Monday, December 26, 2005

Tiny Bubbles

AS a child, Einsten when given the gift of the compass, immediately reocgnized the mystery in nature? If such a impression could have instigated the work that had unfolded over timein regards to Relativity, then what work could have ever instigated the understanding of the Pea as a constant reminder of what the universe became in the mind of a child, as we sleep on it?

Hills and Valley held in context of Wayne Hu's explanations was a feasible product of the landscape to work with?

'The Princess & The Pea' from 'The Washerwoman's Child'

If Strings abhors infinities, then the "Princess's Pea" was really a creation of "three spheres" emmanating from the "fabric of spacetime?" It had to be reduced from spacetime to a three dimensional frame work?

Spheres can be generalized to higher dimensions. For any natural number n, an n-sphere is the set of points in (n+1)-dimensional Euclidean space which are at distance r from a fixed point of that space, where r is, as before, a positive real number. Here, the choice of number reflects the dimension of the sphere as a manifold.

a 0-sphere is a pair of points
a 1-sphere is a circle
a 2-sphere is an ordinary sphere
a 3-sphere is a sphere in 4-dimensional Euclidean space

Spheres for n ¡Ý 3 are sometimes called hyperspheres. The n-sphere of unit radius centred at the origin is denoted Sn and is often referred to as "the" n-sphere. The notation Sn is also often used to denote any set with a given structure (topological space, topological manifold, smooth manifold, etc.) identical (homeomorphic, diffeomorphic, etc.) to the structure of Sn above.

An n-sphere is an example of a compact n-manifold.

Was it really fantasy that Susskind was involved in, or was there some motivated ideas held in mathematical structure? People like to talk about him without really understandng how such geometrical propensities might have motivated his mind to consider conjectures within the physics of our world?

Bernhard Riemann once claimed: "The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean." His prophesy was realized later with Einstein's general theory of relativity. It is futile to expect one "correct geometry" as is evident in the dispute as to whether elliptical, Euclidean or hyperbolic geometry is the "best" model for our universe. Henri Poincaré, in Science and Hypothesis (New York: Dover, 1952, pp. 49-50) expressed it this way.

You had to realize that working in these abstractions, such work was not to be abandon because we might have thought such abstraction to far from the tangible thinking that topologies might see of itself?

Poincaré Conjecture Proved--This Time for Real
By Eric W. Weisstein

In the form originally proposed by Henri Poincaré in 1904 (Poincaré 1953, pp. 486 and 498), Poincaré's conjecture stated that every closed simply connected three-manifold is homeomorphic to the three-sphere. Here, the three-sphere (in a topologist's sense) is simply a generalization of the familiar two-dimensional sphere (i.e., the sphere embedded in usual three-dimensional space and having a two-dimensional surface) to one dimension higher. More colloquially, Poincaré conjectured that the three-sphere is the only possible type of bounded three-dimensional space that contains no holes. This conjecture was subsequently generalized to the conjecture that every compact n-manifold is homotopy-equivalent to the n-sphere if and only if it is homeomorphic to the n-sphere. The generalized statement is now known as the Poincaré conjecture, and it reduces to the original conjecture for n = 3.

While it is very dificult for me "to see" how such movements are characterized in those higher spaces, it is not without some understanding that such topologies and genus figures would point to the continuity of expression, as "energy and matter" related in a most curious way? Let's consider the non-discretium way in which such continuites work, shall we?

From one perspective this circle woud have some valuation to the makings of the universe in expression, would identify itself where such potenials are raised from the singular function of the circular colliders. Those extra dimensions had to have some basis to evolve too in those higher spaces for such thinking to have excelled to more then mathematical conjectures?

We can also consider donuts with more handles attached. The number of handles in a donut is its most important topological information. It is called the genus.

It might be expressed in the tubes of KK tower modes of measure? That such "differences of energies" might have held the thinking to the brane world, yet revealled a three dimensional perspective in the higher diemnsional world of bulk. These had to depart from the physics, and held in context?

Clay Institute

If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.

While three spheres has been generalized in my point of view, I am somewhat perplexed by sklar potential when thinking about torus's and a hole with using a rubber band. If the formalization of Greene's statement so far were valid then such a case of the universe emblazoning itself within some structure mathematically inclined, what would have raised all these other thoughts towards quantum geometry?

In fact, in the reciprocal language, these tiny circles are getting ever smaller as time goes by, since as R grows, 1/R shrinks. Now we seem to have really gone off the deep end. How can this possibly be true? How can a six-foot tall human being 'fit' inside such an unbelievably microscopic universe? How can a speck of a universe be physically identical to the great expanse we view in the heavens above?
(Greene, The Elegant Universe, pages 248-249)

Was our thoughts based in a wonderful world, where such purity of math structure became the basis of our expressions while speaking to the nature of the reality of our world?

Bubble Nucleation

Some people do not like to consider the context of universe and the suppositions that arose from insight drawn, and held to possibile scenario's. I like to consider these things because I am interested in how a geometical cosistancy might be born into the cyclical nature. Where such expression might hold our thinking minds.

Science and it's Geometries?

Have these already been dimissed by the physics assigned, that we now say that this scenario is not so likely? Yet we are held by the awe and spector of superfluids, whose origination might have been signalled by the gravitational collapse?

Would we be so less inclined not to think about Dirac's Sea of virtual particles to think the origination might have issued from the very warms water of mother's creative womb, nestled.

Spheres that rise from the deep waters of our thinking, to have seen the basis of all maths and geometries from the heart designed. Subjective yet in the realization of the philosophy embued, the very voice speaks only from a pure mathematical realm, and is covered by the very cloaks of one's reason?

After doing so, they realized that all inflationary theories produced open universes in the manner Turok described above(below here). In the end, they created the Hawking-Turok Instanton theory.

The process is a bit like the formation of a bubble
in a boiling pan of water...the interior of this tiny
bubble manages to turn itself into an infinite open
universe. Imagine a bubble forming and expanding at the
speed of light, so that it becomes very big, very quickly.
Now look inside the bubble.

The peculiar thing is that in such a bubble, space and time
get tangled in such a way that what we would call today's
universe would actually include the entire future of the
bubble. But because the bubble gets infinitely large in
the future, the size of 'today's universe' is actually infinite.
So an infinite,open universe is formed inside a tiny, initially
microscopic bubble.


  1. It is tragic that 't Hooft spreads falsehoods abusively about Ivor Catt's lifetime of work on capacitors:

    Electric energy flows at light speed, so it goes along the capacitor plate
    at that speed. Maxwell's equations ignore all of the processes inside the

    Maxwell has no mechanism or physics, zero, nada, zilch.

    How many kids have to be killed before Nobel laureate Hoof gets off his high
    horse and understands the problems?

    ----- Original Message -----
    From: "Nigel Cook"
    To: "Hooft 't G."; "'Ivor Catt '";;
    Cc:;;;;;;;;;;;;;;;;;;;;;;;;;;;;; "Hooft 't G.";;
    Sent: Tuesday, December 27, 2005 3:10 PM
    Subject: t'Hooft shows what happens to Nobel Prize Winners who lose touch
    with reality

    > t'Hooft, please stop this abuse. You won the Nobel Prize for
    > renormalisation work in quantum field theory which was dismissed by Dirac,
    > so that doesn't excuse your abuses of other people. Your pet theory is
    > wrong:
    > ml. You should not associate it with my work as you do there, if you are
    > unwilling to study the facts behind classical electromagnetism. Being
    > abusive about Catt's work does not prove anything.
    > t'Hooft cannot claim he knows more about capacitors than Ivor Catt, who
    > spent his entire career measuring their response to transients.
    > Maxwell ignored the light-speed spread of energy along a capacitor plate.
    > His equation for the charging of a capacitor plate is a continuous curve,
    > be contrasted with the experimentally and theoretically validated correct
    > step-wise plot
    > Oliver Heaviside showed when signalling with Morse Code in the undersea
    > cable between Newcastle and Denmark in 1875 that electrical energy is
    > transmitted at the speed of light for the insulator of a cable: it
    > up' just like a capacitor! This is because all electromagnetic energy
    > consists of such fields, even photons, and the varying electric field
    > throughout a photon does not violate conservation of charge, because
    > number is not conserved in quantum mechanics!
    > Lack of physical understanding kills people. Ivor Catt in Electronics
    > September 2003 issue, 'EMC - A Fatally Flawed Discipline' pages 44-52:
    > 'during the Falklands War, the British warship HMS Sheffield had to switch
    > off its radar looking for incoming missiles ... This is why it did not see
    > incoming Exocet missiles, and you know the rest. How was it that after
    > decades of pouring money into the EMC community, this could happen ...
    > community has gone into limbo, sucking in money but evading the real
    > problems, like watching for missiles while you talk to HQ.'
    > More deaths linked to the suppression of Catt's work: Electronics World,
    > January 2003, pp12-14:
    > 'In July last year, problems with the existing system were highlighted by
    > the tragic death of 71 people, including 50 school children, due to the
    > confusion when Swiss air traffic control noticed too late that a Russian
    > passenger jet and a Boeing 757 were on a collision path. The processing of
    > extensive radar and other aircraft input information for European air
    > is a very big challenge, requiring a reliable system to warn air traffic
    > controllers of impending disaster. So why has Ivor Catt's computer
    > for Air Traffic Control been ignored by the authorities for 13 years?
    > Cook reports.' - and
    > How on earth does the media (e.g., the author of most of the popular books
    > on quantum entanglement, Dr John 'Jupiter Effect' Gribbin) worship 'string
    > theory' which Dr Peter Woit has proved is 'not even wrong', while ignoring
    > the proved experimental facts of electromagnetism which contradicted the
    > textbook formula for Maxwell's displacement current but allowed Ivor Catt
    > design the world's first wafer-scale integration product, a 160 MB solid
    > state memory right back in 1988, which won the 'Product of the Year Award'
    > from the U.S. journals Electronic Design (on 26 October 1989) and also
    > Electronic Products (in January 1990), after Sir Clive Sinclair's offshoot
    > computer company, Anamartic, invested £16 million (see
    > ----- Original Message -----
    > From: "Hooft 't G."
    > To: "'Nigel Cook '" > Sent: Tuesday, December 27, 2005 12:52 PM
    > Subject: RE: Editor Jeremy Webb discredits integrity of the New Scientist
    > > Please remove me from this list. I don't want my in-box to be polluted
    > > all this nonsense about Maxwell's equations. The Maxwell equations
    > correctly
    > > describe the propagation of signals as well as the conservation of
    > in
    > > capacitors, period. Keep me out of any further discussions.
    > > G. 't Hooft.

  2. "It does not make any difference how smart you are, who made the guess, or what his name is - if it disagrees with experiment it is wrong." - Feynman, Character of Physical Law, 1965, p156.

    The Maxwell equation for displacement current is wrong as it is not stepwise. When corrected, taking into account that an atom is a charged capacitor, you get quantum theory. The capacitor charges in steps equal to the time for energy travelling at light speed to transit a capacitor plate and reflect back.