| Topic: |
Science > Physics |
| User: |
"Jack Sarfatti" |
| Date: |
11 Sep 2005 12:13:35 AM |
| Object: |
Exotic particles & parastatistics |
typo-corrected & expanded
On Sep 10, 2005, at 10:01 PM, Jack Sarfatti wrote:
There are q qth roots of unity
e^i2pip/q
p = 1, 2, .... q
Therefore a local frame must rotate q times to get the phase factor
e^i2pip/q to equal 1.
Note that this is a periodic cyclic group mod q, so that it is the
denominator q that controls the physics, not the numerator p.
The spinor corresponds to q = 2, p =1, note that p = is the trivial
root of unity, i.e. 1 itself. Only one particle max per single-particle
state allowed.
We now have a physical interpretation.
Consider the simple spinor S = 1/2.
Consider a very slow-moving single neutron of spin S = 1/2 in a
Mach-Zender interferometer with a Stern-Gerlach magnet in one path. Let
the beam splitter be 50-50 and the physical path lengths identical.
Adiabatically turn the Stern-Gerlach once by 2pi as the neutron passes
through it and see a relative phase shift of pi. You need to turn it
twice to get back to zero phase shift.
Suppose we had an exotic magnetic particle with q = 3, p =1 or p = 2, in
either case one one have to adiabatically turn the magnet 3 times by 2pi
to cancel any relative phase shift. Presumably there could be 2 such
particles in the same single particle quantum state. q = 4 with p = 1 or
p = 2 or p = 3 i.e. max of 3-particles per state.
On Sep 10, 2005, at 7:20 PM, Jack Sarfatti wrote:
Standard quantum field theory starts with Fock occupation number space.
For a given "mode" a and a* are destruction and creation operators.
Bosons of spin 0, 1, 2, ... for non-exotic states obey
aa* - a*a = 1
Note that 1 = e^i2piN where N is any integer positive or negative
Fermions of spin 1/2, 3/2 ...
obey
aa* + a*a = 1
In general, for NON-exotic identical quanta of spin S = 0, 1/2, 1, 3/2,
2 ...
aa* - e^i2piSa*a = 1
a*a* = aa = 0 for S = 1/2, 3/2, ...
Note that 3/2 ~ 1/2 mod 2
because 1 ~ 3 mod 2
In contrast if we had an exotic particle say of spin S = 1/3
aa* - e^i2piSa*a = 1 true in general?
a*a*a* = aaa = 0
etc.
On Sep 10, 2005, at 11:32 AM, Jack Sarfatti wrote:
Remember the key to the practical low-power metric engineering of Warp &
Wormhole using dark zero point energy is the simple "Josephson" type
equation
/\zpf ~ (coherence length of Vacuum ODLRO)^-1(coherence length of ANYON
ODLRO)^-1cos(Vacuum Phase - Anyon Phase)
/\zpf > 0 is universally repulsive anti-gravity negative exotic vacuum
pressure
/\zpf < 0 is universally attractive gravitating positive exotic vacuum
pressure
where
Guv + /\zpfguv = 0 is Einstein's field equation for exotic vacuum (both
dark energy and dark matter)
Gennady Shipov's torsion field permits
/\zpf^,v =/= 0
in order than
Guv^;v = - /\zpf^,vguv =/= 0
a necessary condition for weightless warp drive and for the manufacture
of traversable wormhole star gates for instant space and time travel.
Note to go back in time you need to find a wormhole that already existed
in the past you want to go back to. If you do go back you create an Igor
Novikov globally self-consistent time loop locked into the "Destiny Matrix."
Bohm & Hiley's "The Undivided Universe" has a similar idea to the notion
of "emergence" below in the non-mechanical contextual form-dependence of
the fragile soft micro-quantum potential with signal locality. However,
they do not have macro-quantum ODLRO explicit there where the quantum
potential for the local order parameter stiffens.
The stiff macro-quantum local order parameter PSI(x) in the Galilean
relativity static limit is for an on-mass-shell condensate
Q(x) ~ PSI(x)|^-1(h^2/2m)(Grad)^2|PSI(x)|
This Q(x) is immune to environmental decoherence and allows signal
nonlocality.
The Schrodinger equation is replaced by the macro-quantum LOCAL "mean
field" L-G equation (without normal micro-quantum noise coupling in zero
order approximation)
ihPSI,t = -(h^2/2m)(GradPSI)^2 + VclassicalPSI + b|Psi|^2Psi
The "BCS" state in second-quantized Fock space
PSIk ~ <0|uk + vkak|0> is replaced by a macro-quantum squeezed Glauber
coherent state
PSI ~ e^(s*a*a* - saa)e^(z*a* - za)|0>
[a.a*] = 1
for bosons
This generalizes for 2D high Tc films of anyon condensates with fractal
parastatistics (e.g. fractional Quantum Hall Effect)
i.e. PSI changes by e^i2pi(p/q) in a closed loop about a topological
defect of the ODLRO parameter in 3D space, with p & q integers.
Note for bosons q = 1
For fermions p = (2n + 1), q = 2, n = 0, +-1, +- 2 ....
In general
aa* - e^iwpi(p/q)a*a = 1
When q = 1 for all p
aa* - a*a = 1 i.e. bosons
Indeed you can think of p as the spin in that case.
When p = (2n + 1) & q = 2
aa* + a*a = 1 fermions
So for these two non-exotic cases, the usual spin-statistics connection is
aa* - e^i2piSa*a = 1
S is the SPIN of the quantum field.
S = 0, 1, 2, ... all give +1 for the exponential
S = 1/2, 3/2 ... all give -1 for the exponential
A single-particle micro-quantum wave function gets a phase factor
e^i2piS when the reference frame is rotated by 2pi.
Can we have exotic fields of any spin S?
ex 1 S = 2/3, rotate the frame by 3pi/2 to get -1 for the phase shift
exponential. This suggests some kind of dislocation defect. We can
think of local macro-quantum order parameters only partially as quantum
wave functions. They do not have all the properties of quantum waves,
i.e. they have a physically measurable scale that micro-quantum waves do
not have, i.e. |order parameter|^2 ~ physical condensate density unlike
micro-quantum waves that are invariant under multiplication by an
arbitrary constant complex number z. The macro-quantum local order
parameter is the fusion of IT with BIT. In contrast a micro-quantum wave
is pure BIT and it lives in configuration space. The order parameter is
local and lives in ordinary space.
Suppose
aa* + a*a = 1
Therefore
N = a*a = 1 - aa*
Consider
Na*a*|0> = a*aa*a*|0> = a*(1 - a*a)a*|0> = a*a*|0> - a*a*aa*|0>
a*a*aa*|0> = a*a*(1 - a*a)|0> = a*a*|0> - a*a*a*a|0>
But a|0> = 0
Therefore, a*a*aa* = a*a*|0>
Therefore,
Na*a*|0> = a*a*|0> - a*a*|0> = 0
That is we have derived the Pauli exclusion principle that a*a*|0> = 0,
i.e. no more than one fermion in a single-quantum state. Is this true
also off-mass-shell?
So one set of NON-FRACTAL para-statistics is
a*...a*|0> = 0, i.e. a cyclic group of integer order p', i.e. no more
than p' para-fermions in a single-particle state.
Is there any physical meaning to taking roots of this, some kind of
FRACTAL interpretation?
.
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