Unruh: Loop Quantum Cosmology paper (new)

marcus

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.

Chronos

Fascinating paper. Thanks for the link.

marcus

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 cant see because we arent----it was like Hawking radiation because one of the virtual particles falls behind and cant 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?

Chronos

Yes, but,I am reluctant to give any numbers fearing how they might be abused. Oh well.. 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.

marcus

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 dont 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 dont 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

Chronos

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:

Chronos

4E-23a is approximately correct. The pi factor is unnecessary, it cancels in translation.

marcus

I think you and I can maintain our dignity in whatever pen we are herded
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 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:





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?]

Chronos

Looks good from here
http://en.wikipedia.org/wiki/Hawking_radiation
http://relativity.livingreviews.org/...1-6/node3.html

marcus

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,a...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.