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.
Please bare with me as I'm a beginner with this stuff, and am just learning lol But I was wondering if I did the right math to figure out the momentum of the Space Shuttle.
Linear Momentum, in classical mechanics, is the product of the mass (the measure of an objects resistance to acceleration...
I am curious why a more intimate relationship between light and empty space is not something one ever hears about when I think about the three obvious examples of why there seems to be a relationship. 1) Light follows a curve when in a curved spacetime (a gravitational field), 2) photons at...
After talking to a coworker, I looked into the wikipedia article on "Gravity of Earth". I found that the Earth's gravity is not uniform, which makes sense (never thought about it). I have always wondered why satellites de-orbit over time. Someone told me that there is enough space dust to slow...
Homework Statement
[/B]
Driving to work, a commuter passes through a sequence of three traffic lights. At each light he either stops, denoted by s, or continues, denoted by c. Assume that the outcome c or s for each traffic light is independent of the outcome of other traffic lights.
(a)...
This is basically just a comprehension question, but what makes elements of the Hilbert space exist in infinite dimensions? I understand that the number of base vectors to write out an element, like a wavefunction, are infinite:
\begin{equation*}
\psi(x) = \int c_s u_s (x) ds = \sum_k^{\infty}...
Hello.
I was thinking about gravity and how matter bends the ST (space time) creating gravity.which lead on to singularities. I wondered how much mass it would take to either make a hole in spacetime, or how much it would take to make a black hole. So I googled it.
This is where my confusion...
Hi All,
what is the reason why very close to an electromagnetic source (Fresnel Region), the wave impedance Z0 in free space for electric field and magnetic field is not the same? Z0 for magnetic field increases and for electric field decreases by increasing the distance from the source...
A few years ago, a Australian guy jumped from a platform that was attached to a weather balloon, from roughly 24 miles or so in the atmosphere. News articles claimed he jumped "From the edge of space".
https://en.wikipedia.org/wiki/Felix_Baumgartner
But did he?, I mean clearly 24 miles is an...
the moment there was matter there was time and thus even as time was shaping up to be the dimension we now know there must have been another dimension let's call it :"time2" in which our time was forming، can you say that? This is because time is matter as it forms the fabric of space and time.
I was thinking about the age of the universe which is said to be 13.8 billion years approximately. I read that this is derived from two sources , calculating the life of the oldest stars in the observable universe and from extrapolating backwards the distance which is radius from Earth to all...
Specifically, what I am wondering is gravity considered to be a physical contraction of space? For instance the space between any two points A and B shrinks as gravity grows stronger. Is this the right concept?
Homework Statement
Question is uploaded
I have completed till part iii and obtained correct answers
i. 2
ii. Basis for R:- { ( 2 3 -1 ) , (1 4 2 ) }
Cartesian equation; 2x-y+z=0
iii. Basis for Null:- { ( -3 2 0 1 ) , (2 -3 1 0 ) }
2. The attempt at a solution
I have problem in last part. I...
Homework Statement
How many functions y(t) satisfy both y''+t^2*y=0 and y(0)=6?
2. The attempt at a solution
As this is a second order differential equation, two initial conditions (for y and y') would be needed to obtain a unique solution (cf. existence and uniqueness theorem). So the...
Hey everyone,
So, my school club was approached by a local entrepreneur that sends up cubesats as well as ping-pong ball sized "satellites." The original intent of these (what he likes to call) Pongsats was to get kids excited about STEM and space. He send them up for free via weather balloon...
Homework Statement
The question is:
if vectors v1, v2, v3 belong to a vector space V does it follow that:
span (v1, v2, v3) = V
span (v1, v2, v3) is a subset of V.[/B]
2. The attempt at a solution:
If I understand it correctly the answer to both questions is yes.
The first: the linear...
ok so this has been on my mind for a while. If the hotter a stars burn or flame the further it goes on the spectrum correct so what if it burned so hot it is literally invisible wouldent that be considered a dark matter then it's a dark matter sun
Homework Statement
2 large plates are separated by a distance d and a space charge of uniform charge density p is placed between them and a potential difference V is applied across the plates. Find the electric field stength at a distance x fromt the positive plate
The answer is -V/d...
Here's an interesting article from Quanta magazine:
https://www.quantamagazine.org/20170223-bootstrap-geometry-theory-space/
and some backstory:
https://en.wikipedia.org/wiki/Bootstrap_model
In another forum, the question was raised, "could a ship with 1G acceleration escape the gravity well of a planet with 1G gravity?"
A popular response is, if the craft is aerodynamic, it could accelerate laterally until it reached escape velocity and then manage to get to space.
I don't...
Homework Statement
Let γ : I → R3 be an arclength parametrized curve whose image lies in the 2-sphere S2 , i.e. ||γ(t)||2 = 1 for all t ∈ I. Consider the “moving basis” {T, γ × T, γ} where T = γ'.
(i) Writing the moving basis as a 3 × 3 matrix F := (T, γ × T, γ) (where we think of T and etc...
I have a question. If something stands absolutely still in the space can it time travel?? I mean can it fall out of this universe? I am not a Physicist and forgive me for my mistakes in English.(I am foreigner) Just a question.
I've been stuck on this physics problem for several years now. I would be very grateful if someone could explain how to solve this problem. The farthest a human could travel from Earth in one lifetime theoretically is limited only by the acceleration a human can withstand, and the length of...
Based on classical physics all things attract one another due to their own gravity pull, so theoretically the Earth is drawn closer to a tennis ball even if its impossible to detect. Knowing this and Einsteins theory of relativity of spacetime could I not assume then that every physical body...
Homework Statement
The equation given:
dy/dt = 3*y
A basis for the space of solutions is required.The Attempt at a Solution
According to me it is e^(3*t) but it has turned out false. Why? I am considering the answer "The basis is the set of all functions of the form c*e^(3*t) but a...
In a nutshell, does Newton's "action = -reaction" law apply to massless particles? If a spaceship directs a condensed light beam on its own heat-resistant photon sail, what would happen?
Homework Statement
Consider the set V + {all periodic *complex* functions of time t with period 1} Draw two example functions that belong to V.
Show that if f(t) and g(t) are members of V then so is f(t) + g(t)Homework EquationsThe Attempt at a Solution
f(t) = e(i*w0*t))
g(t) =e(i*w0*t...
Hello all,
at the beginning, let me say that I haven't studied General relativity yet, I might have some knowledge at popsci level only... So I apologize if the question looks stupid...
At cosmological scale we observe that universe is expanding. If I understood well, this includes only the...
Our Professor said there will be still an electric field in empty space even without charges.Hows that possible.Space-time has a some quantum property that acts like this ?
Hello there. I'm currently trying to come to terms with the aforementioned topics. As I am self studying, a full understanding of these concepts escapes me. There's something I'm not grasping here and I would like to discuss these to clear away the clouds.
As I understand it, a basis for some...
Why does an object is attracted towards Earth according to Einstein?? I only know that celestial objects are attracted due to curve made by another massive object but what happens in case of objects attached to Earth??[emoji26] [emoji26]
Hello PF,
I built a small application which I figured some users here may be interested in. The app aggregates news and events in the space industry, allows you to view launch schedules, track the space station, and more.
It's called Luna and an early version is available on the Play Store...
Maybe there's a tiny battery somewhere, just to make it realistic. The wire is also very thin, and thus needs little to no force to be bent.
What happens to the wire? Does it twist on itself because each piece of the wire experiences a Lorentz force due to the magnetic field of the wire on the...
Homework Statement
Prove the following form for an inner product in a complex space V:
##\langle u,v \rangle## ##=## ##\frac 1 4####\left| u+v\right|^2## ##-## ##\frac 1 4####\left| u-v\right|^2## ##+## ##\frac 1 4####\left| u+iv\right|^2## ##-## ##\frac 1 4####\left| u-iv\right|^2##
Homework...
If some function is element of space ##L^2(0,1)## then
\int^1_0|f(x)|^2dx< \infty. What in the case when it is not so simple to calculate this integral. For example ##f(x)=x^{-1}(C_1+C_2 \ln x)##. How to find is it this function in ##L^2(0,1)## for some ##C_1,C_2##?
I just read Carlo Rovelli new book "Reality is Not What It Seems: The Journey to Quantum Gravity" in one sitting and quoting the relevant passage:
"The world is not made up of space + particles + electromagnetic field + gravitational field. The world is made up of particles + fields, and...
I've read Sir Arthur C Clerk's space odyssey series and curious of the propulsion technologies used in those ships. Ships like Universe and Galaxy of space odyssey 2061 use just water. The fiction speaks of "muon propulsion" too. The main spacecraft s that we see in his 'space odyssey' series...
Someone asked me the other day that
a photon is traveling at c and he is also traveling at c (suppose)
then to him the photon is at rest and so it must have a mass
I could not answer him and so I need some help
I am not sure I can express clearly my thoughts on this one, but I am going to try.
The effect of mass on space, and the resulting gravity, is sometimes described, in a two dimensions graphic, as a bowling ball applying pressure on the surface of a mattress, or something equivalent.
Thus, the...
By space, I mean a vector space which could be a representation of a group or even have some expanded algebraic structure. So I am not sure if this question goes here or in the Algebra subforum.
Consider the tensor square r\otimes r of an irreducible group representation r with itself, and...
GR lacks absolute space, but does Newtonian physics also? If not what does GR lacking absolute space mean?
I had thought in Newtonian physics that there existed an absolute space in which Newton's laws are true, and that an inertial frame was a reference frame in relative uniform motion to...
Homework Statement
Build the matrix A associated with a linear transformation ƒ:ℝ3→ℝ3 that has the line x-4y=z=0 as its kernel.
Homework Equations
I don't see any relevant equation to be specified here .
The Attempt at a Solution
First of all, I tried to find a basis for the null space by...
I know that the span of any subset of vectors in a vector space is also a vector space (subspace), but is it true that every vector space has a generating set? That is, the moment that we define a vector space, does there necessarily exist a spanning set consisting of its vectors?
There is this science gadget that consists of two parobolic mirrors, one with a hole in it and you place an item in the bottom of one, turn the other mirror with the hole on top of it, and you can see the image of the item standing above the hole in the top mirror. How is this done? Are the...
If a line in space has no thickness, how can I distinguish the line from its surroundings when I look at the line such that I can't see its length? After all, in three dimensional space, you can look at a line from different angles.
Dear forum,
I am trying to understand what a separable vector space is. I know we can perform the tensor product of two or more vector space and obtain a new vector space. Is that vector space separable because it is the product of other vector spaces?
thanks