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. DarkMattrHole

    I Question about the limits of space contraction near light speed

    Hi all. I have a question about something Nima Arkani-Hamed said in his lecture on space-time about space contraction near light speed. I included a link to the lecture at the point where he refers to contraction of two space ships with a 'cable' between them, they are accelerating towards the...
  2. karush

    MHB Set of vectors form a vector space

    this is what is given so by addition $$\begin{bmatrix}x_1\\y_1\\5z_1\end{bmatrix} \oplus \begin{bmatrix} x_2\\y_2\\5z_2 \end{bmatrix} = \begin{bmatrix} x_1+x_2\\y_1+y_2\\5z_1+5z_2 \end{bmatrix} = \begin{bmatrix} X\\Y\\10Z \end{bmatrix}$$ uhmmmm really?
  3. karush

    MHB Determine vec {{x},{y},{3x+2y}} in R^3 form a vec space

    Determine if the set of vectors $\begin{bmatrix} x\\y\\3x+2y \end{bmatrix}$ $\in \Bbb{R}^3$ form a vector space (with the usual addition and scalar multiplication for vectors in $\Bbb{R}^3$).OK first of all this doesn't have z in it. So I don't know if this meets the requirement of...
  4. karush

    MHB Is This a Valid Vector Space with Unusual Operations?

    On the set of vectors $\begin{bmatrix} x_1 \\ y_1 \end{bmatrix}\in \Bbb{R}^2 $ with $x_1 \in \Bbb{R}$, and $y_1$ in $\Bbb{R}^{+}$ (meaning $y_1 >0$) define an addition by $$\begin{bmatrix} x_1 \\ y_1 \end{bmatrix} \oplus \begin{bmatrix} x_2 \\ y_2 \end{bmatrix} = \begin{bmatrix} x_1 + x_2 \\...
  5. Zack K

    B How did Einstein come up with the thought of a space fabric?

    I've always wondered how we came to come up with such an idea. Was he one day sitting around and thinking, then made a random assumption and go "ah hah!". Or did his idea come up through his calculations on the nature of how gravity should cause interaction? Is their a literal fabric of space...
  6. D

    Would an astronaut be able to get back to the space station?

    Would an astronaut really bale able to make it back to the space station by throwing a wrench in the opposite direction if his cable broke and floated away? I heard this question as it relates to Newton's third law. Wouldn't the astronaut need to throw the wrench faster than he is moving before...
  7. J

    I Does all orbiting space debris eventually fall and why?

    Just read somewhere that we have left some 500,000 pieces of debris orbiting around earth. Some probably are near enough to touch a little atmosphere so it is reasonable to expect they will fall eventually. But what about the ones a little further? Will they never return to earth?
  8. M

    Show that a space is a Banach space

    Homework Statement Show the following space equipped with given norm is a Banach space. Let ##C^k[a,b]## with ##a<b## finite and ##k \in \mathbb{N}## denote the set of all continuous functions ##u:[a,b]\to \mathbb R## that have continuous derivatives on ##[a,b]## to order ##k##. Define the...
  9. R

    How Do You Calculate the Probability of No Events Occurring?

    Homework Statement 1. Suppose that A, B, and C are 3 independent events such that Pr(A)=1/4, Pr(B)=1/3 and Pr(C)=1/2. a. Determine the probability that none of these events will occur. Is it just: (1-P(a))(1-P(b))(1-P(c)) = 3/4 * 2/3 * 1/2 = 1/4 Homework EquationsThe Attempt at a Solution I...
  10. SebastianRM

    Problem 9.2 Classical Mechanics: Astronaut in a rotating space station

    Homework Statement Acceleration experienced by an astronaut in a rotating space station. Homework Equations What force would he experience is his own rotating frame of reference. The Attempt at a Solution Newton's second Law for a rotating frame is: mr'' = F net+ Fcor + Fcf Fnet (In the...
  11. Antony Death

    B Is the current definition of gravity accurate?

    The current definition of Gravity is: The force of attraction between bodies as a result of their mass. Gravity affects both the space and time of the area surrounding a mass, diminishing with distance, so is the current accepted definition truly accurate? Do I have the correct definition and if...
  12. GlassBones

    How to show a subspace must be all of a vector space

    Homework Statement Show that the only subspaces of ##V = R^2## are the zero subspace, ##R^2## itself, and the lines through the origin. (Hint: Show that if W is a subspace of ##R^2## that contains two nonzero vectors lying along different lines through the origin, then W must be all of...
  13. S

    How to determine if the space ship is moving or stopped?

    Homework Statement Tom is in a spaceship without windows and can not know outside condition. How can he know if the ship is moving with constant speed or stops? a. Measure the apparent speed of light in the spaceship b. Measure your precision watch. If it runs slower, the spaceship is moving c...
  14. Z

    B Earth from Space: What Would Hubble See?

    Assume the Hubble Space Telescope was in orbit around Pluto. What would it see when pointed toward Earth? I know the scene would change due to rotation and seasonal changes, but would our planet be blue? White? Green?
  15. A

    Phase space trajectories can't intersect...

    Phase space trajectories can't intersect each other is it due to the fact that at the intersection point there will be more than one possible path for the system to evolve with time??
  16. MattIverson

    What are phase space coordinates and how do you plot them?

    Homework Statement I have phase space coordinates (x0,y0,z0,vx,vy,vz)=(1,0,0,0,1,0). I need to analytically show that these phase space coordinates correspond to a circular orbit. Homework Equations r=sqrt(x^2+y^2+z^2) maybe? The Attempt at a Solution My core problem here is maybe that I...
  17. A

    Flight Path Angle and Velocity During Atmospheric Re-entry

    A space vehicle enters the sensible atmosphere of the Earth (300,000 ft) with a velocity of 25,000 ft/sec at a flight-path angle of -60 degrees. What is its velocity and flight-path angle at an altitude of 100 nautical miles during descent? (Assuming no drag or perturbations, two body orbital...
  18. D

    B How high can a helium baloon rise to space?

    Hey i have these ideas in which i use helium baloons. I wonder how high does it go and what is the gravity force and pressure at this point?
  19. K

    I Which function space do square waves span?

    Hello! As the topic suggests I´m interested which functions space square waves span? Lets say we define them as https://wikimedia.org/api/rest_v1/media/math/render/svg/5b8953debf86627276f45bf8822140ff2bbaee56 . Do they span the same space as the sines and cosines in Fourier analysis? :/ Thanks!
  20. N

    B Skydiving from Space -- maximum altitude?

    Hi everyone. I'm a skydiver. i would like to know the maximum altitude from where i can jump from the space and to be able to free fall back to Earth without geting lost in space. i think the actual record is 41425m. here is a brief story about world record spacedive...
  21. Arman777

    I Pair Production in Empty Space

    I am not sure this question has been asked here before but I am curious about it. From the Modern Physics Course, I learned that we need a nucleus to create an electron and positron pair (with a photon). And the reason is stated as to conserve linear momentum. If this is the case then how the...
  22. F

    I Space and time dependence of entangled particles

    It seems that the entanglement of two particles does not change with time and can cross long distanced as long an neither particle decoheres with the environment. This makes me wonder if the wave function for that entanglement can have any time or space dependence? I only did a brief search for...
  23. N

    Received power for free space optics

    Hello everyone, I have calculated the received power for free space optic (FSO) using the equation: Lsystem (system loss) is set to 8dB. PTotal can be calculated as: where Ntx (number of receiver) = 1 and PTx (transmitted power) =7.78 dBm. LGeo can be calculated as: where d2R (receiver...
  24. Prez Cannady

    I Inhomogeneous Wave Eq. & Minkowski Spacetime Interval

    Answer is probably not, but is there some connection between the inhomogeneous wave equation with a constant term and the spacetime interval in Minkowski space? $$ 1) ~~ \nabla^2 u - \frac{1}{c^2} \frac{\partial^2 u}{\partial t^2} = \sum_{i=0}^2 \frac{\partial^2 u}{\partial x_i^2} -...
  25. A

    So how is it accelerating (two rockets in space)

    Assume that there are 2 rockets in deep space or a place where there is nothing around to compare their motion to. Rocket A starts its thrusters but the observer in rocket A doesn't know about it. So my question is, if rocket A is considered to be stationary by the observer then how can he...
  26. Demigod

    B Hyperloop - Orbital Space Launch

    I'm hoping I can get my idea debunked or with some words of encouragement, continue my investigation in what could be an ideal way to solve some propulsion issues in space travel. What I'm suggesting is building a large circular "maglev" accelerator in space, similar to CERN, which wouldn't...
  27. Johnnyallen

    I Gaia Space Telescope and Lagrangian Point 2

    I'm confused (what else is new) about L2. While watching a video from PBS Digital Spacetime about the latest data drop from Gaia Space Telescope, Matt O'Dowd showed a CGI animation of the telescope leaving Earth then circling/orbiting L2 perpendicular to the Earth/sun plane. I thought that the...
  28. A

    B Collider in Space? LHC Possibilities Beyond Earth

    What could change if a collider like LHC would be built and made function in Earth's orbit or on another planet like Mars?
  29. H

    I Curvature of space in large regions: zero or not?

    I have read numerous times that the overall curvature of space in extremely large regions -1000s of megaparsecs say - is zero. I also keep reading that the expansion rate of the universe is increasing, and that the universe is resultantly positively curved. I would be interested in a...
  30. M

    B Space Time fabric graphic is misleading

    This has been bothering me for some time, and would like to get a physicist's view of it. If my understanding or contention is in error, please correct me (gently). I only have under grad physics from 1970, and was a microbiologist, though am interested in quantum physics, cosmology. My...
  31. QuasarBoy543298

    I Volume in phase space- Louviles theorem

    I was looking at the following proof of Louviles theorem : we define a velocity field as V=(dpi/dt, dqi/dt). using Hamilton equations we find that div(V)=0. using continuity equation we find that the volume doesn't change. I couldn't figure out the following : 1- the whole point was to show...
  32. V

    MHB Can Vector Space $(V,O_1,O_2)$ Represent 2 Graphs?

    Given a basis of a vector space $(V,O_1,O_2)$ can it represent two different non-isomorphic graphs.Any other inputs kind help. It will improve my knowledge way of my thinking. Another kind help with this question is suppose (V,O_1,O_2) and (V,a_1,a_2) are two different vector spaces on the...
  33. T

    I Lorentz Transformation in One-Dimensional Space

    If space only had one dimension would Einstein's speed of light postulate still lead to Lorentz transformation for motion along that one dimension? Relativity of simultaneity can obviously be demonstrated in one dimension (lightning bolts hitting opposite ends of stationary and moving train)...
  34. R

    B Standard candles in a stretching fabric of space

    I'm just trying to figure somethings out concerning the accelerating expansion of the universe and the measured redshift, etc. If a light emitting object moves away from us, because of the expansion of the universe, the speed of that object causes a redshift in this light. But this light, from...
  35. A

    I Expansion of 3-D positively curved space

    The metric of a 3-D positively curved space is dr2+ Sk(r)2(dθ2+sin2θdΦ2). Now if this space expands with a scale factor a(t) from r to r'. Whether the change in the radial component be a(t)dr and angular component be Sk(r')dθ and Sk(r')sinθdΦ since the change due to expansion is already...
  36. E

    Space With Schwarzschild Metric

    This is a problem from Tensor Calculus:Barry Spain on # 69 Prove that a space with Schwarzschild's metric is an Einstein space, but not a space of constant curvature. The metric as given in the book is $$d\sigma^2=-\bigg(1-\frac{2m}{c^2r}\bigg)^{-1}dr^2-r^2d\theta^2-r^2\sin^2 \theta...
  37. K

    Mathtype: extra space after inline equation

    Hello, i use mathtype 7.3 in word - in office 365 for equations. Everything is okay, but when inserting an inline equation, an extra space is inserted after the equation in Word. It looks ugly. i found http://dessci.com/en/support/mathtype/tsn/tsn143.htm but it didnt help me. It does not work...
  38. sarumman

    Proving or Disproving Null Space Containment in F(n) for A and A^2

    Homework Statement given I am required to proove or disprove:[/B] Homework Equations rank dim null space The Attempt at a Solution I tried to base my answer based on the fact that null A and null A^2 is Contained in F (n) and dim N(A)+rank(A)=N same goes for A^2.
  39. G

    Converting a household space heater to DC

    Hello, Basically, I use a portable electric space heater to keep my room warm during the winter, and it works quite well, except it makes a very loud hum that keeps me awake, so my options right now are poor sleep due to hum or having my room drop to about 12 C over night if I turn the heater...
  40. A

    Quantum energy of a particle in a 2 dimensional space

    Homework Statement [/B]Homework Equations Doing this problem like e.g setting the determinant of potential matrix and the ω2*kinetic matrix equal to 0 ,det(V-ω2T)=0,I got the frequency of the normal modes of vibration to be 2ω0 and ω0 where ω0 is the natural frequency, But sir how to treat...
  41. A

    Quantum energy of a particle in 2 dim space

    Homework Statement Homework Equations Doing this problem like e.g setting the determinant of potential matrix and the ω2*kinetic matrix equal to 0 ,det(V-ω2T)=0,I got the frequency of the normal modes of vibration to be 2ω0 and ω0 where ω0 is the natural frequency, But sir how to treat this...
  42. wlc88

    B The Red Light Shift and Space Debris

    Hi, As I understand it the theory that the universe is expanding is in part based off the red light shift. My question is could atoms in space, dust etc cause the red light to travel faster. I realize that space isn’t a medium, but could the aforementioned atoms and dust exist in such...
  43. Rafid Mahbub

    A Exploring parameter space of inflation models

    I have been studying primordial black hole formation through inflation for a while and I was curious to know how the parameters in an inflation model are determined such that they are consistent with CMB constraints. In my literature reviews, there are quite a few models that exhibit an...
  44. J

    B When light arrives at the end of space, what happens?

    In the big bang theory, inevitably we have the end of space. Expansion ratio is same everywhere in space. The end of the universe moves from us at the very high speed, but there space also hardly expands(Ho << 1). Then what happens to the light that arrives at the end of space? Will it stop...
  45. Math Amateur

    MHB The Space of All Derivations at a point p .... Tu, Theorem 2.2 .... ....

    I am reading Loring W.Tu's book: "An Introduction to Manifolds" (Second Edition) ... I need help in order to fully understand Theorem 2.2 and the remarks after the theorem ...Theorem 2.2 and the remarks after the theorem read as follows: My questions on the above text from Tu are as follows...
  46. D

    Heating efficiency of a Heat Pump and a Space Heater

    Homework Statement Instead of pumping heat into the cabaret air from the outside air, you could simply put an electric space heater inside the cabaret. A space heater turns electrical energy directly into thermal energy. Why would operating a space heater consume more electric power than...
  47. G

    I Existence of Directional Derivative in Normed Linear Space

    Given a finite-dimensional normed linear space ##(L,\lVert \cdot \rVert)##, is there anything that suggests that at every point ##x_0 \in L##, there exists a direction ##\delta \in L## such that that ##\lVert x_0 + t\delta \rVert \geqslant \lVert x_0 \rVert## for all ##t \in \mathbb{R}##?
  48. A

    Conservation of Momentum Space Ship Problem

    Homework Statement The payload of a spaceship accounts for 20% of its total mass. The ship is traveling in a straight line at 2100km/hr relative to some inertial observer O. When the time is right, the spaceship ejects the payload, which is moving away from the ship at 500km/hr immediately...
  49. D

    I A surface integral over infinite space

    Hi. If a function f is normalizable ,ie f→0 as | x | → infinity or r→ infinity then I presume the following surface integral f dS over infinite space is zero ? But I thought about this again and it seems like a case of zero x infinity. The function is zero at the infinite surface but the area...
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