Carroll Definition and 32 Threads

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...

Summary:: hodge Duality... Does anybody has idea for solving these 2 problems?

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?

Hi, Page 166, theorem expressed as 7.2, does anybody know it's name? Many thanks

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?

Greg Bernhardt submitted a new PF Insights post Interview with a Physicist: Sean Carroll Continue reading the Original PF Insights Post.

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...

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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...

http://preposterousuniverse.blogspot.com/2005_05_01_preposterousuniverse_archive.html#111509098797695398 anyone know what happened?

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...