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.
(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...
Hi all,
Consider a system of ##N## noninteracting, identical electric point dipoles (dipole moment ##\vec{\mu}##) subjected to an external field ##\vec{E}=E\hat{z}##. The Lagrangian for this system is...
In dynamic programming:
1. what is the definition of the space of subproblems? does it have a mathematical definition?
2. why is it necessary to have an arbitrary index for the subproblem to vary?
To elaborate on question 2, I've taken the following paragraph from chapter 15.3 in...
Given that we know experimentally that time slows and space bends in the presence of matter, what is the actual physical mechanism that enables matter to bend space and slow time?
Science fiction is of course full of all kind of futuristic ideas about interstellar space travel and ways of propulsion, some more physically plausible then others.
But within the current realm of what is physical possible, what could interstellar space travel be like?
First you need a source...
If an infinite amount of energy were available to create the lift mechanism for a space launch. What would be required to fire a 200lb object into low Earth orbit(160km) after speeding it up in a way similar to how the large hadron collider speeds up a particle.
Assuming the launch vehicle...
I attatched an example plot where I created the histogram for the differential distribution with respect to the energy of the d-quark produced in the scattering process. My conception is that the phase space generator can "decide" how much of the available energy it assigns to the respective...
What do you guys think of this soberly elegant proposal by Sean Carroll?
Reality as a Vector in Hilbert Space
Fundamental reality lives in Hilbert space and everything else (space, fields, particles...) is emergent. Seems to me a step in the right conceptual direction.
So carbon nanotubes are incredible. Is a macrtube a possibility? If we stretched one out for centuries, and landed it on another planet, would it transfer gravity?
Hi,
How do I left align the text below? Also, how do I create vertical spaces above and below the line stating "Subbing the following expressions..."? Could you please help me with it?To derive 14(ii) m_{0} \gamma^{2} \frac{d^{2} y}{d t^{2}}=e E_{y}^{\prime} from 13(ii) m_{0} \frac{d^{2}...
Summary:: Given a known closed space/apparatus ( e.g. constant volume, pressure, density, current, temperature, voltage, spark gap distance - let me know if I missed something) how would I compute the change in gas temperature.
Hello,
Given a known closed space/apparatus ( e.g. constant...
Is the following a correct demonstration that quantum mechanics can be done in a real vector space?
If you simply stack the entries of density matrices into a column vector, then the expression ##\textrm{Tr}(AB^\dagger)## is the same as the dot product in a complex vector space (Frobenius inner...
Hello, I have problems with this exercise
Let $(X,\mathcal{B} , \mu)$ a measurement space, consider
$\bar{\mathcal{B}} = \{ A \subseteq{X} \; : \; A\cap{B} \in \mathcal{B}$ for all that satisfies $\mu(B) < \infty \}$, and
for $A \in \bar{\mathcal{B}}$ define
$\bar{\mu}(A) = \left \{...
It is said that: It is not possible to write a position vector in a curved space time. What is the reason?
How can one describe a general vector in a curved space time?
Can you please suggest a good textbook or an article which explains this aspect?
I consider three material points O, O', M, in uniform rectilinear motion in a common direction, so that in relation to the point O, the points O' and M move in the same direction with the constant velocities v and u (u>v>0). Assuming that at the initial moment (t0=0), the points O, O', M were in...
From "standard" formula we have that the gravity acceleration a = GM/r^2 and that the Schwarzschild radius rs = 2 GM / c^2
Is it possible to compute the gravity acceleration at Schwarzschild radius putting r = rs?
In this case we will have a = c^4 / (4GM) This mean that a very very...
So I am a layman in physics, I admit I am trying to grasp big ideas piecemeal via articles, wikipedia and YouTube. I don't pretend to be educated in this regard but I am curious and willing to learn!
The idea of the multiverse intrigues me. Sidestepping for a second the fact that the idea has...