# What is Carroll: Definition and 34 Discussions

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.

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1. ### I Carroll GR: Tangent Space & Partial Derivatives

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...
2. ### I Carroll GR: Geodesic Eq from Var Principles

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...
3. ### Understanding Proper Time better

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...
4. ### Sean Carroll podcast on Issues Related to Basketball Analytics

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...
5. ### Exercise 16, chapter 3 (Tetrad) in Carroll

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...
6. ### Carroll chapter 2 questions 9 and 10 on Manifolds

Summary:: hodge Duality... Does anybody has idea for solving these 2 problems?
7. ### What is the problem that the Many Worlds Interpretation aims to solve?

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...
8. ### Math Courses to Understand General Relativity (by Sean Carroll)

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
9. ### Finding killing vector fields of specific spacetime

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...
10. ### I Sean Carroll podcast on many worlds interpretation

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...
11. ### Bob from Nevada City, CA

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...
12. ### I Help with integration conventions in "Spacetime and Geometry" by Sean Carroll

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?
13. ### A Schwarzschild Derivation: Sean Carroll Notes - Theorem Name?

Hi, Page 166, theorem expressed as 7.2, does anybody know it's name? Many thanks
14. ### BBC Horizon S55E13: Sean Carroll at His Best

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...
15. ### B Sean Carroll on Why Does Time Exist at All?

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?
16. ### Insights Interview with a Physicist: Sean Carroll - Comments

Greg Bernhardt submitted a new PF Insights post Interview with a Physicist: Sean Carroll Continue reading the Original PF Insights Post.
17. ### A Meaning of ds^2 according to Carroll

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...
18. ### I Confusion about killing horizon in Carroll

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...
19. ### TOV Equation in (2+1)-dimensions for Perfect Fluids

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...
20. ### Error in Carroll's Spacetime Geometry?

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...
21. ### Error in Carroll's Lecture Notes on General Relativity pg. 186

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}...
22. ### Carroll Problem #15 of chapter 3 - As trivial as it seems?

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...
23. ### Relativity Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carroll

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...
24. ### Astrophysics An Introduction to Modern Astrophysics by Bradley W. Carroll and Dale A. Ostlie

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:
25. ### Derivation of the Geodesic equation using the variational approach in Carroll

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...
26. ### Automotive Carroll Shelby: Engineering Genius & Racing Legend

Carrol Shelby, Brilliant Engineer, world class driver and one hell of a racer
27. ### News Carroll Shelby RIP: Race Car Designer Passes at 89

http://msn.foxsports.com/motor/story/Carroll-Shelby-dies-race-car-designer-cobra-age-89-051112/
28. ### Compare Carroll & Ostlie's Astrophysics Texts: Any Suggestions?

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...
29. ### Sean Carroll and the immortality of the soul

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...
30. ### How did Sean Carroll manage to survive Villanova?

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.
31. ### Penrose, Carroll, and Inflation

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...
32. ### Uncovering the Mystery: The Disappearance of Sean Carroll

http://preposterousuniverse.blogspot.com/2005_05_01_preposterousuniverse_archive.html#111509098797695398 anyone know what happened?
33. ### What is Sean Carroll's Cosmology Primer?

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...
34. ### News What are some quotes from Sean Carroll that Kerry should use in the debates?

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...