THE CONSERVATION OF MENTAL ENERGY INFORMATION AT DEATH—A hypothetical Mathematical Model..
ΨR = Ψ(t=d) * e^-(t-d)/τ

In a previous write up on “ Information is not lost at death”, we had an overview of how we could draw parallels from Hawkings radiation to model the conservation of mental -information at death and beyond.
In this article we will briefly explore some possible ways in which we can model this concept mathematically..
It is important to note that the model described herein is still conceptual and speculative .Nevertheless it’s a theory worth noting…
We know that according to the laws of quantum mechanics, information is never truly destroyed, it can only change forms. In the same way that Hawking radiation emits from black holes due to quantum effects near the event horizon, the quantum information that comprised a person’s consciousness may continue to radiate or leak out even after biological death.
When a living brain generates consciousness, it does so through intricately networked quantum processes operating below the level of neurons. This ongoing ultra-fast flux of subatomic particles and interactions could preserve some “echo” or residue of the consciousness information even when the physical brain ceases to function.
Perhaps this residual quantum information imprint retains some subtle memory or influence of the consciousness it once generated. Just as Hawking radiation retains imprints of what fell into a black hole, consciousness information may persist in quantum form after death of the body. Interactions between this radiated consciousness information and other quantum systems could theoretically allow at least some aspects of the conscious experience to continue distributed across nature on the quantum level, though not in a localized, subjective way perceivable to others.
So in summary, the Hawking analogy proposes that quantum processes underlying consciousness may prevent absolute loss of information at death, similar to how Hawking radiation retains remnants of collapsed objects. Of course, this remains hypothetical – but the growing interface between physics and consciousness does suggest information is not so easily destroyed as once believed.

Here is an attempt to express the concept mathematically:
Let C = the total quantum information representing a person’s conscious experience at any given moment.
C is composed of innumerable quantum states and interactions between fundamental particles in the brain over picosecond timescales. It can be conceptualized as a complex wavefunction Ψ that changes continuously over time.
At the moment of biological death (t=d), when the brain can no longer sustain coherent neural activity, the localized wavefunction Ψ collapses.
However, due to the quantum nature of consciousness information, some remnant of Ψ persists and begins to radiate outward in accordance with the equation:
ΨR = Ψ(t=d) * e^-(t-d)/τ
Where:
ΨR is the radiated or residual consciousness wavefunction
Ψ(t=d) is the value of the full consciousness wavefunction at the time of death
τ is the characteristic lifetime of ΨR as it dissipates into the environment
t-d-The time elapsed since death.
e-The base of the natural logarithm, approximately equal to 2.71828.
By analogy to Hawking radiation persisting as a form of information leakage from black holes, ΨR represents the subtle “echo” or imprint of the conscious experience that may remain extant on a deeper quantum level, even after death of the physical brain and collapse of Ψ.
Over successive quantum interactions, ΨR would gradually approach zero, though its integrated information may live on distributed throughout nature in perpetuity.
Below is a link to a book titled;
“THE SCIENTIFIC ACCEPTABILITY OF REBIRTH” by Dr Granville Dharmawardena
https://www.buddhanet.net/pdf_file/rebirthscience.pdf

