archived as http://www.stealthskater.com/Documents/Pitkanen_19.doc

(also …Pitkanen_19.pdf) => doc pdf URL-doc URL-pdf

more from Matti Pitkänen is on the /Pitkanen.htm page at doc pdf URL

note: because important websites are frequently "here today but gone tomorrow", the following was archived from http://matpitka.blogspot.com/2009/09/condensed-matter-monopoles-found.html on September 5, 2009. This is NOT an attempt to divert readers from the aforementioned website. Indeed, the reader should only read this back-up copy if the updated original cannot be found at the original author's site.

Condensed Matter Monopoles found?

by Dr. Matti Pitkänen / September 5, 2009

Postal address:

Köydenpunojankatu 2 D 11

10940, Hanko, Finland

E-mail:

URL-address: http://tgdtheory.com

(former address: http://www.helsinki.fi/~matpitka )

"Blog" forum: http://matpitka.blogspot.com/

K.R.A.M. sent me a New Scientist story telling about the finding of condensed matter monopoles. I decided to write something about this. But Lubos was faster than me in his reactions and I can only recommend his blog for explanation what Dirac monopoles are and what the condensed matter monopoles are not. Lubos gives also a link to a popular article in Nature and also other links. Unfortunately, the article "Dirac Strings and Magnetic Monopoles in Spin Ice Dy2Ti2O7" itself is not freely accessible.

As Lubos tells, the monopoles are not Dirac monopoles with quantized magnetic charge (which are not allowed by the gauge invariance of Maxwell equations in topologically trivial space-time). They do not seem to be GUT monopoles either. Rather, they seem to correspond to magnetic flux tubes having opposite effective magnetic charges at their ends.

These kind of objects are imaginable even in the standard Maxwellian theory. It is important, however, to notice that the flux must continue beyond the ends by a conservation of magnetic flux if Maxwell's equation in flat space are true so that the ends are fictive to some extent. What one can think of in Minkowski space is the analog of a bar magnet with return flux dispersing at the ends of magnet.

These Dirac strings are very interesting from the TGD point-of-view since CP2 has a non-trivial topology. The fact that the second homology group is non-trivial (i.e., integers) means that there are non-contractible 2-surfaces in CP2. These surfaces are characterized homologically by integer valued Kähler magnetic flux. These monopoles are not Dirac monopoles but homological monopoles for which the topological half of Maxwell's equations remains true (Faraday's induction law and vanishing of divergence of magnetic field).

Since the projection of Kähler form to space-time defines Maxwell's field (part of electromagnetic field and under some conditions all of it), these homological monopoles can appear at the space-time level.

1. If space-time surfaces are orientable, these monopoles appear always as pairs with opposite Kähler magnetic charges.

2. For CP2 type vacuum extremals representing elementary fermions, the flux is confined inside CP2 rather than flowing radially out. Same is true for a piece of CP2 type vacuum extremal representing gauge boson as a wormhole contact.

3. If one allows non-orientable space-time surfaces so that homology becomes Z2 valued, genuine monopoles carrying even value of magnetic charge are also possible. I would guess that CP2 projection of space-time surface must be non-orientable in this case. Klein bottle and Möbius strip imbedded in CP2 could serve as basic examples. By gluing handles, one obtains more complex non-orientable 2-surfaces.

Let us restrict the consideration mostly to the orientable case.

A. Magnetic flux tubes at the ends of string like objects (cosmic strings with enormous string tension) would be the basic realization. The simplest extremal is just the Cartesian product X2×Y2 where X2 is string orbit in M4 and Y2 a complex sub-manifold of CP2.

Cosmic strings are basic objects in TGD-inspired very early cosmic string dominated cosmology when space-time sheets had not yet emerged. During cosmic evolution, these flux tubes would widen to magnetic flux tubes carrying arbitrary weak magnetic field. These flux tubes could (dare I say "would"?) be still present. I would guess that non-orientable 2-surfaces of CP2 do not allow a representation as complex manifolds so that I would not expect them to give rise to cosmic string-like objects.

B. Fermions correspond in the TGD Universe to light-like 3-surfaces separating so called CP2 type vacuum extremal with Euclidian signature of metric from space-time sheet with Minkowskian signature of metric. This light-like 3-surface can be interpreted as an orbit of a partonic 2-surface and besides fermionic quantum numbers could carry magnetic charge so that magnetically-charged variants leptons and quarks could exist.

A good guess is that these states are very massive. One would have a long-ranged radial magnetic field and the second member of monopole pair could correspond to the outer boundary of the space-time sheet. Whether boundary conditions allow this is not clear.

C. Also, bosonic variants of monopoles are possible. Gauge bosons are identified as wormhole contacts (piece of CP2 type vacuum extremal) connecting space-time sheets with Minkowskian signature of metric and there would be pair of throats carrying opposite magnetic charges. Throats could carry fermionic and anti-fermionic quantum numbers so that all gauge bosons and possible Higgs particle could have magnetically charged variants.

In a two-sheeted space-time picture, one would have magnetic dipoles with magnetic charges extremely near to each other. From the point-of-view of either space-time sheet, one would have monopole carrying Classical magnetic field giving rise to a genuine force.

D. I have proposed that the magnetic flux in superconductors could be transferred between space-time sheets through these kind of wormhole contacts carrying at its throats opposite magnetic charges possibly also carrying other elementary particle numbers and behaving as bosons. The magnetic flux tubes observed in superconductors could enter to the superconductor from a larger space-time sheet and return to it through this kind of wormhole throats.

There is also a much more mundane possibility but still representing something new. Flux tubes could be just flux tubes with outer boundary (of form X2×S2, D2 disk, rather than of form X1×Y2, Y2 closed manifold in CP2) and beginning from the boundary of space-time sheet or from wormhole throat and carrying magnetic flux which need not satisfy Dirac condition. Condensed matter monopoles could be these kind of objects.

Notice that spin glasses in which the Dirac fluxes are observed are systems in which the direction of magnetization is frozen in a given patch but varies from patch-to-patch. In TGD framework, the notion of 4-D spin glass landscape emerges naturally from the vacuum degeneracy of Kähler action meaning same for 4-D space-time region so that kind of dynamical spin glass would be in question.

For background, see the chapters "General View About Physics in Many-Sheeted Space-Time: Part I" and "General View About Physics in Many-Sheeted Space-Time: Part II" of Physics in Many-Sheeted Space-Time.

Readers' Comments

1. At 3:02 AM, Anonymous said...

Excuse me, Matti,

What is the difference between the Meisner field and the magnetic field of the discovered monopoles?

2. At 4:43 AM, Matti Pitkanen said...

Meisner field appears in superconductors as flux tubes. In this case, the total area of flux quanta is minimized (positive surface energy).

In another kind of superconductors near criticality, there are very complex structures looking locally like thin walls. In this case, the area of structure is maximixed (i.e., negative surface energy).

I just realized that both kind of magnetic configurations also appear in the TGD-inspired Quantum Biology. Flux sheets assumed to traverse DNA and defined hierarchy of genomes would naturally correspond to negative surface energy and magnetic flux tubes to positive surface energy.

In the recent, situation one does not have superconductivity. The basic anatomy of magnetic flux tubes would be however same.

I do not have any detailed information about the finding so I cannot say more.

3. At 8:28 AM, Anonymous said...

But the experiments are made at the terms for superconductivity (near-Zero Kelvin). Is that accidentally? And what is your last opinion on the ORMEs elements?

4. At 10:50 AM, Matti Pitkanen said...

I do not have access to the article. But on basis of the its abstract, I understand the experiments in question are for the spin glass phase. This is magnetized material but with a decomposition to magnetized regions with magnetization direction varying randomly. These materials are extremely complex due to the huge degeneracy of ground states.

if on the Internet, Press <BACK> on your browser to return to

the previous page (or go to www.stealthskater.com)

else if accessing these files from the CD in a MS-Word session, simply <CLOSE> this file's window-session; the previous window-session should still remain 'active'

4