A fractal has an axis of scale symmetry - "move about", ie: move up and down in scale, and the world remains the same.
See for example coastlines and menger sponges
http://library.thinkquest.org/26242/full/ap/ap4.html
http://mathworld.wolfram.com/MengerSponge.html
Even in a universe...
But Rade this is just holding a mirror to one scale - how you imagine the very small Planck scale to be. So of course you see a simple reflection symmetry.
There is also the second possible axis of symmety, the asymmetric one that is local~global or fractal in nature.
Seems to me you have in mind questions of conservation laws and entropy - why is the creation of more void, an expanding universe, allowed? Why does the universe expand in short.
The "points" of the universe are Planck-scale. You could also ask why they don't expand as the Universe grows...
Take your point but it is probably right to say that the vacuum would be the lowest possible state of the system, the natural end state. Give the universe enough time and all those pesky matter/gravity bumps will be flattened out - dissipated - to make a flat spacetime void.
Hi Richard
You raise a number of points that we will be forbidden to discuss as they will be deemed "not physics".
So I only offer quick replies.
Salthe is a theoretical biologist, but has developed a mathematically general framework that can apply to any kind of system.
There are...
google on Stan Salthe but I think his stuff on the web mostly concerns his "specification" hierarchy rather than his "scalar" hierarchy. It is in his 1985 book evolving hierarchical systems.
I would explain but the posts would get censorsed as "not physics".
Nice question. I would expect the conventional answer is that space - being homogenous and isotropic - would be self-dual. The reflection would be the same.
This would be a reflection of space at the same scale - across the axis of symmetry.
But there may be also the axis of asymmetry -...
Still seems crazy that you would pick on that of all things to "correct". There is endless other stuff I write that could do with actual correction.
Anyway, in that post I was flagging the FRACTAL sphere packing story in a perhaps too subtle hint that people should consider instead a dynamic...
Would it have helped to have said that there are two regular ways of stacking? But, of course, you could mix the binary choice made with each layer to generate an infinity of "different" outcomes?
If that is all you are saying here, it seems a puzzlingly pedantic point. And is neither here...
Hi Josh - why is it ugly?
There seem two alternative views on the landscape.
1) The first is that it is a set of crisp probabilities. That is, every possible solution actually has existence and we happen anthropically to be in one outcome in which existence can be reported.
2) The...
Hi Carl - that's an interesting point. Do you know of any references or further material that argue the case or explain the reason?
Cheers - John McCrone.
Whoops! You are quite right. The visible Universe is flat (which implies it is at the critical density) and the rate of expansion is a separate issue to the geometry.
The old story was that the rate was decelerating due to gravity acting on mass - the coasting to a halt scenario. The new...
Yes, there are three alternatives. You can have flat space (which coasts to a halt at infinity), closed space (that will collapse) or openly expanding space (which has hyperbolic curvature and accelerates away).
The recent fuss about dark energy, quintessence or cosmological constant is due...
..and another who likes phonons....
Olaf Dreyer (Perimeter Institute) http://arxiv.org/hep-th/0409048 [Broken]
There are currently two competing views of the role
quantum field theory plays in our theoretical understand-
ing of nature. In one view, quantum field theory describes
the...
Professor Xiao-Gang Wen, winner of OYRA in 1994, received his B.S. degree from the Univ of Sci. Tech of China in 1982, his M.S. in 1983 and Ph.D. in 1987 both from Princeton Univ.
His Ph.D. thesis director was Prof. Ed Witten.......
Hi Richard - some actual figures on sphere packing.
Random packing achieves density of about 65 percent. There are two ways of stacking that achieve the maximum possible density of 74.048 percent.
See - http://mathworld.wolfram.com/KeplerConjecture.html
Or for some neat fractal pix...
When you think of a cube, that is flat space. When you think of a sphere, that is curved space - so curled that it makes a circle. Add in open or hyperbolic curvature, where all paths diverge, and you have covered all three possibilities.
Cheers - John McCrone.
Better still you can follow Linde and others who prefer to start from the "largeness" of eternal inflation rather than the smallness of a singularity. This reverses things so that instead of an explosion of a hot point you get a bubble of cooling in a hot field.
And perhaps even the idea of...
Thanks, that is clear now.
We can observe certain things like redshift and we then have to assume that the reason is the expansion of space. Agreed. And the expansion of space would move two observers apart for "no reason". Although the two observers would have to be far enough apart for...
Which does not address the point I made about red-shifting, just restates the fact that speed of light must always look the same to an embedded observer.
The essential question here is whether the Hubble flow expansion kicks in at a certain distance that is not the Planck distance - say at...
Speed of light stays the same but wavelengths get stretched or red-shifted. That is what we see at astronomical distances to get a measure on the Hubble flow. And it is what we see at every point of space as the CMB effectively - the way the hot glow aftermath of the Big Bang got stretched out...
An alternative view is that stringiness emerges via a system of constraint. So the fact that it is "approximations" all the way down the hierarchy is simply a reflection of the fact that physical reality is constructed by an asymptotic approach to limits.
String theories model the harmonics...
Marcus said - "although I hate the number two. if there is more than one metric then there ought to be an infinite number, not just two."
This is an instinctual reaction. So where does it come from?
Fundamental physics is riddled with dualities. QM demands complementary properties, not to...
Isn't there some confusion in this thread between when the Hubble flow really kicks in (probably Planck scale) and when it is observeable (large scale)? The situation is much like classical vs relativity - relativity applies even at "Newtonian" scales, but is a correction so small it does not...
Seeing the Universe as a dissipative structure suggests far more radical thoughts than that!
But you should check out Lineweaver - http://www.mso.anu.edu.au/~charley/papers/LineweaverChap_6.pdf
The heat death would indeed be asymptotic as the event horizon - in black body fashion - would...
"I think we should get rid of the swamp metaphore, but not of the swamp itself. What are we really trying to talk about? Can't we be more descriptive, and use real terms instead of a handwaving metaphore?"
Hard to tell if any of your grumbling was directed at me. But I certainly live on a...
For sure. This is true of many people who worked hard to get things right and then find the world still ignores them (Nobel or not, chemists don't count in the grand scheme of things).
On the other hand, some of those who are most deeply wrong - like Francis Crick was about consciousness -...