Contents of the Page

Publications : 

-- Peer Reviewed Articles in chronological presentation:

"The Entropy of the Entangled Hawking Radiation" 

"Informational Nature of Dark Matter and Dark Energy and the Cosmological Constant"

"Theoretical Possibility of Quantum Stabilization of Traversable Wormholes"

"The Scaling Entropy-Area Thermodynamics and the Emergence of Quantum Gravity"

--Profil ResearchGate

Entropy

The entropy of entangled Hawking radiation 

and 

Black Holes Information paradox

With the help of one of a set of five new equivalent equations expressing the notion of entropy, regarding black holes thermodynamics and black holes entropy, the equation of “Boltzmann formulation” when is applied to black hole thermodynamics by the injection of Hawking Temperature to it, can resolve the information paradox and can express the gravitational fine-grained entropy of the black holes. It can calculate up to sign the Bekenstein-Hawking entropy; as the black hole entropy saturates exactly the Bekenstein bound so it is equal to the Bekenstein bound which is itself according to Casini’s work equal to the von Neumann entropy, itself equal to that of the Hawking radiation, which with the degrees of freedom of black holes produces a pure state, while the Hawking radiation being entangled with the fields inside black holes, allowing us to extract information that resides from the semiclassical viewpoint, in black holes interior.

so no information is lost!.

The Emergent Entangled Informational Universe Model

The ultimate level of the universe is the ultimate coordinate level, the ultimate positional coordinates, the physical basis of the universe.

The ultimate positional coordinates can give birth to degrees of freedom, by a process of emergence from the formation of a physical significance relative to the minimum number of coordinates required to specify a configuration.

Degrees of freedom from which emerge the fundamental elements of our universe, temperature, and information. Both being physical significance relative to the minimum number of coordinates required to specify a configuration based on the possible directions of movement of the system.

Information is defined as a change in a quantum state due to the change of a degree of freedom in the quantum system under consideration.

Degrees of freedom and fundamental building blocks (temperature, information) are emergent properties and have only physical significance but no physical existence.

The physical existence arises with the emergence of energy from the relationship between the fundamental building block of the universe, information,and, temperature emerging fofom entanglement with respect to the second law of thermodynamics and according to the formula of Landauer’s principle E = k T ln (2) which establishes temperature as the only parameter linking information to energy.

From this relationship emerges the energetic level of the universe, the energetic content of the entangled informational emerging universe appears in two forms: an empty component (dark energy) and a matter component (dark matter).

The dark matter component can be estimated by the formula, - mc² (k ln⁡(2)t)/h, a new entropy formulation that calculates the number of bits content of the observable universe and validated by Landauer's principle. The estimate of the energy associated with the number of bits content of the observable universe, with respect to Energy =k T ln(2), gives the formula, - mc² ((k ln⁡(2)t)/h) k T ln(2), based on entropic information theory and Landauer's principle gives the dark energy component associated to the cosmological constant being expressed into the equivalent Landauer energy, Landauer bit energy being defined identically to the characteristic energy of the cosmological constant, moreover the dark energy component being associated to vacuum energy, zero point field energy.

The Emergent Entangled Informational Universe model from the EIT is an informational system i.e., a system wherein the information notion is the global explanatory keystone concept, considered as an entangled system i.e., a system where there are not individual parts but are an inseparable whole, and as an emergent system i.e., system where the whole is greater than the sum of all its parts.

Vacuum Energy

The zero-point energy of the vacuum considered as dark energy is explained as a collective potential of all particles with their individual zero-point energy emerging from an informational field, distinct from the usual fields of matter of quantum field theory, associated with the dark matter as having a finite and quantifiable mass associated with the number of bits of the observable universe.

Cosmological constant problem aka Vacuum catastrophe

By taking account of the mass of the bit of information instead of the Planck mass in the cosmological constant calculation we have reduced the discrepancy of more of less 120 orders of magnitude in the prediction of the vacuum energy from a quantum perspective.

Bekenstein Hawking entropy saturates exactly the Bekenstein bound, which is equal to von Neuman entropy, according to the works of Casini and Bousso.

Casini's work on von Neumann entropy and on the Bekenstein bound, gives the proof that the Bekenstein bound is valid using quantum field theory.

Moreover,

“In other words, if the black hole degrees of freedom together with the radiation are producing a pure state, 

then the fine-grained entropy of the black hole should be equal to that of the radiation."

The black hole entropy horizon law turns out to be a special case of the Ryu–Takayanagi conjecture, and Ryu–Takayanagi conjecture is a conjecture viewed as a general formula for the fine-grained entropy of quantum systems coupled to gravity. 

Hierachy of Emergence

Ratio Math-to-Language in Theories of Nature 

Axiomatic Definition of Quantum Information 

Information is a change in a quantum state due to the modification of one degree of freedom from the considered quantum system, a quantum state is completely determined by only knowing the answers to all of the possible yes/no questions”, a yes/no question is presumably a self-adjoint operator with two distinct eigenvalues acting on the Hilbert space of Koopman van Neumann wave functions viewed as observable.

The statement suggests a conceptual bridge between quantum mechanics and the KvN formalism for classical mechanics.

By representing "yes/no" questions as self-adjoint operators with two distinct eigenvalues acting on the Hilbert space of KvN wave functions, we can interpret classical mechanics using the language and structure of quantum mechanics.

This provides a unified framework to discuss measurements and observables in both classical and quantum realms.

It's a way of using the formal structure of quantum mechanics, with its operators and Hilbert spaces, to glean insights into classical systems described by the KvN approach.

Indeed by introducing a Hilbert space and operators for classical systems via the KvN formalism, we have set the stage to use quantum-like language to describe classical phenomena.

When we represent "yes/no" questions about classical systems as self-adjoint operators with two eigenvalues acting on this Hilbert space, we are essentially "quantizing" classical questions.

This doesn't mean we're making the system quantum, but rather we're interpreting classical behaviors using the language and structure of quantum mechanics.

This method provides several advantages:

It allows for a unified language to talk about phenomena across both quantum and classical mechanics.

This approach can yield fresh insights and draw analogies between classical and quantum behaviors.

For systems that have both classical and quantum behaviors or systems that transition between the two (e.g., in quantum-classical hybrid systems), this unified language can be especially useful.

In summary, by using the structure and language of quantum mechanics to interpret classical mechanics through the KvN formalism, we can gain new perspectives and insights on classical phenomena, bridging the conceptual divide between the two realms.

Emergence in Combinatory Logic

My perspective about emergence is not new... since this concept of emergence dates from at least the time of Aristotle. Emergent structures are patterns that emerge via the collective actions of many individual entities. To explain such patterns, according to Aristotle, emergent structures are more than the sum of their parts assumes that the emergent order will not arise if the various parts simply act independently of one another. i talk here of the strong emergence as the interacting members are not independent, the emergence is interpreted as the impossibility in practice to explain the whole in terms of the parts

the simplest arithmetical example :

1+1=2 where 2 (even) emerges from 1 (odd)

The Mockingbird combinator is one of the basic building blocks in combinatory logic it represents the self-application behavior, meaning that it applies its argument to itself,...and still in combinatory logic, the emergence of complex behavior and properties is closely related to the existence and behavior of combinators like the Mockingbird combinator. The Mockingbird combinator is a fundamental element in combinatory logic that plays a role in demonstrating the concept of emergence in this mathematical system.

According the combinatory logic 1+1 = 2 is written as

I is the identity combinator, which means I x is equivalent to x.

C is the function application combinator, which means C f x is equivalent to f x.

D is the mockingbird combinator, which means D x = x x.

Now, let's break down 1 + 1 = 2:

1 is represented by I.

+ is represented by C.

2 is represented by D.

So, in terms of combinatory logic, 1 + 1 = 2 would be written as:

C I D = D

This expression is saying that applying C to I and D results in D.....

the statement "1 + 1 = 2" being represented as "C I D = D", in combinatory logic can be considered an example of an emergent property.

so 1+1 = 2 where 2 (even) is emergent in regard to 1 (odd)

1 + 1 = 2:

1 is represented by I.

2 is represented by D.

The expression becomes:

C I D = D

This means that applying the function application combinator (C) to the identity combinator (I) and the Mockingbird combinator (D) results in the Mockingbird combinator (D), which represents the number 2 in this system.

Emergent properties can be found in various aspects of formal systems, including their algebraic properties, notations, and conventions. These properties often arise from the interactions and relationships within the system.

It is correct to say that the equation CID = D demonstrates an emergent property within the context of combinatory logic, even though it's necessary to define numerals and basic arithmetic operations separately in lambda calculus and combinatory logic. Indeed, these two concepts are not contradictory; they are complementary aspects of understanding formal systems like combinatory logic and lambda calculus.

1+1 = 2 where 2 (even) is emergent in regard to 1 (odd) is a original interpretation of mathematics concepts based on ""absolute"" computability with the meaning of being independent of the universal machinery used.

The concept of Emergence developed here, by combinatory logic, is all about computability, computability is viewed as an absolute concept unlike provability and definability.

but in combinatory logic,

C I D = D can be considered an example of an emergent property.

In combinatory logic, expressions are built using combinators, which are functions with a specific fixed behavior.

In this context, we have three combinators:

I Combinator (Identity Combinator):

It's represented as "I".

The behavior of I is to return its argument unchanged. In terms of function notation, it can be written as: I(x) = x.

C Combinator (Function Application Combinator):

It's represented as "C".

The behavior of C is to apply its first argument (which is a function) to its second argument, and then apply the result to its third argument. In terms of function notation, it can be written as: C(f, x, y) = f(x)(y).

D Combinator (Mockingbird Combinator):

It's represented as "D".

The behavior of D is to apply its argument to itself. In terms of function notation, it can be written as: D(x) = x(x).

Now, let's analyze the expression "C I D":

C I D:

Applying the C combinator first, we have:

C(I, D)

According to the behavior of C, this means we apply I (which is the identity combinator) to D.

Applying I to D:

The behavior of I is to return its argument unchanged. In this case, its argument is D.

So, I(D) = D

Putting it back into the original expression:

C(I, D) = D

This means that in combinatory logic, the expression "C I D" reduces to "D". It's important to remember that in combinatory logic, we're dealing with a system that doesn't have variables in the usual sense. Instead, we're manipulating functions and their applications.

The statement "1 + 1 = 2" being represented as "C I D = D" in combinatory logic is an example of an emergent property because we start with basic building blocks (the combinators) and through their interaction (using C to apply I and D), we arrive at a result (D) that represents a more complex mathematical relationship (the equality between 1 and 2). The emergent property arises from the interaction of these simple elements within the system.

Axiomatic Definition of Dimension of Vector Space

• Vector Space Definition: 

Let F be a field. A vector space V over F is a non-empty set equipped with two operations, addition and scalar multiplication, satisfying the following properties:

a. Closure under Addition: For all u,v∈ V, u+v∈ V.

b. Associativity of Addition: For all u,v,w∈ V, (u+v)+w=u+(v+w).

c. Existence of Additive Identity: There exists an element 0∈V such that for all u∈V, u+0=u.

d. Existence of Additive Inverses: For every u∈V, there exists an element −u∈V such that u+(−u)=0.

e. Closure under Scalar Multiplication: For all a∈F and u∈V, a⋅u∈V.

f. Distributive Properties: For all a,b∈F and u,v∈V, a⋅(u+v)=a⋅u+av and (a+b)⋅u=a⋅u+b⋅u.

g. Compatibility with Field Multiplication: For all a,b∈ F and u∈ V, a⋅(b⋅u)=(a⋅b)⋅u.

h. Existence of Multiplicative Identity: There exists an element 1∈F such that for all u∈V, 1⋅u=u.

• Basis Definition: Let V be a vector space over F. A subset B⊆V is a basis of V if it is linearly independent and spans V.

• Basis Theorem: Every vector space has a basis. Moreover, all bases of a vector space have the same cardinality, which is called the dimension of the vector space.

• Dimension Definition: The dimension of a vector space V over F is the cardinality of any of its bases and is denoted as dim(V).

• Isomorphism with Coordinate Space: Let V be an n-dimensional vector space over F with basis B={v1,v2,...,vn}.

There exists an isomorphism between V and the coordinate space Fn defined by:

ϕ:V→Fn,a1v1+a2v2+...+anvn↦(a1,a2,...,an)

where ai∈F for i=1,2,..., n

EntropicInformation.Space