the Mother of All Energy

[Martin]

when Relativity is quantized you get a maximum energy density

 

a good recent paper is

http://arxiv.org/gr-qc/0407074

Genericity of the Big Bounce in isotropic loop quantum cosmology

Date and Hossain

 

When it is quantized, the big bang does

not contain a singularity (a place where energy density and curvature increase out of control and the model blows up)

Instead of being infinite the density has a finite limit and they calculate it.

 

when relativity is quantized so that you get a quantum model of cosmology, it approximates the classical very closely exept around the ex-singularity of the big bang----and there you get a "bounce"----a changeover from contraction to expansion. At the changeover the density reaches a maximum and then it turns around.

 

So they calculate, among other things, the maximum energy density that occurred right at the crossover between end of contraction and the onset of expansion

 

In quantized relativity it seems handier to talk about the ENERGY density instead of a mass density. You can always convert mass into an equivalent energy so fundamentally there's no difference but they seem to prefer to work with an energy density

 

What they calculate is actually equivalent to some 10⁹⁴ times the density of water, but then imagine all that superdensematter being converted to a superdense flash of light by E=mc²

 

In ordinary metric units, and trying to be more precise, the energy density is, they say, on the order of Planck unit density (one planck energy unit per planck unit of volume)

And that is

4.6 E113 joules per cubic meter.

4.6 x 10¹¹³ joules per cubic meter

 

So with the help of Date and Hossain's paper we have an idea, in joules per cubic meter, what is the mother of all energy densities.

 

I guess it is to be expected because the big bounce that they and other Loop Quantum Cosmology people are now studying, is a physical representation of the "Planck era". so if figures that the temperature would be planck unit temperature and the density would be planck unit density. and so on.

 

as a followup, have a look at

http://arxiv.org/gr-qc/0407069

Genericity of inflation in isotropic loop quantum cosmology

Date and Hossain

 

to paraphrase their abstract, once relativity is quantized, inflation comes naturally without fine-tuning or elaborate additional assumptions. If you have questions, you might click on the link and read their summary, which spells this out in more detail.

[Martin]

in a nearby thread Gun asked for someone to explain coulomb law

 

this is a surprise for Gun in case he looks in here.

 

here's an example, worked out in natural units---planck units.

 

spread your thumb and tip of forefinger apart as far as you can

that is about E34 planck length units.

Imagine two charges E34 units apart.

 

typical amounts of charge for something to have is E12 electrons

so imagine the two charges are each E12 electrons.

 

multiply the charges together---E12 times E12 is E24

 

square the distance----E34 times E34 is E68

 

divide E24 by E68 and it gives E-44

 

there is a natural unit of force and E-44 of that unit is a force of about 123 grams------roughly an eighth of a kilo weight or a quarter of a pound.

Teachers dont like you to use grams or pounds or kilos of force they like you to use "newtons" and E-44 is right around 1.2 newtons.

 

So we are almost done, we got E-44 for the force. But dont forget to divide by 137 The actual force between that amount of electrons that distance apart is NOT E-44

it is, instead, 1/137 times that.

[math]F = \frac{1}{137} \times 10^{-44}\mbox{ natural units of force}[/math]

 

So it would be 1.2 newtons divided by 137, whatever.

Or 123 grams divided by 137. In other words about a gram.

 

why such a small force. Because each charge is only E12 electrons (a trillion) and the electron is a small bit of charge and also you put the two charges pretty far apart----the spread of your thumb and finger.

[Martin]

I just checked amazon.uk and Penrose book is in 34th place

 

It came out in midJuly, went to 3rd place in first week of august and

has been staying steady around 34th for a while

doing pretty good for two months now

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this maximum energy density is likely to turn out to be the density at the center of black holes

 

quantizing removes the BB and BH singularities and makes there be a finite (very high) density instead of an infinity.

 

Leonardo Modesto's paper this summer removed the BH singularity.

In case anyone wants to look it is

Disappearance of Black Hole Singularity in Quantum Gravity

http://arxiv.org/gr-qc/0407097

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trying to figure what is the best way to think of this maximum density.

 

in the case of the big bang one thinks "hot" with all the matter changed to light or some intense radiation, so I guess the Planck temperature says it:

 

1.4 x 10³² kelvin

 

but at the center of a black hole one might want to think in terms of a mass density like

 

10⁹⁴ grams per cubic centimeter

10⁹⁴ times standard density of water

 

since mass can be measured equivalently as energy maybe the most multipurpose way to think of it is as an energy density----joules per unit volume. (and that is incidentally the same unit as pascals: newtons per unit area)-----only trouble it's not as intuitive or familiar a measure for most people