We know that ion current flows in through the axons, and the delivered charge produces local transient voltages [80, 81] on the membrane around the arbor of the synaptic connection. Furthermore, the ions form ”packets” when immediately before issuing an AP they arrive at the AIS [50]. We hypothesize that for the period of generating an AP (furthermore, for the period of receiving synaptic inputs), the membrane does not remain equipotential. The membrane is a two-dimensional, very thin, elastic, semipermeable, insulator surface (a long and narrow rectangle) with a high concentration of ions on the extracellular side. Axon tubes are connected to the intracellular side at some points of the long rectangle and AIS at the other end. The membrane attempts to remain equipotential and forwards the charge toward regions at lower potential. This way, the ionic charge forms a “slow” current and gets distributed over the membrane’s surface along some potential gradient for about a few hundred microseconds.
Due to that charge, a new epoch begins when the membrane potential reaches its threshold value. That voltage opens the valves (ion channels) in the membrane’s wall, ions rush into the intracellular space (a positive current). The intense “slow” current quickly increases the membrane’s potential, so the axonal inflow stops. The membrane has a single flow-out point, the AIS, where a less intense “slow” current leaves the cell with a delay and arrives at the very beginning of the axon. In the first phase, the axon pumps the received current out to the extracellular space (a negative current), causing a measurable macroscopic current. Later, the pumped-in and pumped-out ions along the axon are balanced and begin transferring the spike along the axon.
”Action potentials (APs) have been measured using electrophysiological methods and understood as electrical signals generated and propagating along the axonal membrane” [95], and ”the AP is accompanied by fast and temporary mechanical changes” (such as axonal radius, pressure, optical properties, the release and subsequent absorption of a small amount of heat, and shortening of the axon at its terminus).
Interestingly, even the paper [146] that attempts to describe non-ideal membranes, considering also mechanical deformations, uses only “fast” waves. Similarly, the model in [95] predicts a “traveling wave of voltage” without seeing that it also means a traveling wave of current, i.e., a finite speed (“slow”) current (“we emphasize that the driven waves we consider will travel at the speed of the electrical AP that drives them”). The electrostatic repulsion leads to mechanical stress on the membrane.
An interesting parallel with science is that ’classic physics’ is based on the abstraction that position-related phenomena do not depend on time (the time derivative of the position) and that the ’classic physiology’ is based on the abstraction that the charge-related phenomena do not depend on time (the time derivative of the current). In ’modern physics’, although mathematics, based on the Newtonian abstraction, perfectly describes a wide range of phenomena, near to the limiting speed the Einsteinian abstraction entirely different mathematics must be used to describe nature perfectly. Similarly, in the ’modern physiology’ the time derivative of charge movement must also be taken into account when describing the dynamic physiological behavior of neurons that needs different approximations. Neglecting the time derivative of the position may result in calculating speed above the limiting speed (the speed of light), and neglecting considering the time derivative of charge movement may result in a wrong understanding of the neuronal electric operation.