Space Definition and 1000 Threads

I don't want to post this in a math forum because it's very basic and I just want a straightforward answer, not something math heavy . What's the definition of angle in a cuved space embedded in a higher eucledian space? Like when I have a spherical surface in 3d eucledian space and want to work...

Anyone know what honeycombs "tile" Minkowski space?

Let C2x2 be the complex vector space of 2x2 matrices with complex entries. Let and let T be the linear operator onC2x2 defined by T(A) = BA. What is the rank of T? Can you describe T2? ____________________________________________________________ An ordered basis for C2x2 is: I don't...

what is the reason for that the energy hypersurfaces in a phase space, which belong to systems with constant energy are closed? ( see picture )

I was wondering if humans send spacecraft far enough into space in the future (for example Alpha Centauri or other star systems further away), is there any particular distance where it might make more sense to communicate between star systems by making a star blink with some sort of shutter...

Please explain how we know that it is space itself that is expanding rather than an expansion due to an explosion such as the big bang. In either case wouldn’t every object appear to be moving away from us? How do we determine that space/ time is expanding? Tex

Could one derive a set of coordinate transformations that transforms events between different reference frames in the de Sitter metric using the invariant line element, similar to how the Lorentz Transformations leave the line element of the Minkowski metric invariant? Would these coordinate...

He draws an n-manifold M, a coordinate chart φ : M → Rn, a curve γ : R → M, and a function f : M → R, and wants to specify ##\frac d {d\lambda}## in terms of ##\partial_\mu##. ##\lambda## is the parameter along ##\gamma##, and ##x^\mu## the co-ordinates in ##\text{R}^n##. His first equality is...

I have a question about operators in finite dimension Hilbert space. I will describe the context before asking the question. Assume we have two quantum states | \Psi_{1} \rangle and | \Psi_{2} \rangle . Both of the quantum states are elements of the Hilbert space, thus | \Psi_{1} \rangle , |...

Given an orthonormal basis ##\{e_1,\ldots, e_n\}## in a complex inner product space ##V## of dimension ##n##, show that if ##v_1,\ldots, v_n\in V## such that ##\sum_{j = 1}^n \|v_j\|^2 < 1##, then ##\{v_1 + e_1,\ldots, v_n + e_n\}## is a basis for ##V##.

Another noob relativity / cosmology question (although at least this time won't turn out to be a coding bug, as no code is involved...) AIUI, according to relativity, there is no privileged reference frame, and any inertial reference frame is as "correct" as any other. But... In practice, in...

Definition of linear operator in quantum mechanics "A linear operator ##A## associates with every ket ##|\psi\rangle \in \mathcal{E}## another ket ##\left|\psi^{'}\right\rangle \in\mathcal{E}##, the correspondence being linear" We also have vector operators ##\hat{A}## (such as a position...

Hi, In my calculus book,I found this vector form of line equation in space (bold means vector): Given point (x1,x2,x3) lies on line L & v=<a,b,c>, then equation of line is : r = <x1,x2,x3> + t <a,b,c> with t any number. Now, my question if I plug any number for t, then result will be vector...

In Sakurai Modern Quantum Mechanics, I came across a statement which says probabiliy flux integrated over all space is just the mean momentum (eq 2.192 below). I was wondering if anybody can help me explain how this is obtained. I can see that ##i\hbar\nabla## is taken as the ##\mathbf{p}##...

As I've mentioned in a few previous threads, at the midpoint of my sci-fi story on a generation ship, I need a disaster that wipes out about a third of the (male half of) the crew. Several people have suggested things like "a virus that disproportionately affects men", but that didn't quite cut...

Suppose there is a pressurized gas canister in space, at rest. With a mass "m" of gas inside of it at a pressure "P". Next the valve of the canister is opened. The canister will accelerate in the opposite direction to the valve opening. When all the gas has left the canister, it will be moving...

Is there a way to create a map from satellites showing how much light pollution there is on earth? For example if you wanted to do astro photography and wanted to know how far away from city you need to drive to see certain levels of detail from galaxy?

Umm.. yes I think. Not sure what I’m getting into, but the pursuit of knowledge eh? Teach me please. I’m just here to share thoughts and bounce between fellow big brains. Haha this strange. Good luck!

So I have a random question with all these talks of the pictures released from NASA by JWST. So these galaxies, stars, etc, are like 40 million light years away, so that light must've left these galaxies 40 million years ago, which means things have obviously changed. So are there any tests or...

Quantum spin is orientable so it takes place in a space with an even number of dimensions. What is that space? If the space had an odd number of dimensions, then spin in that space wouldn't be orientable. But quantum spin is orientable. We could say that it is Minkowski space, but that space...

Hi, Also, I read this article, What Do You Mean, The Universe Is Flat? (Part I), on Scientific American; URL: https://blogs.scientificamerican.com/degrees-of-freedom/httpblogsscientificamericancomdegrees-of-freedom20110725what-do-you-mean-the-universe-is-flat-part-i/ I have few questions about...

##f : [0,2] \to R##. ##f## is continuous and is defined as follows: $$ f = ax^2 + bx ~~~~\text{ if x belongs to [0,1]}$$ $$ f(x)= Ax^3 + Bx^2 + Cx +D ~~~~\text{if x belongs to [1,2]}$$ ##V = \text{space of all such f}## What would the basis for V? Well, for ##x \in [0,1]## the basis for ##V##...

In the paper C. S. Lent and P. D. Tougaw, "A device architecture for computing with quantum dots," in Proceedings of the IEEE, vol. 85, no. 4, pp. 541-557, April 1997, doi: 10.1109/5.573 about quantum dots, it is stated that the basis vectors in the space of quantum states for a single cell...

I'm interested in describing a 6-dimensional space of which three are compactified to small circles. Globally this space looks 3-dimensional, like a 2-dimensional cylinder looks 1-dimensional globally. Kaluza and Klein did a similar thing in the context of 4-dimensional spacetime. They extended...

Hi, The quote below has been taken from this article, https://math.ucr.edu/home/baez/einstein/node2.html, which I came across. The quote doesn't make any sense to me, especially the part in boldface. Could you please help me with it?

I am having difficulty writing out ##\bra{p',\lambda}\psi^{\dagger}(-\frac{z^-}{2})\gamma^0\gamma^+\psi\frac{z^-}{2})\ket{p,\lambda}## in momentum space. Here, I am working in light-cone coordinates, where I am defining ##z^-=z^0-z^3##, ##r'=r=(0,z^{-},z^1,z^2)##. My attempt at this would be...

I am concerned that this question may instead be a philosophical one although if it it mathematical, any insights would be very appreciated. The question is this; could an object of N dimensions exist entirely in N-1 dimensions? In other words, could an infinitely flat object have 3 degrees of...

can you theoretically put a mirror in space, take a photo of earth/dirts reflection and see it in the past?

I first apologize if this has been posted more than once; sorry. There is a lack of clarity at my end as to whether I am logged on here? Say we have two galaxies, the Milky Way (MW) and galaxy A separated along a straight line 20 x the radius of the Universe visible to us. If I understand...

Hi, may I ask a question, please? Say we have two galaxies, the Milky Way (MW) and galaxy A separated along a straight line 20 x the radius of the Universe visible to us. If I understand correctly then the rate of the physical expansion of space between MW and A could be at the rate of say...

And if there are an infinite amount of frequencies, doesn't that mean that an extraterrestrial civilization could be reaching out without us being able to receive their signals. And even if we did receive their signals, how would we understand their form of communication? What if they...

let's say i would like to drop by one of my pals on a certain planet, 7ly away. I got to 42 years but it doesn't really sound correct.

The two most unscientific words in Star Trek are probably "full stop". :wink: The Impulse Drive is described in the Voyager Technical Manual as 0.25 c (25% of the speed of light). Whatever g forces are required to "immediately" come to a halt from that speed - it's certainly way beyond what the...

Hello, I have a question. If a star tracker in space faces the sun directly then could it be possible that the sun completely burns the image sensor? To be specific we are a student satellite team (Student satellite program IIT Bombay) developing a star tracker and we don't have an exact idea...

You might have seen such a 3-D map of the stars before: And I was wondering about a 3-D map if space was non-Euclidean, what would be the best ways to display it. To keep it simple, if you're considering elliptic space, you can consider the entire "global" map. Just like we have world maps of...

We derive the most basic laws of physics from several fundamental symmetries (those from Noether's theorems, gauge symmetries, Lorentz symmetry...). But are there any types of spacetime where no symmetries, no matter how fundamental, would be valid? Any special metric, geometry or shape?

Does electron beam in empty space generate magnetic fields around them just as with current in conductor. If yes, then is it experimentally proven that two parallel electron beam would attract each other.

I'm about 25,000 words into my latest novel and the story arc is coming together nicely, but one aspect I need thoughts on please is what would happen inside a spaceship that has been grievously damaged in battle to the point that it has been abandoned by the fleet as a 500m long wreck...

I'm hoping this is basic and obvious, but assume it's not to the general public. Ignore quantum mechanics and diffraction and assume a gun that can fire photons that each hit the center of a remote target. Place one of these and a conventional gun that shoots bullets at 1000 m/sec inside of a...

Suppose we have a rotating body like a bicycle wheel in space away from gravity. This body stops after a while due to friction between the wheel and wheel axles. Is not the conservation of angular momentum violated?

So I'm looking for some advice on a problem that I am trying to solve for a project. I'm an engineer but my background in vector mathematics is very minimal so I'm looking for some assistance. Lets assume we have a permanent magnet. We know the characteristics of this magnet, such as it's...

Does a body accelerating at 1g in outer space create a gravitational field around it ?

Summary:: This is similar to the examples of electrical circuit state space analysis, I have been trying to find the state space equations from the following non linear first order differentials but I keep getting stuck. Any help? A) Started off from non linear equations: $$y' =...

How to represent this system in state space form? where: $$ x' = Ax + Bu \text{ and }y = Cx + Du$$ I am trying to create a state space model based on these equations on simulink, need to find A, B, C and D but like I mentioned, i cannot find the solution when the differentials are not of...

What does mean spinel structure has F d3m space group? I know F is for face centred cubic, 3 is 3-fold symmetry and m is mirror, but I don't know what means "d"?

*Pathria, Statistical mechanics*"The microstate of a given classical system, at any time, may be defined by specifying the instantaneous positions and momenta of all the particles constituting the system. Thus. If ##N## is the number of particles in the system, the definition of a microstate...

A little more clear: I'm looking for a video or animation where I can visualize/see radiation on space ice (Europa or the Galilean moons). I know that radiation is invisible, but what does the ice actually look like or how does it change visually when its bombarded with gamma rays? Because its...

I want to share my recent results on the foundation of classical mechanics. Te abstract readWe construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered...

Some physicists prefer to explain the problem of conservation of energy in General Relativity by considering the gravitational potential energy of the universe that would cancel all the other energies and therefore the energy in the universe would be conserved this way. However, many other...

Hello everyone, I am trying to find level shifter/voltage translation solutions that are space-qualified (ideally radiation hardened, etc.) that can logic level translate from FPGA I/O at 1.5V to and ADC at 1.8V while supporting uni- or bi-directional I/O and OE capabilities . This is for high...