Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Saturday, July 14, 2007

Penrose's Landscape

The friday night public lecture by Sir Roger Penrose was held in the large Convention Centre auditorium. Penrose has a remarkable ability to convey complex ideas with real clarity. He used his traditional colourful handdrawn overheads, and although the talk only contained a couple of simple equations, one cannot say it was aimed at the general public. In fact, what he did was outline his latest view of cosmology, which he considers an improvement on current fashionable ideas.

Brace yourself for this: the basic elements of this view, motivated by the second law of thermodynamics, include slowly decaying masses over cosmic time (so we cannot compute them), a Dark Energy and genuine information loss into black holes. Penrose gave a wonderful explanation of what entropy is, using the interaction of the sun and earth as an example of how important entropy is for understanding the cosmos. He explained how the CMB was black body radiation and that this meant a high entropy state, whereas the Big Bang should be a low entropy state. The resolution is to realise that gravity behaves very differently to other matter, and that gravity is also needed to describe the initial singularity. That is, entropy increases with gravitational clumping and so a smooth initial state can correspond to a low entropy state. Finally, the new ingredient is the idea that time loses its meaning in the early universe. Treated as a conformal boundary, matter should be considered massless and since such boundaries may be attached to earlier eons (he assumes a cosmic cyclic time) the singularity effectively disappears.

The mathematical argument hinges on the concept of conformal boundary, so Penrose went to the trouble of explaining Weyl curvature by showing images of distorted galaxies in gravitational lensing rings. The extra scalar factor needed to describe clocks in the massive regime arises as structure internal to all the light cones, namely a sequence of internal hyperboloids for ticks of a clock. In other words, clocks only make sense when there is mass, as indicated by frequency = m.constant (assuming hbar and c constant). It is necessary here for the late universe to also lose its concept of time, as everything forms black holes which only evaporate away incredibly slowly. Penrose's solution was to say, well, there will be no humans, just a bunch of photons, which don't see time anyway.

Of course, this idea is full of holes. The first thing one is tempted to do is to pile all the eons on top of each other and try to find some multiverse picture that still respects the second law in this elegant way. Perhaps this cosmology is useful in that sense. Penrose also predicted that conformal structure would be detected in the WMAP data, and perhaps this carries over to a more quantum viewpoint also. He did mention that a serious problem might arise from issues in the foundation of quantum mechanics. I think the biggest conceptual issue is the lack of a concept of 'NOW'. In a cosmology with time asymmetry, any observer must have a means of distinguishing the past from the future, and this suggests a time mark with the meaning of now, but in Penrose's picture there is nothing special about any given era within the cosmic epoch, and there is no quantitative means of measuring the complexity of interesting physical systems, such as life.

6 Comments:

Blogger Matti Pitkanen said...

Kea,

thank you for a nice summary of Penrose's talk and also for the previous comments. Penrose manages to touch in his talks fundamental questions. I would be happy to say same about string theorists. A little comment about TGD based solution of low entropy problem.

In very early TGD Universe highly tangled cosmic strings dominate. These strings then decay to ordinary matter and transform to magnetic flux tubes with reduced string tension.

Thanks to progress that I made in hadronic mass calculations I can now make microscopic statements about these effectively string like objects. They contain mostly what I call super-canonical bosons characterized by only spin and color but having no ew quantum numbers, dark matter in ew sense.

Their topological condensation on background space-time sheets creates what I would call super-canonical blackholes. These blackholes appear in all length scales: hadronic space-time sheet is example of this kind of blackhole like structure in the hadronic length scale. Super-camonical bosons give dominating contribution to proton mass and valence quarks only 170 MeV ("Pomeron"): they also explain the spin puzzle. RHIC experiments demonstrated the creation supercanonical blackholes by fusion of hadron space-time sheetes to a larger one in heavy nucleus collisions. Ordinary blacholes are what is created in RHIC but involving very many neutron space-time sheets fused together and differ in no dramatic manner from neutron and quark stars.

These cosmic strings decay to shorter cosmic strings with smaller string tension and ordinary matter much like blackholes evaporate and decay increasing their total horizon area and create entropy since the p-adic version of second law of blackhole thermodynamics holds true. At the bottom of the decay sequence you have ordinary hadrons.

July 14, 2007 2:25 PM  
Blogger CarlBrannen said...

Kea, WordPress allows LaTex in posts and comments now. You do it by writing $latex \pi$. When you get back home and things calm down I'll set up a private blog over there.

July 14, 2007 8:47 PM  
Anonymous Anonymous said...

Do you know if a podcast of Dr. Penrose' talk will be made available to the public?

July 16, 2007 4:49 AM  
Blogger Doug said...

Hi Kea,

Thanks for the Penrose update.

With respect to the discussion of time, I wonder if Penrose meant that Earth NOW_time is the intersection of past light cones reaching Earth?

By this I mean that all light reaching Earth comes from the past, ranging from about 8 light seconds from the sun apparently up to 13 million light years from the most distant known source.

Technically we H sapiens live only the NOW. Fortunately we can recall past experiences and look forward to [even predict trends to some degree] future experiences.

This interpretation [of what I think Penrose may mean] seems to border upon philosophy?

I am just as confused about massless matter with respect to conformal boundary?
Perhaps Pebrose is suggesting treating mass as inductance and energy as voltage shifting from mechanics to an all electromagnetism perspective?

July 16, 2007 9:21 AM  
Blogger nige said...

Thanks for your criticism of Sir Roger Penrose's talk. It reminds me that about a decade ago, Penrose gave a lecture in London about "The Large, the Small and the Human Mind".

David A. Chalmers, a retired physicist who worked as an electronics engineer, attended the lecture and was impressed by Penrose's energy and enthusiasm for physics generally, but he told me tha he tried to object to some of Penrose's assumptions during the question-and-answer session.

Chalmer's point concerned Young's double slit experiment: he did an experiment with a laser to prove that there is a serious problem with the popular claim that, when you fire photons one at a time, the dark fringes are not formed from photons arriving out of phase and causing destructive intereference. That would destroy the principle of conservation of energy.

All these mainstream physicists tend to ignore the principle of conservation of energy where it suits them to ignore it: they ignore the application of the principle of conservation to light in the double slit experiment, and to gauge bosons in renormalized quantum field theory (where the polarized vacuum shields charge, reducing the effective flux of gauge bosons involved in maintaining the electric field).

Penrose, according to Chalmers, obfuscated, misunderstood or ignored the point Chalmers was making, then talked about his own ideas. This is classical communication breakdown: you would think that if someone pushes hard enough and has a valid point, someone will listen. I was editor of Science World, ISSN 1367-6172, at that time, so I published Chalmers' paper in the February 1997 issue. Sadly, Chalmers died a couple of years later with no recognition.

His point is that the mainstream 'explanation' of the double slit experiment with light implies that 50% of the photons arrive at dark fringes on the screen and are somehow cancelled out by interference.

If that were true, the total light reflected from the screen would be at best (i.e. for perfectly reflecting screen) only 50% of the energy transmitted through the two slits (which can easily be calculated from the areas of the slits, their distance from the light source, and the intensity of the light source).

Actually, 100% of the photons going through the slits end up in the bright fringes on the screen, none of them end up in the dark fringes! This is an experimental fact from the principle of energy conservation and measurements made by firing laser light through two small holes.

This seriously changes the mainstream interpretation of path integrals, a simple application of which is the double slit experiment: photons don't travel all routes and then interfere upon arriving at the screen! (If they did, they would be arriving in the dark fringes and cancelling out there somehow, breaking the conservation of energy.) Instead, photons interfere with themselves at the double slit, as Feynman argued: interference occurs on small scales, and when the slits are very close together, part of the photon goes through each slit, causing diffraction at the edges of the slit and some chaotic randomness in direction when the photon comes out of that small space on the other side of the slit:

‘When we look at photons on a large scale ... there are enough paths around the path of minimum time to reinforce each other, and enough other paths to cancel each other out. But when the space through which a photon moves becomes too small ... these rules fail ... The same situation exists with electrons: when seen on a large scale, they travel like particles, on definite paths. But on a small scale, such as inside an atom, the space is so small that there is no main path, no ‘orbit’; there are all sorts of ways the electron could go, each with an amplitude. The phenomenon of interference [due to pair-production of virtual fermions in the very strong electric fields (above the Schwinger threshold electric field strength for pair-production) on small distance scales] becomes very important, and we have to sum the arrows to predict where an electron is likely to be.’- R. P. Feynman, QED, Penguin, 1990, p. 84.

This is key to quantum mechanics and it's a pity that Penrose and other big shots can't keep their minds off speculative ideas for long enough (a few minutes) to check the foundations of the subject carefully.

Path integrals clearly don't represent real particles as going on all possible routes unless the path transverses small spaces with strong electric fields, where pair production (deflections due to virtual particles) causes chaos:

(1) In the case where a real photon goes from place A to place B, the path integrals formulation allows you to work out the probability of that one event actually occurring, out of all possibilities (the sum over histories or path integral), and it allows you to work out the path of least action which is taken by the average particle which travels from A to B.

(2) For virtual particles, i.e. the path integral for Coulomb's electric force law (where force is mediated by virtual photons, the gauge bosons of electromagnetism), the path integral over all histories is real, because gauge bosons are travelling all around a charge (they mediate the force field effect).

So there is a complete difference in the required physics: for real particles, the sum over histories or 'path integral' is the not representing reality: it is just a way of estimating the path of least action for a particle going between two points, or the probability of one interaction occurring out of all possibilities.

For virtual particles, however, the siuation is reversed: the path integral represents what really does happen, because there are lots of gauge bosons mediating every possible kind of interaction.

‘Light ... ‘smells’ the neighboring paths around it, and uses a small core of nearby space.’ - R. P. Feynman, QED, Penguin, 1990, page 54.

To summarise: for real particles, the path integral doesn't represent the particles as taking all possible paths, but only paths near tha path of least action. But for virtual particles, the path integral does represent all paths taken. I think that there is a tremendous amount that can be done by having a correct understanding of the physical processes behind the maths of quantum field theory. It's just weird that this is totally opposed by many people, who also claim that they think there may be something wrong with the foundations of quantum mechanics. It's totally delusional of them to ignore and censor out experimentally verified facts.

July 16, 2007 10:20 AM  
Blogger Kea said...

Thanks for the comments. No, I'm not sure if there will be a podcast, but I doubt it, although there were a few cameras so something may end up on Aussie TV.

July 16, 2007 1:45 PM  

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