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Les auteurs de cet article
ont bien voulu le rédiger spécialement pour
nos lecteurs, sous une forme accessible aux non-spécialistes
du formalisme quantique. Ils ont pensé, à
juste titre, que nous intéresserions à des
rapprochements entre la modélisation des comportements
des insectes sociaux et certaines théories récentes
intéressant la non-localité, celles impliquant
notamment la non-localité dans le temps. Nous les
en remercions vivement.

En
l'espèce, il s'agit de montrer comment des systèmes
adaptatifs macroscopiques, comme des fourmilières,
se comportent à leur échelle comme des systèmes
physiques. Une fourmi isolée est un système
aléatoire, une fourmilière devient un système
déterministe. De même une particule décrite
par la mécanique quantique est aléatoire,
tandis qu'un grand ensemble de particules devient déterministe.

Les
auteurs s'intéressent à l'interprétation
transactionnelle de John Cramer, qu'il énonce ainsi
(citation dans le texte ci-dessous):

"Le
processus (transaction) décrit ici peut être
décrit comme celui suivi par un émetteur adressant
une onde de reconnaissance "probe wave" dans toutes les directions, à la recherche
d'une réponse. Si un récepteur, recevant l'une
d eces ondes, répond par une onde de reconnaissance
"verifying wave" qu'il adresse à l'émetteur,
il scelle la transaction et permet le transfert d'énergie
et d'impulsion. Ceci ressemble beaucoup à la procédure
du "handshake" utilisée dans l'industrie informatique
comme protocole de communication entre ordinateurs et périphériques.
De la même façon les banques ne considèrent
un transfert de fonds comme définitif que s'il est
confirmé et vérifié par les parties
à la transaction".

Les fourmis fourragères
"émises" par une fourmilières prospectent
dans toutes les directions. Mais seules les voies présentant
le plus fort taux de phéromones sont "confirmées"
par la collectivité, comme les plus avantageuses
en termes d'économie de moyens. On a d'une certaine
façon l'équivalent d'une transaction telle
que décrite par la TQM La transaction est formée
de deux ondes, l'une du passé vers le futur de la
source et l'autre, émanant d'un récepteur
et scellant la transaction, du futur vers le passé.

L'analogie
avec les collectivités d'abeilles et de fourmis pourrait
permettre de comprendre pourquoi toutes les entités
microscopiques théoriquement présentes dans
l'espace et le temps quantique n'apparaissent pas toutes
dans le monde macroscopique. Seules émergent celles
ayant conclu entre elles des transactions plus "robustes"
que les autres.

L'article
vise à proposer aux lecteurs de discuter la théorie
du "temps caché" qu'ils développent
actuellement à l'Intitut Keldysh et qu'ils pensent
très prometteuse, en vue de d'éclairer un
certain nombre de questions non résolues par la physique
contemporaine. Nous ne pouvons que conseiller à nos
lecteurs intéressés de prendre contact avec
eux, s'ils ne l'ont déjà fait.

Abstract In the paper we briefly
tell a story about what is quantum theory, quantum non-locality
and delayed choice. Then we tell about most promising transactional
interpretation of quantum mechanics, designed by John Cramer to
explain these paradoxes, and how we introduce bees’ flights and
hidden time into John Cramer’s approach.

What is quantum theory?

Quantum
particles like atoms, molecules or electrons are known to have no
smooth trajectories like bodies in classical mechanics. Instead
such particles can be in so called quantum states, and make transitions
between them. Say, an electron can be placed at some point. This
is one kind of quantum state. Or, it can have some definite momentum
(and thus no definite position).

Any
transition has a probability which is calculated in quantum theory
by some very strange formal mathematical procedure. This procedure
provides a recipe to calculate a quantity called amplitude. The
square of absolute value of this amplitude gives a probability of
correspondent transition.

What is quantum non-locality?

Non-locality
of quantum mechanics was widely spoken for the last decade due to
quantum computations, quantum teleportation, EPR correlations. Still,
non-locality of quantum behavior of particles is not necessarily
connected to these exotic phenomena. Non-locality is present in
any quantum transition.

Non-locality
is intrinsic property of any quantum transition. It is most clearly
seen if we use Feynman’s
formulation of quantum mechanics. This formulation is
popularly told by R. P. Feynman in his brilliant book “QED – a strange
theory of light and matter” [1] (QED = quantum electrodynamics).
More technical explanation is in his another book “Quantum mechanics
and path integrals” [2].

Main
idea is that a particle, after leaving a source, reaches (in some
sense) the detector by all possible paths. Each path provides a
complex number, which is a value of some integral along the path.
Total sum of such numbers over all paths gives the amplitude of
transition. Being squared, this amplitude gives a probability of
transition. From here we shall talk about states with definite position
and transitions among them only.

So,
here’s the real sense of quantum non-locality: amplitudes depend,
generally speaking, on the whole Universe! To be true, only a small
set of paths actually matters, while the income of others into total
sum tends to be negligible.

Still,
the paths that matter can be separated essentially. Here’s the most
illustrating classical example from classical paper of David Deutsch
on quantum computations (Fig. 1).

If
we suppose that a photon (a quantum of light) moves either this
or that way after passing the beam splitter, then both of detectors
A and B will work with equal probabilities at many runs of experiment.
Still the detector B never works. In quantum mechanical language
we say that path integrals at two paths sum to zero amplitude for
that detector. In some way a photon “knows” about positions of both
mirrors we use. It is true non-locality.

What
is delayed choice?

Delayed
choice [3] is a kind of analogue of non-locality for time dependence
of quantum amplitudes, contrary to spatial dependence, as discussed
above. Imagine the same classical experiment as at Fig. 1 (such
an installation is known as Mach – Zehnder interferometer).

Let
now all the distances between mirrors and detectors be so large
that it takes essential time for a photon to travel across the arms
of the interferometer. Let us also take off the beam splitter BS2
at the moment just before the photons should come to it. In this
case, according to predictions of quantum mechanics, the photon
can hit either of detectors A and B with equal probabilities.

In
the previous section we agreed that the photon travels both paths,
i.e. arms of the interferometer. But it is not valid in current
situation: hitting any of two detectors should be equivalent to
traveling some single path only!

It
looks as if the photon first moves both paths, but at the former
place of BS2 it decides to turn back and start his travel once more,
this time one path only. In other words, the photon decides what
a history he had at a final instant only. It is delayed choice paradox.

What
is transactional interpretation of quantum theory?

Transactional
interpretation of quantum mechanics (TIQM) is suggested by Prof.
John Cramer, University of Washington (Seattle, USA). It provides
a very illustrative and comprehensive explanation of quantum non-locality
and delayed choice.

Which
is the difference between an interpretation and a full-value physical
theory? It is normally assumed that an interpretation provides a
way of thinking and no predictions. Instead, a full-value physical
theory provides quantitative predictions that can be tested experimentally.
Though, Afshar
experiment seems to verify TIQM, as John
Cramer supposes.

The
core of TIQM is idea that a single act of a particle transition
(consisting of both emitting and absorbing) should be treated as
a single transaction between a source and a detector. Transaction
is formed by two waves: a retarded offering wave (from past to future)
from a source and an advanced (from future to past) confirmation
wave from a detector. An illustrating space-time diagram is in John
Cramer’s paper. The two waves interfere in such an adjusted
way, that there are no any waves before emitting and after detection.

Nature,
according to TIQM, allows different transactions with probabilities,
which correspond to quantum theory, but in each case only one happens.
We could even formulate in the following way: do focus on transitions
(= transactions) rather than emitting and detecting events separately;
do view a transaction as a single physical phenomenon, a single
event. To be true, such a formulation is our own “re-interpretation”
of transactional interpretationJ.

In
this case non-locality and delayed choice make no surprise. Say,
in standard Mach – Zehnder experiment (Fig. 1) transaction is formed
by waves in both arms of the interferometer (Fig. 2a).

And
in delayed-choice experiment one of two possible transactions happens,
each within a single choice (Fig. 2b, 2c).

All
figures 2a, 2b, 2c imply blue line for retarded offering wave, while
red line means advanced confirmation wave.

Why
2 waves in transactional interpretation?

What
for the two waves are needed? In fact, John Cramer is not inventor
of “backward – in - time” propagation. It is an idea of R. Feynman
and J. Wheeler, which is explained in John Cramer’s paper in detail.

Two
waves are necessary to accomplish correlation of boundary conditions
on both sides of transaction. This correlation takes place in many
- particles effects like EPR, quantum teleportation, etc., which
we do not examine here for simplicity, but which were the object
of intense investigation and popularity for last decade. One can
read a very good introduction
by Prof. David Harrison of Toronto University.

“The process described above can also be thought of as
the emitter sending out a "probe wave" in various allowed directions,
seeking a transaction. An absorber, sensing one of these probe waves,
sends a "verifying wave" back to the emitter confirming the transaction
and arranging for the transfer of energy and momentum. This is very
analogous to the "handshake" procedures that have been devised by
the computer industry as a protocol for the communication between
subsystems such as computers and their peripheral devices. It is
also analogous to the way in which banks transfer money, requiring
that a transaction is not considered complete until it is confirmed
and verified”.

What
is hidden time model of quantum phenomena?

Explaining
force of transactional interpretation is great indeed, but new questions
arise, and they are obvious. As we pointed before, quantum transitions
are probabilistic: one of many possible transitions (= transactions)
can occur. Any particle can be either emitter or detector; it should
emit retarded and advanced waves in all directions, to all possible
“partners” in transaction. How it happens, that some definite transaction
happens? Why this, not other?

We
propose a simple idea of how some definite choice can be done. Our
basic idea can be illustrated most clear by an analogy with bees.
This analogy is proposed by Prof. Howard
Bloom.

Imagine
a beehive full of bees. They all have different jobs. Worker bees
want to gather the harvest, but first they need a good decision
about where to fly for most profit. Scout bees, (who are much less
numerous than workers) fly in different directions to find a better
lawn (Fig. 3a).

Each
scout finds the best (in her opinion) lawn. Then she comes back
home and starts agitating for her findings (Fig. 3b). As you might
know, scout bees agitate by dancing special 8
– looking dances. Worker bees attentively “listen” to
agitators. They wonder whose arguments are most convincing. Dances
can take an essential time, especially if the deed is not about
a good lawn, but about a new hive. At swarming the dances can long
for several days, and agitating scouts can even die of emaciation!

Finally worker
bees make their joint decision and fly to some certain lawn (Fig
3.c).

One
can easily see that it looks very much like transactional interpretation.
But instead of 2 waves, including offer and confirmation, we have
3 passes here. We add the third pass of, but it is a pay to explain
why some certain transaction happens of many possible.

This
also explains why in Feynman’s
formulation of quantum mechanics uses all paths to calculate
quantum mechanical amplitude of a transition. In bees’ language,
scouts explore all lawns, but final collective decision is a single
lawn.

So where is hidden time in bees’ flights?

One can claim
here: “Hay! It takes time for scouts to fly back and forth. What
about speed of light? If we talk of a photon, it must reach the
detector with the light speed! It can not jump back and forth 3
times between all possible detectors. It is crazy because it takes
huge time!”

Yes!
This is why we hide scout flights in hidden time. Physical time
simply does not tick while scouts investigate the Universe. We suggest
a very simple but original decision: physical time instants correspond
to completed transitions, while such transitions correspond to final
jumps only, like at Fig 3c. Scouts flights are simply excluded from
the physical time.

More
detailed arguments about why such a scheme is physically correct
(including agreement with special relativity) are in our preprint
and this
article.

Another
analogy: ants

Besides
bees, there is another very promising, as we believe, analogy between
quantum particles and living adaptive systems. These are ants. Whereas
collective of bees in a hive is, in our opinion, an analogue to
a single quantum particle, ant colony behaves much like a classical
body which is a huge collective of particles.

Ant
colony can perform optimization tasks like finding the shortest
way from a nest to a food source. Ant algorithms are now very popular
due to investigations by Marco
Dorigo. Still, for the purposes of enlightening the analogy,
main idea deserves at least a short description.

While
different ants travel both short and long way from a nest to a food
source (Fig. 4), they leave a smelling track of pheromones. At each
of two crotches a traveling ant has a choice to go this way or that
way. The probability of certain choice is proportional to intensity
of smell, left by previous travelers.

Even
implying equal parts of ants’ choices at the 1st passage from the
nest to food source we can estimate that the shorter way becomes
more preferable very soon. The reason is that a longer way needs
a longer time to pass and thus the smell of pheromone melts faster
here than at a shorter way. As ants make many passes back and forth,
more and more travelers prefer the shorter way, while the longer
way becomes empty.

It
is notable, that a single ant is rather random system, while a collective
becomes a deterministic system. The same we have in physics: a single
particle is random (according to laws of quantum mechanics), while
a huge collective behaves in a deterministic manner.

Classical
body (= a huge collective of particles) minimizes
a physical quantity named action, while it moves. Say,
a classical beam of light minimizes the length of propagation way
(Fermat’s
principle). Doesn’t it look too much like what an ant
colony makes?

Many
paths and many passes, as we believe, is a too strong analogy to
ignore. We believe that Feynman’s formulation of quantum mechanics
(“many – paths formulation”) paired with transactional interpretation
(assuming passages back and forth) shows that elementary particles
are complex adaptive systems very much like those we have in living
nature.

Which are the perspectives of hidden - time hypothesis?

We
now want to point only 2 features of our hidden time program, which
we believe will attract new generation of courage mathematicians
and revolutionary physicists.

1)
3 passes of signal, or, in other view, 3 kinds of signals (emit
scout, send scout back and send final choice or final refusal) imply
3 kinds of elementary operations an electric charge can do (we mean
that these are charged particles that emit and scatter photons).

These
operations can be implemented by a single “device” using a unified
algorithm; either 3 distinct algorithms, implemented by 3 distinct
devices, can perform the whole procedure.

Thus
we are courage to suggest that hidden time concept implies by itself
existence of partial charges in addition to whole charges. In other
words, hidden time concept “predicts” quarks. We are not confused
by the fact that they are already openedJ, because nowadays quantum
electrodynamics, which describes photons and electrons, and quantum
chromodynamics, which describes quarks, are different theories.
We suggest a unified approach.

2)
we suggest that hidden time program can possibly lead to uniting
quantum theory and gravity. In other words, we claim to compete
to superstrings
theory and quantum
loop gravity theory at their home fields.

Our basic hypothesis
here, which can quite be wrong, of courseJ, is as follows. To be
true, we don’t talk about attraction of masses yet. Instead we suggest
that the idea of exchanging signals in hidden time provides for
free slowing of physical time.

Imagine
that some particle develops scout signals from lots of other particles.
The core of hidden time approach is that all queries stand in a
queue until the “detector” fully develops the first query in this
queue. “Fully” means sending the scout back and waiting until final
confirmation or final refusal from corresponding has come (in hidden
time, of course). See our preprint
for technical details.

Imagine
that the “detector” particle is inside a huge bulk of other particles.
Although all the development of scout signals occurs in hidden time,
a large number of queries (= scout signals) indirectly “stops for
a while” physical time.

These
two hypotheses are a qualitative estimation only. They can quite
turn to be wrong! But we believe they deserve a more detailed analysis.
Even if they are incorrect, it is very important to test that a
very simple concept like hidden time can indeed or cannot unify
quarks, light and gravity.

Our
understanding of being a scientist tells us we have no right to
pass by such a simple and possibly powerful concept. Because, even
if proved to be wrong, it will provide us some very fundamental
knowledge about what our Universe cannot be. Namely, a web of messaging
agents.

References (1) R. P. Feynman.
“QED – a strange theory of light and matter”. Princeton, New Jersey:
Princeton University Press, 1985.
(2) R. P. Feynman, A. Hibbs. “Quantum mechanics and path integrals”.
McGraw-Hill Book Company. New York 1965.
(3) Avshalom C. Elitzur, Shahar Dolev, Anton Zeilinger. “Time –
reversed EPR and Choice of Histories in Quantum Mechanics”. ArXiv:
quant-ph/0205182.