Science has created abstract concepts such as space and time, mass and charge. It based its concepts and laws on abstractions/idealizations that were concluded by approximations and contained only one of these concepts. The recognition of discreteness of energy led to quantum mechanics. Connecting the features of the microscopic discretete constituent objects to the macroscopic continuous features led to thermodynamics. The recognition of non-independence of space and time led to creating the theory of relativity. All realizations had far-reaching consequences. In addition, we understood that under certain circumstances we must treat particles as a kind of continuous wave, and continuous waves as particles. These micro-objects interact with their environment, including our measuring instruments. With a measurement method suitable for particle detection, we see them as particles, and with an instrument suitable for wave measurement, we see them as waves. (How one micro-object sees the other remained cryptic.) This kind of micro-level behavior is inherent in nature; our methods of description and measurement must be adapted to nature and not the other way round. We understood that the Newtonian approach has its limitations; finite-velocity interactions can only be described with a different kind of mathematics: by introducing the concept of space-time. In another approach, mass is also related to space and time; taking this into account, we can describe nature with curved space-time. We can also say that according to classical physics, we can describe phenomena with sufficient accuracy using only the aforementioned concepts (the zeroth derivatives). According to modern physics, however, for a more accurate description, we must take into account the first derivative with respect to time, and even the second derivative with respect to time for a general description.
Science’s first principles could serve as a firm base for all its disciplines. As we discuss, its disciplines use abstractions based on limited-validity approximations based on the same first principles. However, the approximations are different even for its different disciplines, and even more for biology and physics. In physics, most processes we observe are fast enough so that we can use the abstraction that they are essentially jumps between states. In most cases, the approach can be –more or less– successful. For the slower, well-observable processes, we have the laws of motion that describe how the processes happen under the effect of some driving force. We also experienced that nature is not necessarily linear (in the sense that it depends only on space coordinates but not on their derivatives), which we can describe by ”nice” mathematical formulas. A century ago, A. Einstein invented that the approximations I. Newton introduced two centuries earlier are not sufficiently accurate for describing the movement of bodies at high speeds. In other words, a new paradigm, the constancy of the speed of light (today: the maximum speed of interactions), must have been introduced that caused a revolution in physics and led to the birth of ”modern physics”.
Science, unfortunately, is separated into classical and modern science based on whether the theoretical description assumes infinitely fast interaction (the Newtonian model) or acknowledges the finite interaction speed (the Einsteinian model) or acknowledges the discrete nature of some quantities or connects the discrete and continuous views. Experience shows that the generated forces, regardless of their origin, can be summed, and one can apply Newton’s laws of motion. The finite interaction speed is erroneously associated with the speed of light and frames of reference moving relative to each other with speeds approaching the speed of light. Assuming that the interaction speed is finite is sufficient to build up the special theory of relativity [88] (using the speed of light as the value for its external parameter). Still, the Minkowski-mathematics [89] behind the special theory of relativity works with any speed parameter . The same mathematics describes technical [25] and biological [26] computing systems, where there are no moving reference frames, but the finite interaction speed has noticeable effects on the operation of the system. Furthermore, connecting the discrete and continuous views needs care in the case of biological objects and processes.
The so-called modern physics was born when experiments began to contradict the idea that all phenomena of nature could be described in such a simple way. Neuroscience has similarly accumulated a number of experiences that contradict theory, although mainstream neuroscience has either ignored them or explained them with ad-hoc flawed and unfounded hypotheses. It happens despite Hodgkin’s opinion above. In this field (and in the physical foundation of biology in general), a similar modern approach is needed, which first requires reviewing the fundamental assumptions of the underlying physics.
Quotation: ”How can the events in space and time which take place within the spatial boundary of a living organism be accounted for by physics and chemistry?” [12]
The closed volume of the biological objects and the finite speed of the charge carriers is also a problem of finite resources. In biology, we cannot use the fundamental assumption of physics that, although a field acts on the ion in question, the ion does not affect the field (the other ions generate). The material transport represents simultaneously mass and charge, so the transport itself gradually changes the gradients. The transferred ions decrease the field in the volume they departed from and increase it in the volume where they arrived (a problem of finite resources). We must consider that the resources are finite. A main source of confusion is that the phenomena happen in a limited and closed region of space, and we study processes (in a period instead of a moment) where the environment is not ”infinitely far” from the studied object and the studied process interacts with its environment. The boundaries of closed volume may exert constraint forces and fundamentally affect the processes inside the volume.
Due to the field-dependent speed within the electrolyte, we must consider the autonomous change between the microvolumes where the ion traverses. This process keeps the entire volume of the electrolyte in a (more or less intense) continuous change, which makes life possible. The more distant parts of the biological cell will see any change in the local values of the state variables with a delay. Furthermore, biological objects inside the cell can absorb ions and charge up. With their potential, they alter local gradients, accelerating or decelerating ions. Not to mention that biological objects can be active in the sense that (depending on the environmental conditions) they can let ions from one separated volume part into the other, thus changing the number of charge carriers in the volume under study. Co-existing processes may affect each other by changing resources: changing one quantity changes the other. Mathematics descibes such processes by linked differential equations, such as the Lotka-Volterra (or ”predator-prey”) equations. For details, see section 2.8.2.
These processes are what E. Schrödinger coined as ”the construction is different from anything we have yet tested in the physical laboratory” [12]. Consequently, measurements must be designed and carried out with care; the routine methods used for measuring objects from inanimate nature, cannot surely be applied to living objects.