You Will Not Tunnel Through a Wall

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We periodically get questions on PF about people wanting to know of a tennis ball, a ping pong ball, a person, a cow, etc. can tunnel through a wall, or fall through the ground. This is due to an aspect or a consequence of quantum mechanics in which quantum particles have the probability of tunneling through a potential barrier and come out on the other side of it.

This is a very good time for a lot of people, especially those who did not learn physics (or have not learned physics) formally, to make the realization that physics isn’t just “What goes up, must come down”. Physics is also “Where and when it comes down”. This means that physics isn’t just a qualitative description of something, it also contains a quantitative description of that something. There must be calculational numbers that come out that we can compare and verify with experiments.

So apply to this case. It isn’t just sufficient to indicate that there’s a possibility that tunneling of something is “possible”. One must also calculate the probability of that occurring. This is where the magnitude of it happening makes a huge difference. If the probability is extremely small, so much so that the chances of it occurring is negligible within the age of the earth, or the universe, then call me crazy, but I’d say that it doesn’t occur! So when dealing with something like this, one has to consider both parts: the phenomenon is valid, and the quantitative aspect of it.

I did my PhD work in tunneling spectroscopy in High-Tc superconductors. All I can say is that, throughout the 3 years of my experimental work, I WISHED it would occur as easily as people seem to make it! And I was doing tunneling by electrons, which is not a composite particle. In considering the tunneling of composite objects (objects made of more than one fundamental particle), there are extra complications that are not present when dealing with tunneling of fundamental particles. Let me explain.

In electron tunneling, for example, the electron itself can already be described via the straight-forward wavefunction. And all we care about is the probability of that single electron tunneling across the potential barrier. However, when you have a composite particle, say an H2 molecule, for that to tunneling across, the whole molecule must tunnel across together! Think about it for a second. The molecule consists of 2 protons and 2 electrons. Already, due to their different charges, they see different potential barriers. If you set up a potential barrier to the electrons, the protons see this as being a potential well! It is almost impossible to set up one barrier that is uniform and identical to both the electrons and protons. What this results in is that the probability of tunneling for the protons and electrons will be very different from each other! Different parts of the molecule have different tunneling probability and different chances of coming out on the other side of the barrier. Essentially, this makes it very difficult to imagine the whole entity making it through together! This extra factor is not present in tunneling of a fundamental particle.

Not only that, there is another issue at hand. When we try to detect quantum effects of larger objects, such as buckyball, etc., the most important characteristics that the system must have is that the entire entity (buckyball, 10^11 electrons, etc.) must be in a coherent state with each other. Having such phase coherence is one of the most fundamental aspect of a quantum property. This is why in experiments done on buckyball interference, the molecule had to be cooled down and isolated until all parts of the buckyball are in coherence with each other. It wasn’t easy to detect quantum state at this scale, and one had to go through a lot of crazy gymnastics for that to occur. And this is to do something “simpler”, i.e. 2-slit interference. Think of how much more difficult it is to make that buckyball tunnel through a potential barrier, consider the extra difficulty factor that I mentioned above.

This is why many of us in physics shake our heads when someone outside of physics only understands a phenomenon or a principle superficially, and then decides to extrapolate it into other areas. The Deepak Chopras of the world often like to justify and validate many of their pseudo-scientific beliefs by invoking the “mystical” consequences of quantum mechanics. They do this without any kind of a quantitative understanding of quantum mechanics, and thus, are completely clueless to the scale of such events, and whether such things are well-defined and likely to occur.

The short and sweet answer if a tennis ball, a bowling ball, or any other kind of ordinary macroscopic object can tunnel through a wall is NO.

PhD Physics

Accelerator physics, photocathodes, field-enhancement. tunneling spectroscopy, superconductivity

11 replies
  1. kmm
    kmm says:

    Maline. I would think of it like this. The probability of flipping a coin heads is 1/2. The probability of flipping two heads consecutively is 1/2*1/2=1/4. This is analogous to a the probability of a composite particle tunneling. So if you have an electron that has some probability X of tunneling through some potential barrier, and you have a proton with some probability Y of going through the barrier. Then the composite particle consisting of one electron and one proton will have a probability X*Y of tunneling and since Y<1, X*Y<X. That's what I expect anyway..

  2. kmm
    kmm says:

    I should note, I don't think X*Y is the exact probability of electron and proton tunneling at the same time, but I expect the actually probability to have a similar form.

  3. kmm
    kmm says:

    @maline I wasn't trying to show that the probability was merely less than one. I was attempting to show why the probability of transmission of the electron is higher than  the transmission probability of electron + proton. But I think I see your concern now. In the OP it was stressed that the reason it's tougher to have an H2 molecule tunnel is because the protons and electrons have different probabilities of transmission. I think you understood this as implying that if the protons and electrons had equal probabilities of transmission, they would be more likely to tunnel, and you want to know why. Is that correct?

  4. DavidLloydJones
    DavidLloydJones says:

    I.I. Rabi did a thesis  in school on the proposition "How likely is it that a brick will spontaneously leap one foot into the air?"  I think he did his undergrad at Buffalo, which would account for that archaic "one foot" thing. I remember the answer as being "It'll happen about once in every 64 times the age of this universe."  On the other hand my memory may be fooling me; it may have been once in every 10^64 times the age of the universe.In speeches he also took to givin gout the quantim likelihood of a Mack truck making it through a gap a foot too narrow.  This is rather less likely than the jumping brick.I think, however,  there may be a solution for people who need a lot of bricks lifted or trucks driven into narrow places.  An electric hoist works for bricks, and there are some surprisingly skillful drivers of Mack trucks — though they do need spaces an inch or so wider than the truck.Where hoists and skilled rivers are not available, or for spaces actually narrower than the truck, I would recommend that you get Deepak Chopra teamed up with Russell Targ, he of the Advanced Studies  Institute at Texas U, and very knowledgeable about quantum mind-bending of spoons.  They have access to more powerful quantum methodology than people like I.I. Rabi, a mere Nobel laureate, recognized in 1944 for his discovery of nuclear magnetic resonance.  Bricks in seconds, trucks in inches. Ommmm.-dlj.

  5. Jeff Rosenbury
    Jeff Rosenbury says:

    Does entanglement extend to tunneling?My understanding of entanglement is that it causes some dependence (usual examples are full dependence) of one random variable with another. So is it possible to entangle particles so if one tunnels, the other one must, or at least be more likely to tunnel? Not that it really affects the answer. The difference between 1 in 10^82 and 1 in 10^164 may be huge numerically, but it seems of little practical significance. Still, it's an interesting question about the nature of the universe.

  6. Gary Feierbach
    Gary Feierbach says:

    What is the process by which hydrogen gas H2 escapes from a metal container by going through the metal matrix? Is that a type of tunneling? There is a negative charge barrier from the metal electrons tor the electrons circling the H2 gas molecules but they are treated as a package with a negative charge.

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