Quantum Tunneling 11/23/21

Science with Richard Bleil

One of the most bizarre models in science is quantum theory.  Newly discovered sub-atomic particles (electrons, photons and the like) defied known physics, showing properties of both waves and particles.  This led Schrödinger to try treating these particles in accordance with their wave-like properties instead of as particles.  He took the equations of waves and applied them to these particles, which is why sometimes quantum theory is periodically referred to as “wave mechanics”.  He built kinetic and potential energy expressions into his equation, but it kept much of the wave functionals.  For those who remember trigonometry, the sine and cosine functions look very much like waves, and factor heavily into the solutions of Schrödinger’s equation. 

The thing to remember about quantum mechanics is that the solutions that you may have learned are actually solutions to the mathematical model built by Schrödinger.  Sometimes we forget this as we begin talking about properties of the solution, such as orbitals, for example, as letters (such as the s orbital, the p orbital and so forth).  These letter designations have actually been adopted (from spectroscopic experiments that were done before Schrödinger introduced his equation) and represent specific numbers in the solutions of the equation. 

And people still don’t want to believe it.  See, this equation makes predictions that seem impossible to you and me and paint the picture of a world that might resemble a Picasso painting, looking like it might be something representing what we know but wholly impossible to take as reality.  When I was working as a visiting scientist at Harvard (how’s THAT for a name-drop?) we had a thermodynamicist give a seminar on his model of sub-atomic behavior using classical thermodynamics equations, and it worked.  The problem is that to make it work, he had to add terms that he couldn’t justify.  The reality is that you can make any equation fit any situation if you add enough terms, so nobody took him seriously.  Schrödinger’s equation followed known equations from wave mechanics and well-established mathematical terms for kinetic and potential energy which is why it is so powerful.  The reason some physicists today can’t accept it is because the predictions that come out of it seem to us logically impossible, but, the truly amazing thing is that every one of these seemingly impossible predictions that can be studied have been from physicists far more clever than I, has been demonstrated experimentally. 

For example, and here is something that I don’t even understand and won’t even bother to try to explain, is “quantum entanglement”.  Einstein referred to this as “spooky science at a distance”, and he is correct to do so.  For example, as it turns out, two electrons can be paired, even in a space as small as an orbital, provided their spin is opposite.  Spin is one of the least well understood ideas as science authors try to explain this unexplainable phenomenon.  They are misguided by the term “spin”, a word that really has no physical meaning.  Authors try to say that electrons are “spinning” clockwise or counter-clockwise, but this presupposes that electrons are spheres (they are not, they’re as much waves as they are particles) and spinning on an axis (which is an odd comment since the axis would have to be oriented to some alignment which is impossible at that level).  Actually, spin is a mathematical solution to Schrödinger’s equation that fell out naturally as + ½ or – ½ .  These are not charges; all electrons are negatively charged, but rather it’s just a natural solution to the equation.  Unfortunately, somebody called the positive solution “spin up”, and the negative “spin down” to keep them straight and provide a simple graphical representation.  But, they are just mathematical solutions.

The idea of these spin is that, if two electrons are paired, one must be spin up and the other must be spin down.  Typically they’re pared in a very small space (an orbital), but what would happen if we could take these paired electrons and greatly increase the distance between them, say, opposite sides of the laboratory, or opposite sides of the world?  If they’re paired, they must have opposite spin, but will they remain paired?  There’s no reason to believe that they will at such a distance, but quantum theory predicts that it is possible, and as bizarre as this is, it’s been experimentally verified.  Paired electrons have been separated by an enormous distance, and the spin has been measured.  As it turns out, if you flip the spin on one of the electrons, the spin on the other will flip as well to maintain opposite spin.  This is beyond our ability to fathom, but it is also the guiding principle behind quantum entanglement security that is currently being developed and tested. 

One of my favorite concepts is “quantum tunneling”.  As I’ve mentioned, Schrödinger’s equation has terms built in for both kinetic and potential energy.  What if there is a potential barrier for electrons that should be insurmountable, including, for example, an infinitely large potential energy barrier far greater than the sum total of all kinetic energy in the universe?  Surely the electrons could never get past it, and yet, in the solution to the equation, as it turns out there is a finite (albeit very small) probability of finding that electron on the wrong side of that wall. 

As it turns out, this is not an abstract “could never happen” scenario.  In fact, it’s quite common.  In quantum theory, the solutions to Schrödinger often have “nodes”, which can be nodal points, or nodal planes wherein a plane in infinitely small and infinitely large in both directions of the plane.  A “node” is a region of space (point or plane) where the electron can never, ever, exist.  For example, if you’ve ever seen a diagram of a “p” orbital, it looks like a figure 8.  Where the two lobes cross is the nucleus of the atom, and the electron can never exist in the atom’s nucleus (or all matter would decompose).  People often think of orbitals as the path electrons move, but that would be wrong.  Instead, they represent regions of space where the electron is most likely to be found (usually with 90% or 95% probability).  The p orbital has actually a nodal plane (not just a point) separating the two lobes.  The electron can be found in either one lobe or the other, but never, ever, in the nodal plane.  So which lobe does an electron occupy?  Both.

We cannot understand how an electron can occupy two regions of space separated by a plane where the electron can never exist.  This defies logic in our universe but is very common in the quantum-verse.  To try to get a handle on this concept, of an electron somehow getting across a barrier it cannot cross, scientists have dubbed the term “quantum tunneling”.  Somebody deduced that if the electron cannot get over a barrier, perhaps it can just tunnel underneath it.  We can’t really explain this since the plane is infinite in both directions, and that’s what quantum tunneling is.  Basically, it says that we cannot understand how, and yet somehow the electron can get to either side.  It’s another spooky and experimentally verified concept from quantum theory, and frankly, we’ll never fully understand it simply because it is beyond our ability to comprehend. 

But it sure is fun to contemplate.

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