Mount Carroll is a city in Carroll County, Illinois, United States. It is the Carroll County seat. The population was 1,717 at the 2010 census and as of 2018, the population had dropped to an estimated 1,587.Due to its elevation and northwesterly location, Mount Carroll is subject to unusually cold winter weather. From 1930 to 1999, Mount Carroll held the record for the lowest temperature ever recorded in Illinois, −35 °F (−37 °C), recorded on January 22, 1930. The record was beaten by Congerville in 1999, by one degree Fahrenheit. 20 years later, on January 31, 2019 during an extreme cold snap, Mount Carroll regained the title of coldest city in Illinois when a new Illinois state record low temperature of −38 °F (−39 °C) was officially recorded.
He draws an n-manifold M, a coordinate chart φ : M → Rn, a curve γ : R → M, and a function f : M → R, and wants to specify ##\frac d {d\lambda}## in terms of ##\partial_\mu##.
##\lambda## is the parameter along ##\gamma##, and ##x^\mu## the co-ordinates in ##\text{R}^n##.
His first equality is...
On pages 106-107 of Spacetime & Geometry, Carroll derives the geodesic equation by extremizing the proper time functional. He writes:
What I am unclear on is the step in 3.47. I understand that the four velocity is normalized to -1 for timelike paths, but if the value of f is fixed, how can we...
Let us denote the events in spacetime before the trip has started by subscript 1 and those after the trip is over by subscript 2. So before the trip has begun, the coordinates in spacetime for A and B are
##A = (t_{A_1},x,y,z)## and ##B = (t_{B_1},x,y,z) = (t_{A_1},x,y,z)##.
After the trip is...
Its is podcast #138, guest = Daryl Morey, analytics inclined GM of the Philly team.
Apple Podcasts: https://podcasts.apple.com/us/podcast/sean-carrolls-mindscape-science-society-philosophy/id1406534739?i=1000513079530
It covers higher level issues like: how good's your data? Balance between...
My attempt at solution:
in tetrad formalism:
$$ds^2=e^1e^1+e^2e^2+e^3e^3≡e^ae^a$$
so we can read vielbeins as following:
$$
\begin{align}
e^1 &=d \psi;\\
e^2 &= \sin \psi \, d\theta;\\
e^3 &= \sin \psi \,\sin \theta \, d\phi
\end{align}
$$
componets of spin connection could be written by using...
Sean Carroll's most recent book is called Something Deeply Hidden, and is premissed on the idea that the Everett interpretation of the 'observer problem' in quantum physics is correct. Carroll, and several other prominent scientific popularisers including David Deutsche and Max Tegmark, are...
Hi.
What are the math courses should I take in order to understand the mathematics involved in a book such as Sean Carroll in general relativity.
Thanks
I have been at this exercise for the past two days now, and I finally decided to get some help. I am learning General Relativity using Carrolls Spacetime and Geometry on my own, so I can't really ask a tutor or something. I think I have a solution, but I am really unsure about it and I found 6...
Interpretation of quantum mechanics is something that is discussed at length on pf so it would be interesting to get views of the quantum guys on this short (30 mins) podcast. Thanks...
Hi. I'm a retired software engineer who has always been fascinated in science. I was a math major in college, before the time that computer science majors were a thing. My key areas of interest these days are particle physics and quantum mechanics.
I'll be asking some questions that have...
I am reading Spacetime and Geometry by Sean Carroll. In section 1.10 on classical field theory, he uses this formula (1.132)
The curly L is a Lagrange density. S is an action, Φ is a vector potential.
Could the integral also be written as follows?
On this forum sometimes people moan about badly presented or just plain wrong media output about science.
They should, though I thought this one was OK.
http://www.watchseriesgo.to/link/vidto.me/6951511
If th link doesn't work anymore then it's BBC Horizon S55E13,
Also Sean Carroll here at...
Interesting TedTalk from Sean Carroll last month.
At the end he asks the question of whether the big bang was really the beginning. Is this simple multiverse talk? Thoughts?
Hi all, I need some help- I was reading Carroll's GR book, and on pages 71-71 he discusses the metric in curved spacetime. I have a few questions regarding this section:
(1) He says
In our discussion of path lengths in special relativity we (somewhat handwavingly) introduced the line element...
In the opening paragraph of section 6.3 Carroll defines a killing horizon to be a null hypersurface Σ where some killing vector field χμ becomes null. Later (on page 247 if you have the book) when distinguishing between static and stationary space times, he says that in a stationary, but not...
Homework Statement
Consider a perfect fluid in a static, circularly symmetric (2+1)-dimensional spacetime.
Derive the analogue of the Tolman-Oppenheimer-Volkov (TOV) equation for (2+1)-dimensions
Homework Equations
Schwarzschild metric
The Attempt at a Solution
Okay. I'm trying to think...
On page 161 of Carroll's Spacetime and Geometry, Carroll writes that
\delta g_{\mu\nu}=-g_{\mu\rho}g_{\nu\sigma}\delta g^{\rho\sigma}.
##\delta g_{\alpha \beta}## denotes an arbitrary, infinitesimal variation of the metric.
Why is there a minus sign? By the regular rules of raising and...
Mistake in Carroll's Notes?
On the page 186 of Lecture Notes on General Relativity, where he writes the line element in both ##\tilde{u}## and ##\tilde{v}## coordinates , I think he missed a minus sign. Can someone check it, please?
Also, why he writes ##(d\tilde{u}...
Hey guys! Problem #15 of Chapter 3 in Carroll's text says: Use Raychaudhuri's equation to show that if a fluid is flowing on geodesics through space - time with zero shear and expansion, then space - time must have a time - like killing vector.
As background: Raychaudhuri's equation and all the...
Author: Sean M. Carroll
Title: Spacetime and Geometry: An Introduction to General Relativity
Amazon Link: https://www.amazon.com/dp/0805387323/?tag=pfamazon01-20
Download Link: http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll_contents.html
Prerequisities:
Contents:
Contents:
1...
Author: Bradley W. Carroll (Author), Dale A. Ostlie (Author)
Title: An Introduction to Modern Astrophysics
Amazon Link: https://www.amazon.com/dp/0805304029/?tag=pfamazon01-20
Prerequisities:
Contents:
Hello Everybody,
Carroll introduces in page 106 of his book "Spacetime and Geometry" the variational method to derive the geodesic equation.
I have a couple of questions regarding his derivation.
First, he writes:" it makes things easier to specify the parameter to be the proper time τ...
Hey everyone,
I'm just wondering what the main difference is between Carroll and Ostlie's "An Intro to Modern Astrophysics" and "An Intro to Modern Stellar Astrophysics". I already have the former and have gone through a significant part of it. Does the latter contain any new information, or is...
Has anyone else read Sean Carroll's guest blog post at Scientific American on http://www.scientificamerican.com/blog/post.cfm?id=physics-and-the-immortality-of-the-2011-05-23
Please read the link above so that we are all talking about the same thing.
If I understand his post well enough, he...
He's one of the most outspoken atheists on the Internet (far more hardcore than most atheists I know), and yet he graduated from a religious university. Hmm, this sounds interesting.
Without inflation, only extremely special conditions in the past produce the universe we now see. Or so the story goes.
Penrose has long argued that conditions necessary for inflation are actually more special that the necessary past conditions without inflation. Its seems that Sean Carroll...
Sean Carroll has posted a Cosmology Primer
explaining contemporary cosmology for general audience
It could be very handy for us to have at PF to refer to.
Here, for example, is the FAQ
http://pancake.uchicago.edu/~carroll/cfcp/primer/faq.html
for other sections, go to the TOC and click on...
http://preposterousuniverse.blogspot.com/2004/10/come-lately.html
Sean Carroll is a cosmologist, and also a pretty entertaining blogger
http://preposterousuniverse.blogspot.com/
you get a mix of interesting science news, politics, personal events/comment, jazz, even lately some witty...