Nomological Unification and Phenomenology of Gravitation. Thought of the Day 110.0

Calabi-Yau-manifold

String theory, which promises to give an all-encompassing, nomologically unified description of all interactions did not even lead to any unambiguous solutions to the multitude of explanative desiderata of the standard model of quantum field theory: the determination of its specific gauge invariances, broken symmetries and particle generations as well as its 20 or more free parameters, the chirality of matter particles, etc. String theory does at least give an explanation for the existence and for the number of particle generations. The latter is determined by the topology of the compactified additional spatial dimensions of string theory; their topology determines the structure of the possible oscillation spectra. The number of particle generations is identical to half the absolute value of the Euler number of the compact Calabi-Yau topology. But, because it is completely unclear which topology should be assumed for the compact space, there are no definitive results. This ambiguity is part of the vacuum selection problem; there are probably more than 10100 alternative scenarios in the so-called string landscape. Moreover all concrete models, deliberately chosen and analyzed, lead to generation numbers much too big. There are phenomenological indications that the number of particle generations can not exceed three. String theory admits generation numbers between three and 480.

Attempts at a concrete solution of the relevant external problems (and explanative desiderata) either did not take place, or they did not show any results, or they led to escalating ambiguities and finally got drowned completely in the string landscape scenario: the recently developed insight that string theory obviously does not lead to a unique description of nature, but describes an immense number of nomologically, physically and phenomenologically different worlds with different symmetries, parameter values, and values of the cosmological constant.

String theory seems to be by far too much preoccupied with its internal conceptual and mathematical problems to be able to find concrete solutions to the relevant external physical problems. It is almost completely dominated by internal consistency constraints. It is not the fact that we are living in a ten-dimensional world which forces string theory to a ten-dimensional description. It is that perturbative string theories are only anomaly-free in ten dimensions; and they contain gravitons only in a ten-dimensional formulation. The resulting question, how the four-dimensional spacetime of phenomenology comes off from ten-dimensional perturbative string theories (or its eleven-dimensional non-perturbative extension: the mysterious, not yet existing M theory), led to the compactification idea and to the braneworld scenarios, and from there to further internal problems.

It is not the fact that empirical indications for supersymmetry were found, that forces consistent string theories to include supersymmetry. Without supersymmetry, string theory has no fermions and no chirality, but there are tachyons which make the vacuum instable; and supersymmetry has certain conceptual advantages: it leads very probably to the finiteness of the perturbation series, thereby avoiding the problem of non-renormalizability which haunted all former attempts at a quantization of gravity; and there is a close relation between supersymmetry and Poincaré invariance which seems reasonable for quantum gravity. But it is clear that not all conceptual advantages are necessarily part of nature, as the example of the elegant, but unsuccessful Grand Unified Theories demonstrates.

Apart from its ten (or eleven) dimensions and the inclusion of supersymmetry, both have more or less the character of only conceptually, but not empirically motivated ad-hoc assumptions. String theory consists of a rather careful adaptation of the mathematical and model-theoretical apparatus of perturbative quantum field theory to the quantized, one-dimensionally extended, oscillating string (and, finally, of a minimal extension of its methods into the non-perturbative regime for which the declarations of intent exceed by far the conceptual successes). Without any empirical data transcending the context of our established theories, there remains for string theory only the minimal conceptual integration of basic parts of the phenomenology already reproduced by these established theories. And a significant component of this phenomenology, namely the phenomenology of gravitation, was already used up in the selection of string theory as an interesting approach to quantum gravity. Only, because string theory, containing gravitons as string states, reproduces in a certain way the phenomenology of gravitation, it is taken seriously.

10 or 11 Dimensions? Phenomenological Conundrum. Drunken Risibility.

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It is not the fact that we are living in a ten-dimensional world which forces string theory to a ten-dimensional description. It is that perturbative string theories are only anomaly-free in ten dimensions; and they contain gravitons only in a ten-dimensional formulation. The resulting question, how the four-dimensional spacetime of phenomenology comes off from ten-dimensional perturbative string theories (or its eleven-dimensional non-perturbative extension: the mysterious M theory), led to the compactification idea and to the braneworld scenarios.

It is not the fact that empirical indications for supersymmetry were found, that forces consistent string theories to include supersymmetry. Without supersymmetry, string theory has no fermions and no chirality, but there are tachyons which make the vacuum instable; and supersymmetry has certain conceptual advantages: it leads very probably to the finiteness of the perturbation series, thereby avoiding the problem of non-renormalizability which haunted all former attempts at a quantization of gravity; and there is a close relation between supersymmetry and Poincaré invariance which seems reasonable for quantum gravity. But it is clear that not all conceptual advantages are necessarily part of nature – as the example of the elegant, but unsuccessful Grand Unified Theories demonstrates.

Apart from its ten (or eleven) dimensions and the inclusion of supersymmetry – both have more or less the character of only conceptually, but not empirically motivated ad-hoc assumptions – string theory consists of a rather careful adaptation of the mathematical and model-theoretical apparatus of perturbative quantum field theory to the quantized, one-dimensionally extended, oscillating string (and, finally, of a minimal extension of its methods into the non-perturbative regime for which the declarations of intent exceed by far the conceptual successes). Without any empirical data transcending the context of our established theories, there remains for string theory only the minimal conceptual integration of basic parts of the phenomenology already reproduced by these established theories. And a significant component of this phenomenology, namely the phenomenology of gravitation, was already used up in the selection of string theory as an interesting approach to quantum gravity. Only, because string theory – containing gravitons as string states – reproduces in a certain way the phenomenology of gravitation, it is taken seriously.

But consistency requirements, the minimal inclusion of basic phenomenological constraints, and the careful extension of the model-theoretical basis of quantum field theory are not sufficient to establish an adequate theory of quantum gravity. Shouldn’t the landscape scenario of string theory be understood as a clear indication, not only of fundamental problems with the reproduction of the gauge invariances of the standard model of quantum field theory (and the corresponding phenomenology), but of much more severe conceptual problems? Almost all attempts at a solution of the immanent and transcendental problems of string theory seem to end in the ambiguity and contingency of the multitude of scenarios of the string landscape. That no physically motivated basic principle is known for string theory and its model-theoretical procedures might be seen as a problem which possibly could be overcome in future developments. But, what about the use of a static background spacetime in string theory which falls short of the fundamental insights of general relativity and which therefore seems to be completely unacceptable for a theory of quantum gravity?

At least since the change of context (and strategy) from hadron physics to quantum gravity, the development of string theory was dominated by immanent problems which led with their attempted solutions deeper. The result of this successively increasing self- referentiality is a more and more enhanced decoupling from phenomenological boundary conditions and necessities. The contact with the empirical does not increase, but gets weaker and weaker. The result of this process is a labyrinthic mathematical structure with a completely unclear physical relevance

Simultaneity

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Let us introduce the concept of space using the notion of reflexive action (or reflex action) between two things. Intuitively, a thing x acts on another thing y if the presence of x disturbs the history of y. Events in the real world seem to happen in such a way that it takes some time for the action of x to propagate up to y. This fact can be used to construct a relational theory of space à la Leibniz, that is, by taking space as a set of equitemporal things. It is necessary then to define the relation of simultaneity between states of things.

Let x and y be two things with histories h(xτ) and h(yτ), respectively, and let us suppose that the action of x on y starts at τx0. The history of y will be modified starting from τy0. The proper times are still not related but we can introduce the reflex action to define the notion of simultaneity. The action of y on x, started at τy0, will modify x from τx1 on. The relation “the action of x on y is reflected to x” is the reflex action. Historically, Galileo introduced the reflection of a light pulse on a mirror to measure the speed of light. With this relation we will define the concept of simultaneity of events that happen on different basic things.

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Besides we have a second important fact: observation and experiment suggest that gravitation, whose source is energy, is a universal interaction, carried by the gravitational field.

Let us now state the above hypothesis axiomatically.

Axiom 1 (Universal interaction): Any pair of basic things interact. This extremely strong axiom states not only that there exist no completely isolated things but that all things are interconnected.

This universal interconnection of things should not be confused with “universal interconnection” claimed by several mystical schools. The present interconnection is possible only through physical agents, with no mystical content. It is possible to model two noninteracting things in Minkowski space assuming they are accelerated during an infinite proper time. It is easy to see that an infinite energy is necessary to keep a constant acceleration, so the model does not represent real things, with limited energy supply.

Now consider the time interval (τx1 − τx0). Special Relativity suggests that it is nonzero, since any action propagates with a finite speed. We then state

Axiom 2 (Finite speed axiom): Given two different and separated basic things x and y, such as in the above figure, there exists a minimum positive bound for the interval (τx1 − τx0) defined by the reflex action.

Now we can define Simultaneity as τy0 is simultaneous with τx1/2 =Df (1/2)(τx1 + τx0)

The local times on x and y can be synchronized by the simultaneity relation. However, as we know from General Relativity, the simultaneity relation is transitive only in special reference frames called synchronous, thus prompting us to include the following axiom:

Axiom 3 (Synchronizability): Given a set of separated basic things {xi} there is an assignment of proper times τi such that the relation of simultaneity is transitive.

With this axiom, the simultaneity relation is an equivalence relation. Now we can define a first approximation to physical space, which is the ontic space as the equivalence class of states defined by the relation of simultaneity on the set of things is the ontic space EO.

The notion of simultaneity allows the analysis of the notion of clock. A thing y ∈ Θ is a clock for the thing x if there exists an injective function ψ : SL(y) → SL(x), such that τ < τ′ ⇒ ψ(τ) < ψ(τ′). i.e.: the proper time of the clock grows in the same way as the time of things. The name Universal time applies to the proper time of a reference thing that is also a clock. From this we see that “universal time” is frame dependent in agreement with the results of Special Relativity.

Duality’s Anti-Realism or Poisoning Ontological Realism: The Case of Vanishing Ontology. Note Quote.

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If the intuitive quality of the external ontological object is diminished piece by piece during the evolutionary progress of physical theory (which must be acknowledged also in a hidden parameter framework), is there any core of the notion of an ontological object at all that can be trusted to be immune against scientific decomposition?

Quantum mechanics cannot answer this question. Contemporary physics is in a quite different position. The full dissolution of ontology is a characteristic process of particle physics whose unfolding starts with quantum mechanics and gains momentum in gauge field theory until, in string theory, the ontological object has simply vanished.

The concept to be considered is string duality, with the remarkable phenomenon of T-duality according to which a string wrapped around a small compact dimension can as well be understood as a string that is not wrapped but moves freely along a large compact dimension. The phenomenon is rooted in the quantum principles but clearly transcends what one is used to in the quantum world. It is not a mere case of quantum indeterminacy concerning two states of the system. We rather face two theoretical formulations which are undistinguishable in principle so that they cannot be interpreted as referring to two different states at all. Nevertheless the two formulations differ in characteristics which lie at the core of any meaningful ontology of an external world. They differ in the shape of space-time and they differ in form and topological position of the elementary objects. The fact that those characteristics are reduced to technical parameters whose values depend on the choice of the theoretical formulation contradicts ontological scientific realism in the most straightforward way. If a situation can be described by two different sets of elementary objects depending on the choice of the theoretical framework, how can it make sense to assert that these ontological objects actually exist in an external world?

The question gets even more virulent as T-duality by no means remains the only duality relation that surfaces in string theory. It turns out that the existence of dualities is one of string theory’s most characteristic features. They seem to pop up wherever one looks for them. Probably the most important role played by duality relations today is to connect all different superstring theories. Before 1995 physicists knew 5 different types of superstring theory. Then it turned out that these 5 theories and a 6th by then unknown theory named ‘M-theory’ are interconnected by duality relations. Two types of duality are involved. Some theories can be transformed into each other through inversion of a compactification radius, which is the phenomenon we know already under the name of T-duality. Others can be transformed into each other by inversion of the string coupling constant. This duality is called S-duality. Then there is M-theory, where the string coupling constant is transformed into an additional 11th dimension whose size is proportional to the coupling strength of the dual theory. The described web of dualities connects theories whose elementary objects have different symmetry structure and different dimensionality. M-theory even has a different number of spatial dimensions than its co-theories. Duality nevertheless implies that M-theory and the 5 possible superstring theories only represent different formulations of one single actual theory. This statement constitutes the basis for string theory’s uniqueness claims and shows the pivotal role played by the duality principle.

An evaluation of the philosophical implications of duality in modern string theory must first acknowledge that the problems to identify uniquely the ontological basis of a scientific theory are as old as the concept of invisible scientific objects itself. Complex theories tend to allow the insertion of ontology at more than one level of their structure. It is not a priori clear in classical electromagnetism whether the field or the potential should be understood as the fundamental physical object and one may wonder similarly in quantum field theory whether that concept’s basic object is the particle or the field. Questions of this type clearly pose a serious philosophical problem. Some philosophers like Quine have drawn the conclusion to deny any objective basis for the imputation of ontologies. Philosophers with a stronger affinity for realism however often stress that there do exist arguments which are able to select a preferable ontological set after all. It might also be suggested that ontological alternatives at different levels of the theoretical structure do not pose a threat to realism but should be interpreted merely as different parameterisations of ontological reality. The problem is created at a philosophical level by imputing an ontology to a physical theory whose structure neither depends on nor predetermines uniquely that imputation. The physicist puts one compact theoretical structure into space-time and the philosopher struggles with the question at which level ontological claims should be inserted.

The implications of string-duality have an entirely different quality. String duality really posits different ‘parallel’ empirically indistinguishable versions of structure in spacetime which are based on different sets of elementary objects. This statement is placed at the physical level independently of any philosophical interpretation. Thus it transfers the problem of the lack of ontological uniqueness from a philosophical to a physical level and makes it much more difficult to cure. If theories with different sets of elementary objects give the same physical world (i. e. show the same pattern of observables), the elementary object cannot be seen as the unique foundation of the physical world any more. There seems to be no way to avoid this conclusion. There exists an additional aspect of duality that underlines its anti-ontological character. Duality does not just spell destruction for the notion of the ontological scientific object but in a sense offers a replacement as well.

Do there remain any loop-holes in duality’s anti-realist implications which could be used by the die-hard realist? A natural objection to the asserted crucial philosophical importance of duality can be based on the fact, that duality was not invented in the context of string theory. It is known since the times of P. M. Dirac that quantum electrodynamics with magnetic monopoles would be dual to a theory with inverted coupling constant and exchanged electric and magnetic charges. The question arises, if duality is poison to ontological realism, why didn’t it have its effect already at the level of quantum electrodynamics. The answer gives a nice survey of possible measures to save ontological realism. As it will turn out, they all fail in string theory.

In the case of quantum-electrodynamics the realist has several arguments to counter the duality threat. First, duality looks more like an accidental oddity that appears in an unrealistic scenario than like a characteristic feature of the world. No one has observed magnetic monopoles, which renders the problem hypothetical. And even if there were magnetic monopoles, an embedding of electromagnetism into a fuller description of the natural forces would destroy the dual structure anyway.

In string theory the situation is very different. Duality is no ‘lucky strike’ any more, which just by chance arises in a certain scenario that is not the real one anyway. As we have seen, it rather represents a core feature of the emerging theoretical structure and cannot be ignored. A second option open to the realist at the level of quantum electrodynamics is to shift the ontological posit. Some philosophers of quantum physics argue that the natural elementary object of quantum field theory is the quantum field, which represents something like the potentiality to produce elementary particles. One quantum field covers the full sum over all variations of particle exchange which have to be accounted for in a quantum process. The philosopher who posits the quantum field to be the fundamental real object discovered by quantum field theory understands the single elementary particles as mere mathematical entities introduced to calculate the behaviour of the quantum field. Dual theories from his perspective can be taken as different technical procedures to calculate the behaviour of the univocal ontological object, the electromagnetic quantum field. The phenomenon of duality then does not appear as a threat to the ontological concept per se but merely as an indication in favour of an ontologisation of the field instead of the particle.

The field theoretical approach to interpret the quantum field as the ontological object does not have any pendent in string theory. String theory only exists as a perturbative theory. There seems to be no way to introduce anything like a quantum field that would cover the full expansion of string exchanges. In the light of duality this lack of a unique ontological object arguably appears rather natural. The reason is related to another point that makes string dualities more dramatic than its field theoretical predecessor. String theory includes gravitation. Therefore object (the string geometry) and space-time are not independent. Actually it turns out that the string geometry in a way carries all information about space-time as well. This dependence of space-time on string-geometry makes it difficult already to imagine how it should be possible to put into this very spacetime some kind of overall field whose coverage of all string realisations actually implies coverage of variations of spacetime itself. The duality context makes the paradoxical quality of such an attempt more transparent. If two dual theories with different radii of a compactified dimension shall be covered by the same ontological object in analogy to the quantum field in field theory, this object obviously cannot live in space and time. If it would, it had to choose one of the two spacetime versions endorsed by the dual theories, thereby discriminating the other one. This theory however should not be expected to be a theory of objects in spacetime and therefore does not rise any hopes to redeem the external ontological perspective.

A third strategy to save ontological realism is based on the following argument: In quantum electrodynamics the difference between the dual theories boils down to a mere replacement of a weak coupling constant which allows perturbative calculation by a strong one which does not. Therefore the choice is open between a natural formulation and a clumsy untreatable one which maybe should just be discarded as an artificial construction.

Today string theory cannot tell whether its final solution will put its parameters comfortably into the low-coupling-constant-and-large-compact-dimension-regime of one of the 5 superstring theories or M-theory. This might be the case but it might as well happen, that the solution lies in a region of parameter space where no theory clearly stands out in this sense. However, even if there was one preferred theory, the simple discarding of the others could not save realism as in the case of field theory. First, the argument of natural choice is not really applicable to T-duality. A small compactification radius does not render a theory intractable like a large coupling constant. The choice of the dual version with a large radius thus looks more like a convention than anything else. Second, the choice of both compactification radii and string coupling constants in string theory is the consequence of a dynamical process that has to be calculated itself. Calculation thus stands before the selection of a certain point in parameter space and consequently also before a possible selection of the ontological objects. The ontological objects therefore, even if one wanted to hang on to their meaningfulness in the final scenario, would appear as a mere product of prior dynamics and not as a priori actors in the game.

Summing up, the phenomenon of duality is admittedly a bit irritating for the ontological realist in field theory but he can live with it. In string theory however, the field theoretical strategies to save realism all fail. The position assumed by the duality principle in string theory clearly renders obsolete the traditional realist understanding of scientific objects as smaller cousins of visible ones. The theoretical posits of string theory get their meaning only relative to their theoretical framework and must be understood as mathematical concepts without any claim to ‘corporal’ existence in an external world. The world of string theory has cut all ties with classical theories about physical bodies. To stick to ontological realism in this altered context, would be inadequate to the elementary changes which characterize the new situation. The demise of ontology in string theory opens new perspectives on the positions where the stress is on the discontinuity of ontological claims throughout the history of scientific theories.

Dance of the Shiva, q’i (chee) and Tibetan Sunyata. Manifestation of Mysticism.

अनेजदेकं मनसो जवीयो नैनद्देवाप्नुवन्पूर्वमर्षत् ।
तद्धावतोऽन्यान्नत्येति तिष्ठत् तस्मिन्नापो मातरिश्वा दधाति ॥

anejadekaṃ manaso javīyo nainaddevāpnuvanpūrvamarṣat |
taddhāvato’nyānnatyeti tiṣṭhat tasminnāpo mātariśvā dadhāti ||

The self is one. It is unmoving: yet faster than the mind. Thus moving faster, It is beyond the reach of the senses. Ever steady, It outstrips all that run. By its mere presence, the cosmic energy is enabled to sustain the activities of living beings.

तस्मिन् मनसि ब्रह्मलोकादीन्द्रुतं गच्छति सति प्रथमप्राप्त इवात्मचैतन्याभासो गृह्यते अतः मनसो जवीयः इत्याह ।

tasmin manasi brahmalokādīndrutaṃ gacchati sati prathamaprāpta ivātmacaitanyābhāso gṛhyate ataḥ manaso javīyaḥ ityāha |

When the mind moves fast towards the farthest worlds such as the brahmaloka, it finds the Atman, of the nature of pure awareness, already there; hence the statement that It is faster than the mind.

नित्योऽनित्यानां चेतनश्चेतनानाम्
एको बहूनां यो विदधाति कामान् ।
तमात्मस्थं योऽनुपश्यन्ति धीराः
तेषां शान्तिः शाश्वतं नेतरेषाम् ॥

nityo’nityānāṃ cetanaścetanānām
eko bahūnāṃ yo vidadhāti kāmān |
tamātmasthaṃ yo’nupaśyanti dhīrāḥ
teṣāṃ śāntiḥ śāśvataṃ netareṣām ||

He is the eternal in the midst of non-eternals, the principle of intelligence in all that are intelligent. He is One, yet fulfils the desires of many. Those wise men who perceive Him as existing within their own self, to them eternal peace, and non else.

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Eastern mysticism approaches the manifestation of life in the cosmos and all that compose it from a position diametrically opposed to the view that prevailed until recently among the majority of Western scientists, philosophers, and religionists. Orientals see the universe as a whole, as an organism. For them all things are interconnected, links in a chain of beings permeated by consciousness which threads them together. This consciousness is the one life-force, originator of all the phenomena we know under the heading of nature, and it dwells within its emanations, urging them as a powerful inner drive to grow and evolve into ever more refined expressions of divinity. The One manifests, not only in all its emanations, but also through those emanations as channels: it is within them and yet remains transcendent as well.

The emphasis is on the Real as subject whereas in the West it is seen as object. If consciousness is the noumenal or subjective aspect of life in contrast to the phenomenal or objective — everything seen as separate objects — then only this consciousness can be experienced, and no amount of analysis can reveal the soul of Reality. To illustrate: for the ancient Egyptians, their numerous “gods” were aspects of the primal energy of the Divine Mind (Thoth) which, before the creation of our universe, rested, a potential in a subjective state within the “waters of Space.” It was through these gods that the qualities of divinity manifested.

A question still being debated runs: “How does the One become the many?” meaning: if there is a “God,” how do the universe and the many entities composing it come into being? This question does not arise among those who perceive the One to dwell in the many, and the many to live in the One from whom life and sustenance derive. Despite our Western separation of Creator and creation, and the corresponding distancing of “God” from human beings, Western mystics have held similar views to those of the East, e.g.: Meister Eckhart, the Dominican theologian and preacher, who was accused of blasphemy for daring to say that he had once experienced nearness to the “Godhead.” His friends and followers were living testimony to the charisma (using the word in its original connotation of spiritual magnetism) of those who live the life of love for fellow beings men like Johannes Tauler, Heinrich Suso, the “admirable Ruysbroeck,” who expressed views similar to those of Eastern exponents of the spiritual way or path.

In old China, the universe was described as appearing first as q’i (chee), an emanation of Light, not the physical light that we know, but its divine essence sometimes called Tien, Heaven, in contrast to Earth. The q’i energy polarized as Yang and Yin, positive and negative electromagnetism. From the action and interaction of these two sprang the “10,000 things”: the universe, our world, the myriads of beings and things as we perceive them to be. In other words, the ancient Chinese viewed our universe as one of process, the One energy, q’i, proliferating into the many.

In their paintings Chinese artists depict man as a small but necessary element in gigantic natural scenes. And since we are parts of the cosmos, we are embodiments of all its potentials and our relationship depends upon how we focus ourselves: (1) harmoniously, i.e., in accord with nature; or (2) disharmoniously, interfering with the course of nature. We therefore affect the rest: our environment, all other lives, and bear full responsibility for the outcome of our thoughts and acts, our motivations, our impacts. Their art students were taught to identify with what they were painting, because there is life in every thing, and it is this life with which they must identify, with boulders and rocks no less than with birds flying overhead. Matter, energy, space, are all manifestations of q’i and we, as parts thereof, are intimately connected with all the universe.

In India, the oneness of life was seen through the prism of successive manifestations of Brahman, a neuter or impersonal term in Sanskrit for divinity, the equivalent of what Eckhart called the Godhead. Brahman is the source of the creative power, Brahma, Eckhart’s Creator; and also the origin of the sustaining and supporting energy or Vishnu, and of the destructive/regenerative force or Siva. As these three operate through the cosmos, the “world” as we know it, so do they also through ourselves on a smaller scale according to our capacity. Matter is perceived to be condensed energy, Chit or consciousness itself. To quote from the Mundaka Upanishad:

By the energism of Consciousness Brahman is massed; from that: Matter is born and from Matter Life and Mind and the worlds . . .

In another Hindu scripture, it is stated that when Brahma awakened from his period of rest between manifestations, he desired to contemplate himself as he is. By gazing into the awakening matter particles as into a mirror, he stirred them to exhibit their latent divine qualities. Since this process involves a continuous unfoldment from the center within, an ever-becoming, there can never be an end to the creativity — universal “days” comprising trillions of our human years, followed by a like number of resting “nights.”

We feel within ourselves the same driving urge to grow that runs through the entire, widespread universe, to express more and more of what is locked up in the formless or subjective realm of Be-ness, awaiting the magic moment to come awake in our phase of life.

Tibetan metaphysics embraces all of this in discussing Sunyata, which can be viewed as Emptiness if we use only our outer senses, or as Fullness if we inwardly perceive it to be full of energies of limitless ranges of wave-lengths/frequencies. This latter aspect of Space is the great mother of all, ever fecund, from whose “heart” emerge endless varieties of beings, endless forces, ever-changing variations — like the pulsing energies the new physicists perceive nuclear subparticles to be.

In the Preface to his Tao of physics Fritjof Capra tells how one summer afternoon he had a transforming experience by the seashore as he watched the waves rolling in and felt the rhythm of his own breathing. He saw dancing motes revealed in a beam of sunlight; particles of energy vibrating as molecules and atoms; cascades of energy pouring down upon us from outer space. All of this coming and going, appearing and disappearing, he equated with the Indian concept of the dance of Siva . . . he felt its rhythm, “heard” its sound, and knew himself to be a part of it. Through this highly personal, indeed mystical, experience Capra became aware of his “whole environment as being engaged in a gigantic cosmic dance.”

This is the gist of the old Chinese approach to physics: students were taught gravitation by observing the petals of a flower as they fall gracefully to the ground. As Gary Zukav expresses it in his Dancing Wu Li Masters: An Overview of the New Physics:

The world of particle physics is a world of sparkling energy forever dancing with itself in the form of its particles as they twinkle in and out of existence, collide, transmute, and disappear again.

That is: the dance of Siva is the dance of attraction and repulsion between charged particles of the electromagnetic force. This is a kind of “transcendental” physics, going beyond the “world of opposites” and approaching a mystical view of the larger Reality that is to our perceptions an invisible foundation of what we call “physical reality.” It is so far beyond the capacity or vocabulary of the mechanically rational part of our mind to define, that the profound Hindu scripture Isa Upanishad prefers to suggest the thought by a paradox:

तदेजति तन्नैजति तद्दूरे तद्वन्तिके ।
तदन्तरस्य सर्वस्य तदु सर्वस्यास्य बाह्यतः ॥

tadejati tannaijati taddūre tadvantike |
tadantarasya sarvasya tadu sarvasyāsya bāhyataḥ ||

It moves. It moves not.  It is far, and it is near. It is within all this, And It is verily outside of all this.

Indeed, there is a growing recognition mostly by younger physicists that consciousness is more than another word for awareness, more than a by-product of cellular activity (or of atomic or subatomic vibrations). For instance, Jack Sarfatti, a quantum physicist, says that signals pulsating through space provide instant communication between all parts of the cosmos. “These signals can be likened to pulses of nerve cells of a great cosmic brain that permeates all parts of space (Michael Talbot, Mysticism and the New Physics).” Michael Talbot quotes Sir James Jeans’ remark, “the universe is more like a giant thought than a giant machine,” commenting that the “substance of the great thought is consciousness” which pervades all space. Or as Schrödinger would have it:

Consciouness is never experienced in the plural, only in the singular….Consciouness is a singular of which the plural is unknown; that; there is only one thing and that, what seems to be a plurality is merely a series of different aspects of this one thing, produced by a deception (the Indian Maya).

Other phenomena reported as occurring in the cosmos at great distances from each other, yet simultaneously, appear to be connected in some way so far unexplained, but to which the term consciousness has been applied.

In short, the mystic deals with direct experience; the intuitive scientist is open-minded, and indeed the great discoveries such as Einstein’s were made by amateurs in their field untrammeled by prior definitions and the limitations inherited from past speculations. This freedom enabled them to strike out on new paths that they cleared and paved. The rationalist tries to grapple with the problems of a living universe using only analysis and whatever the computer functions of the mind can put together.

The theosophic perspective upon universal phenomena is based on the concept of the ensoulment of the cosmos. That is: from the smallest subparticle we know anything about to the largest star-system that has been observed, each and all possess at their core vitality, energy, an active something propelling towards growth, evolution of faculties from within.

The only “permanent” in the whole universe is motion: unceasing movement, and the ideal perception is a blend of the mystical with the scientific, the intuitive with the rational.

Weyl, “To understand nature, start with the group Γ of automorphisms and refrain from making the artificial logical distinction between basic and derived relations . . .”

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Gauge transformations appear of primarily descriptive nature only if we consider them in their function as changes of local (in the mathematical sense) changes of trivializations. In this function they are comparable to the transformations of the coordinates in a differentiable manifold, which also seem to have a purely “descriptive” function. But the coordinate changes stand in close relation to (local) diffeomorphisms. Therefore the postulate of coordinate independence of natural laws, or of the Lagrangian density, can and is being restated in terms of diffeomorphism invariance in general relativity. Similarly, the local changes of trivializations may be read as local descriptions.

The question as to whether or not the automorphisms express crucial physical properties  has nothing to do with the specific gauge nature of the groups, but hinges on the more overarching question of physical adequateness and physical content of the theory. The question of whether or why gauge symmetries can express physical content is not much different from the Kretschmann question of whether or why coordinate invariance of the laws, respectively coordinate covariance description of a physical theory, can have physical content. In the latter case the answer to the question has been dealt with in the philosophy of physics literature in great detail. Weyl’s answer is contained in his thoughts on the distinction of physical and mathematical automorphisms.

Let us shed a side-glance at gravitational gauge theories not taken into account by Weyl. In Einstein-Cartan gravity, which later turned out to be equivalent to Kibble-Sciama gravity, the localized rotational degrees of freedom lead to a conserved spin current and a non-symmetric energy tensor. This is a structurally pleasing effect, fitting roughly into the Noether charge paradigm, although with a peculiar “crossover” of the two Noether currents and the currents feeding the dynamical equations, inherited from Einstein gravity and Cartan’s identification of translational curvature with torsion. The rotational current, spin, feeds the dynamical equation of translational curvature; the translational current, energy-momentum, feeds the rotational curvature in the (generalized) Einstein equation. It may acquire physical relevance only if energy densities surpass the order of magnitude 1038 times the density of neutron stars. By this reason the current cannot yet be considered a physically striking effect. It may turn into one, if gravitational fields corresponding to extremely high energy densities acquire empirical relevance. For the time being, the rotational current can safely be neglected, Einstein-Cartan gravity reduces effectively to Einstein gravity, and Weyl’s argument for the symmetry of the energy-momentum tensor remains the most “striking consequence” in the sense of  rotational degrees of freedom.

On the other hand, the translational degrees of freedom give a more direct expression for the Noether currents of energy-momentum than the diffeomorphisms. The physical consequences for the diffeomorphism degrees of freedom reduce to the invariance constraint for the Lagrangian density for Einstein gravity considered as a special case of the Einstein-Cartan theory (with effectively vanishing spin). Besides these minor shifts, it may be more interesting to realize that the approach of Kibble and Sciama agreed nicely with Weyl’s methodological remark that for understanding nature we better “start with the group Γ of automorphisms and refrain from making the artificial logical distinction between basic and derived relations . . . ”. This describes quite well what Sciama and Kibble did. They started to explore the consequences of localizing (in the physical sense) the translational and rotational degrees of freedom of special relativity. Their theory was built around the generalized automorphism group arising from localizing the Poincaré group.

When is the Spacetime Temporally Orientable?

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In both general relativity and Newtonian gravitation, forces are represented by vectors at a point. We assume that the total force acting on a particle at a point (computed by taking the vector sum of all of the individual forces acting at that point) must be proportional to the acceleration of the particle at that point, as in F = ma, which holds in both theories. We understand forces to give rise to acceleration, and so we expect the total force at a point to vanish just in case the acceleration vanishes. Since the acceleration of a curve at a point, as determined relative to some derivative operator, must satisfy certain properties, it follows that the vector representing total force must also satisfy certain properties. In particular, in relativity theory, the acceleration of a curve at a point is always orthogonal to the tangent vector of the curve at that point, and thus the total force on a particle at a point must always be orthogonal to the tangent vector of the particle’s worldline at that point.

More precisely, we take a model of relativity theory to be a relativistic spacetime, which is an ordered pair (M, gab), where M is a smooth, connected, paracompact, Hausdorff 4-manifold and gab is a smooth Lorentzian metric. A model of Newtonian gravitation, meanwhile, is a classical spacetime, which is an ordered quadruple (M, tab, hab, ∇), where M is again a smooth, connected, paracompact, Hausdorff 4-manifold, tab and hab are smooth fields with signatures (1, 0, 0, 0) and (0, 1, 1, 1), respectively, which together satisfy tabhbc = 0, and ∇ is a smooth derivative operator satisfying the compatibility conditions ∇atbc = 0 and ∇ahab = 0. The fields tab and hab may be interpreted as a (degenerate) “temporal metric” and a (degenerate) “spatial metric”, respectively. Note that the signature of tab guarantees that locally, we can always find a field ta such that tab = tatb. In the special case where this field can be smoothly extended to a global field with the stated property, we call the spacetime temporally orientable.

Typicality. Cosmological Constant and Boltzmann Brains. Note Quote.

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In a multiverse we would expect there to be relatively many universe domains with large values of the cosmological constant, but none of these allow gravitationally bound structures (such as our galaxy) to occur, so the likelihood of observing ourselves to be in one is essentially zero.

The cosmological constant has negative pressure, but positive energy.  The negative pressure ensures that as the volume expands then matter loses energy (photons get red shifted, particles slow down); this loss of energy by matter causes the expansion to slow down – but the increase in energy of the increased volume is more important .  The increase of energy associated with the extra space the cosmological constant fills has to be balanced by a decrease in the gravitational energy of the expansion – and this expansion energy is negative, allowing the universe to carry on expanding.  If you put all the terms on one side in the Friedmann equation – which is just an energy balancing equation – (with the other side equal to zero) you will see that the expansion energy is negative, whereas the cosmological constant and matter (including dark matter) all have positive energy.

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However, as the cosmological constant is decreased, we eventually reach a transition point where it becomes just small enough for gravitational structures to occur. Reduce it a bit further still, and you now get universes resembling ours. Given the increased likelihood of observing such a universe, the chances of our universe being one of these will be near its peak. Theoretical physicist Steven Weinberg used this reasoning to correctly predict the order of magnitude of the cosmological constant well before the acceleration of our universe was even measured.

Unfortunately this argument runs into conceptually murky water. The multiverse is infinite and it is not clear whether we can calculate the odds for anything to happen in an infinite volume of space- time. All we have is the single case of our apparently small but positive value of the cosmological constant, so it’s hard to see how we could ever test whether or not Weinberg’s prediction was a lucky coincidence. Such questions concerning infinity, and what one can reasonably infer from a single data point, are just the tip of the philosophical iceberg that cosmologists face.

Another conundrum is where the laws of physics come from. Even if these laws vary across the multiverse, there must be, so it seems, meta-laws that dictate the manner in which they are distributed. How can we, inhabitants on a planet in a solar system in a galaxy, meaningfully debate the origin of the laws of physics as well as the origins of something, the very universe, that we are part of? What about the parts of space-time we can never see? These regions could infinitely outnumber our visible patch. The laws of physics could differ there, for all we know.

We cannot settle any of these questions by experiment, and this is where philosophers enter the debate. Central to this is the so-called observational-selection effect, whereby an observation is influenced by the observer’s “telescope”, whatever form that may take. But what exactly is it to be an observer, or more specifically a “typical” observer, in a system where every possible sort of observer will come about infinitely many times? The same basic question, centred on the role of observers, is as fundamental to the science of the indefinitely large (cosmology) as it is to that of the infinitesimally small (quantum theory).

This key issue of typicality also confronted Austrian physicist and philosopher Ludwig Boltzmann. In 1897 he posited an infinite space-time as a means to explain how extraordinarily well-ordered the universe is compared with the state of high entropy (or disorder) predicted by thermodynamics. Given such an arena, where every conceivable combination of particle position and momenta would exist somewhere, he suggested that the orderliness around us might be that of an incredibly rare fluctuation within an infinite space-time.

But Boltzmann’s reasoning was undermined by another, more absurd, conclusion. Rare fluctuations could also give rise to single momentary brains – self aware entities that spontaneously arises through random collisions of particles. Such “Boltzmann brains”, the argument goes, are far more likely to arise than the entire visible universe or even the solar system. Ludwig Boltzmann reasoned that brains and other complex, orderly objects on Earth were the result of random fluctuations. But why, then, do we see billions of other complex, orderly objects all around us? Why aren’t we like the lone being in the sea of nonsense?Boltzmann theorized that if random fluctuations create brains like ours, there should be Boltzmann brains floating around in space or sitting alone on uninhabited planets untold lightyears away. And in fact, those Boltzmann brains should be incredibly more common than the herds of complex, orderly objects we see here on Earth. So we have another paradox. If the only requirement of consciousness is a brain like the one in your head, why aren’t you a Boltzmann brain? If you were assigned to experience a random consciousness, you should almost certainly find yourself alone in the depths of space rather than surrounded by similar consciousnesses. The easy answers seem to all require a touch of magic. Perhaps consciousness doesn’t arise naturally from a brain like yours but requires some metaphysical endowment. Or maybe we’re not random fluctuations in a thermodynamic soup, and we were put here by an intelligent being. An infinity of space would therefore contain an infinitude of such disembodied brains, which would then be the “typical observer”, not us. OR. Starting at the very beginning: entropy must always stay the same or increase over time, according to the second law of thermodynamics. However, Boltzmann (the Ludwig one, not the brain one) formulated a version of the law of entropy that was statistical. What this means for what you’re asking is that while entropy almost always increases or stays the same, over billions of billions of billions of billions of billions…you get the idea years, entropy might go down a bit. This is called a fluctuation. So backing up a tad, if entropy always increases/stays the same, what is surprising for cosmologists is that the universe started in such a low-entropy state. So to (try) to explain this, Boltzmann said, hey, what if there’s a bigger universe that our universe is in, and it is in a state of the most possible entropy, or thermal equilibrium. Then, let’s say it exists for a long long time, those billions we talked about earlier. There’ll be statistical fluctuations, right? And those statistical fluctuations might be represented by the birth of universes. Ahem, our universe is one of them. So now, we get into the brains. Our universe must be a HUGE statistical fluctuation comparatively to other fluctuations. I mean, think about it. If it is so nuts for entropy to decrease by just a little tiny bit, how nuts would it be for it to decrease enough for the birth of a universe to happen!? So the question is, why aren’t we just brains? That is, why aren’t we a statistical fluctuation just big enough for intelligent life to develop, look around, see it exists, and melt back into goop. And it is this goopy-not-long-existing intelligent life that is a Boltzmann brain. This is a huge challenge to the Boltzmann (Ludwig) theory.

Can this bizarre vision possibly be real, or does it indicate something fundamentally wrong with our notion of “typicality”? Or is our notion of “the observer” flawed – can thermodynamic fluctuations that give rise to Boltzmann’s brains really suffice? Or could a futuristic supercomputer even play the Matrix-like role of a multitude of observers?

Physical Congruences of Nāgārjuna’s Mūlamadhyamakakārikā, Yukti-sastikâ, śūnyatā and Pratītyasamutpāda. Note Quote

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The Middle Way of Mādhyamaka refers to the teachings of Nāgārjuna, very interesting are the implications between quantum physics and Mādhyamaka. The basic concept of reality in the philosophy of Nāgārjuna is that the fundamental reality has no firm core but consists of systems of interacting objects. According to the middle way perspective, based on the notion of emptiness, phenomena exist in a relative way, that is, they are empty of any kind of inherent and independent existence. Phenomena are regarded as dependent events existing relationally rather than permanent things, which have their own entity. Nāgārjuna middle way perspective emerges as a relational approach, based on the insight of emptiness.  śūnyatā (emptiness) is the foundation of all things, and it is the basic principle of all phenomena. The emptiness implies the negation of unchanged, fixed substance and thereby the possibility for relational existence and change. This suggests that both the ontological constitution of things and our epistemological schemes are just as relational as everything else. We are fundamentally relational internally and externally. In other words, Nāgārjuna, do not fix any ontological nature of the things:

  1. they do not arise
  2. they do not exist
  3. they are not to be found
  4. they are not
  5. and they are unreal

In short, an invitation do not decide on either existence or non-existence (nondualism). According the theory of  śūnyatā, phenomena exist in a relative state only, a kind of ’ontological relativity’. Phenomena are regarded as dependent (only in relation to something else) events rather than things which have their own inherent nature; thus the extreme of permanence is avoided.

In the Mūlamadhyamakakārikā, a tetralemma is pointed out: “Neither from itself nor from another, nor from both, nor without a cause, does anything whatever anywhere arise”. In the Yukti-sastikâ, Nāgārjuna says, “That which has arisen dependently on this and that that has not arisen substantially (svabhavatah, स्वभावतः). What has not arisen substantially, how can it literally (nama) be called ‘arisen’? […] That which originates due to a cause and does not abide without (certain) conditions but disappears when the conditions are absent, how can it be understood as ‘to exist’?”

By the notions of ‘to arise’ and ‘to exist’, Nāgārjuna does not mean the empirical existence but the substantial existence. When in many passages of Mūlamadhyamakakārikā Nāgārjuna states that things do not arise (7.29), that they do not exist (3.7, 5.8, 14.6), that they are not to be found (2.25, 9.11), that they are not (15.10), that they are unreal (13.1), then clearly this has the meaning: things do not arise substantially. They do not exist out of themselves; their independence cannot be found. They are dependent and in this sense they are substantially unreal. Nāgārjuna only rejects the idea of a substantial arising of things which bear an absolute and independent existence. He does not refute the empirical existence of things as explained in the following: “It exists implies grasping after eternity. It does not exist implies the philosophy of annihilation. Therefore, a discerning person should not decide on either existence or non-existence”. (15.10)

For Nāgārjuna, the expression ‘to exist’ has the meaning of ‘to exist substantially’. His issue is not the empirical existence of things but the conception of a permanent thing i.e. the idea of an own being, without dependence on something else. Nāgārjuna refutes the concept of independent existence which is unchangeable, eternal and existing by itself. Things do not arise out of themselves, they do not exist absolutely and are dependent. Their permanent being or existence cannot be found. The many interpretations of Nāgārjuna which claim that he is also refuting the empirical existence of objects, are making an inadmissible generalization which moves Nāgārjuna near to subjectivism, nihilism and instrumentalism. Such interpretations originate in metaphysical approaches which themselves have a difficulty in recognizing the empirical existence of the data presented. This is not at all the case with Nāgārjuna. Nāgārjuna presents the dependence of phenomena mainly in images.

Pratītyasamutpāda (Sanskrit: प्रतीत्यसमुत्पाद; Pali: पटिच्चसमुप्पाद paṭiccasamuppāda) is an indication of dependence. Dependent bodies are in an intermediate state, they are not properly separated and they are not one entity. Secondly, they rely on each other and are influenced or determined by something else. Thirdly, their behaviour is influenced by something in-between, for example a mover is attracted by gravitational force, a viewer is dependent on rays of light between his eyes and the object, a piano player’s action is determined by the fine motor skills of his fingers, an agent is dependent on his act. Pratītyasamutpāda is an indication of dependence and of something that happens between the objects. One object is bound to the other without being identical to it. The implicit interpretations of Pratītyasamutpāda, are in terms of time, structure and space.

The following citations and references illustrate the term Pratītyasamutpāda. Pratītyasamutpāda is used:

1. as Dependence in Nāgārjuna’s Hymn to the Buddha: “Dialecticians maintain that suffering is created by itself, created by (someone) else, created by both (or) without a cause, but You have stated that it is dependently born”.

2. as an intermediate state by Nāgārjuna: Objects are neither together nor separated

3. as bondage in the Hevajra Tantra: “Men are bound by the bondage of existence and are liberated by understanding the nature of existence”.

4. as an intermediate state by Roger Penrose: “Quantum entanglement is a very strange type of thing. It is somewhere between objects being separate and being in communication with each other”.

5. as something between bodies by Albert Einstein: “A courageous scientific imagination was needed to realize fully that not the behaviour of bodies, but the behaviour of something between them, that is, the field, may be essential for ordering and understanding events”.

6. as the mean between things in modern mathematics: to quote Gioberti: “The mean between two or more things, their juncture, union, transit, passage, crossing, interval, distance, bond and contact – all these are mysterious, for they are rooted in the continuum, in the infinite. The interval that runs between one idea and another, one thing and another, is infinite, and can only be surpassed by the creative act. This is why the dynamic moment and dialectic concept of the mean are no less mysterious than those of the beginning and the end. The mean is a union of two diverse and opposite things in a unity. It is an essentially dialectic concept, and involves an apparent contradiction, namely, the identity of the one and the many, of the same and the diverse. This unity is simple and composite; it is unity and synthesis and harmony. It shares in two extremes without being one or the other. It is the continuum, and therefore the infinite. Now, the infinite identically uniting contraries, clarifies the nature of the interval. In motion, in time, in space, in concepts, the discrete is easy to grasp, because it is finite. The continuum and the interval are mysterious, because they are infinite.”

Whitehead’s Non-Anthropocentric Quantum Field Ontology. Note Quote.

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Whitehead builds also upon James’s claim that “The thought is itself the thinker”.

Either your experience is of no content, of no change, or it is of a perceptible amount of content or change. Your acquaintance with reality grows literally by buds or drops of perception. Intellectually and on reflection you can divide them into components, but as immediately given they come totally or not at all. — William James.

If the quantum vacuum displays features that make it resemble a material, albeit a really special one, we can immediately ask: then what is this material made of? Is it a continuum, or are the “atoms” of vacuum? Is vacuum the primordial substance of which everything is made of? Let us start by decoupling the concept of vacuum from that of spacetime. The concept of vacuum as accepted and used in standard quantum field theory is tied with that of spacetime. This is important for the theory of quantum fields, because it leads to observable effects. It is the variation of geometry, either as a change in boundary conditions or as a change in the speed of light (and therefore the metric) which is responsible for the creation of particles. Now, one can legitimately go further and ask: which one is the fundamental “substance”, the space-time or the vacuum? Is the geometry fundamental in any way, or it is just a property of the empty space emerging from a deeper structure? That geometry and substance can be separated is of course not anything new for philosophers. Aristotle’s distinction between form and matter is one example. For Aristotle the “essence” becomes a true reality only when embodied in a form. Otherwise it is just a substratum of potentialities, somewhat similar to what quantum physics suggests. Immanuel Kant was even more radical: the forms, or in general the structures that we think of as either existing in or as being abstracted from the realm of noumena are actually innate categories of the mind, preconditions that make possible our experience of reality as phenomena. Structures such as space and time, causality, etc. are a priori forms of intuition – thus by nature very different from anything from the outside reality, and they are used to formulate synthetic a priori judgments. But almost everything that was discovered in modern physics is at odds with Kant’s view. In modern philosophy perhaps Whitehead’s process metaphysics provides the closest framework for formulating these problems. For Whitehead, potentialities are continuous, while the actualizations are discrete, much like in the quantum theory the unitary evolution is continuous, while the measurement is non-unitary and in some sense “discrete”. An important concept is the “extensive continuum”, defined as a “relational complex” containing all the possibilities of objectification. This continuum also contains the potentiality for division; this potentiality is effected in what Whitehead calls “actual entities (occasions)” – the basic blocks of his cosmology. The core issue for both Whiteheadian Process and Quantum Process is the emergence of the discrete from the continuous. But what fixes, or determines, the partitioning of the continuous whole into the discrete set of subsets? The orthodox answer is this: it is an intentional action of an experimenter that determines the partitioning! But, in Whiteheadian process the world of fixed and settled facts grows via a sequence actual occasions. The past actualities are the causal and structural inputs for the next actual occasion, which specifies a new space-time standpoint (region) from which the potentialities created by the past actualities will be prehended (grasped) by the current occasion. This basic autogenetic process creates the new actual entity, which, upon becoming actual, contributes to the potentialities for the succeeding actual occasions. For the pragmatic physicist, since the extensive continuum provides the space of possibilities from which the actual entities arise, it is tempting to identify it with the quantum vacuum. The actual entities are then assimilated with events in spacetime, as resulting from a quantum measurement, or simply with particles. The following caveat is however due: Whitehead’s extensive continuum is also devoid of geometrical content, while the quantum vacuum normally carries information about the geometry, be it flat or curved. Objective/absolute actuality consist of a sequence of psycho-physical quantum reduction events, identified as Whiteheadian actual entities/occasions. These happenings combine to create a growing “past” of fixed and settled “facts”. Each “fact” is specified by an actual occasion/entity that has a physical aspect (pole), and a region in space-time from which it views reality. The physical input is precisely the aspect of the physical state of the universe that is localized along the part of the contemporary space-like surface σ that constitutes the front of the standpoint region associated with the actual occasion. The physical output is reduced state ψ(σ) on this space-like surface σ. The mental pole consists of an input and an output. The mental inputs and outputs have the ontological character of thoughts, ideas, or feelings, and they play an essential dynamical role in unifying, evaluating, and selecting discrete classically conceivable activities from among the continuous range of potentialities offered by the operation of the physically describable laws. The paradigmatic example of an actual occasion is an event whose mental pole is experienced by a human being as an addition to his or her stream of conscious events, and whose output physical pole is the neural correlate of that experiential event. Such events are “high-grade” actual occasions. But the Whitehead/Quantum ontology postulates that simpler organisms will have fundamentally similar but lower-grade actual occasions, and that there can be actual occasions associated with any physical systems that possess a physical structure that will support physically effective mental interventions of the kind described above. Thus the Whitehead/Quantum ontology is essentially an ontologicalization of the structure of orthodox relativistic quantum field theory, stripped of its anthropocentric trappings. It identifies the essential physical and psychological aspects of contemporary orthodox relativistic quantum field theory, and lets them be essential features of a general non-anthropocentric ontology.

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It is reasonable to expect that the continuous differentiable manifold that we use as spacetime in physics (and experience in our daily life) is a coarse-grained manifestation of a deeper reality, perhaps also of quantum (probabilistic) nature. This search for the underlying structure of spacetime is part of the wider effort of bringing together quantum physics and the theory of gravitation under the same conceptual umbrella. From various the- oretical considerations, it is inferred that this unification should account for physics at the incredibly small scale set by the Planck length, 10−35m, where the effects of gravitation and quantum physics would be comparable. What happens below this scale, which concepts will survive in the new description of the world, is not known. An important point is that, in order to incorporate the main conceptual innovation of general relativity, the the- ory should be background-independent. This contrasts with the case of the other fields (electromagnetic, Dirac, etc.) that live in the classical background provided by gravitation. The problem with quantizing gravitation is – if we believe that the general theory of relativity holds in the regime where quantum effects of gravitation would appear, that is, beyond the Planck scale – that there is no underlying background on which the gravitational field lives. There are several suggestions and models for a “pre-geometry” (a term introduced by Wheeler) that are currently actively investigated. This is a question of ongoing investigation and debate, and several research programs in quantum gravity (loops, spinfoams, noncommutative geometry, dynamical triangulations, etc.) have proposed different lines of attack. Spacetime would then be an emergent entity, an approximation valid only at scales much larger than the Planck length. Incidentally, nothing guarantees that background-independence itself is a fundamental concept that will survive in the new theory. For example, string theory is an approach to unifying the Standard Model of particle physics with gravitation which uses quantization in a fixed (non-dynamic) background. In string theory, gravitation is just another force, with the graviton (zero mass and spin 2) obtained as one of the string modes in the perturbative expansion. A background-independent formulation of string theory would be a great achievement, but so far it is not known if it can be achieved.