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gib65

quantum tunneling & "borrowing" energy

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My understanding of the phenomenon of quantum tunneling is that a particle surrounded by a barrier may be detected outside that barrier due to the fact that its wavefunction spans across the barrier (i.e. there's a small portion of the particle's wave that reaches beyond the barrier). Therefore, there's a small chance the particle will be found outside the barrier when measured.

 

What I don't understand is why some physicists feel this has to be accounted for by the particle "borrowing" energy from a parallel universe. As I see it, the idea that a particle exists as a probability wave means that we don't need any sort of energy-borrowing account. I can see that we would in the context of classical mechanics - in that case, the particles needs extra energy in order to penetrate the barrier. But by the standards of quantum mechanics, there is no "penetrating". There is only the probability that the particle will turn up outside the barrier.

 

So why the theory of "borrowing"?

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If we make two measurements, in the first the particle is on this side and in the next it appears on the other side, then you will have to ask the question: how did it get there ?

 

If it didn't penetrate the barrier the which way did it take ?

 

Without the "borrowing" it would be as Magic.

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If we make two measurements, in the first the particle is on this side and in the next it appears on the other side, then you will have to ask the question: how did it get there ?

 

If it didn't penetrate the barrier the which way did it take ?

 

Without the "borrowing" it would be as Magic.

 

No, it would be quantum mechanics. The concept of borowing energy is an attempt to hang on to some classical notions, but there are plenty of "purely" QM phenomena where there is no classical pastiche, so why not this one as well? I think it has more to do with pedagogy; tunneling often appears very early in a QM class and it takes a while to acclimate to all of the quantum weirdness.

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Does anyone know about that 3-box experiment? Where they got some particles to arrive in the end box, without going through the middle one?

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No, it would be quantum mechanics. The concept of borowing energy is an attempt to hang on to some classical notions, but there are plenty of "purely" QM phenomena where there is no classical pastiche, so why not this one as well? I think it has more to do with pedagogy; tunneling often appears very early in a QM class and it takes a while to acclimate to all of the quantum weirdness.

Since I don't know much of quantum mechanics, I have failed to acclimate to its wierdness... :embarass:

 

If a particle is moving from one side to the other side of a barrier, without penetration, it sounds like Magic to me.

(EDIT: Without a 'classical' explanation of how it manages to get there. :) )

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Without the "borrowing" it would be as Magic.

 

What you call "Magic", others simply call "indeterminacy" - as in, the particle's position is not determined, and so could very well turn out to be on the other side of the barrier. The weirdest it gets, IMHO, is when one measures the particle's position and it turns up on the one side of the barrier, and then measures it again a short while after and it turns up on the other side. Then, we know that it somehow got from one side to the other. I guess some feel that this "somehow" can't be explained unless we bring in the concept of "borrowing" energy. I feel that quantum indeterminacy does the job just as well, but I'm no expert.

 

Does anyone know about that 3-box experiment?

 

No, please tell us.

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p17. New Scientist 29 Sep. 2007:

 

"Quantum bodies go here or there, but not in between

...waves of atoms can move between three boxes separated by impenetrable barriers. Ordinarily a quantum particle starting at one end will tunnel through the first barrier, move into the middle box, and spend some time there before tunnelling through the second barrier to reach the third box.

...particles can skip the middle box. The team built a computer model of the movement through a Bose-Einstein condensate,...they could make the waves in the middle box cancel each other ...only a few atoms ever occupied the middle box....may be useful for controlling matter waves..."

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What you call "Magic", others simply call "indeterminacy" - as in, the particle's position is not determined, and so could very well turn out to be on the other side of the barrier. The weirdest it gets, IMHO, is when one measures the particle's position and it turns up on the one side of the barrier, and then measures it again a short while after and it turns up on the other side. Then, we know that it somehow got from one side to the other. I guess some feel that this "somehow" can't be explained unless we bring in the concept of "borrowing" energy. I feel that quantum indeterminacy does the job just as well, but I'm no expert.

Well, I didn't actually call the probability distribution for Magic, what I meant was the lack of explanation of how the particle manages to pass the barrier could be viewed as Magic. Because we had determined it's position.

(Quantum indeterminacy doesn't explain how, it only describes what we observe, but I'm no expert either.)

 

I guess, I am one of those who feel the need for an explanation, like the concept of "borrowing" energy. :)

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quantum tunnelling is a micro and nanoscopic phenomenon in which a particle violates principles of classical mechanics by penetrating or passing through a potential barrier or impedance higher than the kinetic energy of the particle. A barrier is therefore in an energy state.

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I don't know, but this eerily reminds me of flatland. In flatland, a 3d person can poke their finger into a box or someone's body, then move it outside as if by magic, simply because they have an extra spatial dimension that 2d beings cannot detect.

 

If we imagine a ball bouncing continuously, we take a snap shot and it is on one side of a "barrier", then the next snapshot, it is on the other side. But, I guess in that case, the probability distribution would be equal? Just a thought from left field.

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I thought of an experiment that might be able to tell us whether the particle really is passing through the barrier in virtue of having acquired the necessary energy spontaneously: see if a correlation can be detected between the probability of finding the particle outside the barrier (after determining that it is inside) and the "penetrability" of the barrier itself. By "penetrability", I mean, the amount of energy it would take the particle to penetrate it if it were to rely on the processes of classical mechanics only. You could adjust the penetrability by the density of the barrier's material, or the type of material, or its temperature, or whatever else would affect the amount of energy needed to penetrate it. If, in doing so, you can affect the probability of finding the particle on the other side - namely, decreasing it as a function of increasing the barrier's penetrability - this supports the theory that the particle is acquiring extra energy spontaneously and using it to pass through the barrier. The assumption this experiment makes is that the more energy needed, the less likely are the chances that the particle will get that much energy spontaneously, and therefore the less likely it is to penetrate the barrier

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How is that distinguishable from the tunneling? The QM probability depends on particle energy and barrier height.

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The QM probability depends on particle energy and barrier height.

 

If this is a fact, then I take it experiments have been done to verify it. I'd say these experiments are exactly the kind I was trying to describe in my last post (not word-for-word, but close enough). If particle energy and barrier height do have an effect on the QM probability, as you say, then to me this proves favorable for the "borrowing" theory.

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hen to me this proves favorable for the "borrowing" theory.

 

Why?

 

Where in the theory does this borrowing come from?

 

If you work through the maths you can clearly see how the energy and barrier height change the probabilities.

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Why?

 

Where in the theory does this borrowing come from?

 

If you work through the maths you can clearly see how the energy and barrier height change the probabilities.

 

I'm not denying that the math says this.

 

The particle needs a certain amount of energy to penetrate the barrier (or maybe leap over the barrier if height has something to do with it). It gets this energy spontaneously and the amount of energy it gets is random. I'm assuming this is the way it works because ASAIK, according to QM, energy is one of the variables that can be uncertain. The probabilities are that the greater the energy, the less likely it will be that the particle will get it. The higher the barrier, the more energy the particle needs to "leap over" it, and since the acquisition of high energy is less likely to happen than low energy, it will be less likely that the particle will leap over the barrier, and thus the less likely it will be found on the other side of the barrier.

 

If the "borrowing" concept was not correct, the barrier height shouldn't have anything to do with the likelihood of finding the particle on the other side. Nor should its energy. The particle's position is distributed over its waveform, some of which reaches passed the barrier. It is not clear how this distribution is affected by barrier height or energy. There is no reason to predict that a higher barrier or lower energy will change the probability distribution of the particle's position. There should always be the same likelihood that the particle might be found on the other side of the barrier.

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I'm pretty sure you can jump barriers larger than that of which the uncertainty principle would come into play.

 

We're not really talking about particles here, but wave-particles, they don't act classically so there's no reason to say they need to jump over.

 

The barrier height is important because it dictates where the bottom the barrier is, so the level of the lowest energy level of the particle.

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The barrier height is important because it dictates where the bottom the barrier is, so the level of the lowest energy level of the particle.

 

What do you mean by this? Maybe I've misunderstood "barrier height". Does it mean how tall the barrier is (like we would say a wall is 5 feet tall, 10 feet tall, 15 feet tall, etc.), or what position the barrier is at (like we would say a painting on the wall is 5 feet up, 10 feet up, 15 feet up, etc.)?

 

Also, what does "level of the lowest energy level" mean?

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What do you mean by this? Maybe I've misunderstood "barrier height". Does it mean how tall the barrier is (like we would say a wall is 5 feet tall, 10 feet tall, 15 feet tall, etc.), or what position the barrier is at (like we would say a painting on the wall is 5 feet up, 10 feet up, 15 feet up, etc.)?

 

Also, what does "level of the lowest energy level" mean?

 

Height meaning energy, or something related (like a potential), just as height in a kinematic sense relates to potential (gh) or potential energy (mgh).

 

Particles in confinement have quantized energy levels. The ground (lowest) state has some minimum kinetic energy.

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Height meaning energy, or something related (like a potential), just as height in a kinematic sense relates to potential (gh) or potential energy (mgh).

 

Particles in confinement have quantized energy levels. The ground (lowest) state has some minimum kinetic energy.

 

See, to me that supports the idea that the particle is somehow "tunneling" through the barrier. It doesn't proove it, it supports it. I don't know how to imagine that without denying the wave/particle duality of the particle, but it does suggest that there's something funny going on whereby the particle needs extra energy in order to be found on the other side of the barrier (or for the likelihood of finding it there to go up).

 

That's just what I gather from it. I don't know the math very well and I'm not as familiar with this phenomenon as others, so maybe other have better ways of explaining it.

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See, to me that supports the idea that the particle is somehow "tunneling" through the barrier. It doesn't proove it, it supports it. I don't know how to imagine that without denying the wave/particle duality of the particle, but it does suggest that there's something funny going on whereby the particle needs extra energy in order to be found on the other side of the barrier (or for the likelihood of finding it there to go up).

 

That's just what I gather from it. I don't know the math very well and I'm not as familiar with this phenomenon as others, so maybe other have better ways of explaining it.

 

It doesn't exclude the QM principle, though, so it has no ability to falsify one or the other. The so-called support isn't exclusive, and in science, it needs to be.

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It doesn't exclude the QM principle, though, so it has no ability to falsify one or the other. The so-called support isn't exclusive, and in science, it needs to be.

 

Well, I don't think it would falsify the QM principle outright. What it would falsify, in my mind, is the idea that the distribution of the particle's position is unaffected by the state of the barrier or the particle's energy, which is something the "borrowing" theory would want falsified.

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Are we depicting a scenario with equal potential levels on either side of a potential hump of "relatively small" spatial extent? If that's so then are folks speaking of a temporary "borrowing" of energy"? I am slowly getting accustomed to dealing with the vacuum as a sea of fluctuations. This is part of what you're missing when you think classically. Reading sources I recall that probability amplitudes do depend on the height, which could be, say, a voltage repelling an electron, and that there is exponential falloff in the width of the "wall" region. How do we represent the wall potential for an insulator? <I took out an initial question which was confused.>

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