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.
Homework Statement
In a lab that I did in Physics we calculated the magnetic field of a solenoid while constantly increasing the number of time the wire was wrapped around the electromagnet. After I obtained all the values, plotted it in a graph and found the line of best fit, the slope came...
Since NASA is currently under way with the deep space Ion drive, they plan on using xenon to power this propulsion system. My question is could they harness the already existing radioactive particles in space to power it? If they could then there would be almost an unlimited supply of fuel for...
I just read something that I do not want to misinterpret.
If there are two orthonormal basis that span the same space, which I think implies that each basis can be written in terms of the other basis, then measurements made with respect to each basis will not commute?
Does this mean that...
Another Doubt
Guys, I was watching this video on youtube. it is about weightlessness in space. it states that the astronauts inside a spaceship fly in space not due to zero gravity but due to centripetal force with which the satellite is revolving the earth. My question is "then why the...
Hi all,
I need an algorithm that fills a 3d lattice from any point, always expanding (no return allowed as in ref. http://msl.cs.illinois.edu/~lavalle/papers/KufLav09.pdf). The cells must be visited just once.
My efforts are contained in the attached file. It works ***almost*** correct. Some...
Two questions, underlined:
I have read that the universe began with a singularity.
Then space began expanding.
How can space expanding affect a singularity? Has this conundrum been resolved?
If time was speeding up, is would act the same as space expanding, but it would affect a singularity...
Some posts in another thread lead me to a search which ended when I read the following "kets such as ##|\psi\rangle## are elements of abstract Hilbert Space".
That lead me to this paper.
http://www.phy.ohiou.edu/~elster/lectures/qm1_1p2.pdf
"The abstract Hilbert space ##l^2## is given by a...
I always had this doubt,but i guess i never asked someone. What's the main difference between the Classical phase space, and the two dimensional Hilbert Space ?
Sorry new here trying this question. From the perspective of a light particle leaving its star that particle would arrive everywhere in the universe instantly since it is traveling at the speed of light. But we trust our perspective of time and distance in light years to describe what we are...
Homework Statement
Consider the subspace $$W:=\Bigl \{ \begin{bmatrix}
a & b \\
b & a \end{bmatrix} : a,b \in \mathbb{R}\Bigr \}$$ of $$\mathbb{M}^2(\mathbb{R}). $$
I have a few questions about how this can be decomposed.
1) Is there a subspace $$V$$ of...
If you have two different containers filled with two different gasses at the same temperature, would they have less pressure when connected to each other?
Dalton's law states that each of the gases behave independently when it comes to pressure as they fill the space as if they were the only gas...
When a mass is in a circular motion and suddenly gets released by its centripetal force, it will continue traveling in a straight path (tangent to the circle and perpendicular to the radius in the moment of release) if no other forces acting.
So let’s make a case: We have a space centrifuge...
Hello Experts,
This is @Shubham Jaydeokar, and today I'm going to post a question regarding a software named Space Radio.
I have been working on my project of making a receiving setup for listening to the audio signals sent by ISS at 145.800MHz.
According to AA2TX@amsat.org, Anthony Monteiro, I...
Hi folks,
Tell me please why in classical Newtonian physics one can say that the space and time are independent? But we have equations of motion which clearly show this dependence (x=Vt; x=x0+1/2at^2+v0t).
Thank you.
Would lightning work in space? I think it would but you wouldn't be able to see it?
Let's say I have some sort of device that creates a lightning bolt, if I shot it at a watermelon in a vacuum or another target would it hit the target, or nothing happen because of the vacuum?
##\def \sqx{\frac{1}{\sqrt{2}}}##
If Szu represents spin-up in the z-direction and Szd represents spin-down in the z-direction then the vector which represents spin-up in the x-direction is given by the superposition of the z states \begin{equation}|S_{zu}\rangle =\begin{bmatrix}1 \\...
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 ?