Space Definition and 1000 Threads

In my Thermodynamics course, we recently learned about the saturation pressure and saturation temperature of different substances -mainly water. As you know, the saturation temperature at which a substance begins to boil is specific to a fixed saturation pressure. Water only boils at 100...

In state space, the coordinates are the state variables of a system.So,each point in state space represents a specific value of state variables.Thus,state space representation represents the changes in a dynamical system. The state variables are the minimum number of variables which uniquely...

This is a basic assumption that's made during the derivation of results of special theory of relativity is that space is homogeneous i.e. space intervals shouldn't be given preference based on our choice of origin. However I want to understand more about this assumption and its importance...

Homework Statement https://isaacphysics.org/questions/gcse_ch2_13_q10 https://www.physicsforums.com/attachments/213735 https://i.imgur.com/WnZkt83.jpg The thrust generated by a rocket engine is equal to the mass of propellant burnt each second multiplied by the exhaust velocity of the gas...

I've been reading about this a bit and stumbled across something that said its desirable that the heat source not be something that emits a lot of gamma radiation. Other than hazards to a technician, does this have any effect on the device its being used on? Why would it require extra shielding...

Homework Statement If ##C## is a connected space in some topological space ##X##, then the closure ##\overline{C}## is connected. Homework EquationsThe Attempt at a Solution Suppose that ##\overline{C} = A \cup B## is separation; hence, ##A## and ##B## are disjoint and do not share limit...

Hi, i know that The homogeneity of space and time implies that the Lagrangian cannot contain explicitly either the radius vector r of the particle or the time t, i.e. L must be a function of v only but the lagrangian definition is ##L=\int L(\dot q,q,t)##, so velocity appears in the definition...

How does knowing that galaxies are all moving away from each other and the farthest ones are moving more quickly prove that space is itself expanding and not just that the galaxies are moving through it?

Hey! :o I want to draw the space $D$ that is between the paraboloid with equation $z=x^2+y^2$ and the cone with equation $z=\sqrt{x^2+y^2}$ and I want to calculate its volume. How does $D$ look like? To calculate the volume we have to calculate the integral $\iiint_D dxdydz$. I have done...

Suppose an object is moving away from you. Is there a way to determine, experimentally or otherwise, whether it is moving through space or whether it is sitting still but appears moving because the space between you and the object is expanding? Galaxies that are sufficiently far away from us...

Consider the AdS metric in D+1 dimensions ds^{2}=\frac{L^{2}}{z^{2}}\left(dz^{2}+\eta_{\mu\nu}dx^{\mu}dx^{\nu}\right) I wanted to calculate the Ricci tensor for this metric for D=3. (\eta_{\mu\nu} is the Minkowski metric in D dimensions) I have found the following Christoffel symbols...

Homework Statement I think I have managed to do the first three parts of this problem ok, but I am struggling with part 4. [/B] A 2D negatively curved surface can be described in 3D Euclidean Cartesian coordinates by the equation: ##x^2 + y^2 + z^2 = −a^2##. 1) Find the 2D line element for...

Not much likelyhood of any risk on ground. https://www.theguardian.com/science/2017/oct/13/tiangong-1-chinese-space-station-will-crash-to-earth-within-months

Hello all, I have a theoretical question regarding subspaces. If V is a subset of a vector space, and we wish to show that V is a vector space itself, we need to show 3 things. Some references say we need to show: a) V is not empty b) V is closed under + c) V is closed under scalar...

If we have a small 4-volume of empty spacetime of boxlike dimensions t, x, y, z, then according to the vacuum field equations the change of the shape of this box with respect to time is (I think): \frac{d (xyz)}{dt}=0 or equally: yz\frac{dx}{dt}+xz\frac{dy}{dt}+xy\frac{dz}{dt}=0 in other words...

Hey! :o Defining $u=x^2+y^2$, $v=x^2+y^2-2y$ I want to calculate $\iint_D xe^y dxdy$ using the change of variable, where $D$is the space that is determined by the inequalities $x\geq 0$, $y\geq 0$, $x^2+y^2\leq 1$ and $x^2+y^2\geq 2y$. I have done the following: We have the new variables...

So according to Dr. Frederic Schuller, we need to at least know the topology on the space of all theories in order to know that we are getting closer to the truth. I take that this is because we need to know the topology to establish that convergence is possible in the first place. How does this...

Homework Statement 1. You are consulting for a screenwriter who is working on a science-fiction movie about the trials and tribulations of an space-faring family. She wants the script to be reasonably realistic from a scientific perspective, so she is seeking your advice on a variety of scenes...

I have a doubt about coulomb's force equation in free space..ie 1/4πε0... Actually coulomb found that force exerted b/w charges are directly proportional to the product of charges and inversely proportional to the sqr of the distance bw them.we can measure force exerted and distance of...

I'm reading this proof on the matter: https://math.stackexchange.com/questions/278755/show-that-a-retract-of-a-hausdorff-space-is-closed How do we know that the final neighborhood they come up with is disjoint from A?

let r: X-->A be a retraction. This means that r*i = Id_A, where * is composition of maps and i is the inclusion map from A--->X. How to show that the retract of a connected space is also connected? I was trying to proceed by contradiction. Suppose A is not connected, then A = Union(M,N) where...

I know that path loss is proportional to the square of the distance between the transmitter and receiver AND is also proportional to the square of the frequency in use but what does it mean when a free space calculator shows a negative number? How is it possible to get zero loss? For instance...

I am reading "An introduction to manifolds" by Tu. He starts off in Chapter 1 by introducing some definitions on ##\mathbb{R}^n## that will carry across to general manifolds. In Chapter 1, 2.2, he defines germs of functions as a certain equivalence class of smooth functions ##C^\infty_p##. I...

Let ##P## be a ##U(1)## principal bundle over base space ##M##. In physics there are phenomenons related to a loop integration in ##M##, such as the Berry's phase ##\gamma = \oint_C A ## where ##C(t)## is a loop in ##M##, and ##A## is the gauge potential (pull back of connection one-form of...

Let $(X,\tau)$ an topological space. Show that $x_n\to_{n\to \infty} x$ if and only if $d(x_n,x)\to_{n\to \infty} 0.$ Hello, any idea for begin? Thanks.

Hi, i would like to know how can i plot a three dimentionnal phase space (mathematica), for this kind of differential equations: x'= (z^2(x-4y+z)+y^2(x+z)+z(x*y-x^2))/(z^2+x^2-2) y'=y(y-3)+z(4y-z)+3(1-x^2)-2(y-3z)(z^2(x-4y+z)+y^2(x+z)+z(x*y-x^2))/x(z^2+x^2-2)...

What does object space and image space mean in optics?

I'm currently doing an MSc in Space Science and Technology. I've done engineering, celestial dynamics, astronomy and planetary science at postgrad level. I need to choose a thesis topic, and I'm a little short of ideas. I'm interested in theoretical physics and cosmology, but need inspiration...

according to einstein the mass go straight in the curved space because the sun makes the space curved and so the Earth circle the sun. but i don't understand why this "geometrical" explanation is a replacement for the gravity. how does the mass (of the sun for example) makes the space curved...

$\textsf{Find the area of the triangle determined by the points }$ \begin{align*}\displaystyle &P(1,1,1), \, Q(-2,-7,-1), \, R(-7,-1,4)\\ \end{align*} \begin{align*}\displaystyle \vec{PQ}&=(-2-1)i&+(-7-1)J&+(-1-1)k&=-3i-8j-2k\\ \vec{PR}&=(-7-1)i&+(-1-1)j&+(4-1) k&=-8i-2j-3k...

What is a symplectic manifold or symplectic geometry? (In intuitive terms please) I have a vague understanding that it involves some metric that assigns an area to a position and conjugate momentum that happens to be preserved. What is 'special' about Hamilton's formulation that makes it more...

Or is it something separate that acts on a geometric space? So we know that the Euclidean space is a vector space. But is it geometric? I ask this because in group theory, the group elements are the operators acting on another set, but clearly we see that this doesn't mean that the group...

This process and mechanism is very difficult to explain via the computer and even during presentations many people simply do not grasp the concept so I am trying my best to explain it easily and ask my questions as best as I can so that you guys understand me. I really need help with these few...

I know that absolute zero is impossible to achieve but we can get close. According to google the coldest temperature ever reached in a lab was 0.006K. Do you think this is because while the atoms are moving very slow relative to the observer they are still moving at the velocity of Earth's...

I would like to ask some questions. I am in a spacecraft (I have grip on the floor) and at one end a spring is attached to the wall. I hold the spring and begin to walk backwards, extending the spring. 1) What will happen to the spacecraft as I walk backwards? 2) What will happen to the...

They don't breathe. Their internal pressure greater than space. Radiation. Temperature. Micrometeorites. No picnic? Any recommended reading? Thanks.

Is it assumed that Hilbert space is an infinite manifold that the non-collapsing wave function occupies in Everettian QM? Thank you.

In the following youtube video, at 1:10:15, is he saying that space itself is "entangled" by means of the virtual particles of the vacuum energy being entangled? It sounds like this is one of the main points he is trying to make in the video. But if this is so, then isn't he saying that space...

The Wall Street Journal is definitely interested in space debris - dead satellites, boosters, etc. - as they've run a number of stories on this topic over the past few years. E.g. Wikipedia has a link to a story from 2009 as one of the footnotes to their article on space debris, plus a web...

What are the ways of mathematically defining a space? We usually define a space by stating some common property shared by the points that make up the space in question, that is, a symmetry of that space. For instance, the ordinary 2-sphere is defined as all points ##X## that are at a distance...

A fictitious system having three degenerate angular momentum states with ##\ell=1## is described by the Hamiltonian \hat H=\alpha (\hat L^2_++\hat L^2_-) where ##\alpha## is some positive constant. How to find the energy eigenvalues of ##\hat H##?

Permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. And the inductance of an electric circuit is one henry (H) when an electric current that is changing at one ampere per second results in an electromotive force of one volt across...

Is there any theory law explaining the nature of space and describing what is space and what happens to space when some event take place in space.

Hi, I am currently writing a short story where a character travels to the future. This universe operates much like the George Ellis hypothesis where the future is not defined yet and we are always in the leading edge known as "now". Therefore, by traveling to the future he/she comes to a place...

Hello Maybe my question is dumb but is the bent of space time instant due to gravity? If a mass pops into existence will space time be bent instantly ? Intercations between forces are light speed but gravity is and is not a force depending on pov

I have read some of the other posts about this topic but am still left unsatisfied. Could just be me. :cool: Did the universe, one minute after the big bang, consist of a finite volume of spacetime? If so, then is it not logically inconsistent that the universe can possibly be infinite now...

General relativity suggests that path of light is curved around sun. This curvature is not dependent upon frequency of the photon. What is the physical difference between 'curvature of space' and 'curvature of space-time' ? We can make measurements at two points in space at same time. But there...

Does the universe’s ongoing expansion mean that some finite amount of space-time is stretching, or that there is simply more and more of the same (space-time) being produced? Given the obvious difference between the dense primordial universe and the present, I’m guessing the former, which, if...

<Moderator's note: Moved from a technical forum and therefore no template, which would have helped a lot in this case ...> i know that mark time is duration in which a pulse is present and space time is a duration is which pulse is not present. my attempt to ques is: f= 25000Hz...>...

Why object in the space will continue moving foever if the object is in dynamic equilibrium?