Dear Sir,
You have raised a very vital issue regarding physical constraints on mathematics. Suppose we reverse your example to say every apple is eaten by ½ persons, it is meaningless as there is no such thing as fractional number of persons. Since mathematics is a science of numbers and numbers are a property of all physical objects, it cannot be assigned to unphysical imagery. Hence it is not mathematics. This principle invalidates most of modern 'mathematical physics'. It is not that the physical constraints are not known (like in the above example). But in a hurry to score points, people overlook reason and blindly accept 'established theories'. Thus, even after more than a century of failures to find extra-large or compact dimensions, almost all scientists superstitiously subscribe to such fiction perpetuated by the novel FLAT LANDS. Dimension is the perception of differentiation between internal structural space and external relational space of an object. Since we observe through electromagnetic radiation, where the electric field and the magnetic field move perpendicular to each other and both move perpendicular to the direction of motion, we have three mutually perpendicular dimensions representing length, breadth, height that are invariant under mutual transformation.
Regarding your other example, while we know all about what an electron does, we still do not know 'what an electron is'. So we speculate many things like probability. When a ship moves in sea, it expels water in front to sideways, which reunites at the back. A similar phenomenon is seen in magnetospheric reconnection. Something similar happens with electrons. Positive charge of proton radiates out. Some of it is used up in n-p chain. Whatever escapes is blocked at the orbitals. It becomes visible as electron only at shifting intersections with the right orientation.
Even Schrödinger has followed wrong mathematics. The Schrödinger equation in so-called one dimension (it is a second order equation as it contains a term x2, which is in two dimensions and mathematically implies area) is converted to three dimensional by addition of two similar factors for y and z axis. Three dimensions mathematically imply volume. Addition of three (two dimensional) areas does not generate (three dimensional) volume and x2+y2+z2 ≠ (x.y.z). Similarly, mathematically all operations involving infinity are void. Hence renormalization is not mathematical. Yet we blindly follow these.
Recent discovery of galactic blue-shift, galactic merger and the absence of red-shift in galactic or lesser scales should prove dark energy a myth. Energy is perceived through its interactions. If it is not interacting, it cannot be energy. Fluids are also smooth and persistent. Interpretation of M & M experiment is faulty, as light is a transverse wave, which is background invariant. Like the solar system, the universe is spinning around a galactic center. Dark energy is the universal background structure. This implies the galaxy rotation curve and dark matter concept are also faulty. There is a need to review and rewrite physics.
Regards,
basudeba
