can light travel around an object in space?

    I came across an article about one of the many observations that helped to confirm GR. This observation took place during the 1919 total solar eclipse. Stars that were located directly behind the sun could be seen during the total solar eclipse because the gravitational force of the sun bent the...
  23. S

    B Exploring the Relationship Between Earth's Mass and Time: Debunking the Myth

    Is it true that the time increase (24 hrs becomes 25 or 26 or..)when the mass of Earth is increase? ??
  24. nomadreid

    Self-dual solutions to Maxwell's equations, Euclidean space

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  25. J

    Can you change a planet's orbit by reducing its velocity?

    My question is, take Mars, say, and install a huge rocket engine on the ground pointing out the planet (obviously) and in the opposite direction of its velocity, so that if it is turned on, the planet is slowed. The rocket starts to work and Mars is slowed. If the loss of velocity goes little by...
  26. W

    B Help me understand light traveling through vast distances in space

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  27. V

    I Hyperbolic space simulation in VR

    I have come across an interesting simulation of hyperbolic space. I can't totally wrap my hand around it, though. But I am interested in technical part of it. As far as I see no object in the space would get curved when you are moving. The visual deformation is the result of bent light reached...
  28. J

    I Planck length and space expansion/contraction

    Imagine a cubic volume of space, defined today, with edges of the order of the Planck length. As cosmological time goes forward this volume expands so that the edges of the cube expand with the scale factor. This seems ok. However, as physics is time-reversible, it should be valid to imagine...
  29. A

    I Is zero vector always present in any n-dimensional space?

    In the book, Introduction to Linear Algebra, Gilbert Strang says that every time we see a space of vectors, the zero vector will be included in it. I reckon that this is only the case if the plane passes through the origin. Else wise, how can a space contain a zero vector if it does not pass...
  30. Telemachus

    Plot function of 3 space variables plus time

    Hi there. I am willing to plot a function of three space variables plus time, let's say ##\phi(x,y,z,t)##. The idea is to plot the 3D function for each time, i.e. evolving in time. As I have three independent variables, corresponding to the three Cartesian coordinates, the function is actually a...
  31. A

    I Where does the line element of Minkowiski space come from?

    How is it derived? ds^2 =-cdt^2+dx^2+dy^2+dz^2
  32. genphis

    B Does Mass determine our depth in the fabric of space?

    I have not posted for a while,but something has been bugging me. I would like help understanding that if mass makes a dent in the fabric of space, does it mean celestial bodies are sitting at different depths in the fabric, and does that mean the less mass in an object you are then more likely...
  33. T

    I Quantum entangled image sensor for space camera-telescope

    Could this be a possibility at some point? Since entanglement is not affected by distance, could we send cameras out to extremely distant places and get instantaneous signals? Only the image sensor would have to be entangled. It would still take the same amount of time as usual to get the camera...
  34. A

    So why is space travel so hurdlesome again?

    For some reason, whenever I see these documentaries on space travel, and how NASA explains its projects, they always make it sound like "OMG we'll be able to colonize space MAYBE a million years in the future, with super technology, yadda yadda" and "space travel is so difficult", but aside from...
  35. A

    B Gas Behaviour in Space: Exploring the Mysteries of Gaseous Matter Beyond Earth

    What happens to gases in space? Do they just dissapear? (Yes yes, yawn) Or can they make up a region of space, and stick together via gravity? And what about Jupiter and other gas giants? How do they work, if in space, all gases tend to just shoot out and spread into an even film?
  36. U

    B How are the concepts of space, time, and space-time related?

    I'm having a hard time understanding how changing space means changing time. In books I've read people are saying "space and time" or "space-time " but never explain what the difference is between the two concepts or how they are related. How are the concepts of space, time, and space-time...
  37. D

    A What Hilbert space for a spinless particle?

    I'm looking for a rigorous mathematical description of the quantum mechanical space state of, for instance, a particle with no internal states. At university we were told that it the Hilbert state of wave functions. They gave us no particular restrictions on these functions, such as continuity...
  38. P

    B How much space does a single photon occupy?

    If a photon leaves a source 4,2 light years away how far apart will it be from a similar photon it was adjacent to (say less than 10^3 wavelengths) when it departed. Does the inverse square law mean that individual photons get further apart and stay the same size or do they occupy a larger space...
  39. Sanborn Chase

    Iridium Question -- Why is Iridium plentiful in space rocks but scarce on Earth?

    Why is iridium plentiful in space rocks but scarce on earth?
  40. J

    A Phase Space Factor: Confused About 3D to 4D Conversion

    Hi, I'm recently reading "Particle Physics in the LHC Era" and there is a part about the phase space factor that confuses me. When giving the Lorentz invariant phase space, they wrote: d3p / 2E = θ(E) δ(p2 - m2) d4p This is very confusing as it equates a three dimensional differential to a...
  41. M

    A Constructing a function space to automatically satisfy BCs

    Suppose we have a piecewise function $$f(x) = \begin{cases} f_1(x) & \text{if } -1\leq x \leq \xi_1 \\ 0 & \text{if } -\xi_1\leq x \leq \xi_2 \\ f_2(x) & \text{if } -\xi_2 \leq x \leq 1 \end{cases}$$ where ##\xi_1,\xi_2## are known constants and ##f_1(x),f_2(x)## are unknown functions...
  42. J

    B How Does Group Orbit Theory Relate Torus and Cylinder Structures?

    I was listening to this lecture: and in it, sometime around the 30:00 to 40:00 minute mark, he implies that the torus' sturcture built up from the orbits of the group under addition on the real plane is the same idea as the cylinder's structure being built up from the orbits of the group under...
  43. S

    Planetary motion and a space station

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  44. Deepak K Kapur

    B Mechanism of Curvature of Space: Does it Happen Instantly?

    Hi all, How does matter curve space (what's the mechanism)? Does this Curvature happen instantaneously or does it happen at light speed? Thanks in advance.
  45. C

    Surface density on isolated conductors in space

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  46. Hiero

    B Special relativity implies the space cannot be "closed"?

    I think special relativity would disallow our universe from having the structure similar to an ant on a sphere. What I mean is that it can't be possible to travel in a constant direction and to come back to your original location. Suppose there is an observer S on a planet and an observer S'...
  47. Cota

    How can physics enhance robotics and electronics in school projects?

    Hello, I am a professional trainer in robotics & electronics. I need help to understand better some physics concept to integrate then in my school projects.
  48. Quantum Velocity

    I How stuff in empty space cools down?

    If a body have heat and floating in space do it loss heat? If it does loss heat and the how? Thanks!
  49. M

    How Does State Space Design Compare to Classical PID Controllers?

    Hello everyone. Iam just Learning about State space representation and controller design and have a fundamental question about the difference between classical Control theory and modern Control theory. I understood the state space is of advantage when dealing with MIMO systems or non-linear...
  50. Hiero

    B Special relativity; mixed up time and space due to motion

    I just want to be sure I understand this correctly: Suppose there's a long spaceship moving in uniform motion relative to me (an inertial frame). Now someone in the front* of the spaceship calls someone (on the phone) in the back of the spaceship. *(this long length of the ship is oriented...
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