This was a small article written in very simple and lucid style as it involves two concepts of Physics that the Physicist should be capable of explaining at the drop of the hat. Thus, its appropriate for any kind of readership, who can devote 7 minutes, in understanding two of the most talked about modern day ideas, in Physics. Although while explaining, the attribute of simplicity is not lost, I made it slightly swelled, hope you still like it.
part i . Two ideas of modern physics; Quantum Tunneling and Quantum Fluctuation.
If you hear Physics discourses, which is a very kind and useful action you have taken up in life, you will often hear such phrases, as; Quantum Fluctuation or Quantum Tunneling. If, you are a Physicist, or a closely placed expert, eg, a journalist of science; you may know to some extent what these two ideas mean. Of-course, as a Physicist, you know howto give a technically satisfying answer, of Quantum Fluctuation. And; I know no more than that.
The ready-made answer for Quantum Fluctuation, is; its a fluctuation of the quantum. (I hear chuckles for that answer) And its not an incorrect answer. But then, we need to understand; whats quantum and whats fluctuation, rather than, propel the “bogeys of our semantics joys” to unsuspected dhakkans and bruise their eggos before they bruise ours in mad rush of volition.
In Physics, most terminology, despite of their precise definitions; can often be used vaguely. Because (? your mother is a nappy-headed ho, apart from that), the practicing Physicist often knows, what it really conveys. In academic discourses there might be, “a particular propensity for a particular term”. One field of research, may define terms, with a particular connotation, and another with another. eg traction is defined as a frictional force in Engineering. But traction may simply mean “as pertains to motion“. Hence, in another field, one can define such, with another meaning. Recently, I defined traction; as a higher integral of action. And, I defined, attraction as a higher integral of traction. See the coincidence of semantics; action > traction > attraction. ( — The link that follows describes how I define these terms.)
So, fluctuation and quantum have different connotations, in different contexts, as allowed, by the particular situation.
part ii. The Quantum and its attributes of mixing; what results is uncertainty or indeterminacy.
Quantum is simply an unit of matter or energy. Quantum are described, by the differential equation; called a Schrodinger’s Equation. The Schrodinger’s Equation is a doubled-up equation, in the sense that, its a differential equation: that describes a wave, and, another differential equation: that describes a particle. The mixing of equations like this, is very natural. That is, such mixing are to be; found in nature. Its this mixing of waves and particles, which gives rise to Uncertainty Principle. In this particular case of equation mixing which entails wave and particles, to be mixed, its called; a wave-particle mixing or duality.
But, there could be many more different kinds of example of mixing, of the quantum of waves and particles, eg the masses and the quark content of some particle get mixed up, between themselves. In other words, lets say, in a packet, I keep separated quantum (A, B, C) which are made of certain kind of quark content, of some other quantum (alpha, beta); (each of A, B, C: in terms of alpha + beta always), and in another packet, I will have quantum (D, E, F) that are separated on the basis of the different masses of the constituent quantum (each of D, E, F: in terms of gamma + eta always) of the quantum (D, E, F) in question, paying no attention to the quark content.
alpha, beta, gamma and delta will be, each of them, different quark-types and different mass-value, so A; if has a particular quark-type, will get all possible mass-values of the type, and if A; is specified on mass-value, it will get all possible combinations of quark-type, in other words, the attributes mass-value and quark-type which are represented by separate type of eigen-state or waves or particles, are mixed from each other’s attributes, if we specify one attribute, the other attributes can’t be specified.
As a far simpler analogy, this is akin, to the following example, if, we specify the nationality of candidates, in a competition of sports and music, the other attributes, such as how-good-at-music or how-good-at-sports just got mixed up, and there won’t again be just one way, of having the mixed attribute, but many, as many as permitted. So an American may be good at music, good at sports, bad at music, good at sports, bad at music bad at sports, Argentinian may be good at music, good at sports, bad at music, good at sports, bad at music bad at sports and so on. Same with a Dutch. But if you arrange good musicians, he can be Argentinian, American or Dutch, as long as they are. Therefore (music, sports, nationality) as attributes got mixed up. music and sports, nationalities have types, values, tags and so on. Each attribute is definable in terms of an n-tuple of values, types, tags.
Thats exactly what happens in the world of quantum, each of their attribute is, an n-tuple variable, which gets mixed up with the values, tags, types or simply variable in another n-tuple. In the particle, wave, or quantum world, eg in the sub-atomic world, we have variables like, quark-content, mass, energy, momentum, isospin, spin, baryon number, interaction type, hence specifying one types, say isospin states, gets a mix-up from other permissible types, tags, values, attributes, states, variables.
In the latter (alpha, beta, gamma, eta Vs A, B, C, D, E, F), it amounts to saying; the quark-content-type is mixed from the mass-types and the mass-types are mixed from the quark-content-types. If I chose in nature any packets of quantum, then, the packets will have quantum, that are mixed of the two types of categorization of quantum: quark-content-type also known as quark-flavor-type or flavor-states, and mass-type or mass-eigen-state type or simply mass-state. That is due to; a different kind of mixing of the differential equations, than the wave or particles mixing, through mixing of differential equation, but essentially these are ALL just mixing of attributes of each other.
part iii. The uncertainty principle; has, 3 simpler forms. Phase Space is uncertain.
… and, my recent research is paving a way for more complicated forms, which derive from these simpler forms, and, relates between variables that are not supposed to be relating that way. eg between energy and speed, there should be no uncertainty relation, according to textbook, but my leeway: well there is no minimal uncertainty relation between energy and speed, the way, there is between energy and time, but there is a new form, which I have found. (Read the preceding link for a quick grasp of the concept, actual forms will be linked when there is more review)
( — and this new form answers the OPERA anomaly, making errors of measurement in energy for particles ensures we have made a minimal error on the speed of light, which ran into a few KeV doing a 7.5 kms/sec about speed of light, hence its easy to see, OPERA and all particle physics experiments that measure energy and momentum typically to MeV values, do far worse than 7.5 kms/sec, the observed FLT, neutrino speed above, about speed-of-light was far less than 7.5, hence within the bounds of our insanity and not nature’s problem.)
Hence, there is no inconsistency, with any basic formulation of Quantum Mechanics, as it seems now. To understand the formalism of Physics better and far too much detail, read this article ” Why is energy conserved? “. That article explains, how wave-particle equations were first formulated as wave equations and particle equations separately, and then came; the wave-particle equation called Schrodinger’s equation. ( — or other equivalent formulations of such equations)
Since a quantum can be, a wave or a particle, and in all circumstances, hence, a mix of all possibilities *, the uncertainties that apply to the quantum, are going to spread the parameters of the wave and particles. eg If an electron were to be understood from this angle, one has to see that the electron’s energy bands as they appear eg, on the NMR or any CT scan, or any where; are going to be fuzzier. Threads are, as is my favorite example, going to behave like ribbons and these ribbons of 2-D will behave like ribbonoids in 3D and N-ribbonoids in N-D. Actually the phase space is going to behave like that. In one of my recent articles I described; whats a phase-space. So, the phase space is going to be like N-ribbonoids. This is due to uncertainty and is directly connected to Quantum-Tunneling. In simpler words, there will be uncertainty zones in the form of N-ribbonoids.
* [a mix of all possibilities >> “all spectrum of waves plus all decay and regeneration of particles”.]
eg the energy and the momentum, and the speed and locations etc of the electron; are going to be uncertain. These variables, energy, locations etc, are collectively called, a phase-space, although due their mathematical connectivity, all variables may not be needed, for the description of the physical problems, but only a few, eg 4-vector and the 4-vector (of all the particles) would be called; the phase-space. The description of phase space is given in detail, in the linked article, above.
This uncertainty is called a fluctuation as we would not know; exactly where in the phase-space-N-ribbonoid the electron, is going to be found?Various values for its locations, would show up; if we are to measure the “fuzzy” electron in the NMR or CT-scan.
This whole idea is called Quantum Fluctuation.
part iv. quantum tunneling
The quantum tunneling is similarly; the tunneling of the quantum. (Do you still chuckle? its kind of chilled here, and my tea is here, but I am still to describe this, so what I will do, apply the “principle of similar argument”)
I already explained, the idea of the quantum, hence we need only understand tunneling.
Tunneling is the phenomena; of the electron, finding a loophole in the N-ribbonoid. If the electron were only a particle, or a wave exclusively, it was impossible for it; to jump a barrier whose height is bigger, than, its capability.
In other words the barrier has a bigger energy, and the electron; a smaller energy and hence, it can’t jump that. But this jumping bigger barriers than your capability allows you to; is possible in Quantum Mechanics. In the latter, due to presence of N-ribbonoids in phase space, the electron irrespective of its dual properties of wave and particle in-fact due to such, will tunnel through the N-ribbonoid region. This ribbonoid is like a special allowance of energy, momentum, mass, location, time etc and so on. Even if the electron, does not have enough, of what it takes, its going to go through the region and achieve its goal of jumping the barrier. It didn’t jump but tunneled through, like a tax-rebate or holiday-sale.
Hope you liked this article. It was first written, on October 2, 2012, which it occurs to me was the birthday of Gandhi Papa, and was reviewed and edited today, 18th January 2014. The only 14th year of the century, this day, that I found, was the birth day of a writer, Arno Schmidt, although he was a pessimist.