Quantum tunnelling w/ macroscopic objects

[BWV]

does not occur because the probabilities are of the magnitude of exp[ -1 / h ], give or take a few decimal places, correct? i.e. 1 / some number with > 10^30 zeros after it

(trying to explain this simply to my daughter)

 

[Wolfgang2b]

Are you asking why we cannot walk through walls?

The answer is related to probability I guess but I am not sure if there is any formula like the one you mention. As I understand, particles like electrons tunnel through potential barriers rather often (depending on the width/thickness of the barrier). If we want a ball to pass through a barrier, we need all the electrons, protons and neutrons etc that make the ball to tunnel through simultaneously. The chance of all of them tunneling at the same time is very low (Might be as big as what you say although I don't know the numbers). So we don't see it happen.

 

[StevieTNZ]

But there is still a probability for it occurring at that instance of time. To dismiss it is foolish. Perhaps if it doesn't happen in this life time, you can dismiss it. But if you can calculate a probability for it occurring at a certain instant in time, then you can't dismiss it.

 

[BWV]

the wiki article has this for an approximation of the Transmission coefficient

which would be squared to calculate the tunnelling probability? so with large m, Exp[-2m/h^2] is the order of magnitude of the probability. If the probabilities are the simultaneous tunnelling of all the particles this still seems right - the odds of a proton and electron in a hydrogen atom tunnelling together is very small, call it p then you have p^10^23 for the odds of a mole of hydrogen tunnelling at once

which I guess would be small enough to rule out any macroscopic GT occurring anywhere in the Universe

For example 10^60 moles of "stuff" in the universe colliding every second for 10^17 seconds (the age of the universe) with a probability of one of them tunneling at 1/10^10^30 one would not expect an instance of quantum tunneling at this scale to ever occur even with billions of universes

 

[BWV]

But there is still a probability for it occurring at that instance of time. To dismiss it is foolish. Perhaps if it doesn't happen in this life time, you can dismiss it. But if you can calculate a probability for it occurring at a certain instant in time, then you can't dismiss it.

I may just be a finance guy, but I feel very comfortable dismissing probabilities like exp(-10^36) ;)

 

[salvestrom]

Brian Cox and Brian Greene have, in separate programs, mentioned that macroscopic quantum tunneling is a theoretical possible but the calculation shows you would need to wait longer than the age of the universe to ever see it happen. So David Copperfield can stand with his hands against the Great Wall of China, imma go ride mah bike.

 

[StevieTNZ]

I may just be a finance guy, but I feel very comfortable dismissing probabilities like exp(-10^36) ;)

I stick to deductive reasoning.

 

[ZapperZ]

I stick to deductive reasoning.

There's nothing "deductive" about what you are doing, because you're dismissing realistic scenario. Do you plan your life around the possibility that something suddenly pop up in the middle of nowhere, and that a broken vase can spontaneously reassemble itself into its original shape?

There is a difference between mathematically calculated probability that is prohibitively low, versus something that can realistically happen. The physics that you know AND USE depends very much on the latter! The former is very much like String Theory - might be pretty to look at, but darn impossible to verify in all its many variations and options. So you are essentially accepting something with no empirical evidence just because some estimated calculations can come up with a non-zero number. And let's get this clear here, that minuscule number is an estimate, not a "deductive reasoning".

Now, coming back to the original question, let's first of all look at the simplest case of tunneling that we all know and love, and the one that many of us studied as an undergraduate. We dealt with ONE single quantum particle impinging on a potential barrier. This is very important to realize because we treat this particle as a single, point entity with no constituents. So if it tunnels, the whole object tunnels.

This scenario is no longer true for a macroscopic object. Consider something simpler first, such as an atom. It consist of a nucleus (which in itself is made up of other "particles") and the orbital electrons. If you try to have the whole atom to tunnel through, you have to consider how each of the constituents of the atom will tunnel through. The probability of an electron to tunnel through the barrier is different than the probability of a proton to tunnel through. We can already see this simply due to the different charges. A potential barrier for a proton can easily be an attractive potential for an electron! Are they seeing the SAME potential profile in this barrier? No. And by default, they can't have the same probability to tunnel across, say, a wall!

Most of the rudimentary, back-of-the-envelope calculations/estimations of the tunneling probability do NOT take into account such variation to the tunneling probability of such constituents. I would say that even if in the minuscule event that such an atom undergoes a tunneling phenomenon, there probability that it could tunnel through intact with all of its constituents is even MORE minuscule! How small of a number here before we deem it as being unrealistic?

Note that, when "macroscopic" objects such as buckyballs starts behaving and showing quantum properties (such as exhibiting interference behavior), the experiments had to be performed at extremely low temperature to make sure all the constituents of the buckyball are in "coherence" with each other. It isn't easy to do. And guess what? No one is attempting to do an experiment to see these buckyballs can "tunnel" across something.

So what are the odds that something such as a tennis ball (at room temperature no less where decoherence effect are in abundance and rule its behavior) can tunnel through a wall? For all practical purpose, I would say it cannot! And this comes from someone who did tunneling spectroscopy experiments as a grad student many years ago.

Zz.

 

[StevieTNZ]

There is, in all honesty, no need to have a go at me.

 

[Wolfgang2b]

the wiki article has this for an approximation of the Transmission coefficient

Can you please link the article that you referred? I am just curious to know for what system this was the Transmission coefficient

 

[ZapperZ]

There is, in all honesty, no need to have a go at me.

But there is! How else are you going to learn and think twice before making such type of statements on here, especially when you don't really understand the physics?

Note that I also wrote, at length, an explanation to go along with it. I just didn't go "... because I said so!" You should at least try to LEARN something.

Zz.

 

[akhmeteli]

Now, coming back to the original question, let's first of all look at the simplest case of tunneling that we all know and love, and the one that many of us studied as an undergraduate. We dealt with ONE single quantum particle impinging on a potential barrier. This is very important to realize because we treat this particle as a single, point entity with no constituents. So if it tunnels, the whole object tunnels.

This scenario is no longer true for a macroscopic object. Consider something simpler first, such as an atom. It consist of a nucleus (which in itself is made up of other "particles") and the orbital electrons. If you try to have the whole atom to tunnel through, you have to consider how each of the constituents of the atom will tunnel through. The probability of an electron to tunnel through the barrier is different than the probability of a proton to tunnel through. We can already see this simply due to the different charges. A potential barrier for a proton can easily be an attractive potential for an electron! Are they seeing the SAME potential profile in this barrier? No. And by default, they can't have the same probability to tunnel across, say, a wall!

Most of the rudimentary, back-of-the-envelope calculations/estimations of the tunneling probability do NOT take into account such variation to the tunneling probability of such constituents. I would say that even if in the minuscule event that such an atom undergoes a tunneling phenomenon, there probability that it could tunnel through intact with all of its constituents is even MORE minuscule! How small of a number here before we deem it as being unrealistic?

Zz.

This is an important point indeed. However, its implications are not quite obvious, as this point gives rise to a little-known classical analog of the quantum tunneling: https://www.physicsforums.com/showpost.php?p=1051780&postcount=10 .

 

[Wolfgang2b]

This is an important point indeed. However, its implications are not quite obvious, as this point gives rise to a little-known classical analog of the quantum tunneling: https://www.physicsforums.com/showpost.php?p=1051780&postcount=10 .

Are you saying that a classical particle with total energy less than the barrier height can pass through it? I find it hard to digest...If u have any article/link for this, please share

 

[akhmeteli]

Are you saying that a classical particle with total energy less than the barrier height can pass through it? I find it hard to digest...If u have any article/link for this, please share

Not a "classical particle" (if you mean a point particle), but an extended classical object, for example, a high jumper or a long train moving over a hill. I have no reference to offer right now, but I did read about that in a book in Russian many years ago, and I only remember the last name of the author - Rabotnov. However, I guess this is already a part of "quantum folklore", and what is more important, this is quite obvious and should not be controversial (I am not offering anything revolutionary:-) ): indeed, for example, to pass over a bar, a high jumper does not need to have the kinetic energy equal to or larger than mgh, where m is her mass and h is the height of the bar, as she can bend her body during the jump (e.g., Fosbury flop) in such a way that the center of her mass will pass below the bar. If this comment does not look satisfactory, please advise, and I'll try to improve this reasoning.

 

[ZapperZ]

This is an important point indeed. However, its implications are not quite obvious, as this point gives rise to a little-known classical analog of the quantum tunneling: https://www.physicsforums.com/showpost.php?p=1051780&postcount=10 .

How are these two related or even relevant? A high-jumper is NOT tunneling over anything!

Zz.

 

[ZapperZ]

Not a "classical particle" (if you mean a point particle), but an extended classical object, for example, a high jumper or a long train moving over a hill. I have no reference to offer right now, but I did read about that in a book in Russian many years ago, and I only remember the last name of the author - Rabotnov. However, I guess this is already a part of "quantum folklore", and what is more important, this is quite obvious and should not be controversial (I am not offering anything revolutionary:-) ): indeed, for example, to pass over a bar, a high jumper does not need to have the kinetic energy equal to or larger than mgh, where m is her mass and h is the height of the bar, as she can bend her body during the jump (e.g., Fosbury flop) in such a way that the center of her mass will pass below the bar. If this comment does not look satisfactory, please advise, and I'll try to improve this reasoning.

You are making some serious handwaving and speculative argument here, besides the fact that how this is related to tunneling of quantum object is puzzling.

Zz.

 

[akhmeteli]

How are these two related or even relevant? A high-jumper is NOT tunneling over anything!

Zz.

I'd say there is a direct analogy: the tunneling effect is penetration of a potential barrier by an object having limited kinetic energy. This is what a high jumper can do. If you prefer a strictly one-dimensional classical analog, you can imagine a train of masses connected with springs, which passes a one-dimensional potential barrier - again, if the thickness of the barrier is less than the length of the train, the latter does not have to have the kinetic energy equal to or greater than that of its total mass at the top of the barrier. However, the high jumper example seems more graphic.

 

[akhmeteli]

You are making some serious handwaving and speculative argument here, besides the fact that how this is related to tunneling of quantum object is puzzling.

Zz.

OK, OK, now that you allude to forums' rules..., I had to do something to cover my assets:-) :

A. Cohn, M. Rabinowitz, Classical Tunneling, Int'l Journ. Theor. Phys., v. 29, #3, 1990, p. 215.

I just forgot about this article - I read it so long ago (although Rabotnov's book was published even earlier).

As I said, I did not try to offer anything revolutionary, this is indeed just "quantum folklore".

By the way, I even found a reference to Rabotnov's book: Rabotnov N.S. , Larchik mozhno ne otkrivat': Kvantovyi tunnel'nyi effekt. Polveka zagadok i otkrytii, Moscow, Energoatomizdat, 1983 (in Russian)

 

[ZapperZ]

OK, OK, now that you allude to forums' rules..., I had to do something to cover my assets:-) :

A. Cohn, M. Rabinowitz, Classical Tunneling, Int'l Journ. Theor. Phys., v. 29, #3, 1990, p. 215.

I just forgot about this article - I read it so long ago (although Rabotnov's book was published even earlier).

As I said, I did not try to offer anything revolutionary, this is indeed just "quantum folklore".

By the way, I even found a reference to Rabotnov's book: Rabotnov N.S. , Larchik mozhno ne otkrivat': Kvantovyi tunnel'nyi effekt. Polveka zagadok i otkrytii, Moscow, Energoatomizdat, 1983 (in Russian)

I'd say there is a direct analogy: the tunneling effect is penetration of a potential barrier by an object having limited kinetic energy. This is what a high jumper can do. If you prefer a strictly one-dimensional classical analog, you can imagine a train of masses connected with springs, which passes a one-dimensional potential barrier - again, if the thickness of the barrier is less than the length of the train, the latter does not have to have the kinetic energy equal to or greater than that of its total mass at the top of the barrier. However, the high jumper example seems more graphic.

Sorry, but how is THIS on topic to what is being discussed in this thread?

That "classical tunneling" has nothing to do with quantum tunneling of macroscopic object! Are you claiming that this classical tunneling "proves" that macroscopic object can, in fact, undergo quantum tunneling? As far as I can tell, the OP was NOT looking for an analogy!

Zz.

 

[akhmeteli]

Sorry, but how is THIS on topic to what is being discussed in this thread?

I believe your comment quoted in my post 12 in this thread was indeed "on topic to what is being discussed in this thread", and I just commented on your comment, if I may say so, emphasizing that it is not quite obvious "that even if in the minuscule event that such an atom undergoes a tunneling phenomenon, there probability that it could tunnel through intact with all of its constituents is even MORE minuscule", as tunneling of composite objects is not necessarily less probable than tunneling of their constituents (as exemplified by the examples of "classical tunneling").

That "classical tunneling" has nothing to do with quantum tunneling of macroscopic object! Are you claiming that this classical tunneling "proves" that macroscopic object can, in fact, undergo quantum tunneling?

I am not sure I should commit myself to any opinion on this issue, as this issue seems to depend on the definition of "quantum" (or "quantum tunneling"): indeed, on the one hand, the Planck constant does not appear in any formulas for "classical tunneling", on the other hand, the high jumper is still subject to the laws of quantum mechanics. By the way, this is another reason why my comment may be (at least technically) relevant to the thread called "Quantum tunnelling w/ macroscopic objects".

Anyway, the information I offered seems interesting for some readers of this thread (e.g., Wolfgang2b), and it is definitely little-known. On the other hand, I do appreciate that you determine what is relevant in this thread and this forum.

 

[ZapperZ]

I believe your comment quoted in my post 12 in this thread was indeed "on topic to what is being discussed in this thread", and I just commented on your comment, if I may say so, emphasizing that it is not quite obvious "that even if in the minuscule event that such an atom undergoes a tunneling phenomenon, there probability that it could tunnel through intact with all of its constituents is even MORE minuscule", as tunneling of composite objects is not necessarily less probable than tunneling of their constituents (as exemplified by the examples of "classical tunneling").

Sorry, but I fail to see the relevance of classical tunneling example to the quantum case. You seem to somehow not realize that (i) high-jumper exists and (ii) quantum tunneling of atoms have NOT been observed! That fact alone clearly indicates that these are not the same thing!

I am not sure I should commit myself to any opinion on this issue, as this issue seems to depend on the definition of "quantum" (or "quantum tunneling"): indeed, on the one hand, the Planck constant does not appear in any formulas for "classical tunneling", on the other hand, the high jumper is still subject to the laws of quantum mechanics. By the way, this is another reason why my comment may be (at least technically) relevant to the thread called "Quantum tunnelling w/ macroscopic objects".

Er.. there has to be clear definition of quantum tunneling for you? Are you telling me that you can't tell the difference between what you quoted as classical tunneling with what you see in a standard undergraduate QM text?

Anyway, the information I offered seems interesting for some readers of this thread (e.g., Wolfgang2b), and it is definitely little-known. On the other hand, I do appreciate that you determine what is relevant in this thread and this forum.

You are more than welcome to start a discussion on this classical tunneling. However, what you have done is to derail and confuse the issue. They are distinctly different. And yes, at some point, *I* have to judge what is on-topic in a particular physics thread.

Zz.

 

[akhmeteli]

You are more than welcome to start a discussion on this classical tunneling. However, what you have done is to derail and confuse the issue. They are distinctly different. And yes, at some point, *I* have to judge what is on-topic in a particular physics thread.

I regret that my comment seemed inappropriate. Thank you for your time and input.

 

[Physics Monkey]

Just to amplify what Zz said about tunneling of composite objects like atoms, one should remember that macroscopic objects are subject to a strongly decoherent environment. This makes it that much harder to tunnel. The semiclassical tunneling estimate for point particles already gives absurdly small rates when we put in macroscopic numbers for the mass, etc., but even these super tiny rates are probably far too large since they assume that the object in question is moving coherently. Even small would-be quantum objects can't tunnel in the presence of strong decoherence e.g. nanomagnets coupled to a bath of nuclear spins or phonons.

 

[BWV]

interesting responses - i wonder if the decoherence issue really matters given the order of magnitude of my naive calculation - if you have probabilities like exp(-10^35) simply plugging in macroscopic masses into quantum formulas - a factor of 1000 or a million is not really material. either way, it is essentially impossible.

 

[liquidsnake]

Hello Folks,
I am studying quantum computing now and got a problem with understanding MQT( Macroscopic Quantum Tunneling). Consider a symmetric double-well potential (i.e. of a rf-SQUID) with degenerate quantum levels in the wells. So the question is, how can a MQT through the potential barrier introduce a level splitting (in this image it's $\Delta$ ) ?

 

[I2004]

You are making some serious handwaving and speculative argument here, besides the fact that how this is related to tunneling of quantum object is puzzling.

Zz.

http://www.sciencedaily.com/releases/2009/05/090527130836.htm


proves you wrong? macroscopic tunnelling can occur