Terms Definition and 1000 Threads

Here is the Morris-Thorne Wormhole line element: ds2 = - c2dt2 + dl2 + (b2 + l2)(dθ2 + sin2(θ)d∅2) Now my main question here (even though I've asked this before, but never quite understood) is: What exactly is l? I know that b is the radius of the throat of the wormhole. I know that the rest...

Loosely, in terms of string theory, an electron moving back and forth in a radiating antenna is a string moving in space-time. Far away, the electromagnetic radiation of the antenna is made of strings moving in space-time. Can I think of the near electric and magnetic fields surrounding the...

I know there's a similar post, but i didn't understand it. Why the derivative respect to t in terms of the complex conjugate of ψ is: instead of being the original S.E in terms of ψ* or the equation in terms of ψ with the signs swapped

Hello, guys. I have not understood what it means when one writes ##\pi^+=u\bar{d}##, for example. I though it simply meant that the ##\pi^+## meson was composed of one up-quark and one anti-down-quark. However, that doesn't explain what writing ##\pi^0=\frac{1}{\sqrt{2}}(d\bar{d}-u\bar{u})##...

I'm trying to clarify my terminological understanding of things related to mathematical expressions. Actually, first I want to make sure I understand what an expression is and is not. From my current understanding, an expression is any number, variable, or combination of numbers and...

Homework Statement A particle moves along a straight line so that its acceleration t seconds after passing a fixed point O on the line is (2 - 2t) cm/s2. Three seconds after passing O, the particle has a velocity of 5 cm/s. Find and expression, in terms of t, for the velocity of the particle...

I know two methods as to how to do this, but one of them doesn't seem to work. Say you're given x = 3t^2 + 6t - 4. If you treat x as an unknown variable and movie it over to the other side, you can use completing the square to solve for t. This eventually gets you: t = 1/3*sqrt(3(x+7)) - 1 Then...

It says in Susskind's TM: ##\langle L \rangle = Tr \; \rho L = \sum_{a,a'}L_{a',a} \rho_{a,a'}## with ##a## the index of a basisvector, ##L## an observable and ##\rho## a density matrix. Is this correct? What about the trace in the third part of this equation?

Hey guys, I am not to good in Math and I am having issues solving this equation. 2x-9/3x + 8 = 3/7x How do you solve this equation? The answer is supposed to be x = 0.3956?

I want to ask that how to understand the relation of different concentration terms. Like the relation of Molality, Molarity & Density & related relations of concentration terms. So how to understand the relations easily?

Hi all, (Thank you for the continuing responses to my other questions...) I am gaining more and more understanding of differential forms and differential geometry. But now I must ask... Why the words? I understand the exterior derivative, but why is it called "exterior?" Ditto for CLOSED and...

Find the sum of the first $17$ terms of the arithmetic series: $8+\sqrt{7}$, $6$, $4-\sqrt{7 }$... $a_1=8+\sqrt{7}$; $n=17$; $d=2+\sqrt{7 }$ $\displaystyle\sum_{k=1}^{n}(a_1-kd)=136 \sqrt{7 }-170$ Don't have book answer for this? Much Mahalo

I know formula ## p=\frac{h}{λ} ## p is photon momentum h is plankc constant λ is EM-wave wavelenght but it is only valid for one wave. How to describe most general EM- field in terms of photons? Is there always discrete number of photons? If EM field is given in terms of a)EM-vectorfield...

Homework Statement An atom with an excited-state configuration 1s22s22p63s23p64s23d14p1 With residual electron-electron interactions are taken into account, this configuration splits into atomic terms. List these terms labelled by their L and S quantum numbers Homework Equations L=|l1-l2|...

These are Maxwell´s equations in potential formulation: ∇2φ = DIV(grad(φ)) . Am I right? ∇2A = ROT(ROT(A))=ROT(B)=grad(DIV(A))-Laplace(A) . Am I right? In coulomb gauge in every point and at any time DIV(A)=[PLAIN]https://upload.wikimedia.org/math/4/4/1/44131cc26bd9db464d0edb7459ccca84.png...

Homework Statement What terms are generated by the configuration (e1g)2(e2u)2 in D6h symmetry? Homework Equations configuration (χd)2 gives terms 1(symmetric product) + 3(antisymmetric product) where χ=symmetry of an orbital and d = degenerate (e1g)x(e1g) = A1g + [A2g] + E2g (e2u)x(e2u) =...

Homework Statement The Hamiltonian for a single diatomic molecule of identical atoms is given as $$H=\dfrac{\vec{p_1}\cdot\vec{p_1}}{2m}+\dfrac{\vec{p_2}\cdot\vec{p_2}}{2m}+\dfrac{K}{2}(\vec{r_1}-\vec{r_2})\cdot(\vec{r_1}-\vec{r_2})$$. Find the grand canonical partition function for a gas of...

Two Thermally insulated cylinders, A and B, of equal volume, both equipped with pistons, are connected by a valve. Initially A has its piston fully withdrawn and contains a perfect monatomic gas at temperature T, while B has its piston fully inserted, and the valve is closed. Calculate the final...

OK, so I've gone through probably 90 tutorials on electricity and related topics, and there's a bundle of terms I ran into, used by people ages 12-80 with a dozen different accents and twice as many time zones. (So I'm not sure how many terms are universal and how many are provincial). Live...

This is a question about transforming a probability distribution, using the blackbody spectrum as an example. Homework Statement An opaque, non-reflective body in thermal equilibrium emits blackbody radiation. The spectrum of this radiation is governed by B(f) = af3 / (ebf−1) , where a and b...

when expressing dS as a function of dV and dT, dU was expanded out as you can see in the screenshot below, is there a mathematical rule which allows this? does the fact that the internal energy is expanded out change the meaning of the expression?

If moving inside the event horizon of a super-massive black hole and theoretically surviving we could see the universe pass by at millions of years per second relative to someone on earth, where could we go where time passes at a much faster rate than someone on earth? For example where 2...

Coming to terms with the theory of relativity is a long and difficult process that requires shedding all the popular misconceptions and hype surrounding the subject matter. Science doesn't sell but throw in carefully worded claims of time travel, matter materialization, shape shifting and...

Find the sum of the first 17 terms of the arithmetic series $$8+\sqrt{7}, \ 6,\ 4-\sqrt{7}$$ $$u=8+\sqrt{7}$$ $$S_{17} =\frac{u\left(1-\frac{{6}^{17}} {u} \right)}{u}$$ My first shot at this

Really wishing I had paid more attention in high school. I assumed that reactive meant that the element either needed to gain or lose electrons causing it to "want" to grab onto another or be grabbed. Sodium being an example. If I am correct with that part, this next part is where I am picking...

Homework Statement The bessel function Jn(x) is defined by the integral Jn(x)=1/(inπ)∫0πeixcosφcos(nφ)dφ From this formula, find the first 3 terms of the asymptotic expansion of Jn(x) when x=n and n is a large positive integer. Homework EquationsThe Attempt at a Solution I tried combining the...

I'm trying to build a vague understanding of what a sphaleron is (for context: I'm reading about baryon number asymmetry in the early universe and the word keeps cropping up). I've found a paragraph that seems to get me half way there but still leaves me feeling a bit :oldconfused: : So first...

'Flux' is often used to describe quantities associated with a surface integral. I wonder if there are corresponding terms for the line and volume integrals. Linflux? Volux?

If I show you three face down cards (normal playing cards, so can be either a red or black suit), and tell you that no matter which two you pick, they would be different colors, I have no doubt you'll say I'm being weird (to put it mildly). Well, nature does pretty much the same thing. This is...

As per me rise is the vertical length of the structure. Am I right? I read in Gordon's book "Structures or why things don't fall down" that the rise should be half the span of the bridge. Why? What does span mean?. As per me span means the area between one end where there is a column and the...

Homework Statement Compute the radiation pressure exerted by a gas of photons (according to kinetic theory). There are N photons, each with energy hf, the momentum is hf/c, and the walls are perfectly reflecting. Express the pressure in terms of N, V, and the product hf. Homework Equations...

In special relativity, we can prove that the metric is -+++ for all observers and that is by making use out of lorentz invariance. Some on this forum say that it comes as a result of constancy of light and others say that Minkowski predated einstein in making that metric, which was confusing...

I'm asked to find first two terms of the series $\sin(\sin(2x))$. $\sin(t) = t-\frac{t^3}{3!}+\frac{t^5}{5!}-\cdots$ $\sin(2x) = 2x-\frac{2^3x^3}{3!}+\frac{2^5x^5}{5!}-\cdots$ $\displaystyle \sin(\sin(2x)) =...

How would we define positive and negative work in terms of energy? When the force and displacement are in opposite directions, we say the work done by the force is negative. When the force and displacement are in the same direction, we say the work done by the force is positive. However, how we...

I can't seem to find an answer anywhere to this just by searching. I'm trying to understand samplerate more thoroughly. I know 44000 samples per second means that the highest frequency that can be recorded is 22000 hz but what is each sample? Does it mean there is a constant 44000 snippets of...

I have encountered this general Integral: "∫ 1/ax+b dx = 1/a * ln|ax+b| +C" I was not given a proof, but would like one, along with an easy explanation, please.

Can anyone explain space-time to me, and how it disproves Newtons theory of gravity please? I've heard of the analogy that mass bends space-time like a bowling ball on a rubber sheet, but I don't understand how this happens, nor how this contradicts Newtons theory of gravity.

I want to show that $$\int_0^{\infty} \frac{ds}{s-q^2} \frac{s^{-1-\epsilon}}{s-t \frac{z}{1-z}} = \Gamma(1-\epsilon) \Gamma(\epsilon) \frac{1}{t \frac{z}{1-z} - q^2} \left((-t)^{-1-\epsilon} \left(\frac{z}{1-z}\right)^{-1-\epsilon} -(-q^2)^{-1-\epsilon}\right) $$ I have many ideas on how to...

It is possible to express the boolean AND in terms of boolean OR and boolean NOT: a AND b <=> NOT (NOT a OR NOT b) Similarly, a OR b <=> NOT (NOT a AND NOT b) Why can't we express NOT in terms of OR and AND?

What is the "plane of symmetry", "zero velocity wall" and "free surface" terms which I have seen in Polyflow? It says in Vnormal=Fs=0 for plane of symmetry and Vnormal= Vs= 0 for zero velocity Wall. Now I get when Vs=Vn=0 it means that the wall isn't moving and it's in a static state but didnt...

When I was studying complex manifolds in a Freedman's SUGRA book, I ran across this. In a complex manifold, the metric is...

Behold this array of numbers: 3, 5, 11, 4 Sometimes, the programming limits the number of things that can be recorded in one location to a single number, such as 93240, but sometimes I also need to record an array of numbers such as the one shown above. An example of such platforms include the...

In complex manifold, one writes $$ds^2=g_{ab}dz^adz^b\hspace{3cm}(1)$$ $$ds^2=2g_{\alpha\bar{\beta}}dz^{\alpha}d\bar{z}^{\bar{\beta}}+g_{\alpha\beta}dz^{\alpha\beta}dz^{\alpha}dz^{\beta}+g_{\bar{\alpha}\bar{\beta}}d\bar{z}^{\bar{\alpha}}d\bar{z}^{\bar{\beta}}\hspace{3cm}(2)$$ My question is...

When I read any physics articles online I always end up receiving the wrong message. especially in terms such as 'observe'. what does this term mean when its used to describe exeperiments such as the double slit

Homework Statement The problem is upload below. Homework EquationsThe Attempt at a Solution I was stuck at finding the voltage between the 100k resistor and 200k resistor. Is the voltage zero since the node below there is zero and there is no resistor between them? But if the node voltage is...

Hello, I have been reviewing my textbook lately, and I came across a rather paradoxical statements. all of the convergence tests in my book state that the terms of the series has to be positive. However, when I solved this power series ∑(-1)n-1(xn/n), I found that it converges for -1<x≤1, but...

Hi, some one know the expression of the affine connection Γ in terms of tetrad formalism? I would like also some references if it's possible, i found a hit but i think that is wrong... please help me it's so important!

Does anyone know which formula is used or how to arrive at the righthand side of the equation below, which is the dot product of del and rho*a 2nd order tensor(V V). . represents dot product and X a vector quantity This problem is in connection with transforming cauchy's equation in terms of...

What steps can be taken to solve an equation with a relatively higher power on one side such as: 6977x/1200 = (1 + x/12)60 - 1

Homework Statement (This is a part of the entire problem. I'm just struggling with going to the next step since it involves solving this integral.) Integrate: $$ \int \frac {1}{\sin \theta \sqrt {R^2\sin ^2 \theta - a^2} } d\theta $$ Homework Equations R and a are simply constants. Only $$...