Space Definition and 1000 Threads

Hello everyone. Iam just Learning about State space representation and controller design and have a fundamental question about the difference between classical Control theory and modern Control theory. I understood the state space is of advantage when dealing with MIMO systems or non-linear...

I just want to be sure I understand this correctly: Suppose there's a long spaceship moving in uniform motion relative to me (an inertial frame). Now someone in the front* of the spaceship calls someone (on the phone) in the back of the spaceship. *(this long length of the ship is oriented...

Yeah, pretty much what the title says. Who has cool ideas for the future of space travel?

Hi all, I'm doing some reading about special/general relativity, and have come across the ideas of curved space etc. I've very much a novice in physics, so please excuse my (possibly) stupid questions. For background, I'm interested in writing a sci-fi story, and would like to have at least...

Well, first thing, I am new to this forum and it looks pretty good and I'm looking forward to reading more from it and post more questions. Well rocket propeling (or anything that uses some material to propel up when shooting it down) seems pretty straight forward at first, you have some gas...

Homework Statement Show that X is a Hausdorff space IFF the 'diagnol of x' given by t = {(x,x) | X * X} is closed as a subspace of X*X Homework EquationsThe Attempt at a Solution So since X Is Hausdorff so is X*X and t, because the product of two Hausdorff spaces if Hausdoff and the subspace...

Consider empty spacetime containing a charged capacitor. Is there a simple expression for metric for the spacetime between the capacitor plates in terms of Kaluza–Klein theory? We are told that spacetime tells matter how to move; matter tells spacetime how to curve. Is there a Kaluza–Klein...

I've been reading Fleisch's "A Student's Guide to Vectors and Tensors" as a self-study, and watched this helpful video also by Fleisch: Suddenly co-vectors and one-forms make more sense than they did when I tried to learn the from Schutz's GR book many years ago. Especially in the video...

Hi All This is in relation to the folllowing paper: https://arxiv.org/pdf/1402.6562.pdf See section 3 on examples where standard probability theory is discussed. Is it valid? To me its rather obvious but I had had a retired professor of probability say probability theory doesn't have a state...

Hey there! My name is Laurel, and I'm working on a short story with a friend about, among other thing, space travel. I've just got some questions about exiting the atmosphere in order to fly a spaceship around looking for other stuff. I don't want you to feel you have to over simplify things...

Hello, I am someone who has no experience in physics other than primary/high school and I have a quick simple question about something I can't wrap my mind around as a complete physics newbie. Please have understanding. The question: let's say a train is standing still at a point in space (so...

Double field theory [1] is an attempt to realize T-duality of string theory at the level of field theory. For instance, if a field in ordinary field theory lives in 4 non-compact spacetime dimensions, then a field in double field theory lives in 8 non-compact spacetime dimensions. I don't...

Homework Statement An assembly line is observed until items of both types—good (G) items and items not meeting specification (N)—are observed. Show the sample space. Homework Equations Let G be Good Let N be Not Good The Attempt at a Solution S = {GN, GGN, GG...N, GG..., NG, NNG, NN...G...

There's a question that's been in my mind for quite a while but I cannot figure out what the answer is. I't probably an ill posed question but I will ask it anyway: 1.- Do we know what the dark-matter statistical distribution in our Universe is (at large scales)? 2.- In case we do, could...

I am considering making a small studio space for a video I want to make. It will have to hold a cubic meter of space in which I will have very small fluorescent objects 1 mm cube (see previous thread). Since I am not expecting to have the most flaming hot UV light driving the fluorescence I...

NASA just announced a solar probe to travel quite close to the Sun, about 3.7 million miles from the solar surface: Nasa’s hotly anticipated solar mission renamed to honour astrophysicist Eugene Parker. Renamed the Parker Solar Probe to honour solar astrophysicist who predicted high speed solar...

Hi. I'm working on a science fiction story about colonization of the solar system. Asteroid way stations are an important part of the story. I want to construct a realistic scenario about how we could convert the Eros asteroid into a shuttling habitat in it's current orbit (or something close...

Do any of you have pictures of space objects, planets, moons, galaxies that have not been enhanced?

I've been messing around with some circle theorems and found that you couldn't possibly take a picture of a full Earth from a single shot. Is this impossible? Is their some math to prove otherwise, I'm really stuck.

I've read that when two pieces of the same kind of metal touch in space, they will fuse because there is no way for the electrons to "know" that they are in different pieces of metal. What would happen if two different metals were to touch in space? Would electrons still flow freely between...

Light can get red-shifted due to expansion of space, this leads to a loss of energy. Would it be possible that this energy is what's causing the universe to expand in the first place?

Would you explain when the space should be left when backslash, \, is used? For example some codes using backslash. \ \displaystyle a=\frac{dv}{dt} \ : This one works good because there is space between the first two backslashes. But if the space between the first backslash is removed the code...

What happens to sound when it hits a vacuum? Because there is nothing for the sound wave to vibrate against, what happens to the energy?

I am interested in looking at the metric where time is everywhere normal to space, so gta=0 everywhere, where t is the time coordinate and 'a' is any of the space coordinates. I'm finding it hard to look up in the literature: does it have a name that I can search for? My main interest is in...

Does Geometry of space Changes?

Homework Statement Hello All, I am experiencing Adventures in Topology. So far, so good, but I have an issue here. In the topological space (Real #s, U), show that 1 is not an element of Cl((2,3]).Homework Equations The closed subsets of our topological space are the converses of the given...

Edit: Disclaimer, this post contains faulty ideas I'm a 'pedestrian' to physics trying to wrap my mind around various concepts of relativity, and one of those is a visualization of two, say, planets, say each starting at rest. By my understanding, their mass causes space to relatively...

We are told that space is expanding and that the rate of expansion is speeding up. However, as relativity shows that space and time are inextricably linked, does this mean that time is expanding too?

Hi all! How is humidity related to temperature in a system where temperature is constant in time but not in space? As an example: If we have humid air trapped between two parallel walls with T1 and T2 respectively, how does humidity behave along the line from one to the other wall? Is absolute...

how do we know light stays consistent when traveling through the "not nothingness of space"? how do we know the rate at which light degrades as it travels through the medium that has to be there?

Consider the function $$f(x) = - \frac{1}{2}a^{2}x^{2} + \frac{1}{4}bx^{4} + d^{4}\cos(x/c),$$ where ##a##, ##b##, ##c## and ##d## are arbitrary parameters. For some region(s) of the parameter space, there are oscillations in the function. My goal is to identify these regions of the parameter...

I am doing some mathematical exercises with 3D anti-de sitter face using the metric ds2=-(1+r2)dt2+(1+r2)-1+r2dφ2 I found the three geodesics from the Christoffel symbols, and they seem to look correct to me. d2t/dλ2+2(r+1/r)*(dt/dλ)(dr/dλ)=0...

It's generally understood that nothing can be accelerated up to the speed of light, and that nothing can surpass it. That being said, the expansion of space itself can exceed this "universal speed limit," as the Universe is expanding so fast that light can't catch up to it. Regarding the...

Hello! (Wave) I want to find the solution of the following Cauchy problem and determine the space in $\mathbb{R}^2$ where the initial condition defines the solution. $$u_t+ u_x=4, u|_{t=0}=\sin{x} \text{ for } |x|<1$$ I found that the solution of the above initial value problem is...

From the book, I did not understand, 1. Why does fields coming inwards the sphere contradicts the Gauss law ? 2. I am unable to connect the potential picture and electric field picture. Why does the point P must have lowest or highest potential than neighbouring particles ? 3. I understand...

Homework Statement The question asks me to express the system shown in the image in state-space form, firstly by using the transfer function which was fine but the second part asks to express in state-space form by using the components A,B,C,D as the states x1,x2,x3,x4 Homework Equations U(s)...

We say that in big bang, a highly dense point like structure exploded and expanded. In what did it expand? If so, universe and space would be different entities. Please elaborate.

Hi guys, I am a little confused on the difference between an Algebra and a vector space. I´m guessing there´s a fairly simple distinction. Any guidance would be much appreciated, I accept both hand wavy and hardcore axiom based responses :) Cheers

If a particle can potentially be transported to any place in space limited only by the speed of light, does that potential amount to an expansion of space? And another question: Does it make sense to define space as any place a particle could go to?

Please help me flesh this out: You share a "long haul" freighter with six-ten other people. Everybody can have one pet that runs lose (cats, ferrets, etc.) or more that are permanently confined to the person's private living space. (Gold fish would be an example of the latter.) Tribbles are...

<Mentor's note: moved from general mathematics to homework. Thus no template.> Prove subspace is only a subset of vector space but not a vector space itself. Even a subspace follows closed under addition or closed under multiplication,however it is not necessary to follow other 8 axioms in...

Homework Statement Hi, Question attached: inserting ##\phi (x)= \int \frac{d^4k}{(2\pi)^2}\phi(x)e^{-i k_u x^u}## and similar for ##J(x) ## / ##J(k)## into the action and then integrating over ##k## gives: Solution attached: I AM STUCK on this part, completing the square ; so I see...

Would it be possible to craft a carbon based life form throw dna manipulation and selective breeding that could live in the cold vacuum of space?? Also if I posted the thread in the wrong place I'm sorry I didn't know where else to place it. Once again thank you to anyone that will tack the time...

Is it possible for Low Frequency to distort the fabric of space? If so, how?

how can the universe be expanding if matter nor mass can be created?

I set eyes on the next formulas: \begin{align} E_{\alpha \beta \gamma \delta} E_{\rho \sigma \mu \nu} &\equiv g_{\alpha \zeta} g_{\beta \eta} g_{\gamma \theta} g_{\delta \iota} \delta^{\zeta \eta \theta \iota}_{\rho \sigma \mu \nu} \\ E^{\alpha \beta \gamma \delta} E^{\rho \sigma...

Hi all, If I have a hot object in space (not a star but say an oven or just a hot gas as would be on Earth < 10,000 degrees Kelvin) glowing at a temperature T and I want to know long it takes to come to equilibrium with the vacuum of space around it, how can I calculate such a time? I could...

If $ r<s<t $ then for any $ ϵ>0 $there exists $ C>0 $ such that $ ∥f∥_{(s)}≤ϵ∥f∥_{(t)}+C∥f∥_{(r)} $for all $f∈H_t $ Can you please tell me how to start thinking of this problem? I really feel stuck and don't know where to start!

Hi. I'm trying to prove that [\Omega] = \int dq \int dp \, \rho_{w}(q,p)\,\Omega_{w}(q,p) where \rho_{w}(q,p) = \frac{1}{2\pi\hbar} \int dy \, \langle q-\frac{y}{2}|\rho|q+\frac{y}{2}\rangle\,\exp(i\frac{py}{\hbar}) is the Wigner function, being \rho a density matrix. On the other hand...

Homework Statement Consider the vector space that consists of all possible linear combinations of the following functions: $$1, sin (x), cos (x), (sin (x))^{2}, (cos x)^{2}, sin (2x), cos (2x)$$ What is the dimension of this space? Exhibit a possible set of basis vectors, and demonstrate that...