Interesting fact 2; Give an example of a motion where when we apply a force on the object, the force produces motion of the particles along its own direction, the speed remains finite but does not change. According to F = ma, Newtons laws are valid for the motion but speed remains constant, while F is there, v does not change.

Since a = 0, with nonzero F and constant v, one could see this as a diversion from particle mechanics as formulated by Newton, towards a higher understanding, one could argue this as a great inflection towards Quantum Mechanics.

Also note that we are not talking about circular uniform motion where F does not change v, but there is non zero a. F is transverse to particles motion.

Interesting fact 1, certain forces do not obey any of Newton’s laws, in either its strong form or week form. Magnetic forces unless generalized suitably do not obey any form of the Newton’s law, strong = strict, week = partly strict.

Some discussions on fact 2

#### Andrew Somorjai

Would a quantum of charge in a potential changing energy levels occur without acceleration? I’m not sure if elementary particles change velocity instantaneously or do they accelerate.

MDash

Elementary particles change velocity if they have mass. — If they have mass, they have rest mass.

Photons on the other hand don’t have the property called mass. — So its erroneous to say Photons don’t have rest mass, they just don’t have mass, saying they don’t have rest mass would mean; they have zero velocity in some frames, which is physics wise unacceptable.

So elementary particles except zero-mass particles such as photons, change their speeds under acceleration. “Potential changing energy levels” simply means there is a force and acceleration, hence change in energy, speed, momenta etc of the elementary particle such as electrons in orbits.

— Their quantum numbers are different for different orbits, hence, energy and velocity etc are different. In the orbits the electrons would fall down to a smaller radius if they were to lose energy.

Since they are wave-particles we are talking about average values of radius, which decreases accompanied by some acceleration. So the answer to your query is YES, there is acceleration of these particles, in orbit changing processes. (excitation or de-excitation)

The above point of mass-less particles and particles with mass is what classically separates them as waves and particles. — mass-less = wave and particle otherwise. And speed is a variable if particle mass is non zero and mass keeps on changing as well. But zero mass would mean mass and speed are constants.

So in short waves; speed and mass are constants. mass is zero. speed is constant and finite.

Particles; mass and speed vary from zero towards a finite value as decided by the wave (above).

These are elementary particles and waves which come under two categories; matter waves (such as electrons) and non-mechanical (or em) waves such as (photons).

But the hints to my question lies on considering yet another category of waves viz; mechanical waves.