In physics, measurement means quantifying something relevant to the process under study. A ’complete’ measurement measures all relevant quantities. The different disciplines of physics restrict the measured quantities to the ones which are, in general, that the discipline studies. The remaining quantities remain outside the scope of the discipline. The fundamental physical quantities of mechanics are length, mass, and time, which form the basis for defining all other quantities like velocity, force, and energy in that field. The fundamental physical quantities in thermodynamics are Temperature, Energy (Internal Energy, Heat, Work), and Entropy, which characterize systems at equilibrium and describe energy transformations; Pressure and Volume are also key variables. Those of electricity include electrical charge (Coulomb), the basis of all electrical phenomena; electrical current (Ampere), the rate of charge flow; voltage (Volt), the potential difference driving current; resistance (Ohm), opposition to current; power (Watt), the rate of energy transfer; and energy (Joule), the capacity to do work. As seen, there is little overlap of the studied quantities.
When making a measurement, one must keep in mind that measuring devices are designed for the purposes of determining a quantity interpreted in one of the disciplines of science. It is the task of the experimenter to figure out which physical quantities (that maybe interpreted in different disciplines) play a role in the process and to define the set of quantities that describe the process, instead of pre-deciding which discipline’s set of inanimate science will be used for biology which is not one of the disciplines of inanimate science. In biology, that set does not necessary matches any of the sets used in one of the disciplines. A disciplinary study (such as the electrical and thermodynamic ones in physiology) provides an incomplete set of measured quantities. None of the disciplines alone can describe electrolytes, since they consider different and incomplete sets of physical quantities: thermodynamics misses charge, electricity misses mass. As discussed in connection with the Onsager’s relations, a disciplinary (incomplete) measurement does not discover that an unexpected change (a miracle) in the value of one of the quantities belonging to another discipline is accompanied by a change in the value of the other quantity. This change is clearly the case with the measurements performed in the spirit of HH: the values the electrical instruments provide are accompanied by the values of mechanical/thermodynamic quantities which are not measured, partly due to the obvious measuring difficulties and because they are outside the scope of the discipline electricity. The theory, however, should not remain disciplinary. If one attempts to reduce ion-related phenomena to a single abstraction (see the mentioned theoretical descriptions), one experiences that some quantity (the charge or the mass) changes in an uncontrolled way. The fundamental reason of the incompatibility on the disciplinary theories is that they consider an incomplete set of physical quantities. As Feynman R. P [6] told, ”many of the interesting phenomena bridge the gaps between fields”. The disciplinary separation in classical science does not apply to the study of living matter. We must make a complete measurement and interpret them in a cross-disciplinary way.
Thermodynamics provides a framework for handling ions and determining their thermodynamic properties. However, as good thermodynamic textbooks (including the one on the thermodynamics of the membrane [97]) emphasize, thermodynamics derives its concepts for non-interacting particles, so one cannot expect its validity for ionic solutions [22] (Boltzmann assumed that, in the absence of long-range interaction between the particles, the sizes of cells in the phase space do not change). In addition, he required the presence of a vast number of particles in a homogeneous, isotropic, infinite volume, which is typically not the case in biology.