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**General Science / Re: What is Quantum Tunnelling and how does Quantum Tunnelling work?**

« **on:**01/02/2022 19:41:13 »

Hi again.

So let's see if there are any questions left over from Aeris.

Let's just look at a microscopic objects for a moment (before we speculate and generalise to macroscopic objects).

We're going to consider the typical situation with a square barrier potential between two regions of exactly the same potential (region I and region III).

Here's the diagram again:

We're going to fire a particle toward the barrier (from region I) which has Energy, E < V

Firstly remember that the wave function is not the particle, there isn't anything with properties like a particle until you go looking for it (make an observation to locate the particle). The wave function just indicates the probability of finding the particle at a particular place.

If you go back through the earier discussions and animated diagram you'll notice that the wave function isn't always 0 inside the barrier. There is some time when the particle could be found there.

Now this is where various sources of information (not just PopSci) are going to mess things up or mis-represent what seems to be shown by the mathematics.

Just go back and look at the animated diagram carefully if you want to, instead of doing the mathematics. There are times when the real and imaginary components of the wave function are non-zero at a fixed x position inside the barrier. So the square of the modulus of the wave function is not 0 at that time, this is the probability of finding the particle at that given point x in space and given time t. I'm labouring the point here but we just need to be clear that the probability of finding the particle at that position x in the barrier is not 0 for some of the time. The probability of finding of the particle in the barrier does not drop to 0 until some finite non-zero time has elapsed after the incident wave packet hit the barrier. You will find many articles, some textbooks and countless discussions on Quora and similar websites that discuss qunatum tunneling as if it's instant. Some of them are quite interesting and authoritative and discuss problems like the apparent breech of the speed of light (If the particle could move from one side of a barrier of thickness, d>0, to the other side instantly than that is faster than light speed travel). They're all good in their own way except that the fundamental premise they were based on was bollderdash.

Anyway, the mathematics never implied that tunneling would be instant.

Here's one article (from Scientific American) that describes an attempt to actually measure how long it takes a particle to tunnel through a barrier:

https://www.scientificamerican.com/article/quantum-tunneling-is-not-instantaneous-physicists-show/

The details aren't too important, we just need to note that there may actually be some way of observing or measuring tunneling time in practice and it does not seem to be instantaneous. It can be that the particle spends some time in the barrier.

Anyway, we can now try to generalise this to a macroscopic scale: Basically, there's no reason to assume that the quantum tunneling of your chair from region I to region III would be "instant". It's not going to go "poof" from here and just "poof" into existance over there. It is very likely to spend some time "in the barrier" between the two places. I'm not sure what this would "look like" but it could be a lot less impressive than teleporting. Given a piece of space between the start and end point (i.e. a piece of space in the barrier), then the chair could be found there for a short amount of time during the tunneling. I really don't know how to paraphrase this, applying QM to macroscopic objects is always just going to be speculation anyway. It might look like the chair was just moving from the start position to the end position and occupies at least some but possibly all of the positions between those two points in passing. A whole lot less impressive than teleportation, I'm sorry to dissapoint you.

Another long, post, sorry. In summary the only important thing is that Quantum Tunneling isn't instant and may not look like teleportation.

Best Wishes.

LATE EDITING: I probably should make it clear that the time it takes for a particle to tunnel through a barrier is controversial. This was stated originally but it's worth stating again. You should probably make your own investigations. Personally, I'm sticking to what the Mathematics shows.

So let's see if there are any questions left over from Aeris.

Let's say, hypothetically speaking, a macroscopic object like a table or a chair undergoes Quantum Tunneling and essentially teleports from one location to another while I'm still looking at it. What would that look like? would the object just pop right out of and then immediately back into existence in the blink of an eye?

Let's just look at a microscopic objects for a moment (before we speculate and generalise to macroscopic objects).

We're going to consider the typical situation with a square barrier potential between two regions of exactly the same potential (region I and region III).

Here's the diagram again:

We're going to fire a particle toward the barrier (from region I) which has Energy, E < V

_{0}exactly as before and we've already discussed the wave function and shown animated diagrams of this earlier.Firstly remember that the wave function is not the particle, there isn't anything with properties like a particle until you go looking for it (make an observation to locate the particle). The wave function just indicates the probability of finding the particle at a particular place.

If you go back through the earier discussions and animated diagram you'll notice that the wave function isn't always 0 inside the barrier. There is some time when the particle could be found there.

Now this is where various sources of information (not just PopSci) are going to mess things up or mis-represent what seems to be shown by the mathematics.

**The amount of time over which the particle could be found "in the barrier" is controversial.**Some sources are going to tell you that it "instantly appears" on the other side of the barrier or just that "it will never be found in the barrier" etc. I don't wish to use too much bad language but this is clearly utter bolderdash.Just go back and look at the animated diagram carefully if you want to, instead of doing the mathematics. There are times when the real and imaginary components of the wave function are non-zero at a fixed x position inside the barrier. So the square of the modulus of the wave function is not 0 at that time, this is the probability of finding the particle at that given point x in space and given time t. I'm labouring the point here but we just need to be clear that the probability of finding the particle at that position x in the barrier is not 0 for some of the time. The probability of finding of the particle in the barrier does not drop to 0 until some finite non-zero time has elapsed after the incident wave packet hit the barrier. You will find many articles, some textbooks and countless discussions on Quora and similar websites that discuss qunatum tunneling as if it's instant. Some of them are quite interesting and authoritative and discuss problems like the apparent breech of the speed of light (If the particle could move from one side of a barrier of thickness, d>0, to the other side instantly than that is faster than light speed travel). They're all good in their own way except that the fundamental premise they were based on was bollderdash.

Anyway, the mathematics never implied that tunneling would be instant.

Here's one article (from Scientific American) that describes an attempt to actually measure how long it takes a particle to tunnel through a barrier:

https://www.scientificamerican.com/article/quantum-tunneling-is-not-instantaneous-physicists-show/

The details aren't too important, we just need to note that there may actually be some way of observing or measuring tunneling time in practice and it does not seem to be instantaneous. It can be that the particle spends some time in the barrier.

Anyway, we can now try to generalise this to a macroscopic scale: Basically, there's no reason to assume that the quantum tunneling of your chair from region I to region III would be "instant". It's not going to go "poof" from here and just "poof" into existance over there. It is very likely to spend some time "in the barrier" between the two places. I'm not sure what this would "look like" but it could be a lot less impressive than teleporting. Given a piece of space between the start and end point (i.e. a piece of space in the barrier), then the chair could be found there for a short amount of time during the tunneling. I really don't know how to paraphrase this, applying QM to macroscopic objects is always just going to be speculation anyway. It might look like the chair was just moving from the start position to the end position and occupies at least some but possibly all of the positions between those two points in passing. A whole lot less impressive than teleportation, I'm sorry to dissapoint you.

Another long, post, sorry. In summary the only important thing is that Quantum Tunneling isn't instant and may not look like teleportation.

Best Wishes.

LATE EDITING: I probably should make it clear that the time it takes for a particle to tunnel through a barrier is controversial. This was stated originally but it's worth stating again. You should probably make your own investigations. Personally, I'm sticking to what the Mathematics shows.

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