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Tubulin proteins occur in microtubules. It is known that the peanut-shaped
tubulin protein (Fig.
9.4
) flexes about 30
, giving two conformational shapes
(states). They may qualify to be qubits.
Microtubules are mainly for maintaining cell structure, providing platforms for
intracellular transport and other cellular processes such as mitosis. These ropelike
polymers of tubulin can grow as long as 25
m and are highly dynamic; they, along
with microfilaments, seem to be everywhere in biological cells as in Fig.
9.5
. The
outer diameter of a microtubule is about 25 nm, pictured in Fig.
9.6
. There are
roughly 10
7
tubulins per neuron.
It is proposed by Hameroff that quantum states in one neuron could interact with
quantum states in other neurons via electrotonic gap junctions. These are conduc-
tive junctions through the glial between neurons. If quantum states can extend over
many neurons, a large-scale system may be possible.
Partial justification for such a system is found in observations of gamma
synchrony (a property of brain waves). These indicate that information may propa-
gate through the brain much faster than ordinary neural bursts would permit. The
implication is that entangled qubits are at work using quantum teleportation.
4
The relevance of tubulin qubits is disputed on the grounds that quantum coher-
ence is predicted to be less than a picosecond, that is, 10
12
s[
2
]. This is far too
short to be of practical value in a neural environment. To refute this, Hameroff and
Penrose recalculated that coherence may be for up to about a second, using a
combination of electrostatic (Debye) screening, quantum error correction, and
processes related to cellular maintenance [
10
].
μ
4
Two entangled qubits may have a state vector that looks like
> Þ
0
.
If one qubit is observed to be one, for example, then the other will be forced to be a one when it is
observed, no matter where it is located. But if the first is observed to be zero, the other will be
forced to be zero when it is observed. Note that a coherent quantum system is necessary.
Teleportation is a nonlocal quantum property.
jψ >¼ ηðj
0
> j
0
> þj
1
> j
1
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