Closed magnetic flux tubes (also flux sheets) carrying dark matter are in crucial role in TGD view about criticality.
Dark matter withy large Planck constant would be created at criticality and it would generate the the long
TGD allows the possibility that the magnetic flux quanta associated with
criticality carry monopole flux. In Maxwellian electrodynamics this is not
possible. These flux tubes are associated with elementary particles: in this
case they have open string like portions at parallel space-time sheets
connected at their ends by wormhole contacts to form a closed two-sheeted loop.
Since the magnetic monopole flux is conserved along the flux tube, one has full
reason to wonder whether these closed magnetic flux tubes can be created from
One can imagine two manners to create flux loops: in a continuous energy
conserving manner classically or by quantum jump in which quantum sub-Universe
associated with given causal diamond (CD) is re-created (recall that causal
diamonds define the observable Universes and they have finite size as
intersections of future and past directed light-ones)
Consider for simplicity flux tubes which are circular. How the flux tubes can be
- One possibility is that an existing circular flux tube splits into two.
This would take place by self-reconnection: circular flux tubes evolves first
a figure eight shape, and after that self-reconnects and splits to two circular
flux tubes. Figure eight is necessary because the direction of the conserved
magnetic flux defines orientation and flux tube portions with opposite
orientations cannot join. This mechanism allows replication of flux tubes and
could be behind the 1→ 2 decays of elementary particles and the
reverse reactions. It could be also behind biological replication at both DNA
and cell level, and even higher levels. The reconnection of U-shaped flux tubes
for two systems so that they become connected by a pair of flux tubes is the
reverse of this process and is proposed to define fundamental mechanism of
- Can one imagine a purely classical mechanism in which flux tubes would be
generated from nothing? An idealization as a closed string allows to imagine a
closed string which begins from point and expands: in string models this kind of
closed strings indeed pop up from vacuum. Energy conservation however forbids
the classical occurrence of this process. Therefore this process is possible
only in path integral formalism which allows processes, which are classically
In TGD framework space-time surfaces appearing in the functional integral are
extremals of Kähler action and conserve energy so that this kind of process
is impossible. It is difficult to say what happens when the string is replaced
with a flux tube having a a finite thickness: could this make it possible an
energy conserving process in which initial state would not contain flux tubes
but final would contain flux tubes? At elementary particle level this would
mean generation of a particle or a pair from vacuum but this does not take
place. Note that the development of Higgs expectation can be interpreted as
generation of new vacuum state which contains Higgs bosons: TGD counterpart of
the ground state would be a superposition of states containing various numbers
of flux loops.
- One can however consider a quantum jump generating flux tube
from nothing. The sequence of quantum jumps consist of sub-sequences consisting
of state function reductions to a fixed boundary of CD ("upper" or "lower"). A
sub-sequence defining self corresponds to a sequence of repeated quantum
measurements having no effect on the state in ordinary quantum measurement
theory. In TGD state function reduction has effect on the second boundary. Or
to be precise, on the wave function in the moduli space associated with the
second boundary with moduli characterising among other things the temporal
distance from the fixed boundary. This effect gives rise to the experienced flow
of time as increase of the average temporal distance between the tips of CD and
also to its arrow.
These state function sequences do not last for ever (self has finite
lifetime!): Negentropy Maximization Principle (NMP) eventually forces state
function reduction at the opposite boundary of CD. The new state can contain
flux loops which did not exist in the initial state. These flux loops could
exists also outside the CD but this is not relevant for the physics experienced
by the conscious observer associated with given CD.
The generation of this kind of monopole flux loops from nothing could be seen
as a direct proof for macroscopic quantum jumps re-creating the Universe.
Penrose proposed something similar in Shadows of Mind: quasicrystals are
non-periodic lattices which look like lattices but - unlike ordinary crystals -
cannot be generated by gradual lattice growth but must pop up in quantal manner
For details and references see the new chapter Criticality and dark matter of "Hyper-finite factors and hierarchy of Planck constants" or the article Criticality and dark matter.