Skip to main content

Fulling-Davies-Unruh-Hawking Radiation

G+'er +Jonah Miller pointed out yesterday that Unruh had shown that the radiation predicted by Fulling produced a black body thermal spectrum in the same manner as Hawking radiation[1].  For some reason, I had it in my head that Unruh had actually pointed out prior to Hawking, so I wound up on another search through the research.  The necessary papers are usually fairly close at hand since the main thrust of my current theoretical research is looking at the spectrum of particles created, (or not), when an observer is rotating rather than accelerating in a linear fashion, but I digress.  Here's the chronology of papers to the extent I was able to work them out today.  By they way, Jonah was right!

Fulling[2] was the first to point out that an event horizon coudl muck with your particle creation and annihilation operators producing what might look like particles to the uniformly accelerating observer.

Davies[3] certainly discussed the temperature of the radiation in the same year as Hawking.  If it weren't for the following quote from the article, I'd say that Davies preceded Hawking, since his article was submitted in its final form in 1974, but, you'll see


Since Davies does in fact point out Hawking's treatment of the temperature, it looks like the correct attribution of the thermal nature of the produced particles goes to Hawking after all![4]

Unruh pops in a bit later[5] and points out that the particles produced in Rindler space, (as opposed to the Schwarzschild metric of a black hole), also has a thermal spectrum.

Interestingly, Unruh had looked at the spectrum of particles created in a Rindler metric as early as July of 1974[6].

Two last interesting papers:  Fulling and Davies point out that Hawkings derivation has can be reviewed[7] in terms of their work on radiation from an accelerating mirror[8].

Picture of the Day:
View along the coast near Dingle, Ireland


References:
1.  +Jonah Miller's comment can be found at
https://plus.google.com/108242372478733707643/posts/aNeikFbLWk8

2.  Fulling on the creation of particles by event horizons in Rindler space
http://journals.aps.org/prd/abstract/10.1103/PhysRevD.7.2850

3.  Davies on particle production and the temperature of the radiation 1975
http://iopscience.iop.org/0305-4470/8/4/022

4.  Hawking on the temperature of the radiation 1975
open access on project Euclid:
https://projecteuclid.org/download/pdf_1/euclid.cmp/1103899181

5.  Unruh on the thermal nature of the created particles
http://journals.aps.org/prd/abstract/10.1103/PhysRevD.14.870

6.  Unruh on particle spectrums a bit earlier
http://rspa.royalsocietypublishing.org.lib-ezproxy.tamu.edu:2048/content/338/1615/517.short

7.  Fulling and Davies on Hawking
http://www.jstor.org/stable/79378?origin=JSTOR-pdf

8.  Fulling and Davies on particles from mirrors
http://www.jstor.org/stable/79130


Labels:

Comments

Post a Comment

Please leave your comments on this topic:

Popular posts from this blog

The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1.  While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero.  This is typically explained in the following way.  While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare.  That doesn't stop us from looking for them though! Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2].  Cabrera was utilizing a loop type of magnetic monopole detector.  Its operation is in concept very sim
1 comment
Read more

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
11 comments
Read more

More Cowbell! Record Production using Google Forms and Charts

First, the what : This article shows how to embed a new Google Form into any web page. To demonstrate ths, a chart and form that allow blog readers to control the recording levels of each instrument in Blue Oyster Cult's "(Don't Fear) The Reaper" is used. HTML code from the Google version of the form included on this page is shown and the parts that need to be modified are highlighted. Next, the why : Google recently released an e-mail form feature that allows users of Google Documents to create an e-mail a form that automatically places each user's input into an associated spreadsheet. As it turns out, with a little bit of work, the forms that are created by Google Docs can be embedded into any web page. Now, The Goods: Click on the instrument you want turned up, click the submit button and then refresh the page. Through the magic of Google Forms as soon as you click on submit and refresh this web page, the data chart will update immediately. Turn up the:
Post a Comment
Read more