Nature Quantum Tunneling

What’s nature? Many cultures, in the last two million years, identified nature to God(s). What’s god? The end-all, be-all. Assuredly nature fits the bill.

A more constructive point of view is to introduce the notion of computer. Nature is a computer, and the universe the set of all solutions. 

The notion of computer is not really new: the Greeks had very elaborated mechanical computers. They used it to predict the motions of celestial objects.

As I have argued in “ULTRABIOLOGY”, the 2,500 year old notion of computing has become obsolete. It turns out that Nature is a QUANTUM computer.

Electrons Tunnel, Therefore We Are

Electrons Tunnel, Therefore We Are

What’s the Quantum about? As I argued in QUANTUM WAVE, the Quantum is about emitting and receiving energy by packets, while transmitting it as waves.

A world of waves? It’s going to be fuzzy, because stopping a wave with a wave is not going to be work too well, or be instantaneous. So Quantum waves tend to go through walls a bit.

Indeed, the wave equations proposed to depict Quantum processes are always characterized by having a potential on the right-hand side. Even if the potential changes abruptly, the wave will not. This is what the “Tunnel Effect” is all about.

Matt Strassler wrote an excellent article on Quantum tunneling (abstracted in The Amazing Feat Of Quantum Tunneling). Here are some extracts, although readers are encouraged to read the much more complete original. the quantum world we live in, no object is ever quite stationary for more than an instant, nor is its location exactly knowable.”

Why? Because waves are always moving and waves are never really local.


From Tunneling A QUANTUM Process:

It's Worse Than That: Even The Jitter Jitters, As It's Waving All Over...

It’s Worse Than That: Even The Jitter Jitters, As It’s Waving All Over…

A trap for an electron, which is like a bowl for a marble. (Left) Normal life would lead us to expect that the electron, like the marble, would be stationary if placed at the center. (Right) But quantum `jitter’ assures that the electron is always slightly in motion, and never quite at the center for more than an instant. A blue fuzz evokes the fact that the electron is, in some sense, spread out around the center of the trap.

If  I put an elementary particle like an electron in a magnetic trap that acts like a bowl, tending to push the electron toward the center just the way gravity and the walls of the bowl push the marble toward the bowl’s center in Figure 1, then what is a stable location for the electron? Just as you would intuitively expect, the electron’s average position will be stationary only if I place the electron the center of the trap.

But quantum mechanics adds a wrinkle. The electron cannot remain stationary; there is a sense in which its location is subject to a sort of “quantum jitter”. This causes its position and its motion to be constantly changing, or (better) even to be undefined, by small amounts. [This is the famous “uncertainty principle” in action.]”

[BTW, this uncertainty reflects only the fact that Quantum Physics does not say what an electron “IS”. There is no “IS” there. A wave is all there is. And a wave is hard to define “locally”, it always comes with a neighborhood! Actually, it’s even worse than that: the only way to localize a wave is to make it a “wave packet”]

“Only the average position of the electron is at the center of the trap; if you look for the electron, you’ll typically find it somewhere else in the trap, near but not at the center. And the electron is only stationary in the following sense: it’s typically moving, but its motion is in a random direction, and since it’s trapped by the walls of the trap, on average it goes nowhere.

That’s a bit weird, but it just reflects the fact that electrons aren’t what you think they are, and don’t behave like any object you’ve ever seen.

By the way, it also assures that the electron cannot be balanced on the edge of the trap, in contrast to a marble on the edge of a bowl (as in Figure 1, bottom). The electron’s position isn’t sharply defined, so it can’t be precisely balanced; and so, even without the trap being jiggled, the electron would become unbalanced and almost immediately would fall off.

But the weirder thing is what happens if I have two traps, separated from one another, and I put the electron in one trap. Yes, the center of either trap is a good stable location for the electron. That’s still true… in the sense that the electron can stay there and won’t run away if you jiggle the trap.

However, if I put the electron in trap number 1, and walk away, sealing the room etc., there’s a certain probability (Figure 4) that when I come back the electron will be in trap number 2.

This Process Will Be Exploited In Future Memories

This Process Will Be Exploited In Future Memories

Fig. 4: An electron in one trap can tunnel into a second nearby trap, even though this naively seems as impossible as the marble in Figure 2 moving spontaneously from the blue bowl to the red one. Quantum `jitter’ is ultimately responsible for this remarkable possibility. (Actually the marble can tunnel too, but being vastly heavier, and with the bowls being macroscopically large and distant, the probability is unbelievably small that this will ever happen to any marble anywhere in the universe.)

How did it do that? If you imagine that electrons are like marbles, you will not be able to understand this. But electrons are not like marbles [or at least not like your intuitive notion of a marble], and their quantum jitter offers them an extremely small but non-zero probability of “walking through walls” — of going someplace that it would seem impossible for them to go — and ending up on the other side. This is called, poetically, “tunneling” — but you should not imagine that the electron digs a hole through the wall.  And you’ll never catch the electron in the wall — in the act, so to speak. It’s just that the wall isn’t completely impermeable to things like electrons; electrons are not things that can be easily trapped.

Actually, it’s even crazier than this: because what is true for the electron actually is true for the marble in the bowl. The marble could end up in bowl 2, if you could give it enough time. But the probability of this happening is extremely extremely extremely small… so small that if you waited billions of years, or even billions of billions of billions of years, that still wouldn’t be enough.  For all practical purposes, it will “never” happen.

The point is that our world is a quantum world, and all objects are made from elementary particles and are subject to the rules of quantum physics. Quantum jitter is ever-present. But for most objects that have a lot of mass compared to an elementary particle — a marble, for instance, or even a typical speck of dust — this quantum jitter is too small to observe, except in very specially designed experiments. And the consequent ability to tunnel through walls is also, therefore, never seen in ordinary daily life.

To say it another way: any object can tunnel through a “wall”, but the probability for it to do so typically goes down very rapidly if

  • the object has a large mass
  • the wall is thick (i.e. there is a long distance between its two sides)
  • the wall is hard to penetrate (i.e. to punch through the wall in the usual way would require a lot of energy.)

For a marble to penetrate the lip of a bowl is possible in principle, but in practice might as well be impossible. For an electron to escape from one trap to another may be easy, if the traps are close together and the traps are not very deep, but it may be very difficult, if the traps are far apart or the traps are very deep.”


Knowing about such things as the preceding, and knowing as they fit with different appearances, and knowing how we found them out, is what makes our wisdom different from that of the Ancients.

Not just a different knowledge basis, but also a different meta-knowledge basis (how we established that knowledge).

Just as drastically, recent bits of science provide us with new models for thinking in general.

For example, tunneling implies that there are no absolute separations, and that, instead, interpenetration makes the real world hold together well.

That’s why students of philosophy that have learned nothing new in the last few centuries, ought not to be taken too seriously. Even on poetry, tunneling ought to have an impact.

Tunnel Effect: if you want to be real, you have to dig it.

Patrice Aymé


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22 Responses to “Nature Quantum Tunneling”

  1. Ian Miller Says:

    Actually, Patrice, you don’t know the electron can NEVER be found in the barrier; all you can say is it hasn’t, but who has actually looked using a technique by which it could conceivably be found? Similarly, you can never say there is jitter; all you can say is what you can observe is consistent with it. Now I know some are less than happy with thinking of tunneling as following the Schrodinger wave equation, but if you think of it that way, and think of it as having a real wave, then the limit to tunneling is not really the thickness of the barrier, but rather the ability of the barrier to transmit the wave. Thinking that way, and the marble will always stay in its bowl, and you can’t prove me wrong! At least, not without cheating ! 🙂

    • gmax Says:

      @Ian: Patrice quoted Matt Strassler, an authoritative physicist, extensively. But that does not mean that she agrees with all what Matt said. From what I understand Patrice does not agree with the standard CI.

      I would agree with all you said, BTW

      • Patrice Ayme Says:

        That’s right. I would not have put some of the things the way Matt did. I am more careful than that. But Matt’s formulations are traditional, and not far off the truth (whatever that is). Although I don’t see the electron jitter, I see it delocalizing in a jittery way. It may actually delocalize and relocalize quasi-continuously, in a strong field.

    • Patrice Ayme Says:

      Dear Ian: I would have to switch to my Bohr impersonation here. We have no imaginable tech to detect something within the barrier.

      The reasoning works that way: we have actually three PDEs; before, within, after, the barrier. Then one find a class of solutions for each. Then one adjust them by continuity so as to glue them together. That causes a solution that attenuates strongly within the barrier.

      The “jitter” thing may be an illusion. I prefer to think of it as delocalization of the electron (as it’s a wave!)

      BTW, all what’s detected is that some electrons (waiting long enough) will tunnel through, contrarily to Classical Mechanics. It has never been said they can’t get stuck within the barrier.

  2. Paul Handover Says:

    The early hour of a new morning (it’s 05:40) provides the quiet period in which to read this carefully.

    At one level it’s clear; albeit weird!

    But at the philosophical level it generates the most peculiar of thoughts. Almost that nothing is ever what it seems. Or, tongue in cheek, nothing is where you think it is! Now that’s something I do resonate with – can never find a tool when I need it!

    Than again, what do I mean by the word ‘resonate’? You couldn’t make sense if you said to me, “Paul, you just dropped your resonate behind you!” So it’s not a thing; nothing you could point at! However, there’s a sense that it is real. Like the sun’s heat on your arm.

    Tangible, yet intangible.

    Better stop now! I feel a headache coming on!

    Oh dear, even a headache can’t be defined as a point!

    • Patrice Ayme Says:

      Dear Paul: There is actually a type of logic called “fuzzy logic”. (Its main activist being an Iranian called Sale, I think, who used to be in the logic department at Berkeley.) Fuzzy logic or not, Quantum Mechanics is indeed fuzzy. However, fuzziness, certainly achievable, as you point out, in all circumstances, makes more sense that an un-reachable perfect precision.

      • gmax Says:

        Notice Patrice is saying that tunneling is understandable without getting in the details of equation solving, just by thinking of the electron as a continuous wave.

        • Paul Handover Says:

          Thanks Gmax. “understandable” as an idea, I agree with. Help me out though; please.

          In the back of my brain is the idea that the electron’s ‘distance’ from the central proton/neutron core is comparable to the scale of Planet Earth from the Sun.

          Is that correct?

          • gmax Says:

            I better let Patrice answer that one, that’s up her alley. Nothing at atomic scale is like at astronomical scale.

          • Patrice Ayme Says:

            Agreed, GMax! No time now, but I will come back to the subject.

          • Patrice Ayme Says:

            As I told GMax, I will answer this in the future. This sort of subject is somewhat on the edge of research. It requires to ponder what “dimension” and “measure” are. That’s why the Multiverse guys are all confused.

            Just a few remarks, though:
            0) The dimension of an electron is not known. Especially of a moving electron.
            1) We have no proof electrons have real trajectories.
            2) As an implicit acknowledgement of this hidden remark, “electron trajectories” are called “ORBITALS”.
            3) (Some) Orbitals can go “through” the nucleus of the atom.

          • Paul Handover Says:

            I’ll crawl back to writing part two of Progressing Wisdom! 😉

      • Paul Handover Says:

        Yes, I can understand that!

  3. Roger Henry Says:

    Are radio waves electrons? They penetrate wood ,,certain metals, concrete, etc., but not dense materials such as lead. So which of these materials is the marble bowl made of?

    • Patrice Ayme Says:

      Radio waves are electromagnetic waves, thus made of photons.
      Metals (such as lead) conduct electrical charges, such as electrons. They are actually characterized by an electron cloud floating around inside.

      Now the electromagnetic waves move (and are created by the motion of) electric charges (as discovered in full details by Ampere and Faraday). Both neutralize each other in a metal. So the electromagnetic field does not penetrate a metal (much; a sort of variant of the tunnel effect known as the skin effect).

      Marble bowls are made of non metallic ceramic. The tunnel effect is somewhat indifferent to the nature of the material. It allows an electron to penetrate a semi-conductor, or a metal, wood, whatever.

  4. Roger Henry Says:

    Thank you Patrice,

    • Patrice Ayme Says:

      Anytime. I think, as my friend Feynman did, that one understands physics to perfection, once one can explain it simply. And if one can’t do the later, one does not have the former (Feynman mentioned that specifically about the PCT theorem, nota bene).
      Paradoxically, it’s harder to do this in, say, history.

      • Paul Handover Says:

        Apologies, can’t resist asking if you offer any distance learning courses? 😉 ( My Obsession-Compulsion about “qualifications” showing through again. )

        • Patrice Ayme Says:

          All my stuff tends to have a research ambiance, in the sense that it tends to contain original research, very carefully, but often boldly conducted. Others are welcome to use the material. An essay like on Quantum Tunneling is very basic, though, but, and because, basics of physics ought to be explained better. I have a hint of that on the disintegrating glaciers: people don’t get the inertia, the acceleration, the speed. Not enough physics instinct.

  5. TomAlex Says:

    @Ian: actually observing a particle while tunneling is not just an experimental difficulty; it is more fundamental than that, since it would be impossible to define velocity and hence time in normal terms during tunneling.

    • Patrice Ayme Says:

      Tunneling electrons into a hole in the wall is actually done in the lab for experimental memories, so I do not understand Ian’s objection either. (“Observing” has got to mean to build a hole in the wall; maybe we should ask Pink Floyd?)

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