I'll press on with my studies with this analogy in mind. Thank you for the patient explanation! Your latest response will help me untie my mental knots about this subject.
Argh, none of this makes sense to me at all. It seems like you're saying that in the past, the Universe had both a) higher mass-energy density and b) faster expansion. But that makes no sense, because the gravitation from higher mass-energy density would slow down the expansion, right?
So if...
I'm just looking for conceptual clarification re: the relationship between matter density and the Hubble parameter in the Friedmann equation. Just for quick reference, the equation I'm looking at is
H2 = 8πGρ/3 - ka-2
(I'm working through Liddle's Intro text, and for now we're ignoring the...
My question is why it makes sense to talk about two-dimensional spin-state vectors rotating in ordinary space as if they were ordinary position vectors. Forgive me, but I can't see how your reply helps with that. Can you expound any further?
My question is conceptual but specific. I'm self-studying Townsend's text 'A Modern Approach to Quantum Mechanics.' In Sec. 2.2 pg 33 (in case you have the book handy), he introduces rotation operators, in the context of spin states for spin-1/2 particles.
He states that the rotation operator...
Okay. But it's not like my grandma wrote this stuff, and it's not like it isn't well-established physics. The solution to your objection is for me to point to page 421 of the first edition of Carroll's textbook Spacetime Geometry: An Introduction to General Relativity, published by...
Wow, thanks for trying!
In the first place, nothing in my post implies that I am NOT looking at textbook-level sources. And indeed, I am. But parallel to that steeper learning curve, there is absolutely nothing wrong with trying to get the general lay of the land from popular books. That's...
am reading Sean Carroll's pop-science book 'From Eternity to Here' and am having trouble connecting the links in his discussion of the Holographic Principle.
At the outset, I would ask that you try to answer in terms of Carroll's discussion and without moving into concepts much more advanced...
This is not a homework problem. I'm doing it for fun. But it is the kind that might appear on homework.
Homework Statement
I'm trying to prove that if lim n→∞ |an+1/an| = L < 1, then \Sigma an converges absolutely and therefore converges. Homework Equations
The Attempt at a Solution
Here's...
Thanks for your thorough reply! I'm still thinking on a lot of it, but there is one big question I have about what you're telling me. I think I'm misunderstanding something fundamental about the mechanism. If increased flow results in decreased downstream pressure, would that not mean that...
My brother is a professional plumber and I'm a physics major, so he often comes to me for explanations of some of the physics underlying his job. I'm familiar with the basics of fluid mechanics, e.g. hydrostatic principles, continuity equation, Bernoulli's law, Poiseuille's law. But often I...
Homework Statement
Two small conducting spheres with radii a and b are imbedded in a medium of resistivity ρ and permittivity ε with their centers separated by a distance d >> a, b. What is the resistance R between
them?
Homework Equations
R = V/I
I = ∫JdS = (1/ρ)∫EdS
The...
Ok, I seriously feel like a heel. I see my mistake. The complex exponentials DO describe an oscillating function, according to Euler's equation.
Ugh. Sorry about that :(
As far as what is leading me to go against my own reasoning, every text I've consulted, both physical and online, tells me that in the region x > 0 where V0 > 0 (but E > V0), the solutions to the appropriate Schr. Eqn are of the form
Cexp(ikx) + Dexp(-ikx)
where k is the wave number...