Argument Definition and 375 Threads

Hi, I thought that I understood why, once the free charges stop moving, ##E=0## inside a conductor, but I really don't. Can someone please help me out? I've heard the following arguments, but I don't think I understand any of them: I don't think ##q=0## implies ##\vec{E}=0##. I understand that...

http://web.williams.edu/Mathematics/sjmiller/public_html/302/coursenotes/Trapper_MethodsContourIntegrals.pdf See Type 5 Integrals. I don't understand why J is equal to the original real integral multiplied by a factor of ##2\pi i##. I think the ##2\pi i## comes from the fact that as you go...

Let ##G## be a group. Suppose that the map from ##G## to itself defined by ##\phi (g) = g^{-1}## is a homomorphism. Prove that ##G## is abelian. So I came up with two ways of writing the solution and am wondering whether they are equivalent and which one is preferable: 1) Let ##a,b \in G##...

10.) neg[r\implies neg(w v s)] 13.) r\implies neg(w v s) ----------------------------- R R^(wvs) --------------------------...

Greg Bernhardt submitted a new PF Insights post 3 New Years Tips For Cooling Off Debates Continue reading the Original PF Insights Post.

Homework Statement The picture below. Homework Equations cos2x=1-2sinx sin2x= 2sinxcosxThe Attempt at a Solution I got the modulus by using the Pythagoras theorem which is 2sin theta But I faced difficulty to find the argument. I have no idea why i end up with tan a (alpha) = cot theta which...

Hi guys, maybe you have any idea how to translate this two statements: If we are less than certain the human fetus is a person, then we must give it the benefit of the doubt. If we are certain the human fetus is a person, then we must accord it the right to live.

I don't fully understand the argument below used to derive the Lorentz transformation equation ##y'=y##. Suppose we have a rod of unit length placed stationary in frame S. According to an observer in frame S' (which is moving at a velocity v relative to frame S), this rod is moving and its...

So around 44:00, Susskind begins his argument. He put a variety of items into a region of space, and the added a minimal shell of material surrounding the items, then squeezed that material to form a black hole around the item. Then he said that the amount of original information cannot be...

In his 2005 paper titled 'Lifetime of the universe1' [ https://arxiv.org/abs/hep-th/0510003 ] Canadian physicist Don Page gives an argument that our universe must end on the timescale of 1060 years to avoid having more Boltzmann brains than normal observers. If not the volume of our comoving...

In 1D QM: I understand that if a given potential well, U(x), is symmetric about x = L, then the expectation value for operator [x] would be <x> = L. (I am not even entirely sure why this is, guessing that the region where x<L and x>L are equally probable) Is it possible to draw conclusion...

The Friedmann equation for a spatially flat Universe is given by $$\Big(\frac{\dot R}{R}\Big)^2=\frac{8 \pi G}{3}\rho$$ where ##R(t)## is the proper radius of some spherical volume with us at its center. Let us assume that there is a mass ##M## inside this spherical volume of radius ##R##. The...

this wiki link is down. does anyone know the title of the Okun paper or have a link? "For many years it was conventional to enter the discussion of dynamics through derivation of the relativistic mass, that is the mass–velocity relation, and this is probably still the dominant mode in...

Okay, these are my last questions and then I'll get out of your hair for a while. For 1, I have already done a proof by contradiction, but I'm supposed to also do a direct proof. Seems like it should be simple? For 2, this seems obvious because it's the definition of an integral. My delta is...

Homework Statement Find the modulus and argument of z=((1+2i)^2 * (4-3i)^3) / ((3+4i)^4 * (2-i)^3 Homework Equations mod(z)=sqrt(a^2+b^2) The Attempt at a Solution In order to find the modulus, I have to use the formula below. But I'm struggling with finding out how to put the equation in...

Homework Statement I want to check my understanding of the symmetry arguments that allow for E to come out Gauss's Law and the symmetry arguments that allow for E vector *dA to become EdA. Specifically for an infinitely long cylinder. Homework Equations ∫EdA=q/ε The Attempt at a Solution So...

Is it any argument structure not classified as a syllogism? where premises lead to conclusions which is another premise. It seems that the definition is that in a convergent argument all the premises are independent of each other and support the conclusion only. But how does one know? "I...

Homework Statement Write the given complex number in polar form first using an argument where theta is not equal to Arg(z) z=-7i The Attempt at a Solution 7isin(\frac{-\pi}{2}+2\pi n) The weird part about this problem it asks me to not use the argument, The argument is the smallest angle...

Hello everybody, I'm currently helping a friend on an assignment of his, but we are both stumbled on this exercise, I'm posting it here We define a function ##f## which goes from ##\mathbb{R}## to ##\mathbb{R}## such that its argument maps as $$ x \mapsto...

There is a paper by Arnold Neumaier, where it is argued that Bohmian mechanics, is simply wrong, because it doesn't predict all the results that we observe from experiment. See here. Neumaier wrote down his argument for a particle in the ground state of a harmonic oscillator, but there's...

I will be very grateful if someone could explain to me the following, in the most simple terms, f being a wave function : " ...f = f(x–ct). Let me explain the minus sign and the c in the argument. Time and space are interchangeable in the argument, provided we measure time in the ‘right’ units...

$\displaystyle\text{if} \left| r \right|< 1 \text{ the geometric series } a+ar+ar^2+\cdots ar^{n-1}+\cdots \text{converges} $ $\displaystyle\text{to} \frac{a}{(1-r)}.$ $$\sum_{n=1}^{\infty}ar^{n-1}=\frac{a}{(1-r)}, \ \ \left| r \right|< 1$$ $\text{if} \left| r \right|\ge 1 \text{, the series...

Homework Statement If modulus of z=x+ iy(a complex number) is 1 I.e |z|=1 then find the argument of z/(1+z)^2 Homework Equations argument of z = tan inverse (y/x) where z=x+iy modulus of z is |z|=root(x^2+y^2) The Attempt at a Solution z/(1+2z+z^2) = x+iy / 1+2(x+iy)+( x+iy)2 ...

I am reading Tristan Needham's book "Visual Complex Analysis" and am currently focussed on Chapter 1, Section II Euler's Formula ... in particular I am trying to follow Needham's heuristic argument in support of, or justifying, Euler's formula - Needham calls it 'the moving particle argument'...

I am having trouble understanding the relationship between complex- and real-argument associated Legendre polynomials. According to Abramowitz & Stegun, EQ 8.6.6, $$P^\mu_\nu(z)=(z^2-1)^{\mu/2}\cdot\frac{d^\mu P_\nu(z)}{dz^\mu}$$ $$P^\mu_\nu(x)=(-1)^\mu(1-x^2)^{\mu/2}\cdot\frac{d^\mu...

Dear all, I have a question on the hole argument as presented here by John Norton, http://plato.stanford.edu/entries/spacetime-holearg/ in particular section 3. The hole argument, as I understand it, can be used to show that GR is a gauge theory with the metric as gauge field and general...

Homework Statement So I'm trying to find the modulus and argument of cosh(iπ) Homework EquationsThe Attempt at a Solution so far coshπi = ½(eiπ+e-iπ) I am now a bit stuck as what to do as i have two terms in the form eix and I'm not sure homework to combine them to get the argument?

Homework Statement Find the modulus and argument of 1) cos(i) 2) -3i Homework EquationsThe Attempt at a Solution 1) So for question 1 i tried cos(i) = ½(ei2 + e-i2) = ½(e-1 + e) . However this doesn't (as far as I can see!) lead me to the right answer. I was aiming to get it in the form...

Homework Statement a) The complex number ## 1-i ## is denoted by ##u##. On an argand diagram, sketch the loci representing the complex numbers ## z## satisfying the equations ## |z-u|= |z| and |z-i|=2 ## b) Find the argument of the complex numbers represented by the points of intersection of...

Some layman people are against special relativity and stubbornly persist on their theories. One man put the model that the speed of photon is c + v, where v is speed of source. In such case Michelson interferometer is not a good anti-argument. What is, in your opinion about the most simple and...

In a relativistic treatment of mechanics one can say, that momentum and energy are correlatively conserved. The argument I would use, is that the length of the four-momentum is lorentz-invariant, and therefore, if E is conserved in any frame of reference, so the momentum. But I don't know, if...

Hello, in my QM class we arrived at the expression ##\langle \hat{H} \rangle = \Sigma_{even n} |C_n|^2 E_n = \frac{24}{n^2 \pi^2} \frac{\hbar^2}{2m} \frac{n^2 \pi^2}{L^2}##. The n terms cancel and we are left with ##\langle \hat{H} \rangle = \frac{12 \hbar^2}{mL^2} \Sigma_{even n} 1##. My...

Prove $$\sum_{n=0}^N\cos(nx)=\csc\left(\dfrac x2\right)\sin\left(\dfrac{(N+1)x}{2}\right)\cos\left(\dfrac{Nx}{2}\right)$$ I've tried working from the RHS with various identities but haven't managed to come up with anything that works. I suspect this problem involves some trigonometry that I...

What's the quickest way to calculate the argument of $\displaystyle \pi e^{-\frac{3i\pi}{2}}$?

Homework Statement For an infinite potential well of length [0 ; L], I am asked to write the following function ##\Psi## (at t=0) as a superposition of eigenstates (##\psi_n##): $$\Psi (x, t=0)=Ax(L-x) $$ for ## 0<x<L##, and ##0## everywhere else. The attempt at a solution I have first...

Homework Statement In the argand plane z lies on the line segment joining # z_1 = -3 + 5i # and # z_2 = -5 - 3i # . Find the most suitable answer from the following options . A) -3∏/4 B) ∏/4 C) 5∏/6 D) ∏/6 2. MY ATTEMPT AT THE SOLUTION We get two points ( -3 , 5 ) & ( -5 , -3 ) => The...

Homework Statement Of all complex numbers that fit requirement: ## |z-25i| \leq 15## find the one with the lowest argument. Homework EquationsThe Attempt at a Solution z=a + ib (a, b are real numbers) ## \sqrt{a^2 + (b-25)^2} \leq 15 \\ a^2 + (b-25)^2 \leq 225 ## The lowest possible...

I am hopeful someone can give me a quick lesson here. I have an idea that time does not slow as one's velocity increases (bear with me, please). I'll state this in familiar terms with a person on a train vs platform and the light beam traveling vertically from the ceiling (P1) to the floor of...

(∃x)[P(x) → Q(x)]∧(∀y)[Q(y) → R(y)]∧(∀x)P(x) → (∃x)R(x)

Homework Statement Give a combinatorial proof that (n-r)\binom{n+r-1}{r} \binom{n}{r}=n\binom{n+r-1}{2r} \binom{2r}{r} Homework EquationsThe Attempt at a Solution I interpreted the right side of the equation as: There are n grad students and r undergrads. First, from the n grad students...

I start with the spatially flat FRW metric in conformal co-ordinates: $$ds^2=a^2(\eta)(d\eta^2-dx^2-dy^2-dz^2)$$ This metric has the following non-zero Christoffel symbols: \begin{eqnarray*} \Gamma^0_{\alpha \beta} &=& \frac{\dot{a}}{a} \delta_{\alpha \beta} \\ \Gamma^i_{0j} &=& \Gamma^i_{j0} =...

A minor write stated the following argument about this famous puzzle: "Tristram Shandy, who writes his autobiography so slowly that he covers only one day of his life in a year of writing. the set of days written about cannot in fact always be a subset of the set of days past. Consider any day...

PeterDonis submitted a new PF Insights post The Block Universe - Refuting a Common Argument Continue reading the Original PF Insights Post.

I came across this argument on thinkinghard.com: " To make the contradiction obvious, let the human mathematician who understands that G(G) is non-terminating be the same human mathematician for whom F determines their mathematical ability. If the mathematician was a robot, telling them that...

So during a particle physics lecture, the lecturer used Heisenberg's uncertainty principle to set a lower limit on the KE of the quarks bound in a proton (given the mass,size of proton and the mass of u/d quarks), which is of the order of 100 MeV, while the mass of quarks is about several...

Homework Statement Taken from Discrete Mathematics and its Applications, Seventh Edition: "What is wrong with this argument? Let S(x, y) be 'x is shorter than y.' Given the premise \exists s S(s, Max), it follows that S(Max, Max). Then by existential generalization it follows that \exists x...

Laser action by definition requires the presence of stimulated emission in the laser medium. The typical way of treating this semi-classically is to introduce the Einstein coefficients, in essentially an ad hoc way, then derive the Einstein equations for the various level population transitions...

Find the error in the following argument by providing a counterexample. “The reflexive property is redundant in the axioms for an equivalence relation. If x ∼ y, then y ∼ x by the symmetric property. Using the transitive property, we can deduce that x ∼ x.”

In order to construct a geometric series we do the following: chose a number a such that a does not equal 0 and a second number r that is between (-1,1). We call r the ration because it is the ratio, the progression of each term to its predecessor. We have An=a+ar+ar^2+ar^3...ar^n We multiply...

How can I find an Integral of an exponential with Polynomial argument with finite limits: \int_0^\pi \exp^{-a x^2 -b x^4} dx \\ \int_0^\pi \exp^{-a x^2 -b x^4} (x - x^3)dx