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.
Would it be possible for photons to form some sort of static structure, like a standing waveform, if space-time was curved enough?
It seems like a structure like this exists around black holes. Is there any other distortion or phenomenon that could cause this, such as a neutron star or a galaxy?
First time poster here, and I need some experts to weigh in on a debate that I'm having on the Skeptics Guide to the Universe forum, here (https://sguforums.com/index.php/topic,51110.0/topicseen.html ). In my opinion, a few of the other posters are being pessimistic.
Given recent advances in...
Thanks for being here, this is my first post.
Imagine on a dark night a very powerful beam of light was aimed at the sun from earth
and switched on, at 23:00.
I am observing from side on, in space, at a distance far enough away to get a good view of the beam
as it travels out into space on its...
Hi, I am writing a report on uniqueness theorems and I am at the section for non asymptotically flat spacetime. I know that if we request certain restrictions, there are the existence of certain uniqueness theorems, however for the most part there are (so far) not many and they are hard to find...
The best story from space I remember is how NASA spent a huge pile of money trying to get a pen to work in so little to no gravity in space. They worked and worked away and the Soviets found the solution: using a pencil.
All the white space among words in a text file was lost. Write a C++ program which using dynamic programming to get all of the possible original text files (i.e. with white spaces between words) and rank them in order of likelihood with the best possible runtime.
You have a text file of...
Can the low temperatures in Space be employed to cool a Quantum computer installed on an operational Space vessel doing away with the need of a super fridge or whatever they use here on Earth? Thank you.
Homework Statement
Problem given to me for an assignment in a math course. Haven't learned about roots of unity at all though. Finding this problem super tricky any help would be appreciated. Screenshot of problem below.
[/B]
Homework Equations
Unsure of relevant equations
The Attempt at...
I am reading the book: Multivariable Mathematics by Theodore Shifrin ... and am focused on Chapter 8, Section 2, Differential Forms ...
I need some help in order to fully understand the vector space of alternating multilinear functions ...
The relevant text from Shifrin reads as follows:
In...
I keep hearing in these Science Channel programs that the reason why the Big Bang banged (instead of immediately collapsing into a black hole) is that when it banged it made space to expand faster than the speed of light. I'm always puzzled on how sure and certain the speakers look in these...
When a rocket engine exhausts into Space what happens to the particles or molecules that are thrown out?
My interest is firstly where do they go e.g.: orbit the Earth or other planetary body if from a shuttle, orbit the Sun if ejected outside the capturing influence of a planetary body, or just...
Hi everyone.
I'd like to verify my thoughts about travellig through space using a space curvature.
Imagine you have a spaceship and you want to travel some distance. Your ship launches an object into space that has huge mass and density. It curves space. Now, you enter the curved space and...
Hi PF
Given some linear differential operator ##L##, I'm trying to solve the eigenvalue problem ##L(u) = \lambda u##. Given basis functions, call them ##\phi_i##, I use a variational procedure and the Ritz method to approximate ##\lambda## via the associated weak formulation
$$\langle...
Hello everyone!
I am an undergraduate getting three bachelors in Anthropology/Ecology/Neurosciences (just to show off of course), but sadly no true physics (I don't show off that much, I'm still humble).
I am working on a personal project, a tabletop role playing game, where my main struggle is...
Did a quick search of an explosion in a vacuum and got most of what I was looking for, but on CBS Sunday morning they had a segment on restoring and reevaluating all of the immense footage of America's atmospheric nuclear testing program. They showed some amazing footage of the expansion of the...
I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...
I am currently reading Chapter 12: Multilinear Algebra ... ...
I need some help in order to fully understand the proof of Theorem 12.22 on page 276 ... ...The relevant text reads as follows:
In the above...
Our 4-D space is ##x^1,x^2,x^3 ,t##.
Our sub-manifold is defined by ##(x^1,x^2,x^3)##
Therefore for this sub-manifold to be maximally symmetric and for which the tangent vector ##\frac{∂}{∂t}(\hat t)## orthogonal to this sub-manifold
The metric becomes...
{Moderator's note: Moved to Cosmology forum.]
Dark matter and the fabric of space time,
Can someone with a real knowledge base of physics and the current accepted theories, please explain why the fabric of space is not the candidate for the elusive dark matter?
Having read extensively about...
Greetings: I watched several videos describing so-called "empty space" as being permeated with fields (electron field, quark field, etc.). Is it possible that it is actually these fields that curve about large masses and that the trajectory of light and matter curve because they follow the...
From the geodesic equation
d2xμ/dΓ2+Γμ00(dt/dΓ)2=0,for non-relativistic case ,where Γ is the proper time and vi<<c implying dxi/dΓ<<dt/dΓ.
Now if we assume that the metric tensor doesn't evolve with time (e,g gij≠f(t) ) then Γμ00=-1/2gμs∂g00/∂xs.
If we here assume that the metric components of...
Homework Statement
In the far future, humans have built a space elevator as a cheap
means of access to space. However before that could be done, a few basic principles had to be
worked out. . .
a)
What is the minimum initial speed (in an Earth-centered inertial reference frame) needed
for an...
Hey,
i can't see actual space in tesseract.
Like in 3 dimensional cube, you have squares as faces and between them there is a space.
But in tesseract where you have 8 cubes as faces, this leaves 0 space for actual space inside, i can see only 8 faces and nothing between them.
I first thought it...
Just a random thought: IF a strong rare Earth magnet and a superconductor like YBCO can perform meissner effect that holds them both in place, is it possible to make that in a larger scale, like in space?
I was thinking that since space's temperature is almost 0K, it can cool down...
I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...
I am currently reading Chapter 12: Multilinear Algebra and am specifically focused on Section 12.1: Vectors and Tensors ...
I need help in fully understanding Corollary 12.4 to Theorem 12.2 ... ...
Theorem...
Hey! :o
Let $S_{X,3}$ be the vector space of cubic spline functions on $[-1,1]$ in respect to the points $$X=\left \{x_0=-1, x_1=-\frac{1}{2}, x_2=0, x_3=\frac{1}{2}, x_4\right \}$$ I want to check if the function $$f(x)=\left ||x|^3-\left |x+\frac{1}{3}\right |^3\right |$$ is in $S_{X,3}$...
I am reading Loring W.Tu's book: "An Introduction to Manifolds" (Second Edition) ...
I need help in order to fully understand Tu's section on the dual space ... ... In his section on the dual space, Tu writes the following:
In the above text from Tu, just preliminary to Proposition 3.1 Tu...
I am reading the book: Multivariable Mathematics by Theodore Shifrin ... and am focused on Chapter 8, Section 2, Differential Forms ...
I need some help in order to fully understand some statements of Shifrin at the start of Chapter 8, Section 2 on the dual space ...
The relevant text from...
Hi Physics Forums community.
Let me briefly explain my current state of affairs. Next season, if every goes as planned, I will begin my Master's in Physics. I have, what I call, a positive problem; I like lots of branches of Physics (I study Physics because of pure passion and not because I...
I have a question regarding the nature of 2-forms (indeed k-forms ... but I'll focus the question on two forms ... ) ... Defining 2-forms and the space {\bigwedge}^2 ( \mathbb{R}^3 ) , Jon Fortney in his book: A Visual Introduction to Differential Forms and Calculus on Manifolds, writes the...
Hi all. I have a question about something Nima Arkani-Hamed said in his lecture on space-time about space contraction near light speed. I included a link to the lecture at the point where he refers to contraction of two space ships with a 'cable' between them, they are accelerating towards the...
this is what is given
so by addition
$$\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}$$
uhmmmm really?
Determine if the set of vectors
$\begin{bmatrix}
x\\y\\3x+2y
\end{bmatrix}$ $\in \Bbb{R}^3$
form a vector space
(with the usual addition and scalar multiplication for vectors in $\Bbb{R}^3$).OK first of all this doesn't have z in it.
So I don't know if this meets the requirement of...
On the set of vectors
$\begin{bmatrix}
x_1 \\ y_1
\end{bmatrix}\in \Bbb{R}^2 $
with $x_1 \in \Bbb{R}$, and $y_1$ in $\Bbb{R}^{+}$ (meaning $y_1 >0$) define an addition by
$$\begin{bmatrix}
x_1 \\ y_1
\end{bmatrix} \oplus
\begin{bmatrix}
x_2 \\ y_2
\end{bmatrix}
=
\begin{bmatrix}
x_1 + x_2 \\...
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...
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...
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?
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...
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...
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...
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...
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...
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...
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?
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??
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...
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...