Space Definition and 1000 Threads

Could it be possible for light to not move at all but remain still while space and time moves past it? The light would just exists as the continuum of space time moves past light.

Hi good day. I am trying to find the general Inverted Pendulum on a cart nonlinear state space equations with two degrees of freedom with x, x_dot, theta, theta_dot which represents displacement, velocity, pendulum angle from vertical, angular velocity. However from research, I am seeing...

A question came up about deducing the number of possible energy states within a certain momentum ##p## using momentum space. To make my question easier to understand, I deliberately chose ##p## and not a particular increment ##dp## and I assume a 2 dimensional momentum space with coordinates...

I always had a tough time understanding how QFT relates to reality. Are these quantum fields (electron field, ect) physically real? Are they things that exist in space or are they just mathematical abstractions that help use calculate things?

Hi all. I was wondering if time is dilated whilst traveling in a stable magnetic field that is generated by the object travelling, and if so, does this vary if you reduce or intensify the magnetic field? Also, what happens if the object is generating two opposing magnetic fields, would...

Let's consider two inertial frame S and S'. S' moves with speed v w.r.t S along x-axis towards the right. Now we can draw the two co-ordinates system. The t' axes will make an angle arctan(v/c) with t axes rotated towards x-axis and similarly the x' axis will be tilted towards the t axes...

It is often proposed that gravity could be simulated on a space station by rotating around an axis, such that the astronaut experiences the centripetal force of the space station wall, analogously to gravity. It is usually mentioned that the radius of rotation must be very large to avoid...

Russia has developed a micronized nuclear powered drive for ballistic misiles and cruize misiles. This is obviously a very aggressive and environment polluting action. However, could such nuclear powered drive be used for space ships, that would start in space and do not touch the atmosphere of...

So I'm an Software Engineer, not a physicist, nor a mathematician. So I like to work in the qualitative, not the quantitative. Today I hit on a problem. I've been trying to remove the concept of "down" or "inward" from my thinking of gravity and GR. When people show the concept of space/time...

Homework Statement For the given circuits, identify state variables and derive a state-space model for each. Assume the input is v(t) and the output is vL(t). Homework EquationsThe Attempt at a Solution [/B] So my issue is that I solved this problem using two different methods. First...

I was talking to a graduate physics student about the issue of energy conservation in an expanding universe. I paraphrased the argument against energy conservation as follows - Suppose we have a photon in outer space that is very far from earth. The universe is expanding (by this I meant that in...

Homework Statement A) Use Gauss's Law to derive the electric field in all space for a non-conducting sphere with volumetric charge distribution ρ=ρ0r3 and radius, R. B) Repeat when there is a concentric spherical cavity within the non conducting sphere with radius, A. Homework Equations...

I be grateful for any feedback on this argument: - First assume space is continuous - Then there is an actually infinite amount of information in a spatial volume of 10000 cubic units - There is also an actually infinite amount of information in a spatial volume of 1 cubic unit - But this is a...

TL;DR at bottomIt's a somewhat accepted convention that in realistic scifi space fighters should be impossible to use effectively. In general they are regarded as being easy targets that, at interstellar ranges would be unable to survive in a battlefield that employs current plausible scifi...

Hello, I've a fundamental question that seems to keep myself confused about the mathematics of quantum mechanics. For simplicity sake I'll approach this in the discrete fashion. Consider the countable set of functions of Hilbert space, labeled by i\in \mathbb{N} . This set \left...

nmh{796} $\textsf{Suppose $Y_1$ and $Y_2$ form a basis for a 2-dimensional vector space $V$ .}\\$ $\textsf{Show that the vectors $Y_1+Y_2$ and $Y_1−Y_2$ are also a basis for $V$.}$ $$Y_1=\begin{bmatrix}a\\b\end{bmatrix} \textit{ and }Y_2=\begin{bmatrix}c\\d\end{bmatrix}$$ $\textit{ then }$...

At an L1 LaGrangian point between two bodies, one could - materials science notwithstanding - pit two of Newton's Laws (LM3,UG) against each other to provide thruster-free stationkeeping. Would it be feasible to use that to launch free from the system ? either spit out like a watermelon seed...

I've been trying to wrap my head around the geometry of the expansion of space, from Science Channel shows I vaguely understand the "every point in space is moving away from every other point in space" and iirc this was uniformly so. Is that correct? If not ignore the rest of this post I suppose...

In the 19th century Lord Kelvin made the first numerical calculation of the age of the Earth not based on the Bible.From his initial guess that the Earth started as a molten rock and that today the temperature of the interior increases at a certain rate as you approach the center, he got an age...

To explain the concept of curved space time, we often use analogy of rubber sheet. If we put a heavy ball at the centre of sheet then it creates a depression and now a smaller ball will fall towards that heavy ball because of depression. But in this analogy smaller ball is falling down the slope...

Hello, I am taking a quantum mechanics course using the Griffiths textbook and encountering some confusion on the definition of inner products on eigenfunctions of hermitian operators. In chapter 3 the definition of inner products is explained as follows: $$ \langle f(x)| g(x) \rangle = \int...

In texts treating Hilbert spaces, it's usually given as an example that "any finite dimensional unitary space is complete", but I've found no proof so far and failed prove it myself.

I've plotted out the trajectory of an imaginary electron in 3D; next I represent it's points with the matrix A(x1 y1 z1) "throughout it's orbit": ( -1/2 -1 1 ( -2 -1.5 2 (-1/2 2 3...

Homework Statement "Do there exist any event spaces with just six elements?" Homework EquationsThe Attempt at a Solution Suppose ##F_1## is an event space with a non-trivial event ##A##. Then ##F_1=\{∅,A,A^c,Ω\}##. So ##inf(|F_1|) = 4##, since if you remove any of these events, ##F_1## is no...

Homework Statement If ##\lim_{n \rightarrow \infty} x_n = L## then ##\lim_{n\rightarrow\infty}cx_n = cL## where ##x_n## is a sequence in ##\mathbb{C}## and ##L, c \epsilon \mathbb{C}##. Homework Equations ##\lim_{n\rightarrow\infty} cx_n = cL## iff for all ##\varepsilon > 0##, there exists...

Lagrangian Mechanics uses generalized coordinates and generalized velocities in configuration space. Hamiltonian Mechanics uses coordinates and corresponding momenta in phase space. Could anyone please explain the difference between configuration space and phase space. Thank you in advance for...

Can string theory be made without time equations? According to Carlo Rovelli in his latest book "The Order of Time" https://www.amazon.com/dp/073521610X/?tag=pfamazon01-20 : "The equations of loop quantum gravity on which I work are a modern version of the theory of Wheeler and DeWitt. There...

Hey! :o For a field $K$ and $1<n\in \mathbb{N}$ let $A\in K^{(n-1)\times n}$ aa matrix with rank $n-1$. For a row vector $z\in K^{1\times n}$ let $\left (\frac{A}{z}\right )\in K^{n\times n}$ be the matrix that we get if we add as the $n$-th row of the matrix $A$ the vector $z$. To show that...

The permittivity of free space, ε0, is usually given without any derivation or historical context as to how it was experimentally determined. Could you explain to me how the value of ε0 was first determined experimentally or provide a resource that gives such a derivation? Thanks!

Hi everyone, I need a little help understanding how periodic reciprocal space applies to the Debye model for solids. Many thanks in advance! If we start with the general derivation of a dispersion relation for a 1D system, with atoms coupled by springs, one gets the following relation $$\omega...

Hello! I am a bit confused about the sign in space and time translation operators acting on a state. I found it with both plus and minus sign and I am not sure which one to use when. The equations I am talking about are: $$U(t)=e^{\pm iHt/\hbar}$$ and $$T(x)=e^{\pm ixp/\hbar}$$. Is it a plus or...

So, let me preface by saying I’m neither a scientist nor a mathematician, so am requesting some talented help here checking the accuracy of my source information and math. Regarding star formation, I got curious about how much volume of space in the interstellar medium is actually required to...

Homework Statement "If ##A_1,...,A_m\in O## and ##k\in ℕ##, show that the set of points in ##Ω## (the sample space) which belong to exactly ##k## of the ##A_i## belongs to ##O## (the previous exercise is the case when ##m=2## and ##k=1##)." Homework Equations Event space: O ##O\neq ∅##...

1) space is expanding at an increasing rate, therefore things are getting farther from each other and therefore increasing in velocity. 2) the faster an object moves relative to another, the more mass it has 3) supermassive objects can turn into neutron stars, black holes, etc. Therefore, will...

Homework Statement I am asked to write an expression for the length of a vector V in terms of its dot product in an arbitrary system in Euclidean space. Homework EquationsThe Attempt at a Solution The dot product of a vector a with itself can be given by I a I2. Does that expression only apply...

When we see with open eyes or in visible range of wavelength of e.m. wave we see black space containing some star...but if we see the space in other range of wavelength of the e.m. wave what will we see?? Also why the space is black?? Which matel we find in space mostly? Can we extract those...

In the field of medical physics, specifically in monte carlo simulation of radiation beams produced by electron accelerators, people call ‘phase space’ to a file that contains the data of a large number of particles when they traverse a reference surface in the machine (usually a plane), i.e...

Homework Statement 1.1.3 1) Do functions that vanish at the endpoints x=0 and L=0 form a vector space? 2) How about periodic functions? obeying f(0)=f(L) ? 3) How about functions that obey f(0)=4 ? If the functions do not qualify, list what go wrong.Homework Equations The Attempt at a...

Homework Statement Homework Equations definition of null vector, [/B] The Attempt at a Solution null vector : ## |0 \rangle = (0,0,0) ## inverse of (a,b,c) = ( - a, -b, -c) vector sum of the two vectors of the same form e.g. (c,d,1) + ( e,f,1) = ( c+e, d+f, 2) does not have the same...

For the vector valud function F in the image, the three components of the output vector at a point are functions of (x,y,z)the three coordinates of the point.But while calculating divergence, why is the rate of change of x component of the output along x direction alone is accounted(similarly...

To specify, by fuel I mean fossil, nuclear, chemical and pressurized air. Want to build and design a satellite for my daughter with a camera in it (goPro) with an antenna to be able to view anytime she likes. Want to do a hexagonal approach with solar cells only for power. Want to power the...

I am looking at a couple of very interesting papers, published in MNRAS, that deduce, that the accelerated expansion of the Universe we observe can be attributed to gravitational waves, produced by a very distant merger of two or more universe-mass-scale black holes. The last one is on the...

Homework Statement The book I'm using provided a proof, however I'd like to try my hand on it and I came up with a different argument. I feel that something might be wrong. Proposition: Let ##<X,d>## be a metric space, ##<Y,D>## a complete metric space. Then ##<C(X,Y), \sup D>## is a complete...

I was looking at NASA saying they might not have enough funds to put humans on Mars by 2040. OK, zoom forward maybe 200 years and the cost might be, maybe, just buy a ticket. Or people might already be working there; they will be paid to go there. So, here's the question. What is the least cost...

What's the difference between Euclidean & Cartesian space?

Hello! I am a returning student, 19YO, and will be starting back in community college in a month retaking classes I failed the first go-around with college. This is hopefully less of a "tell me what to do" thread, and more of a "clarify my misconceptions." Basically, I am very interested in a...

as we know light has momentum so theoretically we can use it but is it practical? (also this is it that light only exerts force if incident on something?)

If I consider a tetrahedron of four densely packed spheres of unit radius, what it the radius of the largest sized sphere that can fit in the space in between?

How do you show that there can be only one tangent space at a given point of a manifold? Geometrically it's pretty obvious in 3 dimensions, as one notices that there can be only one tangent plane at a point. But how could we show that using equations?