Space Definition and 1000 Threads

Homework Statement Problem: Let ##A## be an infinite subset of a ##T_1## space, and let ##x## be a limit point of ##A##. Prove that every open neighborhood of ##x## contains infinitely many points of ##A##. Homework EquationsThe Attempt at a Solution First note that if ##\mathcal{O}## is an...

I am trying to understand what space is. Does QM state that Space is made of nothing? In other words it does not exist?

I am picking this up as a continuation and extension of the idea laid out e.g. in @davenn 's thread "The Sun today - 9 July 2017 - nice spot group" https://www.physicsforums.com/threads/the-sun-today-9-july-2017-nice-spot-group.919696/ See also (for continuity purposes)...

Because I just got started on John Varley's Dark Lightning, about an asteroid converted to an interstellar vehicle. Nice word pictures there. Any, some possible help for the person asking the question. Original thread is closed.

I was just wondering. According to Lorentz transformations, if two events are simultaneous in one reference frame, they will generally not be simultaneous in another. The time difference that I get between the two events in the other reference frame is \Delta t^{`} = \gamma\beta\Delta x...

In free space there are two masses: - Metallic sphere of mass M, radius R and total charge equal to 0. It has also a resistivityρ. - Metallic sphere of mass m, radius r and charge q. The distance between the masses is D. We can assume r <<R<<D and m<<M. The masses start accelerating until they...

In this forum I read a thread about centrifuge and learned that, ''There is no difference between centrifuges on Earth and centrifuges in space because gravity is in no way related to how a centrifuge works'' Reference https://www.physicsforums.com/threads/how-do-centrifuges-work.148518/ But...

I have always had this question, and I wonder if someone can explain to me if I am wrong about it. In relativity they say space(time) can curve around massive bodies. Let's just consider space for a moment. For example on the surface of a sphere, you tell someone to walk in a straight line...

I'm not sure if I'm posting in the correct category. Please direct me to the correct one, if I have made a mistake. As I have mentioned in my intro, my knowledge of physics is almost non-existent. I am writing a book series, and I'm trying to base my ideas on science (more or less). This is one...

Say you have an elevator that reaches space. I have 2 questions : 1) say a space rock hits the top of the elevator... that would create a torque = force * distance on the ground... Wouldn't it instantly snap from any light force or space junk hitting the top of the elevator? Would the station...

I came across an article about one of the many observations that helped to confirm GR. This observation took place during the 1919 total solar eclipse. Stars that were located directly behind the sun could be seen during the total solar eclipse because the gravitational force of the sun bent the...

Is it true that the time increase (24 hrs becomes 25 or 26 or..)when the mass of Earth is increase? ??

I am attempting to understand a question posed to me by an acquaintance, who asked me if I could refer him to literature freely available on the Internet on "self-dual solutions to Maxwell's equations on Euclidean space, or pseudo-Euclidean space, not Minkowski space (where there are none)" and...

My question is, take Mars, say, and install a huge rocket engine on the ground pointing out the planet (obviously) and in the opposite direction of its velocity, so that if it is turned on, the planet is slowed. The rocket starts to work and Mars is slowed. If the loss of velocity goes little by...

Hi everyone.Ive been looking for a beginners section on this site but no joy.I am uneducated but physics and Astro physics in particular really interest me.One of the things I don't understand is the vast distance in space.We talk about things being thousands of light years away.Yet light is...

I have come across an interesting simulation of hyperbolic space. I can't totally wrap my hand around it, though. But I am interested in technical part of it. As far as I see no object in the space would get curved when you are moving. The visual deformation is the result of bent light reached...

Imagine a cubic volume of space, defined today, with edges of the order of the Planck length. As cosmological time goes forward this volume expands so that the edges of the cube expand with the scale factor. This seems ok. However, as physics is time-reversible, it should be valid to imagine...

In the book, Introduction to Linear Algebra, Gilbert Strang says that every time we see a space of vectors, the zero vector will be included in it. I reckon that this is only the case if the plane passes through the origin. Else wise, how can a space contain a zero vector if it does not pass...

Hi there. I am willing to plot a function of three space variables plus time, let's say ##\phi(x,y,z,t)##. The idea is to plot the 3D function for each time, i.e. evolving in time. As I have three independent variables, corresponding to the three Cartesian coordinates, the function is actually a...

How is it derived? ds^2 =-cdt^2+dx^2+dy^2+dz^2

I have not posted for a while,but something has been bugging me. I would like help understanding that if mass makes a dent in the fabric of space, does it mean celestial bodies are sitting at different depths in the fabric, and does that mean the less mass in an object you are then more likely...

Could this be a possibility at some point? Since entanglement is not affected by distance, could we send cameras out to extremely distant places and get instantaneous signals? Only the image sensor would have to be entangled. It would still take the same amount of time as usual to get the camera...

For some reason, whenever I see these documentaries on space travel, and how NASA explains its projects, they always make it sound like "OMG we'll be able to colonize space MAYBE a million years in the future, with super technology, yadda yadda" and "space travel is so difficult", but aside from...

What happens to gases in space? Do they just dissapear? (Yes yes, yawn) Or can they make up a region of space, and stick together via gravity? And what about Jupiter and other gas giants? How do they work, if in space, all gases tend to just shoot out and spread into an even film?

I'm having a hard time understanding how changing space means changing time. In books I've read people are saying "space and time" or "space-time " but never explain what the difference is between the two concepts or how they are related. How are the concepts of space, time, and space-time...

I'm looking for a rigorous mathematical description of the quantum mechanical space state of, for instance, a particle with no internal states. At university we were told that it the Hilbert state of wave functions. They gave us no particular restrictions on these functions, such as continuity...

If a photon leaves a source 4,2 light years away how far apart will it be from a similar photon it was adjacent to (say less than 10^3 wavelengths) when it departed. Does the inverse square law mean that individual photons get further apart and stay the same size or do they occupy a larger space...

Why is iridium plentiful in space rocks but scarce on earth?

Hi, I'm recently reading "Particle Physics in the LHC Era" and there is a part about the phase space factor that confuses me. When giving the Lorentz invariant phase space, they wrote: d3p / 2E = θ(E) δ(p2 - m2) d4p This is very confusing as it equates a three dimensional differential to a...

I was listening to this lecture: and in it, sometime around the 30:00 to 40:00 minute mark, he implies that the torus' sturcture built up from the orbits of the group under addition on the real plane is the same idea as the cylinder's structure being built up from the orbits of the group under...

Homework Statement A space station is in orbit between the Earth and the moon. The force due to gravity on the space station from the moon is the same as the force due to gravity from the Earth. (FGmoon = FGearth). How far away from the Earth is the space station? How far from the moon is the...

Hi all, How does matter curve space (what's the mechanism)? Does this Curvature happen instantaneously or does it happen at light speed? Thanks in advance.

Homework Statement There are n isolated condutoctors in space: Sum of charge of all conductors is positive. Show that surface density is postivie everywhere on at least one of conductors Homework Equations Using induction The Attempt at a Solution -It's clear that if we have one conductor...

I think special relativity would disallow our universe from having the structure similar to an ant on a sphere. What I mean is that it can't be possible to travel in a constant direction and to come back to your original location. Suppose there is an observer S on a planet and an observer S'...

Hello, I am a professional trainer in robotics & electronics. I need help to understand better some physics concept to integrate then in my school projects.

If a body have heat and floating in space do it loss heat? If it does loss heat and the how? Thanks!

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...