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.
Hello everybody, new here. Sorry in advance if I didn't follow a specific guideline to ask this.
Anyways, I've got as a homework assignment two cannonical transformations (q,p)-->(Q,P). I have to obtain the hamiltonian of a harmonic oscillator, and then the new coordinates and the hamiltonian...
I am reading Stephen Willard: General Topology ... ... and am currently focused on Chapter 2: Topological Spaces and am currently focused on Section 3: Fundamental Concepts ... ...
I need help in order to fully understand a result or formula given by Willard concerning a link between...
Summary:: I would like to get a career in commercial space technology and business and that is why i started my 2nd bachelors in aeronautics at the age of 30 three years early. I am about to complete my bachelors in aeronautical science from Embry riddles world wide. I don't know what next to...
This exercise is located in the vector space chapter of my book that's why I am posting it here.
Recently started with this kind of exercise, proof like exercises and I am a little bit lost
Proof that given a, b, c real numbers, the set X = {(x, y) E R^2; ax + by <= c} ´is convex at R^2
the...
probably a daft question asked before, but.
if space is expanding at an accelerating rate would that mean time is accelerating too?.
after all Einstein* claims and the maths seems to say that space and time are the same thing, ie space-time.
so if space is expanding faster and faster shouldn't...
I am reading Stephen Willard: General Topology ... ... and am currently reading Chapter 2: Topological Spaces and am currently focused on Section 1: Fundamental Concepts ... ...
I need help in order to fully understand an aspect of the proof of Theorem 3.7 ... ..Theorem 3.7 and its proof...
In a discrete metric space open balls are either singleton sets or the whole space ...
Is the situation the same for open sets or can there be sets of two, three ... elements ... ?
If there can be two, three ... elements ... how would we prove that they exist ... ?
Essentially, given the...
I am reading this book and in there the spacetime defined as a manifold such that an affine space of dimension 4. I am having trouble to understand the affine space. I made some reasearch but I couldn't grasp the idea of it. In the books its also stated that " We are familiar with the structure...
I read (in "The View From The Center") that Jupiter protects the Earth from collision with large space rocks, asteroids, etc.
What I can't get out of my mind is that could it also cause collisions. A large rock (initially not heading for Earth) could be put on a different path by Jupiter's...
Now that gravitational waves are more famous because of LIGO, it got me to thinking about what we (lay people) are usually told would happen, which is that the Earth will continue in a straight line at a tangent to its orbit at that moment that information arrives eight minutes later. Which is...
hi guys
our solid state professor sent us a work sheet that included this example :
i solved it not sure its correct tho :
is it that simple , or this is not the right approach for it ?
Hi
I found this paper on the measurement of unknown velocity vector of a closed space. Does it mean that it is possible to measure the unknown velocity vector of a closed space ? Can someone explain it to me
Summary:: the set of arrays of real numbers (a11, a21, a12, a22), addition and scalar multiplication defined by ; determine whether the set is a vector space; associative law
Question: determine whether the set is a vector space.
The answer in the solution books I found online says that...
The ISS includes a very fancy running machine which astronauts use to maintain fitness. Several astronauts have run Marathons at the same time as the earthly race (London, Boston etc) and, while there have been many press reports of these runs, none has given any indication as to how hard it is...
I am including a link to a B level discussion of this I found on-line to try and anchor my question, not because I think the below article is good or poor - I am not able to assess that.
https://www.einstein-online.info/en/spotlight/changing_places/#The_analogy
In particular I am asking about...
Hey
Could you give me a hint how to explain this example?
Need help to prove statement in red frame.
Example from book (Topics In Banach Space Integration)
by Ye Guoju، Schwabik StefanThank you
Hello,
I am after some help to try and understand SVM implementation is a micro that controls a motor.
As I understand it one of the advantages of using space vector modulation over sinusoidal PWM modulation in motor control is that it can control the phase voltages such that the line-to-line...
Is it correct to say that:
the cotangent is given by the gradients (*) to all the curves passing through a point and it actually spans the same tangent space to a point of a sphere? If you visualize them as geometric planes (**), the cotangent and the tangent spaces are more than isomorphic...
Hi
With displacements, I KNOW that three orthogonal axes cover all of 3D Space.
What about rotations?
How do I KNOW that the Tait or Euler angles cover all orientations?
For Tait, I would almost "expect" it.
The object rotates about the local body axes in order of: one axis, then a second...
I was wondering if it would be possible to see the history of space if one was to stand at the edge of the universe as it expanded faster than the speed of light. If the universe was to be expanding faster than the speed of light right now, and I was able to somehow go there and keep up with it...
From Tong gravity notes pdf page 32 :
We see from the picture that there are more ways to “go to infinity” in a null direction than in a timelike or spacelike direction. This is one of the characteristic features of Minkowski space.
I read that also elsewhere.
Why are there many null-like...
I am reading Tej Bahadur Singh: Elements of Topology, CRC Press, 2013 ... ... and am currently focused on Chapter 1, Section 1.2: Topological Spaces ...
I need help in order to fully understand Singh's proof of Theorem 1.3.7 ... (using only the definitions and results Singh has established to...
Hi,
The following is not a homework question.
My question is:
My answer is:
Total pages required = 2^32/2^7 = 2^25 pages
Thus page table has 2^25 entries
PM = 2^16
Total page frames in PM = 2^16/2^ 7= 9 page frames
Somebody please guide me what is the correct solution for the above.
Zulfi.
I am reading Sasho Kalajdzievski's book: "An Illustrated Introduction to Topology and Homotopy" and am currently focused on Chapter 3: Topological Spaces: Definitions and Examples ... ...
I need some help in order to fully understand Kalajdzievski's definition of a closed set in a...
I just love space rocks :biggrin:
The latest addition to my meteorite collection
NAME (LOCALITY): Huckitta, Huckitta cattle station, NT, Australia
FALL DATE: Unknown, found 1924 (TKW 2300kg)
CLASS: Pallasite, PMG-an
WEIGHT g: 220.1g
METEORITICAL BULLETIN: Never published in the...
If something happened 350 million years ago in space, are we just seeing it/ receiving the light now? From SpacePlace "The nearest large galaxy to us, Andromeda, is 2.5 million light-years away. So, we see Andromeda as it was 2.5 million years in the past." Wow!
In relativity, a flat space is always regraded to be endowed with an invariant metric field ##g_{\mu\nu}(x)= \eta_{\mu\nu}##, So in a flat space the corresponding connection ##\Gamma_{\mu\nu}^\rho(x)=0## It means that if we parallel transport a vector ##v^\nu(x_0)## in the space. Then it...
Space is space with the virtual absence of mass, with the presence of radiation and whatever stray particles that pass over it.
From a scifi perspective space can be used for a type or even types of scifi propulsion.Since space is volume and the virtual absence of mass, any scifi drive that was...
Is a BSc in space science regarded as a valid/competitive degree? It looks like a relatively newer degree. I am currently in Space Science, which is a major in Pnysics with a focus on orbital mechanics and space mission management.
Basically I am just looking for an industry outlook/opinion on...
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...
(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...
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...
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.
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...
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...
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?
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...
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...
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...
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...
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}...
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...
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...
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...
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