Monday, August 27, 2007

Quantum Geckos

This cute photo makes one hungry for papaya! More fond memories are of the beach house on Hanalei Bay, the picture window facing the ocean and geckos that climbed the glass every night. As children we learned that geckos are friends who eat mosquitoes and other pests. From the time of Aristotle, scientists have wondered how geckos can stick to perfectly smooth surfaces. Only in 2002 did this PNAS paper tell of a solution. The gecko's secret lies in the realm of quantum mechanics, virtual particles and the van der Waals effect.

Geckos in the Escher drawing occupy both positive and negative space. Quantum mechanics theorises that apparently empty Space is a sea of virtual particles constantly winking in and out of existence. If two surfaces are extremely close together, quantum particles have no room to pop in. This creates a quantum vacuum, allowing the surfaces to stick. Gecko toes are covered with millions of bristles, each of which is covered with thousands of microscopic hairs. This allows a gecko to get extremely close to any surface, and break free by retracting the hairs.

Researchers have attempted to mimic the gecko's ability to create super-strong adhesives. So far they have difficulty producing gecko-derived adhesive in a usable quantity. Makers of carbon nanotubes face a similiar challenge if they are to build Space elevators. The gecko made use of quantum mechanics long before humans figured it out!

The protons and electrons that we are made of began as virtual particles. Today they pop in and just as quickly pop out, because the Universe has reached a stable density. Near the Big Bang the Universe had not reached this density. Virtual particles could pop in and stay.

Suppose that the Universe is spherical with a radius given by:

R = ct

The volume of this 4-dimensional Riemann sphere is given by :
V = 2 ($\pi$^2) (R^3)

We know that GM = tc^3. For an initial mass M, density $\rho_i$ is just M/V:

$\rho_i$ = M/V = (2 $\pi$^2 G t^2 )^{-1}

But the stable density $\rho_f$ after matter has formed is:

$\rho_f$ = ($6 \pi G$t^2)^{-1}

Difference between $\rho_i$ before matter and $\rho_f$ after matter formation is precisely 4.507034%. This unique prediction of Theory has been verified by the Wilkinson Microwave Anisotropy Probe. Density allows us to check the geometry of the Universe. If it had a different shape, the percentage of baryonic matter would be different.

Why have more people not heard about this? While it is easy to write about strings or "dark energy," theories predicting a changing speed of light are difficult to even publish. Nevertheless, another paper is shortly appearing in a journal and the word is spreading exponentially. The happiest one of all will still be that gecko getting his papaya!

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Blogger Kea said...

Nice to see some real physics on a blog! And thanks for the CUTE gecko picture.

6:53 PM  
Blogger L. Riofrio said...

Thanks for your patience too. One bug with blogger is that one has to hit "publish" button to see how the equations look.

7:01 PM  
Anonymous Anonymous said...

"Nevertheless, another paper is shortly appearing in a journal and the word is spreading exponentially"

Which one exactly do you have in mind? Thanks.

12:46 AM  
Anonymous mendo said...

Geckos are very cool - and great photo! I've seen moorish geckos in southern europe quite a bit, although they're not as brightly coloured as the Hawaiian ones...

VSL papers have been thin on the ground, yet Magueijo, Barrow, Moffat and a fair few other have published papers both on the arxiv and in the peer reviewed journals. Of course in the latter case having a good and understanding referee helps...At least once you're through that stage, getting the paper in print is pretty quick. Good to hear that youre there, and hope to see it soon!

A couple of quick questions about the density calculation. I'd assumed that in GM=tc^3 M is constant, however, since rho_f is greater than rho_i and the volume V increases with t^2, then M must increase at least in this period? Sort of related to that, how long does the increase in density from rho_i to rho_f take, and when does it occur relative to the big bang?



1:35 PM  
Blogger L. Riofrio said...

The paper will appear in a journal with 50,000 readers each week. It has been in editorial a LONG time, over 18 months, longer than this blog has been on. The writer has learned the hard way not to announce ahead of time where she will be publishing or speaking.

For mendo: M does increase, quite quickly after the Big Bang. This is when Black Holes are likely to form. The Universe appoaches but never reaches a critical density, meaning that a tiny amount of matter is being produced today.

The Albrecht/Maguiejo paper can be a help here. Refer to their equation (10). Here e is the deviation from critical density.

edot = (1 + e)e(adot/a)(1 + 3w) + 2(cdot/c)e

Now we have w = 0,
(adot/a) = (2/3t) and (cdot/c) = (-1/3t)

edot = e^2 (2/3t)

Is it not reassuring that the other terms cancel? When t is low e is large and a large edot drives density toward a critical value. Today, when t is billions of years and e is very nearly zero, little mass is being created.

Can you believe some people act as if this isn't a

8:15 PM  
Blogger alex kaplan said...

"If two surfaces are extremely close together, quantum particles have no room to pop in."
It is not exactlly true.The virtual particles are have speicific wavelengths,between two plates while an arbitary outside

6:46 AM  
Anonymous mendo said...

Thanks for the information, I'd been looking at the Albrecht and Magueijo paper and hadn't appreciated (stupidly) that you could plug in your equations for a and c. An interesting thing about the equation

de/dt = e^2(2/3t)

is that its solution (assuming I integrated it correctly...) has a vertical asymptote and hence omega<1 at small t, but for any reasonable values of e at the present time, tracking e back shows that the asymptote happens at Planck scale times. I don't see that as a problem as that's probably well outside the domain of applicability!

Can you believe some people act as if this isn't a Theory?

Yes, because new theories always take time to become fully understood in the wider scientific community and because a broad range of experimental evidence may be lacking. Changing c is pretty radical because it enters in so many equations so a natural question is whether a decreasing c affects for instance stellar astrophysics in critical ways. In this regard I think that building interest and acceptance for new theories is essentially salesman(or woman!)ship to show that the theory can stand up to a battery of experimental evidence.



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