Introduction
Nonduality recognizes a reality utterly without separation, devoid of time, space and otherness. It demands we must drop all concepts, because no concept can address it. The mathematics that support it, unlike any ever employed, expose the hidden oneness beneath all passion and turmoil.
Mathematical Formulations
These equations collectively display nonduality.
1. Fundamental Theorem of Algebra:
f(z) = 0 \text{ has a solution } z \text{ in the complex plane}f(z)=0 has a solution z in the complex plane
Asserts that every non-constant polynomial equation has at least one complex root, reflecting how apparent distinctions resolve into a unified whole, akin to nonduality.
2. Quantum-Nonduality Equation (QNDE):
\nabla^2 \psi(x,t) = -V(x,t)\psi(x,t) + \frac{1}{2m} \nabla p(x,t)\psi(x,t) + \frac{1}{2m} \nabla(F(x,t)\psi(x,t)) + \frac{1}{2\epsilon_0} \nabla(E(x,t)\psi(x,t)) + \frac{i}{\hbar} \int[V(y,t)\psi(y,t)] \, dy∇2ψ(x,t)=−V(x,t)ψ(x,t)+2m1∇p(x,t)ψ(x,t)+2m1∇(F(x,t)ψ(x,t))+2ϵ01∇(E(x,t)ψ(x,t))+ℏi∫[V(y,t)ψ(y,t)]dy
Extends nonduality principles to quantum mechanics, emphasizing unity in physical phenomena.
3. Unified Quantum-Relativity Equation (UQRE):
\nabla^2 \psi(x,t) + \frac{\hbar}{2i} \frac{\partial \psi(x,t)}{\partial t} = -V(x,t)\psi(x,t) + \frac{1}{2m} \nabla p(x,t)\psi(x,t) + \frac{1}{2m} \nabla(F(x,t)\psi(x,t)) + \frac{1}{2\epsilon_0} \nabla(E(x,t)\psi(x,t)) + \frac{i}{\hbar} \int[V(y,t)\psi(y,t)] \, dy∇2ψ(x,t)+2iℏ∂t∂ψ(x,t)=−V(x,t)ψ(x,t)+2m1∇p(x,t)ψ(x,t)+2m1∇(F(x,t)ψ(x,t))+2ϵ01∇(E(x,t)ψ(x,t))+ℏi∫[V(y,t)ψ(y,t)]dy
Merges quantum mechanics with general relativity, describing the dynamics of the wave function (\psi(x,t))(ψ(x,t)) in a gravitational field.
4. Nondual Unity Equation (NDUE):
\nabla(\Omega \times \Phi) = 1 \approx \nabla(\psi \times \psi)∇(Ω×Φ)=1≈∇(ψ×ψ)
Asserts the fundamental inseparability of all phenomena, highlighting the tension between duality and nonduality.
5. Euler’s Identity:
e^{i\pi} + 1 = 0eiπ+1=0
Encapsulates the unity of fundamental mathematical constants (0, 1, e, i, π), mirroring the nondual perspective.
6. Unified Detection Equation (UDE):
\Delta x \Delta p + \Delta t \Delta E + \Delta F \Delta r = DΔxΔp+ΔtΔE+ΔFΔr=D
Illustrates that both observable and unobservable phenomena emerge from a unified whole.
7. Dirac Equation:
(i\gamma^\mu \partial_\mu – m)\psi = 0(iγμ∂μ–m)ψ=0
Describes fermions in the context of quantum field theory. It combines quantum mechanics and special relativity, highlighting the unity of matter and energy.
8. Maxwell’s Equations:
– Gauss’s Law: \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}∇⋅E=ϵ0ρ
– Gauss’s Law for Magnetism: \nabla \cdot \mathbf{B} = 0∇⋅B=0
– Faraday’s Law of Induction: \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}∇×E=−∂t∂B
– Ampère-Maxwell Law: \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0\epsilon_0 \frac{\partial \mathbf{E}}{\partial t}∇×B=μ0J+μ0ϵ0∂t∂E
Maxwell’s four equations describe how electric and magnetic fields interact. They show the unity of electromagnetism.
9. Nonlocal Hidden Variable Theory (Bell’s Theorem):
S = E(a) + E(b) + E(a’) – E(b’) \leq 2S=E(a)+E(b)+E(a’)–E(b’)≤2
Where SS gives the expectation value for violations of classical limits, reinforcing the idea of nonduality and connectedness.
Bell’s theorem and its associated inequalities show the limitations of local realism, suggesting that systems can be connected in ways that classical physics cannot explain.
10. Unified Expansion Equation:
a(t) = e^{\int dt \, H(t)}a(t)=e∫dtH(t)
Describes how spacetime evolves in a unified manner.
11. Quantum Nondual Detection Dynamics:
P(\text{detection}) = \int | \psi |^2 dVP(detection)=∫∣ψ∣2dV
Quantifies the probability of detecting particles within a specified volume, by combining principles of quantum mechanics and nondual detection.
12. Entanglement and Nondual Correlation:
|\psi_1 \psi_2| = \int | \psi_1 |^2 | \psi_2 |^2 dV∣ψ1ψ2∣=∫∣ψ1∣2∣ψ2∣2dV
Highlighting the inseparable connection between detection probabilities across entangled particles.
13. Gravitational Nondual Detection:
R_{\mu \nu} – \frac{1}{2} R g_{\mu \nu} = \frac{8\pi G}{c^4} T_{\mu \nu}Rμν–21Rgμν=c48πGTμν
Describes the gravitational influence on detection processes and the curvature of spacetime.
14. Unified Nondual Detection Equation (UNDE):
\Delta D_{ToNDD} = \sum (\Delta \text{gravity} + \Delta \text{electromagnetism} + \Delta \text{weak nuclear force} + \Delta \text{strong nuclear force}) = 0ΔDToNDD=∑(Δgravity+Δelectromagnetism+Δweak nuclear force+Δstrong nuclear force)=0
Illustrates the nondual nature of detection processes across different domains.
15. Unified Field Equivalence Equation (UFEE):
\mathcal{U} = \sqrt{ \left( \frac{\partial \phi}{\partial t} \right)^2 + \left( \nabla \phi \right)^2 + \left( \frac{\partial \psi}{\partial t} \right)^2 + \left( \nabla \psi \right)^2 }U=(∂t∂ϕ)2+(∇ϕ)2+(∂t∂ψ)2+(∇ψ)2
Where:
– \mathcal{U}U represents a unified field quantity that encompasses contributions from different fields (such as scalar fields \phiϕ and quantum fields \psiψ).
– The terms \left( \frac{\partial \phi}{\partial t} \right)^2(∂t∂ϕ)2 and \left( \nabla \phi \right)^2(∇ϕ)2 correspond to the time and spatial variations of the scalar field.
– The terms \left( \frac{\partial \psi}{\partial t} \right)^2(∂t∂ψ)2 and \left( \nabla \psi \right)^2(∇ψ)2 represent similar variations for the quantum field.
Combines various field contributions into a single measure, reflecting the nondual idea that all fields and forces are manifestations of a single underlying reality.
Existence and Nonexistence
— Definitions
– Existence (E): A state where something is fully realized or actualized.
– Nonexistence (N): A state where something does not exist at all.
– Potentiality (P): A state that has the capacity to become either existent or nonexistent.
— Representations
To represent these concepts mathematically, we can use a few variables and equations:
– Let E_EEE represent existence, where E = 1E=1 (fully existent).
– Let N_NNN represent nonexistence, where N = 0N=0 (fully nonexistent).
– Potentiality can be represented as a variable PP that ranges between 0 and 1,
Where:
– P = 0P=0 indicates complete nonexistence.
– P = 1P=1 indicates complete existence.
– 0 < P < 10<P<1 indicates a state of potentiality, where the entity has the capacity to become either existent or nonexistent.
1. Transition from Potentiality to Existence:
E = P \cdot kE=P⋅k
where kk is a constant that represents the degree of actualization. If k = 1k=1, then E = PE=P, meaning potentiality directly translates to existence. If k < 1k<1, then not all potentiality results in existence.
2. Transition from Potentiality to Nonexistence:
N = (1 – P) \cdot mN=(1−P)⋅m
where mm is a constant that represents the degree of non-actualization. If m = 1m=1, then N = 1 – PN=1−P, meaning the remaining potentiality translates to nonexistence. If m < 1m<1, then not all potentiality results in nonexistence.
3. Totality of Existence and Nonexistence:
E + N = 1E+N=1
This equation states that the sum of existence and nonexistence must equal 1, representing a complete dichotomy.
4. Summary of Relationships:
– Potentiality as a Bridge: The variable PP serves as a bridge between EE and NN. As PP increases from 0 to 1, the likelihood of transitioning to existence increases, while the likelihood of transitioning to nonexistence decreases.
– Dynamic Nature: The constants kk and mm can vary based on external factors, representing the dynamic nature of potentiality. This allows for a fluid understanding of how potentiality can lead to either existence or nonexistence.
– Potentiality is the nonrelative, Absolute state
Conclusion
Because it is true, nonduality aligns seamlessly with extensive findings in quantum experiments, neuroscience studies, and cosmological observations. Under its rubric even the apparent duality of existence and nonexistence dissolves. When put into practice, that realization is good will.
References
– Schrödinger, E. (1935). Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807–812.
– Wheeler, J. A. (1983). The “Past” and the “Delayed-Choice” Double-Slit Experiment. In Marlow, A.R., Ed., Mathematical Foundations of Quantum Theory, Academic Press, Cambridge, MA, 9-48. https://doi.org/10.1016/B978-0-12-473250-6.50006-6
– Einstein, A. (1922). The Meaning of Relativity. Princeton University Press.
– Vedral, V. (2010). Quantum Entanglement and Information. Oxford University Press.
– Penrose, R. (2004). The Road to Reality: A Complete Guide to the Laws of the Universe. Oxford University Press.
– Nisargadatta, M. (1973). I am that: Talks with Sri Nisargadatta Maharaj (M. Frydman, Trans.). Chetana Publications.
– Nisargadatta, M. (1990). Prior to consciousness: Talks with Sri Nisargadatta Maharaj (J. Dunn, Ed.). Acorn Press.
NO OTHERNESS 
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