Infinite Definition and 1000 Threads

Hello, Reading Richard Feynman’s book “Quantum Electrodynamics” (Edited by Advanced Book Classics), I read that the electron’s self-energy is infinite and that has been a trouble for QED during 20 years. Feynman proposed a solution based on a cut-off, but that’s not fully satisfactory and I...

Homework Statement Use Eisenstein's criterion to show that there exists irreducible polynomials over Q or arbitrarily large degree, and from this deduce that the field of algebraic numbers is an infinite extension of Q Homework Equations none The Attempt at a Solution Note that x^n+4x+2 is...

And virtual particles potential energy is infinite too? As more and more dark energy is created does this mean that the potential energy of dark energy is infinite? Does that happen for virtual particles in vacuum and vacuum energy too?

https://en.m.wikipedia.org/wiki/Vacuum_energy And it is this type of energy dark energy or a form of it?

Homework Statement To Determine Whether the series seen below is convergent or divergent. Homework Equations ∑(n/((n+1)(n+2))) From n=1 to infinity. The Attempt at a Solution Tried to use the comparison test as the bottom is n^2 + 3n + 2, comparing to 1/n. However, this does not work as the...

1. ##<x>= \int_{0}^{a}x\left | \psi \right |^{2}dx## ##\psi (x)=\sqrt{\frac{2}{a}}\sin\frac{n\pi x}{a}## then ##<x>= \frac{2}{a} \int_{0}^{a}x \sin\frac{n\pi x}{a}dx## 2. Homework Equations 1) ##y=\frac{n\pi x}{a}## then ##dy=\frac{n\pi}{a}dx## and 2) ##y=\frac{n\pi x}{a}## then...

This is about the legitimacy of a possible operation. Take 0.999999... The operation is defined like this: 1) identify the insertion position with respect to the decimal. in this example we choose "3" as in the third position, 0.999999... 2) from the insertion position, inclusive, to the...

In using the Biot-Savart Law for an finite wire, I am having trouble understanding the angles. I have sintheta1-sintheta2, where theta1 is measured from point P to the horizontal wire and from the vertical axis, to the left of point P. Theta 2 is measured to the right of point P. I am ok until...

I started simply looking at a circuit breaker connection diagram, then I fell down the rabbit hole. So I wondered, if you had a piece of pure copper and getting rid of heat (structural integrity, gravity etc.) was not an issue, just how much current could you push through it before it hit it's...

I'm curious if anyone has ever simulated the infinite monkeys on typewriters using a computer, and managed to generate short sentences or phrases that have appeared in books/print media before. That would demonstrate the effectiveness of the infinite monkey theorem.

Find a group $G$ that contains elements $a$ and $b$ such that $a^2=e$, $b^2=e$, but the order of the element $ab$ is infinite. My attempt: Clearly $G$ cannot be abelian. So I looked at two commonly known non-abelian groups, namely (i) The group of symmetries of the equilateral triangle (ii) 2...

Homework Statement For the particle in a box given in the above question, what is the probability of finding the electron between (i) x = 0.49 and 0.51, (ii) x = 0 and 0.020 and (ii) x=0.24 and 0.26 ( x in nm) for both n=1 and n=2. Rationalize your answers. Homework Equations...

Given the equation ##\frac{d^2 \psi (x)}{{dt}^2}+\frac{2m}{{\hbar}^2}(E-V(x))=0## the general solution is: $$\psi (x)=A_1 e^{ix \sqrt{\frac{2m}{{\hbar}^2}(E-V(x))}} +A_2 e^{-ix \sqrt{\frac{2m}{{\hbar}^2}(E-V(x))}}$$ If we have an infinite potential well: ## V(x)=\begin{cases} \infty \quad x\ge...

In QM, we all know that the wavefunction ψ is zero when x is infinite. However, Is dψ/dx also zero when x is infinite? And the d2ψ/dx2?

hi, I'm solving solving a problem about sums of zeta function and I'm come to the following conclusion $$\sum _{n=2}^{\infty }{\frac {\zeta \left( n \right) }{{k}^{n}}}= \sum _{s=1}^{\infty } \left( {\it ks} \left( {\it ks}-1 \right) \right) ^{-1}=\int_{0}^{1}\!{\frac {{u}^{k-2}}{\sum...

I've been Dealing with a problem of perturbation of the movement of an infinite chain of harmonic oscillator and I tried to apply the von Zeippel-Poincare formalism of canonical perturbation theory just to see what I get. This was too naive since I quickly stumbled into the problem of defining...

Homework Statement The global topology of a ##2+1##-dimensional universe is of the form ##T^{2}\times R_{+}##, where ##T^{2}## is a two-dimensional torus and ##R_{+}## is the non-compact temporal direction. What is the Fermi energy for a system of spin-##\frac{1}{2}## particles in this...

Homework Statement Consider a series of ##N## particles in a line, with the displacement of each particle from its equilibrium position labelled by ##q_{n}## and it conjugate momentum labelled by ##p_n##. Assume that the interaction between the particles is pairwise, so that the Hamiltonian is...

Hi everyone, first post here. Today i crushed into a question. I was going to write it down here, then i crushed into another one. Lets say we want to know the potential energy of a body relative to a center of gravity. I will refer to gravitys acceleration as "g" and to mass as "m". "k" will...

Sorry I couldn't finish the title. I ran out of space. Anyway, here's the question: A uniformly charged, infinitely long line of negative charge has a linear charge density of -λ and is located on the z axis. A small positively charged particle that has a mass m and a charge q is in circular...

Hi Everyone! I used to have a book that explained physics concepts quite simply. I used to read it when I was about 8 or 9 years old and one chapter really stuck with me (I'm 25 now). I'm not sure where the book went, and have been looking for it for some time and think this might be the best...

a. Find the common ration $r$, for an infinite series with an initial term $4$ that converges to a sum of $\displaystyle\frac{16}{3}$ $$\displaystyle S=\frac{a}{1-r} $$ so $\displaystyle\frac{16}{3}=\frac{4}{1-r}$ then $\displaystyle r=\frac{1}{4}$ b. Consider the infinite geometric series...

The magnetic field generated by an infinitely long straight wire represented by the straight line ##\gamma## having direction ##\mathbf{k}## and passing through the point ##\boldsymbol{x}_0##, carrying a current having intensity ##I##, if am not wrong is, for any point ##\boldsymbol{x}\notin...

Calculate the sum for the infinite geometric series $4+2+1+\frac{1}{2}+...$ all I know is the ratio is $\frac{1}{2}$ $\displaystyle\sum_{n}^{\infty}a{r}^{n}$ assume this is used

The (most popular) flat model of Universe is space-infinite. How the infinity is measured? Can you give me references to the papers about the actual infinity of space?

How can the universe be infinite and yet have a finite age?

If I displace an object at rest in space by giving it a force F in X direction and the object tends to move forever, will the work done be infinite? Knowing that work done = force*displacement . Since the space has no external resistance (unbalanced force) to stop the object from moving , making...

Let ##\boldsymbol{l}:\mathbb{R}\to\mathbb{R}^3## be the piecewise smooth parametrization of an infinitely long curve ##\gamma\subset\mathbb{R}^3##. Let us define $$\boldsymbol{B}(\boldsymbol{x})=\frac{\mu_0...

Homework Statement OK, I've worked up my nerve to ask a stupid question about this problem. I've read the various discussions of it, but I'm clearly missing something.2. Homework Equations [/B] The right-hand mass is 1/(1-t). The sum of the left-hand masses (an infinite series) is also...

Homework Statement imgur link: http://i.imgur.com/0Zc8nQe.png Homework Equations Y-Delta transformations The Attempt at a Solution Since it's a proof, I can't check the answer in the back. What I did: I transformed the three impedances in their delta config to a Y config, and my TI89...

I always has the impression that the density of the universe is infinite at the singularity because its just amount of stuff divided by volume and if the distance between stuff is 0 then the volume is 0. So divide by zero and you get infinity. But I have been told by others that dividing by zero...

Homework Statement This is a problem from Spacetime and Geometry by Carroll, Just because a manifold is topologically nontrivial doesn't necessarily mean it can't be covered with a single chart. In contrast to the circle ##S^1##, show that the infinite cylinder ##RxS^1## can be covered with...

The problem \lim_{x\rightarrow \infty} \frac{x^4 + x \ln x}{x + \left( \frac{2}{3} \right)^x} The attempt \lim_{x\rightarrow \infty} \frac{x^4 + x \ln x}{x + \left( \frac{2}{3} \right)^x} = \lim_{x\rightarrow \infty} \frac{x^4(1 + \frac{x \ln x}{x^4}) }{x + \left( \frac{2}{3} \right)^x}...

Say we have a coil connected to a battery in a uniform magnetic field, perpendicular to the magnetic moment of the coil. This is a simple motor. There is a torque on the coil that varies with the angle θ between the field and the moment. Clearly, the angular velocity ω is not constant. Here is...

Homework Statement Hi, I have to find the RMS value of the inifnite series in the image below. Homework Equations https://en.wikipedia.org/wiki/Cauchy_product Allowed to assume that the time average of sin^2(wt) and cos^2(wt) = 1/2 The Attempt at a Solution So to get the RMS value I think I...

A significant number of physicists today postulate that the universe we reside in is infinite in size. It's also thought that if we extrapolate back in time to the big bang that the universe was a singularity of infinite density. Singularities are commonly thought of as a dimensionless point...

Homework Statement An infinitely long line of current $I_1=6[A]$ is following along the positive z-axis in the direction of +$\hat{a_z}$. Another current is following a triangular loop counter clockwise from the points A(0,2,2), B(0,6,2) and C(0,6,6). Homework Equations To start I applied...

If we have an infinite square well, I can follow the usual solution in Griffiths but I now want to impose periodic boundary conditions. I have \psi(x) = A\sin(kx) + B\cos(kx) with boundary conditions \psi(x) = \psi(x+L) In the fixed boundary case, we had \psi(0) = 0 which meant B=0 and...

Let ##V\subset\mathbb{R}^3## be an infinitely high solid cylinder, or a cylindrical shell of radii ##R_1<R_2##, whose axis has the direction of the unit vector ##\mathbf{k}##. For any point of coordinates ##\boldsymbol{r}\notin \bar{V}## external to ##V## the Lebesgue integral (which is...

$\tiny\text{LCC 206 8.8.11 Infinite Intervals of Integration}$ $$\displaystyle I=\int_{1}^{\infty} {x}^{-2} \,dx = 1$$ $$I=\left[\frac{1}{x}\right]_1^\infty=\left| 0-1 \right|=1$$ $\text{the only way apparently to get 1 is to use absolute value ?}$ $\tiny\text{from Surf the Nations math study...

The problem is to find the general term ##a_n## (not the partial sum) of the infinite series with a starting point n=1 $$a_n = \frac {8} {1^2 + 1} + \frac {1} {2^2 + 1} + \frac {8} {3^2 + 1} + \frac {1} {4^2 + 1} + \text {...}$$ The denominator is easy, just ##n^2 + 1## but I can't think of...

What is the metric for the spacetime around an infinitely thin, infinitely long, uniform rod? Could it be written in the form ds2 = A(r)dt2 + B(r)dr2 + C(r)dh2 + r2dθ2 where h is the coordinate along the rod and r is the radial coordinate, or would it be something more complicated?

Is there a notation for the opposite of epsilon (infinitesimal) in the way that infinity is the opposite of zero?

I found a strange theorem and a doubtful method in Stroud's book "Engineering mathematics": I think, every polynomial equation will have two infinite roots (at +infinity and -infinity). I also think that this method of the determination of an asymptote gives wrong results if f(x) is a...

Homework Statement From the picture below, calculate the net resistance between points A and B if ##R_1=12## ##R_2=3.75## Homework Equations 3. The Attempt at a Solution [/B] I cannot think of any way but to find the equivalent resistance od ##R_1## and ##R_2## and add them up but since there...

Could someone explain why we can not use the double split experiment with entangled photon pairs as to communicate information at infinite speed? Switching off and on readers effects whether the other photons displays as interference or as particles; so why can't we use this to send 1 and 0s...

Sorry if this is in the wrong place. Happy for it to be moved. I've heard it said that a multiverse containing an infinite number of universes, would lead to the ridiculous. The argument is something like this: 1) An infinite number of universes contain an infinite amount of matter. 2)...

I am reading Paul E. Bland's book "Rings and Their Modules ... Currently I am focused on Section 2.2 Free Modules ... ... I need some help in order to fully understand Bland's Example on page 56 concerning directly finite and directly infinite R-modules ... ... Bland's Example on page 56...

I am reading Paul E. Bland's book "Rings and Their Modules ... Currently I am focused on Section 2.2 Free Modules ... ... I need some help in order to fully understand Bland's Example on page 56 concerning directly finite and directly infinite R-modules ... ... Bland's Example on page 56...

Suppose the universe is infinitely big, then even the most improbable thing will happen somewhere in the universe, in fact it will happen an infinite number of times. So what we consider to be probable things and what we consider to be improbable things are both infinite. So how do we rule out...