Unruh: Loop Quantum Cosmology paper (new)

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Discussion Overview

The discussion revolves around a recent paper by Bill Unruh related to Loop Quantum Cosmology (LQC), specifically focusing on the challenges associated with positive curvature in cosmological models. Participants explore Unruh's contributions to the field, particularly his concepts of Unruh temperature and radiation, and how they relate to the broader context of LQC and black hole thermodynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants highlight Unruh's research on positive curvature in LQC, noting it contrasts with previous work primarily focused on spatially flat cases.
  • Unruh's concepts of temperature associated with acceleration are discussed, with references to his original work and its implications for understanding thermal radiation in accelerating frames.
  • Participants share calculations related to Unruh temperature, expressing caution about the implications of their numerical results and the potential for misinterpretation.
  • There is a discussion about the relationship between Unruh temperature and black hole thermodynamics, with participants attempting to recall and verify formulas for both phenomena.
  • Some participants express uncertainty regarding the correct formulation of the Unruh temperature and its comparison to Hawking radiation, indicating a need for verification and clarification.
  • Links to external resources are provided to support claims and facilitate further exploration of the topics discussed.

Areas of Agreement / Disagreement

Participants generally agree on the significance of Unruh's work and its implications for LQC, but there is no consensus on the exact formulations of the temperatures discussed or their interpretations. Multiple competing views and uncertainties remain regarding the mathematical details and their implications.

Contextual Notes

Participants express limitations in their calculations and understanding, particularly regarding the assumptions made in deriving formulas for Unruh and Hawking temperatures. There is also mention of technological challenges in measuring effects related to Unruh radiation experimentally.

Who May Find This Useful

Readers interested in advanced topics in cosmology, black hole physics, and theoretical physics may find this discussion relevant, especially those exploring the intersections of quantum mechanics and general relativity.

marcus
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http://arxiv.org/abs/gr-qc/0408074

Bill Unruh has been doing some LQC research

Looking at the positive curvature case
Bojowald and friends mostly looked at the spatially flat case
Unruh found some interesting difficulties with the positive curved universe, especially the kind that eventually collapses

"Difficulties with Closed Isotropic Loop Quantum Cosmology"
Daniel Green and William Unruh


Unruh came up with the Unruh temperature and Unruh radiation about the same time that Hawking came up with Hawking temperature and Hawking radiation. It is nice that Unruh has taken an interest in LQC and something could come of this. It might shake things up and trigger some new growth.

Bojowald is a young guy just barely out of his postdocs and
Unruh is a major figure of the 1970s onwards. Hello.
 
Astronomy news on Phys.org
Fascinating paper. Thanks for the link.
 
Chronos said:
Fascinating paper. Thanks for the link.

yeah, Bill Unruh is neat. glad someone picked up on this Chronos!

I remember when I saw his original article about the temperature associated with any quantity of acceleration.

it was in Phys. Review Series D and the first thing he did was set
G=c=hbar=k=1
where k is Boltzmann constant
this validated natural units for me. the formulas all became incredibly simple.

then he said that if an observer was accelerating he would see a certain radiation which you and I can't see because we arent----it was like Hawking radiation because one of the virtual particles falls behind and can't catch up (oversimplifying) just like at BH event horizon
so the accelerating observer sees a temperature in the universe which is the temperature of this thermal glow----sheer artifact of his acceleration.

this is a creative mind. this is beautiful. I was impressed all getout.

You Chronos probably know some about Unruh temperature.

did you ever take some sample acceleration and calculate the temperature that goes with it?
 
marcus said:
did you ever take some sample acceleration and calculate the temperature that goes with it?
Yes, but,I am reluctant to give any numbers fearing how they might be abused. Oh well.. :devil: It takes some pretty impressive accelerations to generate much of an effect. 1 degree K requires about 2.4E22 cm/s^2. For a temperature of 2.7K, which is what I was curious about, this works out to roughly 7E19 G... [ducking for cover now]. I thought this might somehow relate to the maximum mass of a detectably 'radiating' black hole, but, that is a pretty speculative approach.

Measuring this experimentally is, however, quite the technological challenge. I've heard some proposals involving high energy lasers, but, not about it having yet been tried.
 
Chronos said:
Yes, but,I am reluctant to give any numbers fearing how they might be abused. Oh well.. :devil: It takes some pretty impressive accelerations to generate much of an effect. 1 degree K requires about 2.4E22 cm/s^2. For a temperature of 2.7K, which is what I was curious about, this works out to roughly 7E19 G... [ducking for cover now]. I thought this might somehow relate to the maximum mass of a detectably 'radiating' black hole, but, that is a pretty speculative approach.

Measuring this experimentally is, however, quite the technological challenge. I've heard some proposals involving high energy lasers, but, not about it having yet been tried.

Chuckle. Have i been scolding you about numbers? If I did I am sorry. There is no need to duck for cover!

actually I heard of some experiment at Stanford SLAC around year 2000 IIRC or 2001. But I lost the link to it. I don't know if it was a good experiment.

I vaguely remember that if G=hbar=c=k=1 then the formula for the temperature is
T = a/2pi

I will assume your number is right, as a guide to me in trying to remember.

I know that 1.4 kelvin is E-32
(they have Planck temperature listed with the other constants at NIST)

so one would just multipy that by 2pi to get the acceleration that would produce that temp.

2pi E-32

this acceleration will produce 1.4 kelvin.

It looks like I am done but if I want to interpret that acceleration in metric terms then I have to know that the unit of acceleration (G=c=hbar=1) is 5.56E51 meter per second per second (again from the NIST figures for Planck time and length etc.)

so multiplying by 2piE-32 gives 35E19 meter per second per second.

Wow! I get around the same answer you do! I get 3.5E20 meters which is 3.5E22 cm persecondpersecond. It is the right OOM (order of magnitude)

I happened to be calculating 1.4 kelvin while you were doing 1.0 kelvin but we don't worry about trivial details!

So maybe i remembered right and Unruh formula for temp is really

T = a/2pi

but I'm still unsure and need to check this---earlier remembered something different for the denominator
 
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marcus said:
Chuckle. Have i been scolding you about numbers? If I did I am sorry. There is no need to duck for cover!
Not at all. I was just afraid somebody would use the 'math' to derive some 'fundamental' constant of the universe and push this thread into the 'Theory Development' sub-forum. :surprise:
 
4E-23a is approximately correct. The pi factor is unnecessary, it cancels in translation.
 
Chronos said:
Not at all. I was just afraid somebody would use the 'math' to derive some 'fundamental' constant of the universe and push this thread into the 'Theory Development' sub-forum. :surprise:

I think you and I can maintain our dignity in whatever pen we are herded :smile:
Be not afraid of eviction Chronos

but I felt a brief elbow in my ribs about my blatantly obvious love for
the fundamental physical constants-----especially when their values are all set to unity.

Trouble is, my memory is pulling a blank and I forget if I have the correct Hawking formula for the temp of a BH of mass M.
and the correct Unruh formula for the temperature of a[/size] any give acceleration.
I'm still struggling with this. Want to be able to recapture it. I think it's like this but I or someone should verify:

[tex]T_{BH} = \frac{1}{8 \pi M}[/tex]

[tex]T_{Unruh} = \frac{a}{2 \pi}[/tex]

in any case they are remarkably nice clean formulas, I hope I have the twos and pies right. Maybe with a little practice using them...[edit: I am still at sea. Many people know these---Alejandro for instance. I would welcome a little help. do you have a source for these Chronos?]
 
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  • #10
Chronos said:
Looks good from here
http://en.wikipedia.org/wiki/Hawking_radiation
http://relativity.livingreviews.org/Articles/lrr-2001-6/node3.html

great! thanks for confirming. for some reason I didnt want to go
churning up the mud at google
but just for the formulas to emerge in our conversation out of the fog of memory

there is a new paper called "Time before Time" with absolutely no formulas in it!

I found it by this link I use every weeknight

Last twelve months (e.g. 26 August 2003 to 26 August 2004):
http://lanl.arXiv.org/find/nucl-ex,...m+AND+OR+triply+doubly+special/0/1/0/past/0/1

As I was going to fetch the link I saw that Olias had already
noticed Time before Time and posted a link. It looks like a useful paper.
 
Last edited by a moderator:

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