INTEGRAL WORLD: EXPLORING THEORIES OF EVERYTHING
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Giorgio Piacenza Giorgio Piacenza is a sociologist student in the Certificate program leading to a Master's degree in Integral Theory at JFK University.

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The AMPLITUHEDRON

How Advanced Physics (Overcoming a Modern
Academic Taboo also Affecting Integralists) is Leading
the Way Toward a Useful Recognition of Higher Realms

Giorgio Piacenza

The AMPLITUHEDRON would be the first of many more geometric forms to be discovered as representatives of a deeper and "subtler" level of order.

Physicist Nima Arkani-Hamed and colleagues related with the Institute for Advanced Studies at Princeton discovered a geometric form that is very helpful for solving complex calculations regarding some quantum particle interactions. The volume of this geometric form shows that these interactions emerge from a more fundamental level of reality previous to the emergence of space-time. The search for this level (often referred as a quantum information level) is on its way at the forefront of the Physics community. Performing calculations of particle collisions and interactions and trying to find their probabilities to achieve “unitarity” with a space-time perspective is very complex. It's like trying to solve complexity from the same level of complexity in which it exists. But trying to solve this complexity from the higher, more inclusive level from which that complexity is generated (the bird's eye view) is simpler. All of this relates with Integral Theory, hierarchical levels and holons as well.


Artist's rendering of the amplituhedron.

The following article on the Amplituhedron gives more information: "A Jewel at the Heart of Quantum Physics".

Simpler calculations in relation to the volume of this geometric figure called “Amplituhedron” would ease the complex process of acquiring information about a certain kind of particle interactions which until now were painstakingly deciphered by using complicated FEYNMAN DIAGRAMS to decipher all relevant combinations of “Dispersed Amplitudes” combining probabilities into “Unitarity” or a form of wholeness under the perspective of space-time. My take (and apparently that of some physicists) is that there is a more inclusive level of wholeness displaying another type of wholeness. I think it would be both an ontological and an epistemological level wholeness previous to space-time and generative of space-time and that this is relevant not only for quantum and relativity physics but for Integral Theory applied to physics and applied to a new kind of expanded metaphysics. Understanding this and the principles by which this level of reality might be organized would make Integral Theory more relevant to where current physics is moving to. There would be a grander conjunction between physics and metaphysics.

Not only “unitarity” understood under space-time parameters but space-time itself would be EMERGENT properties. Characteristics of Quantum Field Theory would also derive from a more fundamental order. In a dependent “subsequent” manner and in relation to a classic space-time level of being-experience, the “dispersed probability amplitudes” would generate “unitarity” and “locality.”

The AMPLITUHEDRON was discovered after previous developments. Exploring the complex multidimensional and BEAUTIFUL mathematics of “Twistors” developed by Roger Penrose in the 1970's, Nima Arkani-Hamed was able to identify its “positive” Grassmannian structure. Also, Edward Witten promoter of “Theory M” (that subsumes various previously competing string theories) found a useful way to connect with “twistors.” Witten also seems to be pleasantly surprised about the Amplituhedron.

The AMPLITUHEDRON would be the first of many more geometric forms to be discovered as representatives of a deeper and “subtler” level of order that affects our gross, physical order. This level of order would subsume and transcend the classical physical level of order under different rules of functioning and of logic. This subtler order is also being understood in terms of GEOMETRY and future developments may also be helpful to understand gravity. I suspect that tetrahedra (which have important applications in alternative physical “theories of everything” such as that presented by physicist Nasseem Haramein) are important for the new geometries that disclose what deeper levels of reality (within the vacuum of space and into the Subtle Realm) described by twisting vortical spaces might be like. I suspect that some geometries encode principles through which consciousness transforms information into actualities.

In terms of the sciences of complexity it would also mean that we are finding tools for acquiring more information (in a sense reducing entropy) about complex systems and interactions, something which until now was very difficult, thus rendering the world of quantum events less amenable to a deterministic approach and –in a sense- less “actual” or “real” for us as participatory consciousnesses. Some of the “hidden factors” behind what seemed “indeterministic” are becoming less potentially real and more “actual” and-or capable of being enacted, interpreted and gradually understood. We are beginning to unveil aspects of what - due to a lack of information or a previous inability to access that information – would have been considered to be in a state of “potentiality” in relation to our “actual,” classic world of coherent, linear, physical experiences. Aspects of the elusive subtle “whole” subsuming our physical world might be “standing out” to our consciousness.

At this point the “AMPLITUHEDRON” would be the first geometric form of its kind discovered using the mathematics associated with “positive grassmanian spaces” used in supersymmetric N4 Yang-Mills approaches to quantum phenomena. It and similar geometries would shed light on aspects of the world of non-local existence which (in relation to Integral Theory) may be related to the “insides” of physical quadrants according to integral researcher Lexi Neale ["The AQAL Cube Meta-Theory of Integral Relativity"].

A form of complexity is simplified under a deeper level of order. A simple volume which can be written as one simple term on a small piece of paper can deliver the relevant information necessary for what previously took an enormous number of calculations, even with the fastest digital computers. Complexity is simplified under the level of order that gave rise to it, possibly turning Subtle Realm parameters now a bit more useful for physical science.

But can we speak of information “without a body” or without exterior forms existing at this deeper level? I don't think so. As per Integral Theory, “Exteriors” (albeit in different forms and with different intensities) would exist in every realm where there is duality. At any rate, the “body” inextricably linked to information would be different from what normally accompanies physical information by not being limited by space-time parameters. However, these space-time parameters would be included as a subset of an expression of reality that should transcend but also manifest a distinct, more inclusive type of objective exteriority in the Subtle Realm.

According to Integral Theory, every phenomenon is accompanied by subjective experiential interiors and objective (communally verifiable) exteriors. This would occur within every realm in which there's duality just as holons would also exist in each of these realms. Overcoming the modern era academic stigma attached to thinking about “other worldly” things is crucial for the “integral” advancement of science and philosophy. The basic idea is that there are THREE FUNDAMENTAL REALMS (Physical, Subtle, Causal), each primarily manifesting under their own rules and logics (although they can also interact, interpenetrate and be mutually immanent to each other).

Interiors and exteriors would express in individual and collective ways in each of the three main forms of ontological-subjective reality thus forming FOUR QUADRANTS in each realm. The differences between the realms and the intensities expressed within those quadrants during inter-realm distinctions would be given by three even more fundamental forms of expression. I suppose that the “Amplituhedron” might be one of the first geometric examples of a mathematical relation between the Subtle Realm and the Physical Realm. Off course this might be considered a bit of a stretch but why wouldn't a coherent information realm from which space-time seems to emerge actually be at least an aspect of what esoteric mystics and reluctant integralists have basically understood as the “Subtle Realm?” Why wouldn't this be the non-local “insides” of the four quadrants or at least the “insides” be a nexus between a Subtle Realm of vaster possibilities and a specified-restricted, cohering version of those possibilities which we normally identify as our classic, physical realm?

The “Amplituhedron” would show how some quantum particles (like gluons) can manifest coalescing probabilities in a specific subset of Subtle Realm reality we experience as “our” known Physical Universe.” Understanding why the Amplituhedron has the characteristics it does in relation to known physical parameters might in the future inform us more about how the Subtle Realm interacts with the Physical. While in the Physical Realm objective Exteriors primarily interact under local, external-to-each-other, causal ways under space-time parameters, in the Subtle Realm, Exteriors would be causally effective and inseparable in relation to Interiors. Subject and Object would operate under the same effective causal level in a complementary fashion and under a complementary logic. Unlike our normal experience in the Physical realm, Interiors would manifest Exteriors with the same causal efficacy as exteriors would manifest interiors.

Being willing to work with Integral Theory in relation to the emerging physics apparently coming to recognize the importance of a “Subtle Realm” would not only make that theory more scientifically (and culturally) relevant but also show that this “theory of everything” is particularly universal in scope and not only meant to attract psychologists, self developmentalists and social or environmental activists.




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