Insights You Will Not Tunnel Through a Wall - Comments

[DrChinese]

Just to be clear... my reference to Lloyd was not intended as a favorable one.

As ZapperZ says, the answer should be: it doesn't happen. He has shown why an H2 molecule will not ever tunnel through a wall in any universe. I think it is clear that anything larger won't either. Saying it is theoretically possible is meaningless in this context.

 

[Derek Potter]

Just to be clear... my reference to Lloyd was not intended as a favorable one.

I think everyone understood that.

As ZapperZ says, the answer should be: it doesn't happen. He has shown why an H2 molecule will not ever tunnel through a wall in any universe.

Hmm. I can see where he says it is much more complicated, and fragile, and unlikely than a simplistic model would suggest but I can't see anywhere that he claims the probability is precisely zero.

 

[kmm]

Since I'm an experimentalist (and I was trained in tunneling spectroscopy measurement), I'll show you evidence on why single electron tunneling is much more prevalent (and thus, easier and significantly more probable) than a coherent 2-electron tunneling.

This manuscript (it was published in PRB) shows superconductor-insulator-normal metal (SIN) and superconductor-insulator-superconductor (SIS) tunneling spectroscopy. Pay attention to Fig 4 (near the end of the manuscript on Pg. 13).

http://arxiv.org/pdf/cond-mat/9807389.pdf

These are IV curves (current versus applied voltage across the tunnel junction) for SIS tunneling. The current that you see is dominated by single-electron tunneling. This is where the the Cooper pairs break apart, and single-electrons tunnel through the insulating layer, and then reforming Cooper pairs again on the other side. This is true EXCEPT for the zero-bias region. If you notice, there is a small signal in the current when there's no applied voltage, and no single-electron tunneling. This is the Josephson current, where it is a tunneling of the supercurrent consisting of the coherent Cooper pairs!

But look at the "constraints" here. The current is exceedingly small when compared to the single-electron tunnel current, and it is destroyed once one applies even a small bias to the junction. As someone who had measured and dealt with this current, it is EXTREMELY FINICKY, and can be destroyed very easily! In fact, if the tunnel barrier gets bigger, there is a point where I only observed single-electron tunneling, and not the Josephson current any longer. The Josephson current is extremely sensitive to "phase change", which is why it makes for a very sensitive detector in SQUIDs.

So in this set of measurements, there is a significant and distinct difference in the probability of single-electron tunneling versus 2-electron tunneling, over the same, indentical tunnel barrier! The single-electron tunneling is clearly more probable. In fact, as long as your barrier remains intact, you can crank up the bias potential as high as you want and get more and more tunnel current, while the 2-electron tunnel current is gone!

There are NUMEROUS complications and additional parameters when we deal with coherent tunneling of "composite" particles that are not described in the simple tunneling picture done in undergraduate QM classes. For example, we haven't even discussed the content of the tunneling matrix element which will be relevant as the complexity arises. I simply did not want this to go over the heads of people who haven't even done undergraduate QM classes, but I wanted to point out that many people who talk about macroscopic objects tunneling through a barrier are ignoring the FACT that composite particle/macroscopic object tunneling is extremely different and extremely complicated with compared to single-particle tunneling. The former has a lot more physics that must be considered, and it is not a simple one-to-one correspondence to the latter. The knowledge of single-particle tunneling does not translates as smoothly as one thinks when dealing with composite/macroscopic particles.

Zz.

Thanks for posting this. Very clear explanation.

 

[Dr_Zinj]

So.
Probability of a100 kg mass of liquid H2O (100 cm x 100 cm x 10 cm) at 4 deg C tunneling through a 10 cm barrier of an infinite size sheet of copper is greater than zero; but probably much less than 1/10^82. (10^82 is on of the approximations of the number of particles in the universe.) For comparison, your odds of winning the Powerball with anyone ticket are about 1/10^7.
Don't plan on having any "Harry Potter" or "Men Who Stare At Goats" moments during your lifetime.

 

[DavidLloydJones]

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 giving out the quantum 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 skilful drivers of Mack trucks -- though they do need spaces an inch or so wider than the truck.

Where hoists and skilled drivers 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 University of Texas, 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.

 

[Jeff Rosenbury]

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.

 

[ZapperZ]

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.

You are forgetting that in the SIS tunneling example that I had given, the electrons in the Cooper pair are entangled with each other. So they make up the Josephson current.

Zz.

 

[DaveC426913]

I wish there were an edit function available

There is.

 

[DavidLloydJones]

The difference between 1 in 10^82 and 1 in 10^164 may be huge numerically, but it seems of little practical significance.

I think you're being a little cavalier about that factor of two in there.

Never forget the businessman who made his millions in Popsicles, or whatever it was: "I make them for a nickel and I sell them for a dime, and from that one percent difference I have become rich."

-dlj.

 

[DavidLloydJones]

There is.

Yup. Found it. But thanks, Dave.

 

[Gary Feierbach]

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.

 

[ZapperZ]

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.

Hydrogen gas is too small and can sneak through metal joints, etc. it is not tunneling.

When I do a RGA reading on an ultra-vacuum system, I usually see hydrogen gas, even when we are at low 10^-10 Torr.

Zz.

 

[Gary Feierbach]

I got an answer from the oil and gas industry. In gas pipelines there is moisture and H₂S that reacts with the iron in the metal to make FeS. The Hydrogen from the reaction in the form of ions can penetrate the metal and also accumulate in striations in the metal, combine into H2 and actually form blisters from the pressure buildup. For this reason these pipes are injected with corrosion inhibitors along with the product.

 

[Jeff Rosenbury]

You are forgetting that in the SIS tunneling example that I had given, the electrons in the Cooper pair are entangled with each other. So they make up the Josephson current.

Zz.

I'm not forgetting; I'm ignorant. Shouldn't there be a separate entanglement for tunneling on top of any entanglement for normal pair formation?

As I understand it, the probability of an unentangled pair of electrons tunneling should be the probability of one tunneling times the probability of the other tunneling? (Of course there will be conundrums such as changing potentials and the like.)

But if the particles tunnel together more frequently than the product of their individual probabilities they would be partially entangled for tunneling purposes in addition to being entangled for spin purposes.

Or is there a difference between the shifting probabilities due to changing potentials and entanglement? Perhaps just having the changing probabilities counts as some form of entanglement? (That is a semantic argument, BTW. It depends on how we define entanglement.)