Quantum Tunneling

[ParanoiA]

Ok, so I was just reading about Quantum Tunneling. About the energy a particle has can wildly fluctuate in a short enough time scale. This is somewhat difficult to absorb because it doesn't make any intuitive sense to me about "borrowing" energy and reqlinquishing it within a small timeframe.

 

Where does it borrow this energy from? Other nearby particles?

 

Greene explains that if you were to shoot a plastic pellet at a concrete wall, that the wave functions of the particles making up the pellet all have a tiny piece that spills out through the wall. And so, the pellet has a small chance of going through the wall after repeating the action enough times.

 

I'm not putting this together very well. I dont' see how pieces of a wave function penetrating the wall could equate to all of the particles penetrating the wall at some lucky point.

[GutZ]

I dont know that seems more complex, this is how I understood it.

 

http://www.physicspost.com/articles.php?articleId=173&page=3

[swansont]

The "borrowing" part, I think, is trying to make a quantum idea fit with a classical mindset. Objects behave like waves, and can be transmitted through barriers, even in situations where a classical partical does not have enough energy to get over the barrier. Also, the wave behavior means there can be reflection even when there is enough energy to classically make it over.

[ParanoiA]

The "borrowing" part, I think, is trying to make a quantum idea fit with a classical mindset. Objects behave like waves, and can be transmitted through barriers, even in situations where a classical partical does not have enough energy to get over the barrier. Also, the wave behavior means there can be reflection even when there is enough energy to classically make it over.

 

Hmm...ok so how does that tie in with "probability"? Why is it that eventually the pellet will go through the wall? (assuming you have the millions of years of lifetime to afford shooting a plastic pellet at a concrete wall)

[Klaynos]

Hmm...ok so how does that tie in with "probability"? Why is it that eventually the pellet will go through the wall? (assuming you have the millions of years of lifetime to afford shooting a plastic pellet at a concrete wall)

 

When you work through the boundry conditions for a particle inside a box (the simplist form we can do here) the probability wave of the "particle" decays inside the barrier, so if the barrier is thin enough the wavefunction can have a part on the other side of it. Therefore the particle has a probability, bassed on it's wavefunction of tunnelling through the barrier.

[ParanoiA]

Is this what physicists are referring to when they talk about probabilities in general? Or is this quantum tunneling just one example of probabilities in quantum physics?

 

I'm a little disappointed in Greene's approach on this, because we spent 2 chapters on Relativity, and now just one quickie chapter on Quantum. I think I need to understand this probability theme better before going on.

[Klaynos]

Is this what physicists are referring to when they talk about probabilities in general? Or is this quantum tunneling just one example of probabilities in quantum physics?

 

I'm a little disappointed in Greene's approach on this, because we spent 2 chapters on Relativity, and now just one quickie chapter on Quantum. I think I need to understand this probability theme better before going on.

 

The probabilty function for a particle, is the complex conjugate of the wavefunction timesed by the wavefunction. This is normally what is ment by probability in QM.

[swansont]

Hmm...ok so how does that tie in with "probability"? Why is it that eventually the pellet will go through the wall? (assuming you have the millions of years of lifetime to afford shooting a plastic pellet at a concrete wall)

 

The same reasoning that you will eventually roll snake eyes with a pair of dice. There is a certain probability that it will happen with each interaction.

[ParanoiA]

The same reasoning that you will eventually roll snake eyes with a pair of dice. There is a certain probability that it will happen with each interaction.

 

See, I'm not understanding how there's a probability that would happen. Obviously I'm not grasping this concept quite right.

 

Maybe I need to think more on the wave functionality of a particle. I tend to think of it as a particle that travels like a wave - and I doubt that's the right way to think about it.

[J.C.MacSwell]

Ok, so I was just reading about Quantum Tunneling. About the energy a particle has can wildly fluctuate in a short enough time scale. This is somewhat difficult to absorb because it doesn't make any intuitive sense to me about "borrowing" energy and reqlinquishing it within a small timeframe.

Where does it borrow this energy from? Other nearby particles?

 

Greene explains that if you were to shoot a plastic pellet at a concrete wall, that the wave functions of the particles making up the pellet all have a tiny piece that spills out through the wall. And so, the pellet has a small chance of going through the wall after repeating the action enough times.

 

I'm not putting this together very well. I dont' see how pieces of a wave function penetrating the wall could equate to all of the particles penetrating the wall at some lucky point.

 

I picture this as being borrowed from space itself which is a quagmire of energy fluctuation. Anyone see pitfalls in this idea?

[ParanoiA]

Ok, after doing some re-reading, please tell me if I'm understanding this a little better.

 

In relation to the pellet penetrating the wall...the probability waves - the wave functionality tunnels through the wall and since the particles can be found anywhere in the wave, based on probability, then obviously at some point a particle will find itself located in the area of the wave that tunneled through...????

 

It seems as if the functionality waves are like water waves in that it describes the movement of these particles - except that even when these particles are isolated, they still move AS IF they were surrounded with billions of other particles moving like water. Which is where probability comes in, since there's no apparent intuitive reason why a particle would behave like that when there are no other particles near it to distort its movement like that.

[ParanoiA]

I picture this as being borrowed from space itself which is a quagmire of energy fluctuation. Anyone see pitfalls in this idea?

 

Actually, I wonder if swansont might have this nailed down. Because, he's right in that Greene did use this terminology to explain it in a layman's perspective.

[swansont]

Ok, after doing some re-reading, please tell me if I'm understanding this a little better.

 

In relation to the pellet penetrating the wall...the probability waves - the wave functionality tunnels through the wall and since the particles can be found anywhere in the wave, based on probability, then obviously at some point a particle will find itself located in the area of the wave that tunneled through...????

 

It seems as if the functionality waves are like water waves in that it describes the movement of these particles - except that even when these particles are isolated, they still move AS IF they were surrounded with billions of other particles moving like water. Which is where probability comes in, since there's no apparent intuitive reason why a particle would behave like that when there are no other particles near it to distort its movement like that.

 

Right. When the particle interacts with the wall, a small part of the wave function is on the other side, meaning there is a small chance the particle is there. For every collision.

 

The water wave analogy may get you in trouble. You don't need a medium for these waves to travel through.

[ParanoiA]

Right. When the particle interacts with the wall, a small part of the wave function is on the other side, meaning there is a small chance the particle is there. For every collision.

 

The water wave analogy may get you in trouble. You don't need a medium for these waves to travel through.

 

So when we use the term "wave function" we're not really talking about an actual wave, but rather a result of motion that "appears" as if they were traveling as a wave?

 

Edit:

 

Ok that was silly, for some reason I read the word "wave" in your reply as "particle" - as if you said you don't need a medium for these particles to travel through.

 

Now that I've read your reply correctly, I'm not sure I understand what you mean by it.

[Ragib]

Ok, i have not bothered to read all up, ill just explain it straight. Basically theres this principle in quantum mechanics called Heisenbergs Uncertainty Principle which basically states that there is an inherent uncertainty between conjugate variables such as postion and momentum. It is basically saying it doesn't matter how hard we try, or how good of apparatus we can get, theres always some uncertainty, because the better we observe one of the variables, the less accurate another one is. This is different to the observer effect where observing it changes the outcome. An example of the oberserver effect is, im measuring the position of a particle, but to the measure it i use a light photon, which has momentum and changes the position. However The Uncertainty principle says even with everything perfect we cant measure it perfect. Eg. Time and Wavelength. The Smaller increments of time gets the time measurment better, but we have less time to observe the wavelength so it will be less accurate.

 

Now one of the uncertainty relations of Time and Energy. It basically says Uncertainty of Time times the Uncertainty of Energy is more or at best, equal to plancks constant divided by 2pi. So, in a small enough increment of time, something can have a large uncertainty of energy and still comply with the principle, and we wouldn't be able to measure it. So in quantum tunnelling a particle, for a very short period of time, has enough energy to escape, which it so happens it does.

[swansont]

So when we use the term "wave function" we're not really talking about an actual wave, but rather a result of motion that "appears" as if they were traveling as a wave?

 

Edit:

 

Ok that was silly, for some reason I read the word "wave" in your reply as "particle" - as if you said you don't need a medium for these particles to travel through.

 

Now that I've read your reply correctly, I'm not sure I understand what you mean by it.

 

It's a probability wave. It's not physical, so looking at it as a real wave, in a medium, might confuse things. The jump from classical to quantum is tough enough, because there is often a tendency to try and tie things back to classical behavior.

[5614]

In trying to explain the idea of a probability wave I'm going to assume that you know about Young's Double Slit experiment. If you don't then this will not help you.

 

When you think about a light wave going through both slits at the same time there is logic in that one wave can go through two slits, however when you think about it in terms of photons it no longer makes sense. How can a single particle be in two places at once? One way of looking at the situation can be to imagine that the photon is fired, and as soon as it's fired it disappears and is replace by a probability wave. This probability wave goes through both slits.

 

When the system is observed (maybe it's a detecting screen after the double slit, or a detector on one of the slits, whatever it is) the probability wave disappears and the photon reappears somewhere, randomly, but depending on the probability distribution that the probability wave gives.

 

The probability wave explains how probable it is to find the particle (photon in this case) at any point. It is not a physical entity.

[ParanoiA]

Thanks 5614. That makes sense. That is so strange how that works.

 

Are you of the mind that Einstein was wrong, in that the behavior we observe as probability or we predict using probability, is the result of some basic incompleteness in our understanding?

 

Just curious...

[5614]

Einstein's EPR paradox, I could say a lot on the subject!

 

Einstein is wrong, to the best of our knowledge. Einstein did not like quantum mechanics and specifically did not like the Copenhagen Interpretation. Einstein presented what he thought were faults with QM to Bohr, however Bohr always managed to show that Einstein was wrong, and that QM was correct. These Bohr-Einstein debates (on whether QM is correct or not) are well documented, you can see a summary here:

http://en.wikipedia.org/wiki/Bohr-Einstein_debates

 

Einstein's final argument against QM was that of the EPR paradox. Sadly Einstein was not alive when the solution to this apparent paradox was discovered. In 1964 Bell came up with a thought experiment which, if carried out experimentally, would reveal whether Einstein and the EPR paradox were true, and QM was false, or the other way around.

 

Although originally Bell never planned for his thought experiment (often referred to as Bell's Inequality) to be carried out experimentally. However in 1972 the first experimental results were being released, most showed that Bell's Inequality was violated, meaning that Einstein was wrong, QM is correct.

 

I'll just interrupt at this point to say that Bell set up his inequality assuming that Einstein was correct. Hence if Bell's Inequality holds true then Einstein is correct, however if it is violated then QM is correct.

 

However it wasn't until 1982 when the experiment was carried out by Aspect that physicists were fully convinced that QM was correct. Even to this day there are more tests, and they all violate Bell's Inequality.

 

About 6 months ago (before I knew about the EPR paradox) I was thinking about physics and stumbled across what must have been Einstein's thought pattern when he came up with the EPR paradox. I came on here (SFN) and asked how, when we know QM is correct, could my "paradox" (the EPR paradox) be explained.

 

A few people recognised my question as the EPR paradox re-worded, and started talking about EPR and Bell, I had to take a step back for I realised that I'd reinvented, as it were, the EPR paradox.

 

First I read more regarding the EPR paradox, and thought that Einstein was right (even though I knew QM was right, I couldn't see a solution). Then I read about Bell's Inequality. A great thought experiment, I thought, that couldn't be carried out. But then finally I read about Aspect's experiment, which shows once and for all that the EPR paradox is not a paradox, that Einstein was wrong and that QM is correct.

 

I guess it's taken me all of that to say that I do think QM is the correct explanation of the world, and therefore accept the consequences of this. Yes I do think the universe is based on probabilities, yes I do think that "God plays dice"*.

 

*Just for those who don't know that quote, it's something Einstein said, he actually said he didn't believe that Einstein played dice with the universe, what he was saying is that he didn't accept the probabilistic nature of QM.

[ParanoiA]

I guess I need to read about the EPR paradox then. I didn't think this was a concept that had been proven one way or the other.