Fulling-Unruh Radiation as a Casimir Phenomena

Just a note about vacuum radiation and similarities

Casimir

When we solve for Casimir energy, we first quantize a field in free space and ask what frequency modes it can support. The answer is all of them because free space is isotropic and homogeneous. We then put in boundaries, either conducting or dielectric, and then as what frequency modes the space between the boundaries can support. The answer will in general be different because the boundaries change what frequency modes can be supported. For example, with parallel conductors, only the modes that can fit multiple half-wavelengths perfectly between the conductors will be supported.

Fulling-Unruh Radiation

It's wasn't immediately apparent to me, but Fulling-Unruh-Hawking radiation is a very similar process. The first step is identical: solve for the available frequency modes in free space. The second step is to solve for the modes in a new space-time coordinate system. A Bogoliubov transform will tell you if all the same modes are supported in both systems. If the transform's result is one, then the coordinate transform was unitary and corresponded to a simple rotation or translation. If the transform does not return a one, then the transformation 'stretched' the space-time so that it would no longer support the same frequency modes. An example of this was pointed by Fulling to be motion under constant acceleration which was named hyperbolic motion by Rindler.

Comments

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

Now available as a Kindle ebook for 99 cents ! Get a spiffy ebook, and fund more physics The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems , there seem to be fewer explanations of the procedure for deriving the conversion, so here goes! What do we actually want? To convert the Cartesian nabla to the nabla for another coordinate system, say… cylindrical coordinates. What we’ll need: 1. The Cartesian Nabla: 2. A set of equations relating the Cartesian coordinates to cylindrical coordinates: 3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system: How to do it: Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables. The chain ...

The Alcubierre Warp Drive Tophat Function and Open Science with Sage

I transferred yesterday's Mathematica file with the Alcubierre warp drive[2] line element and space curvature calculations to the +Sage Mathematical Software System today, (the files been added to the public repository [3]). If you haven't used Sage before, it's a Python based software package that's similar in functionality to Mathematica. Oh, and it' free. I also worked a little more on understanding the theory, but frankly, I made far more progress with the software than the theory. What follows will be a little more of the Alcubierre theory, plus, a cool Sage interactive demo of one of the Alcubierre functions[1], as well as a bit about my first experience with using Sage. Theory The theory is fun, but it's moving slowly. Here's the chalk board from this morning's discussion Alcubierre setup the derivation using something called the 3+1 formalism which means we consider space to be flat, (in this case), slices that are labelled ...

How Many Files Can You Add to a GPT Project? An Interview with GPT-5 on Limits, Context Engineering Tips, and Chats

Setting the scene: I’m tinkering with Project TouCans, knee-deep in radio logs, SQLite dumps, and Cesium code. Naturally, I’m wondering if shoving all this into one GPT Project is a recipe for brilliance… or for disaster. So I turn to Vril — you know, after Brainy from the Legion of Super-Heroes , because what else do you call your AI sidekick who always has the answers? Time to ask him straight up. [ As an aside, yes, GPT-5 has decided to sometimes call me Vail. I'm not sure why to be honest. Also, I asked Vril, er GPT-5, to write up our interview for me. Apparently, me asking it to 'Bro' up a few stories, just for fun, has convinced Vril that I use 'Like,' more than I actually might. ] Me (Vail): So Vril, how many files can I throw into a GPT Project before it just starts choking? Like, is there some magic number where the context window taps out and everything falls apart? GPT-5 (Vril): Great question. There’s no single hard file limit. What matters is ...

Copasetic Flow

Search This Blog