De Broglie’s Nobel Prize discovery asserted the duality of particle and wave nature of everything in the physical universe. This idea is simply expressed by the concise equation: p = h/l. This is a quantum mechanical expression. On the other hand, the classical expression for the linear momentum is given by p = mv as the product of mass and velocity of the moving particle. The Planck’s constant of action is given by h. The wavelength is given by l. The following discussion is not a verbatim excerpt of the one found on Page 94 of Dr. M. D. Fayer’s book: Absolutely Small. The value of Planck’s constant of action is approximately 7´10^(-34) joule-second. A standard Major League’s baseball weighs approximately 145 grams. An average fast pitch is about 40 meters per second. By the equality expression p = mv the linear momentum of the baseball is approximately 6 kilogram-meter per second. Then solving for the wavelength of the baseball by the equality expression p = h/l it is approximately 1´10^(-34) meter, roughly 0.000 000 000 000 000 000 1 the size of an average atomic nucleus of 10^(-15) meter, which is beyond the means of precise measurability by the best scientific instrument.
However, although a moving baseball always has a very small wavelength, by the same mathematical equality expression (p = h/l), a baseball that is relatively not moving or at rest has its wavelength infinitely long since its velocity is zero. That is to say any quantity no matter how small when divided by zero gives infinity, which is incidentally not mathematically defined as a number. The answer becomes physically meaningless. Moreover, instead of a baseball, if the particle is an absolutely small particle of light photon then its mass is always zero and again its wavelength is infinity, although as pure energy, a photon has the ability to take on all the values of the wavelength comprising the range of wavelength of the electromagnetic field. The linear momentum of a photon is always defined as its energy divided by its speed: p = E/c. Quantum mechanically speaking, the energy of a particle or wave is always equal to the product of Planck’s constant of action and the defined frequency of the said particle or wave, whatever makes sense, physically speaking. Nevertheless, completely resolving this duality paradox would require simply the redefinition of linear momentum as the ratio of quantized space-time over the space-time continuum: p = H/S. If quantized space-time (H) is defined as the square of energy: H = E and the space-time continuum (S) is defined as the product of energy and the speed of light: S = cE then substituting them into p = H/S gives the correct expression for the linear momentum of light photon accepted by theories of quantum mechanics and quantum fields. This new definition of linear momentum for free and bound particles is mass independent. It depends only on the sums or partial sums for the total energies of the universe.


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