The main problem I see with the idea of the soul (as an entity that can survive the death of the physical body) is how does this soul interact with the physical body while eluding the observation of physicists. If the soul interacted with the body via a very weak force, it might elude the observation of physicists but its influence on the body would seem insignificant. If on the other hand the soul interacted with the body via a relatively strong force, this force should be detectable by physicists.

One possible answer could be that the soul interacts with the body via a relatively strong force that results in measurable changes in brain activity but the soul's influence on the brain would normally be within the usual variance of human behavior and due to the rather limited level of detail at which we can measure complicated brain processes (fMRI, EEG...) and the myriad external influences on the brain, it would be difficult to tell whether the measurable changes in brain activity are or are not entirely caused by known physical forces.

The problem with this answer is that the brain consists of the same elementary particles that physicists observe with high precision in particle accelerators and there they have failed to detect a force other than the known physical forces. A relatively strong force should be detectable in particle accelerators. So if the soul influences the brain in a significant way, this influence would seem to be limited to the brain and maybe to some other complex physical objects where it would be difficult to differentiate this influence from the known physical forces. Why would the soul influence only brains or other complex objects? The only reason that comes to mind is that the soul would want to hide from detection, which seems rather questionable.

So I have searched for a different possible mechanism of interaction between the body and the soul and have come up with a combination of weak force and resonance: the soul might interact with matter via a very weak force and that's why it has not been detected even in precise observations in particle accelerators, but it would be able to influence the brain in a significant way via resonance. Resonance is a familiar physical phenomenon in which a periodic external force or vibrating system drives another system to oscillate with greater amplitude at specific frequencies. Thus the effects of a weak force would be amplified, theoretically without limit if the driven system had no resistance. It might be that only highly complex structures like neural networks provide patterns that can resonate with the soul and so the otherwise weak interaction between soul and matter would be difficult to detect outside the brain.

The interaction between the soul and the brain could also go the other way: via resonance, brain activity would influence the soul, and thus the soul would be able to receive information from the brain, including information that encodes perceptions of the sensory system of the physical body. After the death of the physical body, the soul could continue to exist and hold consciousness but would lose access to further information provided by brain activity.

As a layman in physics, I don't really know if this idea is possible, specifically whether it is possible that a weak force would be able to induce significant resonance on the scope of neural networks without being detected in our current particle accelerators, or whether perhaps gravity could do the job of the weak force. More serious/rigorous physics forums like physicsforums.com and Physics Stack Exchange censor such ideas as too speculative or vague.

If you have any comments on this resonance idea or other proposals for interaction between a putative soul and the body that might be consistent with known physics, share here.