## Monday, August 07, 2006

### The Blue Mountains

Most of Australia's 20 million people live along the coast. For decades the Blue Mountains were a barrier to exploration of the Outback. Aside from the rugged highlands, the lowlands are thick with rainforest. Today Australia's interior is largely empty, which leads to a feeling of being on a frontier. As we learn in quantum mechanics, even "impossible" barriers can be tunneled through!

Thomas Dent left a very intelligent comment on Rob Knop's blog:

"The 'Riofrio equation' G M = t c^3 where M is the 'mass of the Universe' (whatever that means) and t is its age, can be written in Planck units, which are much more sensible to discuss questions of basic cosmology. Then it becomes:

M / M_P = t / t_P

i.e. the mass of the Universe, measured in Planck masses, is proportional to the age of the Universe in Planck times..."

Kudos to Thomas for following this far. As I have written, it is likely that the product hc really is constant. If c ~ t^(-1/3) then h ~ t^(1/3). Then the 'Planck mass' M_P = sqrt{hbar c/G} is constant. Planck time t_P = sqrt{hbar G/c^5} works out to be proportional to age t of the Universe. Written in Planck units, both sides of M / M_P = t / t_P are still equal.

If h and c are related, then Relativity and Quantum Mechanics are linked! An increasing h explains the thermodynamic 'Arrow of Time". The uncertainties represented by h increase with time. The other arrow, the Cosmological Arrow, is simply explained by R = ct. Expansion of Space is indistinguishable from the forward flow of Time.

Behind me is a demonstration of quantum tunneling. The Blue Mountains may have once seemed like a barrier, but enough determined Australians eventually carved a railway through them! As with the "sound barrier" or any other barrier, there will always be those who say it can't be done. You don't have to be Chuck Yeager to push the envelope; sometimes we just need a child to say that the emperor has no clothes. There are no barriers, only challenges.

#### 37 Comments:

Kea said...

No, it's blueshift from the eucalyptus oil in the trees.

2:52 PM
L. Riofrio said...

Right you are, Kea. That is how the Blue Mountains got their name. You are also right in defending our postings on entropy at Cosmic Variance. Perhaps I should add another comment there.

Q9, the missing bit of the Universe ascribed to 'dark energy" could well be Black Holes, hiding in places where cosmologists haven't looked.

4:14 PM
Mahndisa S. Rigmaiden said...

08 08 06

MANUAL TRACKBACK

08 08 06

Hello Louise:
I have finally done another post on LQG, it is a bit more thorough than my first one. I discussed the non separability of the kinematical Hilbert space in the LQG approach, along with a couple of recent innovations designed to fix that problem. I think you might enjoy this, if you have the time. Here is the URL:

NON SEPARABILITY OF HILBERT SPACES IN LQG, CONTINUOUS MODULI LABELLING & COUNTABLE S-KNOT CLASSES WHAT?!

I have tried to engage others in the blogosphere, but no one has the time or they would rather shoot off at the mouth on how one theory is stupid and another is not. So hopefully this can generate some meaningful dialog:)

Warm Regards,
Mahndisa

2:10 AM
QUASAR9 said...

Mandhisa the same thing, I've read your link - but other than paraphrase extracts about LQG, you don't make clear where you are headed. State at the begining where you are intending to reach, and then include all the extracts to support your thinking >>>
It does read like you are just trying to reiterate LQG theory, which is fine if that iswhat your intended aim in.

From Lubos:
Bootstrap
In the context of quantum gravity, many of us more or less secretly believe another version of the bootstrap. I think that most of the real big shots in string theory are convinced that all of string theory is exactly the same thing as all consistent backgrounds of quantum gravity. By a consistent quantum theory of gravity, we mean e.g. a unitary S-matrix with some analytical conditions implied by locality or approximate locality, with gravitons in the spectrum that reproduce low-energy semiclassical general relativity, and with black hole microstates that protect the correct high-energy behavior of the scattering that can also be derived from a semi-classical description of general relativity, especially from the black hole physics.

Don't know if that is helpful or not, but there is clearly no conflict between Quantum Gravity & Strings ...

What there is not is any evidence that as Lee Smolin claims singulariyies in blackholes or blackholes lead to other universes or parallel universes
nor am I of the Susskind landscape version, where on a membrane there are multi pocket universes in his one MegaVerse, at least not as laid out diagramatically. When you look at a book Atlas you do not say that is the globe. The globe can be represented on an Atlas. The Atlas pages represent parts of the globe, but is not the globe or equal to what the globe looks like. Yes obvious - when talking of an Atlas of Earth, it should be equally obvious when talking of the Atlas of the Universe, and the other dimensions have to fit in it. - not be further pocket universes beyond the cosmic horizon.

Beyond the cosmic horizon is more universe as yet unseen to us because of the very essence of the phenomena we call the cosmic horizon.

Now Louise, what effect does a slowing speed of light have on the cosmic horizon we see perceive or rather measure with current instruments.

4:09 AM
Mahndisa S. Rigmaiden said...

08 08 06

Oh Quasar9 thanks for reading the link. this was supposed to be just a review of the theory for my own interests. I started researching LQG rather casually a few months ago, and each time I learn soemthing new I share it.

It is apparent you didn't read the post though, becase new developments to cure the non separability of the kinematical Hilbert space were explored. Thanks.

8:23 AM
Mahndisa S. Rigmaiden said...

This comment has been removed by a blog administrator.

8:23 AM
QUASAR9 said...

Hi Mandhisa, I did read the post:

[It is apparent you didn't read the post though, becase new developments to cure the non separability of the kinematical Hilbert space were explored. Thanks.]
Your header should have read:
"Exploring New Developments ..."

This post is a bituva brain dump on some of my curiosities in LQG. However, there is a common theme. The biggest issue that I explored was the nonseparability of the kinematical Hilbert space in LQG. It turns out that there are two proposed solutions to fixing the problem:
1. Defining an 'almost differentiable set of fields such that they only have a finite number of discontinuities, and therefore changing the uncountability of the s-knot class labellings to being countable, as proposed by Rovelli et al. OR;
2.Defining a completely new embedding independent theory, where algebraic graphs can be embedded in a manifold in any old way but they contain no topological or differentiable structure information-that is to be gleaned from coherent states, proposed by Giesel and Theimann.
I have no idea which approach works, as only further research and eventually experiment will confirm whether gravity is quantized or not. For now, I think it is intriguing to follow the mathematical details (what little I can understand) and figure out the intricacies and quirks of the theory.

You say yourself this post is a bituva brain dump
There are two approaches and you state you have no idea which one works.
And that is what it says, for now it is fun and intriguing to follow the intricacies an quirk of the theory.

Followed by extracts ...
which you hope will help you understand LQG, and which simply reiterate or paraphrase parts of that LQG theory.

12:05 PM
Mahndisa S. Rigmaiden said...

08 07 06

Quasar9:
I see what you are trying to say now. I think I misunderstood your initial comment. Yes, I would need to work on tightening up my introductions and see your point. Thanks. For the next few posts I do I will be more explicit. That post was just an exploration:)

But if you read the whole thing, you sure read fast!

1:16 PM
Anonymous said...

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4:50 PM
Anonymous said...

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5:00 PM
Mahndisa S. Rigmaiden said...

08 09 06

"Don't know if that is helpful or not, but there is clearly no conflict between Quantum Gravity & Strings ..."

Quasar9: I think the conflict lies in the different mathematical approaches to the theories. If you look at the Helling and Policastro paper you will see what I mean. The biggest difference is in the choice of state functional used for quantization. The LQGers impose more strict constraints and that leads to a more restricted set of states that they can use. The diffeomorphism invariance forces some very interesting consequences.

6:37 AM
L. Riofrio said...

Nice posts, everyone! Perhaps we will someday challenge Cosmic Variance for long discussions.

8:29 AM
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