Quantum Field Theory (QFT) is the fundamental dynamical framework for a successful description of the microworld, from molecules to quarks and leptons and their interactions.

The Standard Model of elementary particle physics, encompassing the strong and electroweak interactions of quarks and leptons, the most fundamental point-like constituents of matter presently known, is fully and wholy based on QFT [37].

Nevertheless, when gravitational interactions are included at the quantum level, the whole construction collapses! Uncontrollable infinities appear all over the place, thus rendering the theory inconsistent. This a well-known and grave problem, being with us for a long, long time now.

The resistance of gravitational interactions to conventionally unify with the other (strong and electroweak) interactions strongly suggests that we are in for changes both at the QFT front and at the gravitational front, so that these two frameworks could become eventually compatible with each other.

As usual in science, puzzles, paradoxes and impasses, that may lead to major crises, bring with them the seeds of dramatic and radical changes, if the crisis is looked upon as an opportunity.

In our case at hand, since the Standard Model, based upon standard QFT, works extremely well, we had not been forced to scrutinize further the basic principles of the orthodox, Copenhagen-like QFT. Indeed, the mysterious "collapse" of the wavefunction, as discussed in section 3, remained always lacking a dynamical mechanism responsible for its triggering.

Had gravity been incorporated in this conventional unification scheme, and since it is the last known interaction, any motivation for changing the ground rules of QFT, so that a dynamical mechanism triggering the "collapse" of the wavefunction would be provided, would be looked upon rather suspiciously and unwarranted.

Usually, to extremely good approximation, one can neglect gravitational interaction effects, so that the standard QFT applies. Once more, usually should not be interpreted as always.

Indeed, for most applications of QFT in particle physics, one assumes that we live in a fixed, static, smooth spacetime manifold, e.g., a Lorentz spacetime manifold characterized by a Minkowski metric (guv denotes the metric tensor):

ds^2 = guv dx^u dx^v = dr^2 - c ^2 dt ^2 (18)

satisfying Einstein's special relativity principle.

In such a case, standard QFT rules apply and we get the miraculously successful Standard Model of particle physics.

Unfortunately, this is not the whole story. We don't live exactly in a fixed, static, smooth spacetime manifold. Rather, the universe is expanding, thus it is not static, and furthermore unavoidable quantum fluctuations of the metric tensor guv (x) defy the fixed and smooth description of the spacetime manifold, at least at very short distances.

Very short distances here do not refer to the nucleus, or even the proton radius of 10^-13 cm, but to distances comparable to the Planck length of 10^-33 cm, which in turn is related to the smallness of GN, Newton's gravitational constant.

In particle physics we find it convenient towork in a system of units where c = h = kB = 1, where c is the speed of light, h is the Planck constant, and kB is the Boltzman constant. Using such a system of units one can write

GN = 1/Mp^2 = Lp^2 = 10^-66 cm^2 (19)

where Mp = 10^19 Gev, and Lp = 10^-33 cm.

It should be clear that as we reach very short distances of O(Lp), fluctuations of the metric

and thus the spacetime manifold is not well defined anymore, and it may even be that the very notion of a spacetime description evaporates at such Planckian distances! So, it becomes apparent that if we would like to include quantum gravity as an item in our unification program checklist, we should prepare ourselves for major revamping of our conventional ideas about quantum dynamics and the structure of spacetime.

A particularly interesting, well-motivated, and well-studied example of a singular spacetime background is that of a black hole (BH) [38]. These objects are the source of a singularly strong gravitational field, so that if any other poor objects (including light) cross their "horizon", they are trapped and would never come out of it again. Once in, there is no way out!

Consider, for example, a quantum system consisting of two particles a and b in loose interaction with each other, so that we can describe its quantum pure state by

Imagine now, that at some stage of its evolution the quantum system gets close to a black hole, and that for some unfortunate reason particle b decides to enter the BH horizon. From then on, we have no means of knowing or determining the exact quantum state of the b particle, thus we have to describe our system not anymore as a pure state... , but as a mixed state

The correct equation is

according to our discussion in section 3 (see (10,11)). But such an evolution of a pure state into a mixed state is not possible within the conventional framework of quantum mechanics as represented by (3) or (9). In conventional QM purity is eternal. So, something drastic should occur in order to be able to accomodate such circumstances related to singularly strong gravitational fields.

Actually, there is much more than meets the eye. If we consider that our pure state of the two particles is a quantum fluctuation of the vacuum, then we are in more trouble. The vacuum always creates particle-antiparticle pairs that almost momentarily, and in the absence of strong gravitational fields, annihilate back to the vacuum, a rather standard well-understood quantum process. In the presence of a black hole, there is a very strong gravitational force that may lure away one of the two particles and "trap" it inside the BH horizon, leaving the other particle hanging around and looking for its partner. Eventually it wanders away from the BH and it may even be detected by an experimentalist at a safe distance from the BH. Because she does not know or care about details of the vacuum, she takes it that the BH is decaying by emitting all these particles that she detects.

In other words, while classical BH is supposed to be stable, in the presence of quantum matter, BH do decay, or more correctly radiate, and this is the famous Hawking radiation [38, 39]. The unfortunate thing is that the Hawking radiation is thermal, and this means that we have lost vast amounts of information dragged into the BH. A BH of mass MBH is characterized by a temperature TBH, an entropy SBH and a horizon radius RBH [38, 39, 40]

satisfying, of course, the first thermodynamic law, dMBH = TBHdSBH.

The origin of the huge entropy (MBH^2) should be clarified.

Statistical physics teaches us that the entropy of a system is a measure of the information unavailable to us about the detailed structure of the system.

The entropy is given by the [logarithm of the] number of different possible congurations of the fundamental constituents of the system, resulting always in the same values for the macroscopic quantities characterizing the system, e.g., temperature, pressure, magnetization, etc.

Clearly, the fewer the macroscopic quantities characterizing the system, the larger the entropy and thus the larger the lack of information about the system. In our BH paradigm, the macroscopic quantities that characterize the BH, according to (20), is only it mass MBH.

In more complicated BHs, they may posses some extra "observables" like electric charge or angular momentum, but still, it is a rather small set of "observables"!

This fact is expressed as the "No-Hair Theorem" [38], i.e., there are not many dierent long range interactions around, like gravity or electromagnetism, and thus we cannot "measure" safely and from a distance other "observables", beyond the mass (M), angular momentum ( L), and electric charge (Q). In such a case, it becomes apparent that we may have a huge number of different configurations that are all characterized by the same M;Q; L, and thus the huge entropy (20).

Hawking realized immediately that his BH dynamics and quantum mechanics were not looking eye toeye, and he proposed in 1982 that we should generalize quantum mechanics to include the pure state to mixed state transition, which is equivalent to abandoning the quantum superposition principle (as expressed in (3) or (9)), for some more advanced quantum dynamics [41].

In such a case we should virtually abandon the description of quantum states by wavefunctions or state vectors ... and use the more accomodating density matrix description, as discussed in section 3, but with a modied form for (9).

Indeed, in 1983 Ellis, Hagelin, Srednicki, and myself proposed (EHNS in the following) [42] the following modified form of the conventional Eq. (9)

which accomodates the pure state ---> mixed state transition through the extra term

The existence of such an extra term is characteristic of "open" quantum systems, and it has been used in the past for practical reasons.

What EHNS suggested was more radical. We suggested that the existence of the extra term not due to practical reasons but to some fundamental, dynamical reasons having to do with quantum gravity.

Universal quantum fluctuations of the gravitational field (guv) at Planckian distances .... create a very dissipative and fluctuating quantum vacuum, termed spacetime foam, which includes virtual Planckian-size black holes.

Thus, quantum systems never evolve undisturbed, even in the quantum vacuum, but they are continously interacting with the spacetime foam, that plays the role of the environment, and which "opens" spontaneously and dynamically any quantum system.

Clearly, the extra term ... leads to a spontaneous dynamical decoherence that enables the system to make a transition from a pure to a mixed state accomodating Hawking's proposal [41].

Naive approximate calculations indicate that

where E is the energy of the system, suggesting straight away that our "low-energy" world (E/MP = 10^-16] of quarks, leptons, photons, etc is, for most cases, extremely accurately described by the conventional Eq. (9).

Of course, in such cases is not offensive to talk about wavefunctions, quantum parallelism, and the likes. On the other hand, as observed in 1989 by Ellis, Mohanty, and myself [43], if we try to put together more and more particles, we eventually come to a point where the decoherence term ...is substantial and decoherence is almost instantaneous, leading in other words to an instantaneous collapse of the wavefunction for large bodies, thus making the transition from quantum to classical dynamical and not by decree!

In a way, the Hawking proposal [41], while leading to a major conflict between the standard QM and gravity, motivated us [42, 43] to rethink the "collapse" of the wavefunction, and it seemed to contain the seeds of a dynamical mechanism for the "collapse" of the wavefunction.

Of course, the reason that many people gave a "cold shoulder" to the Hawking proposal was the fact that his treatment of quantum gravity was semiclassical, and thus it could be that all the Hawking excitement was nothing else but an artifact of the bad/crude/unjustifiable approximations.

Thus, before we proceed further we need to treat better Quantum Gravity (QG). String Theory (ST) does just that. It provided the first, and presently only known framework for a consistently quantized theory of gravity [44].

As its name indicates, in string theory one replaces point like particles by one-dimensional, extended, closed, string like objects, of characteristic length 10^-33 cm.

In ST one gets an automatic, natural unification of all interactions including quantum gravity, which has been the Holy Grail for particle physics/physicists for the last 70 years!

It is thus only natural to address the hot issues of black hole dynamics in the ST framework [44].

Indeed, in 1991, together with Ellis and Mavromatos (EMN in the following) we started a rather elaborate program of BH studies, and eventually, we succeeded in developing a new dynamical theory of string black holes [45].

One first observes that in ST there is an infinity of particles of different masses, including the Standard Model ones, corresponding to the different excitation modes of the string. Most of these particles are unobservable at low energies since they are very massive M > 10 ^19 GeV) and thus they cannot be produced in present or future accelerators, which may reach by the year 2005 about 10^4 GeV.

Among the infinity of different types of particles available, there is an infinity of massive "gauge-boson"- like particles, generalizations of the W-boson mediating the weak interactions,

thus indicating the existence of an infinity of spontaneously broken gauge symmetries, each one characterized by a specific charge, generically called Qi.

It should be stressed that, even if these stringy type, spontaneously broken gauge symmetries do not lead to long-range forces, thus classically their Qi charges are unobservable at long distances, they do become observable at long distances at the quantum level.

Utilizing the quantum Bohm-Aharonov effect [46], where one "measures" phase shifts proportional to Qi, we are able to "measure" the Qi charges from a desirable distance!

This kind of Qi charge, if available on a black hole, is called sometimes and for obvious reasons, quantum hair [47].

From the infinity of stringy symmetries, a relevant for us here, specific, closed subset has been identified, known by the name of

with many interesting properties [48]. Namely, these W{1+ infinity} symmetries cause the mixing [49], in the presence of singular spacetime backgrounds like a BH, between the massless string modes, containing the attainable localizable low energy world (quarks, leptons, photons, etc), let me call if the W1-world, and the massive O (10^19 Gev) string modes of a very characteristic type, the so-called global states.

They are called global states because they have the peculiar and unusual characteristic to have fixed energy E and momentum p, and thus, by employing the uncertainty type relations, a la (8), they are extended over all space and time!

Clearly, while the global states are as physical and as real as any other states, still they are unattainable for direct observation to a local observer. They make themselves noticeable through their indirect effects, while interacting with, or agitating, the W1 world.

Let me call the global state space, the W2-world.

The second step in the EMN approach [45] was to concentrate on spherically symmetric 4-D stringy black holes, that can be effectively reduced to 2-D (1 space + 1 time) string black holes of the form discussed by Witten [50].

This effective dimensional reduction turned out to be very helpful because it enabled us to concentrate on the real issues of BH dynamics and bypass the technical complications endemic in higher dimensions. We showed that [45], as we suspected all the time, stringy BH are endorsed with W-hair, i.e., they carry an infinity of charges Wi , corresponding to the W{1+ infinity} symmetries, characteristic of string theories.

Then we showed that [45] this W-hair was sufficient to establish quantum coherence and avoid loss of information.

Indeed, we showed explicitly that [45] in stringy black holes there is no Hawking radiation, i.e., TBH = 0, and no entropy, i.e., SBH = 0!

In a way, as it should be expected from a respectable quantum theory of gravity, BH dynamics is not in conflict with quantum mechanics.

There are several intuitive arguments that shed light on the above, rather drastic results. To start with, the infinity of W-charges make it possible for the BH to encode any possible piece of information "thrown" at it by making a transition to an altered suitable configuration, consistent with very powerful selection rules.

It should be clear that if an infinite number of observable charges is needed to determine a configuration of the BH, then the "measure" of the unavailable-to-us information about this specific configuration should be virtually zero, i.e., SBH = 0!

The completeness of the W-charges, and for that matter of our argument, for establishing that SBH = 0, has been shown in two complementary ways.

Firstly, we have shown that [45] if we sum over the W-charges, like being unobservables, we reproduce the whole of Hawking dynamics!

Secondly, we have shown that the W{1+ infinity} symmetry acts as a phase-space volume (area in 2-D) preserving symmetry, thus entailing the absence of the W{1+ infinity} symmetry-violating ... extra term in (21), thus reestablishing (9), i.e., safe-guarding quantum coherence.

Actually, we have further shown that [45] stringy BHs correspond to "extreme BHs", i.e., BH with a harmless horizon, implying that the infinity of W-charges neutralize the extremely strong gravitional attraction. In such a case, there is no danger of seducing a member of a quantum system, hovering around the BH horizon, into the BH, thus eliminating the raison d'etre for Hawking radiation!

.... one may need to address a rather fundamental problem. The low-energy, attainable physical world W1, is made of electrons, quarks, photons, and the likes, all very well-known particles with well-known properties, i.e., mass, electric charge, etc. Nobody, though, has ever added to the identity card of these particles, lines representing their W-charges. In other words, the W1-world seems to be W-charge blind. How is it possible then for an electron falling into a stringy BH, to excite the BH through W{1+ infinity} -type interactions, to an altered configuration where it has been taken into account all the information carried by the electron? Well, here is one of the miraculous mechanisms, endemic in string theories. As discussed above, it has beeen shown [49] the in the presence of singular spacetime backgrounds, like the black hole one, a mixing, of purely stringy nature, is induced between states belonging to different "mass" levels, e.g., between a Local (L) state |a)L of the W1 world, with the global states (G) |ai)G of the W2 world

(22)

Notice that any resemblance between the symbols in (22) and (2) is not accidental and will be clarified later.

Thus, we see that when a low energy particle approaches/enters a stringy BH, its global state or W2 components while dormant in at spacetime backgrounds, get activated and this causes a quantum mechanical coherent BH transition, always satisfying a powerful set of selection rules.

In this new EMN scenario [45] of BH dynamics, if we start with a pure state .... , we end up with a pure state .... , even if our quantum system encountered a BH in its evolution, because we can monitor the ... part through the Bohm-Aharonov-like Wi charges! So everything looks dandy.

Alas, things get a bit more complicated, before they get simpler. We face here a new purely stringy phenomenon, that has to do with the global states, that lead to some dramatic consequences.

Because of their delocalized nature in spacetime, the global or W2-states can neither:

(a) appear as well-defined asymptotic states, nor

(b) can they be integrated out in a local path-integral formalism, thus defying their detection in local scattering experiments!!!

Once more, we have to abandon the language of the scattering matrix S, for the super-scattering matrix ...., or equivalently abandon the description of the quantum states by the wavefunction or state vector .... , for the density matrix [51].

Only this time it is for real. While string theory provides us with consistent and complete quantum dynamics, including gravitational interactions, it does it in such a way that effectively "opens" our low energy attainable W1 world. This is not anymore a possible artifact of our treatment of quantum gravity, this is the effective quantum mechanics [51, 5, 6] that emerges from a consistent quantum theory of gravity.

An intuitive way to see how it works is to insert .... as given in (22) into (9), where ...., collect all the .... W2 dependent parts, treat them as noise, and regard (9) as describing effectively some quantum Brownian motion,

This is the connection to the Bohm-Vigier theories!

i.e., regard it as a stochastic differential equation, or Langevin equation for

where the pi's depend on ..... the W2 world in a stochastic way [52].

In the EMN approach [51, 52, 5, 6] the emerging equation, that reproduces the EHNS equation (21) with an explicit form for the extra term, reads (dropping the W1 subscripts)

(23)

where Gij denotes some positive definite "metric" in the string field space, while the beta term is a characteristic function .... representing collectively the agitation of the W2 world on the W1 dynamics.

Before I get into the physical interpretation and major consequences of (23), let us collect its most fundamental, system-independent properties, following directly from its specific structure/form [51, 5, 6]

I) Conservation of probability P (see (5) and discussion above (9))

II) Conservation of energy, on the average

III) Monotonic increase in entropy/microscopic arrow of time

due to the positive definiteness of the metric Gij mentioned above, and thus automatically and naturally implying a microscopic arrow of time.

Rather remarkable and useful properties indeed. Let us try to discuss the physical interpretation of (23) and its consequences.

In conventional QM, as represented by (9), one has a deterministic, unitary evolution of the quantum system, and it is only when one feels compelled to "measure"/"observe" the system, that the probabilistic element of QM emerges.

One, of course, tacitly assumes the existence of a fixed, smooth spacetime background that does not "disturb" the system, acting simply as the arena in which things are happening, and thus leaving the system "closed". The characteristics of such "closed" systems include, of course, conservation of energy and no definite arrow of time or no flow of time, which is reflected in the forms of (9), (18), which are invariant under t --> -t .

When we decide to "open" the system we basically perform a "measurement", i.e., we force the system to "decide" what it wants to be, by choosing a very specific state, out of many coexisting possible ones, i.e., we are talking about the "collapse" of the wavefunction.

That's in a nutshell the Copenhagen interpretation of QM, leaving too much to be desired, and too much on the "eye" of the "observer"! We need to do better. In the density matrix mechanics, as represented by (23), and as emerged, in one interpretation from string theory, one has a stochastic, indeterministic evolution of the quantum system, ab initio, due to the unavoidable existence of spacetime foam.

The uncontrollable, universal quantum fluctuations of the spacetime metric at very short distances ..., containing creation and annihilation of virtual Planckian-size BHs, agitate through the global or W2-world states, our low-energy quantum system, rendering it dynamically and spontaneously "open".

This is an objective, universal mechanism, independent of any "observer", that is always "up and working", thus eroding the quantum coherence and eventually leading to a dynamical, spontaneous collapse.

It should be clear that the natural "opening" of our quantum system is due to our inability to take into account all the detailed effects of the global states, because of their delocalized nature, and thus we do truncate them, arriving at the Procrustean Principle, a new universal principle [6] that goes beyond the standard uncertainty principle (8).

Furthermore, since this new dynamical mechanism of the "collapse" of the wavefunction, as emerged in the EMN approach [51, 5, 6], is an objective spontaneous, time-ordered, and thus an orchestrated one, I propose here to call it synchordic collapse.

Schematically, one can represent this new mechanism of the "collapse" of the wavefunction, by using (22), as follows

which makes it apparent that the global or W2-world states are the agents of the synchrodic collapse, as being the raison d'etre of stochasticity in quantum dynamics.

Also, notice the similarity between (2) and (27), rather remarkable and very suggestive! The most amazing and astonishing thing is that, despite the well-known fact that usually open, dissipative systems defy quantization and energy conservation, our naturally "open" system, as represented by (23) and as explicitly indicated in (24), (25), and (26), is different [53, 54]. It is susceptible to quantization, it conserves energy in the mean, and monotonically increases its entropy, leading to loss of information, quantitatively expressed as quantum decoherence, and thus supplementing us with a very natural, universal, objective microscopic arrow of time!

In the EMN approach [51, 5, 6], time is a statistical measure of the interactions (quantum gravitational friction) between the local, low-energy world W1 and the global or W2-world states, in the presence of singular spacetime backgrounds (spacetime foam).

The strong emerging correlation between loss of information, quantum decoherence leading to wavefunction collapse and the dynamical appearance of flowing time, I believe is unprecedented in physics.

Clearly, the role of the magic extra term proportional to beta j in (23), is multifunctional, as exemplified by making use of the dissipation- fluctuation theorem of statistical mechanics [14]. It can be viewed as a dissipative term that destroys quantum coherence, by damping the off-diagonal elements and also it can be seen as a noise term able to drive the system away from its equilibrium position and, after some time, bring it back to the same position or bring it to some other equilibrium position.

In other words, we may interpret (23) as a renormalization group equation (RGE), as discussed in section 2, describing the evolution of the system between different phases, each corresponding to one of the infinite spontaneously broken W{1+ infinity} symmetries.

Clearly, at an equilibrium position, or at a critical point, all beta j do vanish, thus recovering naturally (9) from (23), or equivalently recovering standard QFT as applied to particle physics for the past 70 years.

In principle, in fixed, smooth spacetime backgrounds, hopefully corresponding to critical points in our new stringy language, there is a decoupling of the global states from the local, low-energy states in (22), i.e., all cg's do vanish, and thus implying vanishing beta j in (23).

Before though, we are carried away from the highly promising stringy big quantum picture that emerges here, it should pay to have a closer look at some numerical details, if not for any other reason, just as a reality check! Indeed, one can work out, using (23), the time that it takes for quantum decoherence, or equivalently the quantum coherence lifetime tau(c), as defined by the off-diagonal elements damping factor [43]:

for a system of N constituents of mass m, assuming that its center of mass pinned down within delta X, and is given by

(28)

where M = 10^18 Gev (characteristic string scale of 1/10 Planck mass). What about the value of m? The most natural value for it would be m = m nucleon = 1 GeV for the following reason. Our attainable low-energy world, as far as we know is made up of electrons, protons, and neutrons: that is what constitute us, i.e., our cells, our proteins, our DNA, etc, and also that is what everything else we use, i.e., the "apparatus", is made of.

Of course, protons and neutrons are mainly made of up (u) and down (d) constituent quarks, but for my arguments they are of comparable mass and thus would give the same results.

Now, since the bulk of matter is due to nucleons, and not to electrons (mnucl = 1836me ), the shortest coherence lifetimes that we are interested in would be provided by mnucl.

Furthermore, independent of the complicated structure that you may consider, e.g., a complicated protein polymer structure, a la microtubules (MTs), the virtual Planckian BHs have such high energy that they "see" and interact/agitate with the most fundamental constituents of the complicated structure, i.e., up and down quarks and electrons, thus as explained above, justifying the identification m = mnucl = 1 GeV in (28).

Thus, using M = 10 18 GeV, m = 1 GeV, and delta x = 1nanometer, (28) yields

a rather suggestive formula. In the case of a single (N = 1) hydrogen atom, (29) becomes tau H = 10 ^16 sec, the present age of the universe! In other words, standard QM applies extremely accurately in microsystems, as of course, we want, because of the spectacular successes of QM in the microworld.

On the other hand, if we take a piece of ice, containing say N = NAvogadro = 10^ 24 nucleons, then we get tau ice = 10^-8 sec. a rather short-lived quantum coherence implying that for macroscopic objects .... QM rules fail and classical physics emerges naturally, dynamically, spontaneously, and objectively!

The Schroedinger's cat paradox is automatically resolved: within within 10^-8 sec the cat would be dead or alive, not the ....... Furthermore, the "measurement"/"observation" problem gets a similar satisfactory resolution. Indeed, performing a "measurement"/"observation" on a quantum system implies bringing it in "interaction" with some suitable macroscopic apparatus thus triggering an almost instantaneous "collapse" of the wavefunction of the quantum system, as suggested by (29) ...

The magic step, as indicated in (7), and which constitutes basically the one-half of quantum mechanics it does need not to be postulated, but it comes out from the stochastic dynamics, as provided by the agitating global or W2-world states.

It should not escape our notice that there is no quantum-classical border, but a continous and smooth transition.

Furthermore, as (28) indicates, the Avogadro number, a measure of the macroscopicity of the system, is basically dynamically determined to be the inverse of the dimensionless product of the gravitational strength times the characteristic strong interaction scale ... times the electromagnetic fine structure constant ...

It is highly remarkable that stringy modified QM or density matrix mechanics is offering us, see ((23),(27)), a new unified approach to quantum dynamics, by turning a deterministic wave-type equation into a stochastic differential equation able to successfully describe both evolution and "measurement" of quantum systems.

At the same time, a unified picture of the quantum and classical world is emerging, as promised in section 3, without the need of raising artificial borders between the quantum and the classical, the transition between them is dynamical and smooth.

The fundamental property of string theory that allows all these "miraculous events" to occur is its defining property, i.e., the need of 2-dimensions (1 space + 1 time) to describe a 1-dimensional (1-D) extended object and its accompanying infinity of excitation modes/particles, due exactly to its extended nature.

While a pointlike particle "runs" on a world-line, a string sweeps a world-sheet.

Eventually, all 4-D spacetime physics would be mappings of corresponding physics in the 2-D stringy world-sheet.

The existence of the W{1+ infinity} symmetry was first established in 2-D "world sheet" physics and then mapped into 4-D spacetime physics.

The infinity of spontaneously broken stringy gauge symmetries, and the very existence of the global states, somehow can trace back their origin to the 2-dimensionality of the world-sheet!

In other words, the stringy nature of the modified quantum mechanics prevails, as should be apparent at each and every turn!

The alert reader may have already noticed the stunning similarity between the string dynamics in singular spacetime backgrounds, like black holes and spacetime foam, and the brain mechanics presented in section 2.

Presence or lack of quantum coherence and its cause, the existence of an infinite number of possible equilibrium or critical points corresponding to an infinite number of spontaneously broken "gauge" (stringy) symmetries with appropriate selection rules, the possibility of "running" away from one equilibrium point, and eventually coming back to it, or end up at another equilibrium point, in a timely manner, etc, etc.

If we could only find a structure in the brain that it renders the EMN string dynamics [45, 51, 52, 5, 6] applicable, we would then be able to provide a rather explicit answer to most of the problems raised in sections 2 and 4. Namely, the binding problem; how the brain represents a physical, objectively real, owing time? free will, etc, etc. Well, these brain structures do exist and they are called microtubules.