WAVE/PARTICLE :: UNCERTAINTY=POSITION/MOMENTUM
In Einstein’s 1917 paper The Quantum Theory of Radiation, photons stimulate the emission of photons by striking and being absorbed by molecules and by raising energy to the point at which new photons are emitted, thus lowering the energy (coincidentally, the theory behind the MASER, LASER, and quantum entanglement) by utilizing the equivalence of mass and energy (e=mc2). This posits the existence of the light quantum, radical since photons were not recognized as yet by the physics community, hence the title. Einstein felt his theory had a weakness—he really wanted there to be a “union with wave theory” and found this to be the greatest weakness of the quantum theory of radiation. He is searching for something but cannot reach it. He knows there must be something about this that explains particle-wave duality but cannot come up with it utilizing the level of experimental knowledge of the time, and cannot therefore arrive at ways to experimentally verify what he intuitively “knows” is true.
Now (2014), a hundred years later, the gap is closed. New work (http://www.huffingtonpost.com/2014/12/24/quantum-physics-easier-to-understand_n_6370570.html) suggests wave and particle duality are the equivalent of Heisenberg’s uncertainty principle in which there is a relative duality between position and momentum. That is, like particles vs. waves, position and momentum can only be measured separately—if one measures a particle’s position one can no longer measure it’s momentum–but are really identical. Vice versa if one measures its position and knows where it is, how fast it is going can no longer be measured. This article states that they are relative—two sides of the same coin. To put it bluntly, momentum and position are relative, just as space and time are relative and particle and wave are relative.
The equivalence principle founds much of Einstein’s later work and led to the generalization of the Special Theory of Relativity. It took from 1905 until 1916 to attain this goal in the Theory of General Relativity, which forced physics to relativize space and time. Now the principle of equivalence leads to a further relativisation—particle and wave are now relative not only to each other but to position and momentum. It took a century but Einstein was proven right again. What interests me is the implication that there might be a bridge here between quantum theory and relativity theory.
The implications of equivalence can immediately be applied to cryptology. What simple mathematical formula describes this four-part harmony between matter, energy, where that matter is, and how fast it is moving? With so many variables, we should be able to avoid anyone hacking into and stealing records of our credit cards because they are encrypted on so many levels. For me—leaving cryptologists to the Turing test—I ask the question: what simple mathematical formula describes this four-part harmony? I sense we are approaching unity—the nexus of Einstein’s model of a macro universe and the Copenhagen school quantum theory of Bohr, Heisenberg, Pauli, and Schrödinger. This nexus fascinates me because I do not believe Einstein would have predicted it and neither would Heisenberg. This may throw light on whether or not Schrödinger’s cat is alive or dead.
Einstein’s quest for a unified theory extends: Kaluza-Klein theory adds a 5th dimension, string theory adds six more to that, and still there is no experimental proof that there is a 5th or an 11th dimension. The first—Kaluza-Klein— disappointed Einstein secondary to lack of data, and the second—string theory/M theory—disappoints a couple of generations of string theorists. What if the results of the classical double-slit experiment—the essential paradigm of particle-wave interaction—represent Einstein’s idea that both wave-particle and uncertainty theory are relative to one another? Well, they are, but only if measuring momentum or position are flip sides of the coin of the principle of uncertainty and there is an equivalence between this and wave-particle theory.
I visualize a multidimensional propagating wave whose particle manifestation can be measured either as velocity or position. It’s like one of the Star Trek movies came to life and you can beam up Captain Kirk. Add to this the relativity of space and time and I see the Tardis ripping through the fabric of the elegant universe.
Too bad the article I read skims the finding because, even though I AM NO MATHEMATICIAN, I’D LIKE TO SEE SOME FORMULAE. THE NEXT STEP IS THE FORMALIZATION OF THESE EQUIVALENCIES SO AS TO MAKE PREDICTIONS. THAT’S when the pedal hits the metal!