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.
My understanding of why Mars lost its atmosphere was because it cooled down too much internally and that when this happened, the planet lost its magnetic field that helped protect it from solar winds (which then ended up stripping away the planets atmosphere). Is there anything that people could...
I have some questions linked to the following experimentation:
In 1985, the space shuttle Challenger took on board a cesium atomic clock. The duration of the mission, around our Earth, was seven days and the parameters of the trajectory were as follows: speed equal to 7700 m/s and altitude h...
A station is orbiting a planet at a distance R1, a moon is orbiting the planet at distance R2 with the period T. The planet itself has a radius rp and a mass mp. We know that when an object adds its velocity at a point in the orbit, the height of the opposite orbit will increase. Determine the...
Hi,
In the picture below, M is Milky Way Galaxy in red, both A's are Andromeda Galaxy in positions P1 and P2 , and W is some random galaxy.
Milky Way Galaxy lie in one plane just like all the planets in solar system. In what configuration Andromeda Galaxy lies? Does it lie almost at the same...
Bridge : For k= 1,2,3 ,4 let $N_k$ be the event that North has at least k aces. Let $S_k, E_k, W_k$ be be the analogous events for South, East, West. Discuss the number x of aces in West's possession in the events
a)$W_1', $
b) $N_2S_2,$
c) $N_1'S_1'E_1'$
d) $W_2- W_3$
e)$N_1S_1E_1W_1$
f)...
As we all know, light itself is the fastest thing in the universe, and the cosmic speed limit, basically. That said, it is said to go at 299,792,458 meters per second in a vacuum. That is pretty fast. However, I have a question I want to ask...
Does light really go that fast in a vacuum?
I ask...
As I understand it, photons are subject to the same time and space distortions under SR as anything else, which is why they don't perceive time or space, since they travel at the speed of light. To an outside observer, then, they should appear stationary, immobile at their moment of creation...
Problem: Let ## (X,d) ## be a metric space, denote as ## B(c,r) = \{ x \in X : d(c,x) < r \} ## the open ball at radius ## r>0 ## around ## c \in X ##, denote as ## \bar{B}(c, r) = \{ x \in X : d(c,x) \leq r \} ## the closed ball and for all ## A \subset X ## we'll denote as ## cl(A) ## the...
Hi. I have watched some YouTube videos which suggest space (itself) is expanding. This sounds the same as the distance (itself) between moving objects is increasing. What's the difference? How can this even be proven in a laboratory? It doesn't sound as though it can be measured with a tape...
Why is the Webb placed at L2 (Lagrange point 2)?
I read some articles that said it would be perpetually shaded being on the opposite side of the sun and moon, but that makes no sense when the Webb orbit is so huge?
So why is it at L2?
I would like to know what will be the visibility from the portable telescope aboard the International Space Station.
What could they potentially view, and what are (at least some of) the things they are known to have looked at?
Presumably they use it *inside* the ISS and not outside, and are...
Q1a)
- My current wrong answer is <-5.9e7, -3.3e8, -2.17e8> I used the Fnet = Gm1m2 / d^2 <unit vector> But i keep getting a dif answer each time
Q2a) - I thought i could find net force and then divide it by the mass, and multiply it by the time interval. However I got the answer <-4.5, 4.5...
A space is infinite dimensional when its basis is infinite. But how can I ensure that the basis of the space of all sequences whose limit is zero is infinite?
(After solving that, I would like to have a hint on this very similar problem which says: let V be a Linear space of all continuous...
Greetings, all. Please forgive my ignorance, but this is a question which has been on my mind for many years:
What space does the universe occupy?
To clarify what I mean: I'm in a building which is in the city of Hillsboro, which is the county of Washington, which is in the state of Oregon...
In Quantum Mechanics, how can you justify the use of distributions like the delta functional without introducing a rigged Hilbert space? I see that some texts do not make any reference to this subject.
I'm reading about the engineering of the James Webb and it surprised me that the temperature difference will be about 318 degrees from one side of the telescope compared to the other (85 C on one side and -233 on the other).
I didn't expect space to be that hot about a million miles further...
(a) Knowing ##E##, we can use equation (2) to determine ##V##. However, since ##\vec E## represents the distribution of electric field in space i.e. a function of (x,y,z). For example, ##\vec E = x \hat i + y \hat j + z \hat k##. Here we do not know this function so how can we know ##V## at a...
We can formulate the spacetime in an observer/coordinate independent way, i.e. a particle becomes a worldline in the 4d space. Then relative to each observer, the worldline can be casted to a function in R^3. However, I haven't found any reference on formulating configuration space in a...
Consider a rocket with mass ##m## in space is going to move forward. In order to do so, it needs to eject mass backwards. Let the mass that is ejected has velocity ##u## relative to the rocket. What is the equation for the final velocity?
It is said that after ##dt## second, the rocket will...
Maybe this is more general discussion, but I am excited / nervous about the upcoming launch of the JWST.
https://jwst.nasa.gov/content/webbLaunch/countdown.html
I can't wait to see the observations this endeavor will bring!
By definition of the vector potential we may write
\nabla \times A =B
at least in flat space. Does this relation hold in curved space? I am particularly interested if we can still write this in a spatially flat Friedmann-Robertson-Walker background with metric ds^2=dt^2-a^2(dx^2+dy^2+dz^2) and...
Hello all. I am studying stat mech from Pathria's book.
It says a system is completely described by all positions and momenta of all the N particles. This maybe represented by a single point in 6N-D gamma space. So, each point is a (micro)state.
Now if we restrict the system (N,V,E to E+ΔE)...
I've always had difficulty grasping why the electric and magnetic fields are in phase in EM waves in a vacuum. Of course, Maxwell's Equations imply that is the case, but I had a hard time intuitively visualizing it. Then I found this short video on YouTube. I would appreciate your opinion...
if we assume each photon of light as a very very light piece of matter (by famous E = mc^2 and then: m = E / c^2) and sum up all photons that have been made from the creation time of a galaxy (also considering limitation of speed of light) and also photons that accidentally passing throw that...
When a Mars Simulation Goes Wrong
https://www.theatlantic.com/science/archive/2018/06/mars-simulation-hi-seas-nasa-hawaii/553532/
The article came across my desk (computer screen). Human behavior is complicated.
I'm more interested in the technical side of space travel, specifically the...
Hi,
I don't know if it is the right place to ask for the following: I was thinking about the difference between the notion of spacetime as 4D Lorentzian manifold and the thermodynamic state space.
To me the spacetime as manifold makes sense from an 'intrinsic' point of view (let me say all the...
Looking for the best material for a heat exchanger exposed to vacuum in a space ship. I've initially gone with radiator vanes that are a ceramic blend and typically operate at twenty-five hundred degrees, but then I started wondering if there is a better material...and now I'm here, hoping for...
Hey! :giggle:
Give a probability space and events $A$, $B$ and $C$ such that $P [C \mid A]>P [C \mid A \cup B]$.So we want that $$\frac{P[C\cap A]}{P[A]}>\frac{P[C\cap (A\cup B)]}{P[A\cup B]}=\frac{P[(C\cap A)\cup (C\cap B)]}{P[A\cup B]}$$ But how can we find these events ? :unsure:
When moving around a circular spinning space station (doughnut shaped) Is there any difference in the direction one goes? Is the energy expenditure the same or different?
Would one ever feel like one is climbing?
My gut feeling says no, as the person walking has the angular momentum matching...
Hello everybody,
I am currently in the middle of my PhD in mathematics. In the beginning of the program I was quite sure that I would stay in academia, however it is becoming more and more clear to me that I want to go into industry once I am finished. During the last weeks I have started to...
It's written in one book I've got on solid state physics the following:
Can someone please explain how to get this number of 230 combinatorially?
Thanks!
Apparently, one of the solar arrays on the Lucy spacecraft failed to fully deploy.
https://scitechdaily.com/nasas-lucy-stable-in-cruise-mode-problematic-solar-array-is-75-to-95-deployed/
The fault may not be fatal. They may have enough solar power to complete the mission.
At the same time...
Hi there, experts on three-D space!
while thinking about (physical) space, I have come up with the following (geometry) question: Is it possible to define five points (A, B, C, D, E) in Euclidian space, so that all distances (AB, AC, AD, AE, BC, BD, BE, CD, CE, DE) can be expressed in rational...
On a long trip the photon goes, but it occupies a wavelength of space at any particular time. If the space between start and finish (inspection) is expanding all the way all the journey time, then most of the expansion has no effect on the photon. Like eg second tenth is section currently passed...
We know that ##v = \omega r## where ##r = R_{\text{E}} + h##. To compensate for the motion, the plane must fly along the equator at the same speed as the Earth but in the opposite direction, i.e. from east to west, so
$$\vec{v} = -\vec{ v}_{\text{E}}$$
$$v_{\text{E}} = \omega_{\text{E}}...
Hello!
I am reading "Differential Geometry and Mathematical Physics" by Rudolph and Schmidt. And they have and example of manifold (projective space). I believe that there is a typo in the book, but perhaps I miss something deep.
Definitions are the following
$$\mathbb{K}^n_\ast=\{\mathbf{x}\in...
Hi, I found this problem in Munkres' topology book, and it seems to be contradictory:
Let X be a metric space.
(a) Suppose that for some ϵ>0, every ϵ-Ball in X has compact closure. Show that X is complete.
(b) Suppose that for each x\in X there is an \epsilon>0 such as the ball B(x,\epsilon) has...
I want to develop a 2D random field and its change with time with constant velocity. My process:
1. Define a 2D grid [x, y] with n \times n points
2. Define 1D time axis [t] with n_t elements
3. Find the lagrangian distance between the points in space with the velocity in x and y ...
While learning about Special Relativity I learned that we use the Transformation matrix to alter the space .This matrix differs for Contravariant and Covariant vectors.Why does it happen?,Why one kind of matrix (Jacobian) for basis vectors and other kind(Inverse Jacobian) for gradient...
AFAIK there is no cosmological principle formulated about space and time. If it would be formulated, it would more or less state that spacetime is an interconnected whole, and has no gaps, edges or boundaries. It doesn't need to state wether spacetime is finite or infinite, that is an open...
I'm watching this minutephysics video on Lorentz transformations (part starting from 2:13 and ending at 4:10). In my spacetime diagram, my worldline will be along the ##ct## axis and the worldline of an observer moving relative to me will be at some angle w.r.t. the ##y## axis.
When we switch...
Before that, Lawrence Kraus stated "Empty space is a boiling, bubbling brew of virtual particles that pop in and out of existence in a time scale so short that you can't even measure them" . After reading https://www.physicsforums.com/insights/physics-virtual-particles/ especially this statement...
Guys I have Problems with this task The arrangement consists of a point charge Q at a distance (x0, y0,0) from the origin and two perfectly conductive surfaces in the (x, z) and (y, z) plane
a) Mathematical description of the space charge density p of the original and mirror charge using the...
Hey everyone,
I've read in an article that Newton's 3rd law proves that there is no ether in space. It says, according to Newton's 3rd law, the mass of the space between objects should be 0; then, ether does not actually exist.
Could you please explain to me why Newton's 3rd law imply that the...
An object moving through a fluid, such as the air, experiences a pressure drag caused by the difference in fluid pressure between the front and back surfaces of the object. Similarly, an object moving through a thermalized photon gas, such as the CMB, also experiences a drag. The cause in this...