# Why You Can’t Quantum Tunnel Through a Wall

We periodically get questions on PF about people wanting to know if 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.

To 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 are 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 Ph.D. 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 the tunneling of fundamental particles. Let me explain.

In electron tunneling, for example, the electron itself can already be described via the straight-forward wave function. 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 the 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 characteristic 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 aspects 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 likes 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.

Tags:
64 replies
1. Drakkith says:
maline

Does the differencebetween the proton & electron actually make the tunneling probability lower, or just much more difficult to calculate? if so, why?

maline

Yes, I got all that from the start! But for the seventh time, how does the fact that the individual probabilities are different come into this?Are you asking if/why the probability for electron + proton is less than proton + proton or electron + electron?

2. maline says:

Yes, I got all that from the start! But for the seventh time, how does the fact that the individual probabilities are different come into this?

3. DaveC426913 says:
maline

I have no problem with the fact that the two individual transmission probabilities are different. But what does this have to do with the joint probability of both particles being transmitted?Because the condition for success is that you (all of you) pass through the wall. Otherwise, none of you does. You encounter an impassible barrier.

Think of a mesh bag full of dice. Shake the bag, and each die has an individual chance of falling out of the bag.

But imagine if all the dice were stuck together with strands of gooey gum. Now, no die can literally fall out of the bag onto the floor, and the entire glop of dice will never fall out of the bag no matter how long and how hard you shake it. The chance of the entire glop of dice falling through are virtually zero, because it is a the sum of all the individual chances, which is a very small number.

4. maline says:

Sure, two particles tunneling is less probable than one! But Zapper's statement was that a hydrogen atom is less likely to tunnel than an alpha particle, because of the fact that the proton & electron have different individual transmission probabilities. In your terms, we're comparing X*Y vs Z*Z. With classical probability, it would be completely irrelevant whether X=Y or not. So why is this aspect important here?

5. 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.

6. 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..

7. ZapperZ says:
maline

I have no problem with the fact that the two individual transmission probabilities are different. But what does this have to do with the joint probability of both particles being transmitted?

p.s. with all due respect, I don't think I'm the one who's "not paying attention" here!Then I don't understand why you were using the alpha particle example, especially when clearly it doesn't apply to the "they" in your Post #12, if you are paying attention.

Whether you buy my argument or not, here's a fact: we have no experimental evidence of the tunneling of whole atoms and molecules.

If such an event can't be achieved, then there's no hope of tunneling whole watermelons.

Zz.

8. maline says:

I have no problem with the fact that the two individual transmission probabilities are different. But what does this have to do with the joint probability of both particles being transmitted?

p.s. with all due respect, I don't think I'm the one who's "not paying attention" here!

9. ZapperZ says:
maline

If they did get through with equal probability, as in the case of alpha particles, how does this increase the probability for them both to get through at once?Did you not pay attention to my description of the SIGN of the charges?

Zz.

10. maline says:

If they did get through with equal probability, as in the case of alpha particles, how does this increase the probability for them both to get through at once?

11. ZapperZ says:
maline

What I'm not getting is why the difference in the separate transmission probabilities necessarily leads to a lower probability that for the transmission of two particles with similar individual probabilities.
Thanks for your patience.Because they won't get through the barrier with equal probability! Your right hand might go through, but your left hand stayed behind! (Sorry, but I had to resort to THAT ridiculous analogy.) So ALL of you didn't get through the barrier at the same time! To me, the probably of all of you to tunnel through the barrier is then ZERO.

Goodbye left hand!

Zz.

12. maline says:

What I'm not getting is why the difference in the separate transmission probabilities necessarily leads to a lower probability that for the transmission of two particles with similar individual probabilities.

13. ZapperZ says:
maline

Would you mind putting in a word about what effect this has on the final probability?I'm not exactly sure what you are looking for here. One particle has to tunnel through a barrier, while the other one has to "jump" over a "hole in the ground". Is it not obvious that the transmission probability will be different for each one of them?

So if you want just "a word", it is "DIFFERENT"!

Zz (who thinks explaining physics using "a word" is impossible).

14. maline says:
ZapperZ

This means that the transmission probability for each one of them will be different!Would you mind putting in a word about what effect this has on the final probability?

15. ZapperZ says:
maline

Does the differencebetween the proton & electron actually make the tunneling probability lower, or just much more difficult to calculate? if so, why?Look at the difference in the CHARGE! One sees it is a "barrier", while the other sees it as a "well". This means that the transmission probability for each one of them will be different!

This is not an issue of tunneling of individual particles. It is the tunneling of ALL the particles together, simultaneously, and coherently. We have not seen such a thing yet. The best that we have is the tunneling of alpha particles, which is nothing more than a clump of two protons (and notice that each of them making up the composite particle has the same charge and the same charge sign) while the neutrons have no charge.

Until we can show of tunneling phenomenon by whole atoms and molecules, tunneling by macroscopic object is practically impossible at this moment.

Zz.

16. maline says:

Does the differencebetween the proton & electron actually make the tunneling probability lower, or just much more difficult to calculate? if so, why?

17. Drakkith says:

So I'm not going to tunnel through my chair and into the core of the Earth. Good to know!

18. Markus Hanke says:

Good insight article, very well spoken !

19. gianeshwar says:

Thanks ZapperZ.I have a better understanding now!