[AntonioLao]

The conceptual problem of force.

Max Jammer, in the preface to the 1999 Dover edition of his book entitled ‘Concepts of Force’ originally published in 1957 stated quite clearly that the definition of force in quantum mechanics is conceptually distinct from its definition in general relativity.

In QM, force is defined as a ‘stock exchange’ or ‘momentum exchange’ of ‘stock particles’ called bosons between ‘trader particles’ called fermions. Analogous to the stock market, these exchanges are not physical but mathematical in the sense represented by numbers or prices flashing across the screens or monitors. Both of these exchanges seem to rise (positively attractive – bullish) and fall (negatively repulsive – bearish) from day to days, year to years, and decade to decades, and century to centuries. However, due to the accumulative nature, the trend is always upwardly dynamic or increasing entropy.

In GR, force is defined as a deviation of particles (both bosons and fermions – without exceptions) from their ‘natural’ paths in space-time. These paths deserve the ‘natural’ connotation if and only if the particles felt no force during their motions. This definition seems to hide a subtle physical tautology. If the particles felt no force, what is it that motivates them to move in the first place? Furthermore, as indicated by the nonlinear field equations, if these particles are the causes of these paths or curvatures to begin with, why do they have to move at all? Since there cannot be a unique solution to the field equations, Friedmann in 1917 found one with an expansive cosmological model. This was later supported by Lemaitre independent calculations. Then Hubble found the galactic redshifts and Gamow as a student of Friedmann was responsible for the scientific explanation of the cosmic background radition, while Fred Hoyle, one of the originators of Steady State model, coined the term Big Bang for his rival expansive model. However, the mystery of GR’s force remains to this day.

One of the modern remedies for this theoretical malady was the introduction of quantum gravity. It uses force exchanges with gravitons as the mediating vector bosons. However, the monkeys on the back of QM are the persistent, cringing charges (electric, weak, color). The monkeys on the back of GR are the different types of mass (inertial, gravitational, tensorial, relativistic, negative and dark matter). Nevetheless, the common denominator shared by both monkeys is the 1st power of energy. These monkeys and force share the square of energy (2nd power) as a common denominator. The advantage is the description of infinitesimal spacetime topological structures.

It is important to note that the description of charge is next to impossible using the nonlinear field equations of general relativity, while a complete description of mass at the quantum level requires spontaneous symmetry breaking and subsequent conceptual existence of the Higgs scalar bosons. It seems that the monkeys of QM and GR are now invading each other’s back. Instead of one problem, now there are four fundamental forces to be subdued. As the old nursery rhyme goes:

Ten little Indian boys went out to dine; one choked his little self and then there were nine.

Nine little Indian boys sat up very late; one overslept himself and then there were eight.

Eight little Indian boys traveling in Devon; one said he’d stay there and then there were seven.

Seven little Indian boys chopping up sticks; one chopped himself in halves and then there were six.

Six little Indian boys playing with hive; a bumblebee stung one and then there were four.

Five little Indian boys going in for law; one got in Chancery and then there were four.

Four little Indian boys going out to sea; a red herring swallowed one and then there were three.

Three little Indian boys walking in the Zoo; a big bear hugged one and then there were two.

Two little Indian boys sitting in the sun; one got frizzled up and then there was one.

One little Indian boy left all alone; he went and hanged himself and then there were none.

But now, they all came back bringing tenfold of infinity of infinitesimal Indian boys on their backs.