Mathematical Modeling of Consciousness for Unifying Causation, Relativity and Quantum Mechanics

Quantum physics and gravity are two different concepts which need to be unified in a widely acceptable way. While electromagnetism, weak nuclear force, and strong nuclear force were accurately unified under the framework of quantum field theory, gravity remains elusive and couldn’t be unified with quantum mechanics. However, gravity is accurately understood by the theory of relativity, which is not complementing quantum physics. This elusiveness is due to the missing consciousness dimension in the mathematical frameworks of fundamental physics, which can explain the causation of gravity, quantum mechanics, and reality. Intricately interweaving the dimension of consciousness with the mathematical frameworks of fundamental physics can make our understanding of reality complete.


Introduction
When understanding reality and how things behave in nature, causation plays a crucial role.Some believe causation is primitive, basic or fundamental, while others argue it is derivative, a construct or a byproduct.As per David Hume and Simon Blackburn [1], causation is patterns composed by the human mind in response to regularities in nature.From their viewpoint, the explanation of the cause and effect is unknown, but how things behave can be analysed.Further, causation is not part of reality but a human construct that depends on the laws of nature.In contrast, Richard Swinburne [2] argues causation is a fundamental of reality.Causation cannot be explained by anything else, such as patterns, regularities or laws in nature.Similarly, Robin Le Poidevin [3] describes causation as primitive, which cannot be explained by other constructs or concepts.In fact, the other concept can be explained by causation.Most notably, he argued that time is derived from a change and attributed to cause and effect.That is, to the direction of cause and effect, time flows.However, Huw Price [4] argues that laws of physics do not explain the direction of time, and backward causality is also possible.
In the laws of physics, the notion of time appears as a basis for the progression of states from the past to the present into the future.As per Newtonian physics [5], there exists an absolute time independent from an observer, and it flows from past to future at a consistent pace throughout the universe.However, later based on the theory of relativity [6], Einstein showed that time is relative to the observer, where that is the speed of light (not the time), same for any reference frame.Time emerges from an awareness of change where both change and awareness are important to perceive time.The change underpins causation which implies cause and effect following the laws of thermodynamics.As per the second law of thermodynamics, the total entropy of a process will not decrease.Therefore, entropy gives a physical meaning to the direction of time, sometimes called an arrow of time.Moreover, from relativity, the awareness of the observer on the cause and effect perceiving at a different rate of change creates relativistic time.The awareness of the observer brings consciousness into the picture.
It is not only physical states, but the neural and mental states are also important to understand causation.In fact, the idea of mental causation-the mind's causal interaction with the physical world and behaviour-is a quite old established philosophy evolving even today.About 2500 years ago, the Buddha stated (in Pali), "Manō pubbangamā dhammā -manō setthā manōmayā", which means the mind underpins causation and the mind is supreme.The Buddha referred to the causation as paticca-samuppada, which is discussed in detail in Patthana Pakarana in Abhidhamma Pitakaya [7,8].Walter Sinnott-Armstrong [9] argues that physical states or neural states cannot exist without mental terminology.The interrelation of mental, neural and physical states describes different levels of causation.
The observer and the awareness are discussed in both relativity and quantum mechanics.In relativity, the notion of time on causation is relativistic and depends on the speed and gravity (i.e., the curvature of space-time) [10].On the other hand, quantum mechanics imposes limitations on awareness of the physical world.As per Heisenberg's uncertainty principle [11], it is impossible to be aware of both the position and momentum (or certain pairs of physical quantities) of a particle with perfect accuracy.Eugene Wigner suggested that consciousness interacts with causation at the quantum level.He stated that consciousness causes the collapse of the wave function to experience the quantum reality-the quantum level observation or measurement [12].Recent discoveries suggest that awareness can be faster than light exceeding physical limitations when quantum entanglement creates non-local reality [13,14,15].Because of such developments in fundamental physics, some scholars now hypothesise consciousness as fundamental [16].
The causation of consciousness is still a contemporary research topic.Some believe consciousness is caused by brain function.Roger Penrose initially suggested that consciousness does not correlate with the brain's neural function [17].He argued that a large portion of brain neurons (i.e., the Cerebellum contains ∼80% of the brain's neurons) are not contributing to consciousness.However, later, Roger Penrose supported the hypothesis that consciousness emerges from quantum vibrations in the orchestrated collapse of microtubules inside brain neurons [18].This idea may unify the consciousness with neuroscience and quantum mechanics.In contrast, Artificial Intelligence (AI) imitating the brain's neural computation [19,20] aka deep neural networks (e.g., convolution neural networks (CNN), recurrent neural networks (RNN), transformer models) has achieved impressive developments related to human cognitive functions (e.g., image processing, natural language processing (NLP)).These artificial neural networks proved their ability to self-learn and adapt, which is studied in reinforcement learning-a form of machine learning in which an AI agent learns by trial and error sequentially [21].On the other hand, McFadden posits that consciousness is underpinned by the brain's energy field [22].He suggested that electromagnetic energy correlates with consciousness and interplay with reality.
The hard problem of consciousness [23] articulates how perceptions or subjective experience (e.g., colour, taste, shapes, etc.) map into objective measurements like neural activities in a brain.The recent research on neuroscience, cognitive models and neural correlates of consciousness tries to understand how perception and consciousness are formed in the brain.On the other hand, the observable reality is about 5%, and the rest of the universe consists of dark matter and dark energy, which cannot be observed but interact with reality.Moreover, proof of non-local reality suggests that awareness is beyond physical limitations, such as the speed of light.Being aware of dark matter, dark energy and non-local reality might require driving consciousness beyond our sensory perception (i.e., touch, sight, hearing, smell and taste).
The contributions of this paper are as follows: (i) Explained consciousness and change as the fundamentals of reality underpinning causation, conservation of energy and momentum, relativity, quantum mechanics and other constructs.(ii) Explained how awareness emerges through consciousness and change.This awareness brings experiences on cause and effect or causation.
(iii) Explained how preserved awareness brings integrity in experiences on reality which is the causation of conservation of energy and momentum, relativity, quantum mechanics and other constructs.(iv) Unified relativity and quantum mechanics based on consciousness and change.The newly introduced consciousness dimension in relativity helps to understand what uncertainty means to relativity.(v) Explained gravity based on consciousness and change.The gravity is none other than preserved awareness near mass.

Methods
In our previous paper [24], we bring forward the idea that consciousness is fundamental in the universe creating reality.We suggested: (i) Consciousness is a sequential process that relates to a single state of reality at a given instant and underpins awareness when the process continues, (ii) Consciousness cycle is the shortest duration to be aware of the change of reality by an observer, (iii) Consciousness constructs space-time based on awareness, (iv) Consciousness interplays with energy and matter such that consciousness photons energy transforms into consciousness particles conserving energy and momentum, (v) Consciousness correlates with relativity.When the observer is moving, both time and consciousness dilate, (vi) Consciousness correlates with quantum mechanics and behaves according to wave-particle duality.
We mathematically expressed the above idea such that, where m µ is the rest mass of consciousness particle, h is the Planck constant, c is the speed of electromagnetic waves, v is the speed of consciousness particle and the f µ is the frequency of consciousness wave.Note that Equation 1 unifies matter, energy and consciousness.Further, there is no fundamental time dimension other than consciousness and change.Time is a derivation of consciousness and change.Further, based on our previous paper [24], the established idea of time dilation in relativity, was referred to understand the dilated period of consciousness T v based on the rest period of consciousness T 0 : where the v is the speed of the observer.From now on, note that the dilation of consciousness causes the time dilation effect in causation.Further, the frequency of consciousness f µ was expressed: where, we defined the cycle of consciousness T v as the shortest duration to be aware of the change of reality by an observer.Therefore, f µ implies the state of awareness of an observer in a given frame of reference.Based on Equation 4, only consciousness and change are fundamental, where time is a perception based on the awareness underpinned by consciousness and change.
In physics, four fundamental forces govern the interactions between particles in the universe.These forces are gravity, electromagnetism, the weak nuclear force, and the strong nuclear force.While three of these forces (i.e., electromagnetism, weak nuclear force, and strong nuclear force) have been successfully unified under the framework of quantum field theory, gravity remains elusive and has yet to be successfully reconciled with quantum mechanics.With our consciousness-based mathematical modelling of reality illustrated by Equation 1, relativity and quantum mechanics have been unified.This unification will help to understand the causation of gravity in line with the existing framework of quantum mechanics and relativity.Now on, we consider only consciousness and change are the fundamentals of reality.Based on these two fundamentals, we gain awareness and perceive various secondary constructs.To understand gravity, we postulate: (i) Only consciousness and change are the fundamentals of reality which underpin awareness, (ii) Reality behaves in a way the awareness is preserved, which causes the integrity of the experience.(iii) Gravity is also a perception in awareness caused by consciousness and changes.
As illustrated in Figure 1, the reality behaves in a way the awareness is preserved.That is the cause of the invariance of the speed of light in all uniformly moving reference frames, as postulated in special relativity.Further, space-time is a construct of awareness which is preserved in reality.That can be mathematically expressed by Equation 1, which complements with constructs of conservation of energy and momentum, relativity, and quantum mechanics.

Understanding the Consciousness and Change as Fundamentals
Consciousness is fundamental that underpins heterogeneity, discreteness, causation, time, and memory.In Equation 1, we discussed how consciousness interplays with matter and energy and conserves energy IC-MSQUARE-2023 Journal of Physics: Conference Series 2701 (2024) 012051 and momentum.We discussed how consciousness creates matter which is the fundamental process of the creation of matter.Therefore, consciousness is intricately interweaving with reality and maintains integrity between consciousness and reality.Even though everything is an effect of consciousness, not everything has consciousness.However, everything is changing, so change is a fundamental characteristic.Everything change maintains its integrity with its origin from consciousness.We consider both consciousness and change as fundamental.But, it is equally acceptable to consider consciousness as the ultimate fundamental of characterizing the change.However, since there is no point in discussing consciousness in non-consciousness effects of consciousness, yet the change is the universal characteristic, we consider changing as a fundamental characteristic in reality.Therefore, consciousness can be considered the fundamental cause and change is the fundamental characteristic of reality.
We defined consciousness as a sequential process that relates to a single state of reality at a given instant and underpins awareness when the process continues.Therefore, when considering a given discrete point of consciousness, a set of relationships can be detected, as implied by Equation 1.However, when the discrete process continues, all other constructs emerge.The perception of awareness, causation, correlation, space-time, and all other laws of nature emerge through this consciousness process.The consciousness process is irreversible, and backward causation is not possible.

Understand Consciousness and Change as the Foundation of Fundamental Physics
Fundamental physics can be understood either by relativity or quantum physics.These two fundamental frameworks are not complementing each other.In relativity, we understand reality based on the interaction of mass and energy in space-time.In relativity, both position and momentum are certain.However, when the dimensions of the subject get smaller, that is, either in space or time, reality cannot be understood by relativity anymore, where we need quantum mechanics to explain reality.If we look into the main difference between these two frameworks, the uncertainty of the observation becomes obvious.
The uncertainty of an observation is related to the consciousness of an observer and the complexity of the phenomena.Heisenberg's uncertainty principle [11] describes that it is impossible to be aware of multiple physical quantities or complex scenarios with perfect accuracy at the quantum scale.The more awareness, the less uncertain, and the less awareness, there will be more uncertainty.Awareness has its limits, and like everything discreet, awareness is also discreet and has the shortest duration to be aware of the change in reality.This shortest time is what was defined as the consciousness cycle, the shortest duration that can be perceived in reality.On the other hand, change is a fundamental attribute of reality that brings uncertainty to the observation.In a complex phenomenon, it might be difficult to sample the change with consciousness precisely.Therefore, uncertainty cannot be avoided at the quantum scale, and the quantum nature of reality emerges.In contrast, when the subject is reasonably large in space-time, the observer can reasonably be aware of the behaviour of the subject where uncertainty is irrelevant.In summary, awareness is one of the important concepts for our understanding of reality and an effect of consciousness and change.Observers' consciousness and the complexity of the phenomena determine what can be aware and observed.
If there is the shortest duration to be aware of the change of reality, how to understand time?Time is a construct based on the awareness of change in reality.If the environment is homogeneous, there will be no experience of external change hence no passing of time or boundary of space, assuming the observer is unaware of their own mechanism of awareness or existence.Therefore, space-time is completely perceived by consciousness.The observer's awareness on its own or self-awareness emerged from consciousness, is an attribute of life.Self-awareness is unique to individual life forms.Since consciousness is a sequential process subject to change, self-awareness can experience change based on its own consciousness process without being aware of external change.Therefore, space-time and observations are relativistic experiences based on consciousness and change.That is what was modelled by Einstein's' relativity.
In our previous paper [24], we mapped the dimension of time, which represented all dynamics of fundamental physics, into consciousness and unified the theory of relativity and quantum physics.That unification can be understood by Equation 1.That enabled modelling of the interplay of consciousness, matter, and energy, creating reality.In that way, space-time, energy and matter are not mutually exclusive concepts from consciousness.This relationship causes the natural integrity of the experience of reality and life.That is the fundamental principle of causation.

Understand the Gravity through the Consciousness
Gravity is an exceptional experience in reality.In relativity, the space-time that bends near mass is defined as gravity, which Albert Einstein modelled precisely in relativity.After studying relativity, John Wheeler stated [25], "Space-time tells matter how to move; matter tells space-time how to curve".However, relativity does not explain the causation of bending space-time near mass causing gravity, although it is validated as a correlated phenomenon of light bending due to the curvature of space-time near mass.In physics, many cosmological phenomena re-validated the accuracy of relativity, which lays a strong foundation for our understanding of the behaviour of reality, but not the causation.
Then what is the causation of gravity?To understand this, we use consciousness and change as fundamentals of reality.In relativity, time is relative to the observer and can be experienced through the behaviour of light.This observation is, in fact, an event of change.Similarly, gravity is an experience in reality that brings a unique perception of the behaviour of change (or event) in space and time observable through light.It is important to understand why light bends near mass to understand gravity.In relativity, the bending of space-time causes it.However, we discussed neither space nor time fundamentals of reality.Therefore, it is important to understand why light bends near mass based on consciousness and change -the fundamentals of reality.
We replace the concept of time with awareness since time emerges through the consciousness of an event.We already discussed that consciousness and change are the fundamentals (causes) that bring the perception of time (effect).Therefore, replacing time with awareness doesn't change Einstein's relativity model.However, now with consciousness, it is possible to bring uncertainty into relativity, unify relativity and quantum mechanics, and understand quantum gravity.
First, let's understand the special theory of relativity from the awareness perspective.Please refer Figure 2. Let's assume a reader with a book and an atomic clock in a spaceship.We analyse the system when the spaceship moves at constant speeds of V 1 and V 2 , where V 1 < V 2 .Based on the preserved awareness, the number of consciousness cycles, the atomic clock cycles, and the pages read remain consistent on both occasions.We call that the reader is in preserved awareness, where the reader always experiences integrity in reality.That is how the special theory of relativity is understood through consciousness.
Next, let's understand the general theory of relativity from the awareness perspective.Please refer Figure 3. Let's assume the same reader is moving at V 1 speed, passing a mass.The only freedom by nature the system has in motion is, in a way, the awareness is preserved.If they need to maintain the constant speed V 1 , then they move in a curved space-time such that it is described in the general theory of relativity.However, the causation of this motion is not due to curved space-time but rather constrain in preserved awareness.When the reader moves at constant V 1 speed through the mass, the number of consciousness cycles, the atomic clock cycles, and the pages read remain consistent.

Conclusions
Consciousness and change are fundamentals of reality which govern the causation.They create the perception of awareness and time.Awareness is a construct which emerges from a conscious process.Reality behaves such that awareness is preserved and maintains the integrity of consciousness experiences.By replacing time with consciousness, we described the causation of relativity.We explained the causation of gravity as a phenomenon which maintains the integrity of consciousness experiences or preserved awareness when interacting with mass and energy.Further, the whole The reader with a book and an atomic clock in a spaceship moving in free space.On two occasions, the spaceship moves at constant speeds of V 1 and V 2 , where V 1 < V 2 .In both occasions, the number of consciousness cycles, the atomic clock cycles, and the pages read remain consistent.That is the fundamental of preserved awareness of the reader where they experience integrity in reality.concept of space-time is a construct of consciousness.But the most important contribution of bringing consciousness into fundamental physics is that it enables us to unify relativity with quantum mechanics.In a similar strategy that consciousness is mapped into time to understand the causation of relativity, consciousness is mapped into uncertainty and unpredictability to understand the causation of quantum mechanics.That enabled establishment of consciousness as a common base for relativity and quantum mechanics and unified both frameworks.Most importantly, this enabled us to explain the causation in reality and fundamental physical observations beyond correlation with theoretical frameworks.In future, we will discuss more on the causation of reality based on consciousness and change to better understand the universe.

Figure 1 :
Figure 1: Understand gravity as an effect of consciousness and change.The null geodesics is caused such that awareness is preserved.The curvature of space-time and dilation of time are caused by the dynamics of consciousness and change preserving awareness.

Figure 2 :
Figure2: The reader with a book and an atomic clock in a spaceship moving in free space.On two occasions, the spaceship moves at constant speeds of V 1 and V 2 , where V 1 < V 2 .In both occasions, the number of consciousness cycles, the atomic clock cycles, and the pages read remain consistent.That is the fundamental of preserved awareness of the reader where they experience integrity in reality.

Figure
Figure The reader with a book and an atomic clock in a spaceship moving near mass.The reader maintains the constant speed V 1 and experiences that they move in curved space-time.In this motion, the number of consciousness cycles, the atomic clock cycles, and the pages read remain consistent.The awareness is preserved such that they experience integrity in reality.