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Article
How
bees can possibly explain quantum paradoxes
par
Pavel V. Kurakin, George G. Malinetskii
Keldysh Institute of Applied Mathematics http://www.keldysh.ru/
Russian Academy of Sciences, Moscow
kurakin.pavel@gmail.com
Welcome to our “Yahoo!” - group to discuss
hidden time http://groups.yahoo.com/group/hidtime
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Note:
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. AI.
Fourmilière en dôme, avec fourmis
fourrageant, source http://membres.lycos.fr/dmouli/
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.
Here’s
a very explaining citation from another
paper by John Cramer:
“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.
The novelty
of our approach at Keldysh
Institute of Applied Mathematics in Moscow is to unite
the two approaches and to put these passes into hidden time.
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.
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