Space Definition and 1000 Threads

Hi all, Consider a system of ##N## noninteracting, identical electric point dipoles (dipole moment ##\vec{\mu}##) subjected to an external field ##\vec{E}=E\hat{z}##. The Lagrangian for this system is...

In dynamic programming: 1. what is the definition of the space of subproblems? does it have a mathematical definition? 2. why is it necessary to have an arbitrary index for the subproblem to vary? To elaborate on question 2, I've taken the following paragraph from chapter 15.3 in...

Given that we know experimentally that time slows and space bends in the presence of matter, what is the actual physical mechanism that enables matter to bend space and slow time?

Science fiction is of course full of all kind of futuristic ideas about interstellar space travel and ways of propulsion, some more physically plausible then others. But within the current realm of what is physical possible, what could interstellar space travel be like? First you need a source...

If an infinite amount of energy were available to create the lift mechanism for a space launch. What would be required to fire a 200lb object into low Earth orbit(160km) after speeding it up in a way similar to how the large hadron collider speeds up a particle. Assuming the launch vehicle...

I attatched an example plot where I created the histogram for the differential distribution with respect to the energy of the d-quark produced in the scattering process. My conception is that the phase space generator can "decide" how much of the available energy it assigns to the respective...

When something is described as say 7 billion light years away would't it be more accurate to 7 billoin years ago?

What do you guys think of this soberly elegant proposal by Sean Carroll? Reality as a Vector in Hilbert Space Fundamental reality lives in Hilbert space and everything else (space, fields, particles...) is emergent. Seems to me a step in the right conceptual direction.

So carbon nanotubes are incredible. Is a macrtube a possibility? If we stretched one out for centuries, and landed it on another planet, would it transfer gravity?

Hi, How do I left align the text below? Also, how do I create vertical spaces above and below the line stating "Subbing the following expressions..."? Could you please help me with it?To derive 14(ii) m_{0} \gamma^{2} \frac{d^{2} y}{d t^{2}}=e E_{y}^{\prime} from 13(ii) m_{0} \frac{d^{2}...

Summary:: Given a known closed space/apparatus ( e.g. constant volume, pressure, density, current, temperature, voltage, spark gap distance - let me know if I missed something) how would I compute the change in gas temperature. Hello, Given a known closed space/apparatus ( e.g. constant...

Is the following a correct demonstration that quantum mechanics can be done in a real vector space? If you simply stack the entries of density matrices into a column vector, then the expression ##\textrm{Tr}(AB^\dagger)## is the same as the dot product in a complex vector space (Frobenius inner...

Hello, I have problems with this exercise Let $(X,\mathcal{B} , \mu)$ a measurement space, consider $\bar{\mathcal{B}} = \{ A \subseteq{X} \; : \; A\cap{B} \in \mathcal{B}$ for all that satisfies $\mu(B) < \infty \}$, and for $A \in \bar{\mathcal{B}}$ define $\bar{\mu}(A) = \left \{...

It is said that: It is not possible to write a position vector in a curved space time. What is the reason? How can one describe a general vector in a curved space time? Can you please suggest a good textbook or an article which explains this aspect?

I consider three material points O, O', M, in uniform rectilinear motion in a common direction, so that in relation to the point O, the points O' and M move in the same direction with the constant velocities v and u (u>v>0). Assuming that at the initial moment (t0=0), the points O, O', M were in...

From "standard" formula we have that the gravity acceleration a = GM/r^2 and that the Schwarzschild radius rs = 2 GM / c^2 Is it possible to compute the gravity acceleration at Schwarzschild radius putting r = rs? In this case we will have a = c^4 / (4GM) This mean that a very very...

So I am a layman in physics, I admit I am trying to grasp big ideas piecemeal via articles, wikipedia and YouTube. I don't pretend to be educated in this regard but I am curious and willing to learn! The idea of the multiverse intrigues me. Sidestepping for a second the fact that the idea has...

Could someone explain the green highlight to me, please?

From: https://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics In the section, "Effect of measurement on the state" (aka Postulate 5), it says: If this is just a fancy way of talking about our very own space in which we live (ie, in which an observation has been made), then...

Why doesn't it repel things... or just pass through and leave distance unchanged?

Since it asks for the time evolution of the wavefunction in the momentum space, I write : ##\tilde{\Psi}(k,t) = < p|U(t,t_{0})|\Psi> = < U^\dagger(t,t_{0})p|\Psi>## Since ##U(t,t_{0})^\dagger = e^{\frac{i}{\hbar}\frac{\hat{p^2}t}{2m}}##, the above equation becomes ##\tilde{\Psi}(k,t) =...

I've been trying for a very long time to show that the following integral: $$ I_D=2{\displaystyle \int} \, {\displaystyle \prod_{i=1}^3} d \Pi_i \, (2\pi )^4\delta^4(p_H-p_L-p_R) |{\cal M}({e_L}^c e_R \leftrightarrow h^*)|^2 f_{L}^0f_{R}^0(1+f_{H}^0). $$ can be reduced to one dimension: $$ I_D...

I suspect you're not supposed to ask short questions here. Mine is in the summary.

It's probably more kind of math question. I consider a wave function of a harmonic oscillator, i.e. a particle in a parabolic well of potential. We know that the Hamiltonian is a Hermitian operator, and so its eigenstates constitute a full basis in the Hilbert space of the wave function states...

I first saw note of this about a week ago and I don't think it has gotten enough attention: https://www.cnn.com/2021/06/30/opinions/hubble-telescope-glitch-opinion-lincoln/index.html While I don't want to eulogize too soon, I'm wondering where the HST ranks in the annals of the most...

does np=ni^2 holds even the space charge region of a pn junction diode?

Please help me understand why this is a concept that has not been studied? The laser sail is really the only info I can find in this area using a laser from a fixed source. Using liquid nitrogen to cool the mirrors and reflecting lasers off of them for propulsion. I'm a Doctor of Pharmaceutical...

Summary:: You have a spacecraft the size of a cube (2x2x2 m^3, m=3000 kg. It has 24 thrusters (2N each) and one main engine. For preparing your spacecraft for maneuvers, you want to rotate by 180 degrees. For the rotation, you'll use n=4 attitude thrusters per burn. What am I doing wrong...

Can chameleon inspired capture system function to deorbit or even recover orbital debris? What are the physics challenge?

Electrostatic energy involves a volume integral and a surface integral The question is how to apply this formula to a finite space in which case the 1st term (surface integral) won't vanish. Let's apply to a capacitor and enclose the capacitor by a closed surface. Calculate the energy integral...

The answer in the textbook says 0J but I am not sure what the concept behind it is. Does it have something to do with gravity?

Hi PF, I've one question about vector spaces. There is only one way to define the operations of a vector space? For example if V is a vector space there is other way to define their operations like scalar multiplication or the sums of their elements and that the result is also a vector space?

I can calculate the fields generated by the cylinder and the wire but I don't know how to calculate their vector sum to evaluate it at point A. Cylinder field inside: ρR^2/2rε Cylinder field outside: ρr/2ε Field generated by the wire: λ/2πr I should break the fields into components but I don't...

Hi and thank you for answering questions on complex subjects like this. I’m a non-scientist who is jealous of your brain capacity! Recently, in a discussion with a chemist, he said the particles appearing from nothing might have been the initial cause of the universe. I’m familiar with the...

I've heard it and I've read* it before, so I just want to make sure I understand this so I never have to wonder about it again. So, are tidal forces exactly curvature of space? Here's why I think the answer to that is yes: .I've seen a spacetime interval equation which has a coefficient on...

I read this in the wiki article about Wick rotation: Note, however, that the Wick rotation cannot be viewed as a rotation on a complex vector space that is equipped with the conventional norm and metric induced by the inner product, as in this case the rotation would cancel out and have no...

Let's play this game, let's assume the infinite Hilbert Space, the operators and all the modern machinery introduced by Von Neuman were not allowed. How would be the formalism? Thanks

Hi, I was reading the following article. Source: https://www.forbes.com/sites/startswithabang/2019/01/31/dark-energy-may-not-be-a-constant-which-would-lead-to-a-revolution-in-physics How come the density of dark energy remains constant? Yes, if it's intrinsic to the space itself and more...

Freshly Made Plutonium From Outer Space Found On Ocean Floor May 13, 2021 [discussion split off from here: https://www.physicsforums.com/threads/what-is-theoretically-the-heaviest-isotope-that-the-r-process-could-produce.1000056/ ]

The Earth is spinning and orbiting the Sun, and that is orbiting the center of the Milky Way, and that too moving in some way... Say I were to hop in a spaceship and travel in such a way that it counters all of this motion, leaving me and the spaceship completely motionless, would anything...

Heloo guys, diego here, I was wondering if there exist multiple space dimensions, and we can only see in the 3th dimension, it is entirely possible to have multiple time dimensions. And another thing, we all learn(simplified version coming) 1 dimension is basically a point, 2nd dimension is a...

{a} P = identity Matrix w/ -1 on diagonals {b} eigenvalues = +/- 1

Hi there, first post here! I'm working on a story and at one point there is a ship traveling at 40% of C. The characters are on a long trip, fifteen years or so, I'm wondering in a ship far from any star system going at a % of C, what kind of interesting experiments could one do. The ship has...

I am not sure how does the integral was did here. More preciselly, How to go from the first line to the second line? Shouldn't it be $$\frac{4 \pi}{(2 \pi)^3} \int _{0} ^{\infty} p^2 e^{ip*r}/(2 E_p)$$ ? (x-y is purelly spatial)

I'm trying to figure out alternative ways to lift the roof on a pop-up camper that I'm refurbishing. There is limited space, and it needs to be lifted from beneath. I'm trying to avoid completely gutting it if possible which is what I'd have to do with a standard cable system. Any ideas? It...

In Anthony French's book, Newtonian Mechanics, while explaining the non-Euclidean nature of the 3-d space, he poses a problem (I have rephrased it slightly): Suppose you are on Earth's equator (r = 6,400 km) at the prime meridian (point I). You first walk along the equator 1000 miles east and...

It has been stated unequivocally that there are no naturally occurring elements beyond uranium anywhere else in the universe but on Earth then I read that plutonium has been discovered in space. Assuming it wasn't put there by humans who's right?

Due to gravitational time dilation, the speed of light in outer space will be higher than on Earth. Do astronomers use the corrected value?

One place I used to visit every year was Green Cove Springs Florida. Once there, I could hardly ignore this artifact near the river bank. It has been there since 2013. It is privately owned, so presumably it could be for sale. If you don't recognize it, this picture may help. In the...

I am trying to draw the Poynting vector field for a single electron in free space between two capacitor plates. The electron is moving (and accelerating) to the positive plate at the right. I expected the Poynting vector field lines to converge to the electron, because that is where the work...