B How does quantum tunneling occur without an observer?

[e.bar.goum]

I agree. The crucial question is: does the change of Ψ involve a collapse?

Arg. So leaving this thread. What change in $\Psi$? It's just following the evolution given by the TDSE. Here's a pretty simulation.

Sharp barrier at 0. Evolution of $\Psi$, no collapse required. I'm pretty sure I made a very similar video in second year physics...

 

[Demystifier]

I measured the current using a large glob of electrode. If you think something the size of 2 mm by 2 mm as a "position" measurement, then you have a generous phase space for quantum effects. Besides, this is measured on the surface of the conductor, not at the tunnel junction. If you call this collapse, then the collapse happened OUTSIDE of it, not where all the action was taking place, i.e. at the tunnel junction.

I never said that collapse did not happen outside of it. I agree it did. But I have two points:
1. A collapse did happen.
2. Perhaps another collapse (not detected by you) also happened at the tunnel junction or somewhere also before your detection.

 

[ZapperZ]

I never said that collapse did not happen outside of it. I agree it did. But I have two points:
1. A collapse did happen.

But this has NOTHING to do with tunneling phenomenon. I could measure a current in a conductor and claim the same thing! So why is this relevant in this topic?

2. Perhaps another collapse (not detected by you) also happened at the tunnel junction or somewhere also before your detection.

This is crackpottish! You are shooting in the dark, and hoping that something will stick. Stop being vague! Show me exactly where, in the physics, that there is a detection! Otherwise, you are giving false ideas that people like the OP are clinging to and thinking that they were right, or at least, there is a valid disagreement. There isn't! All you have done is introduce some vague, handwaving argument and forcing me to prove you wrong. How about you actually prove you are right?

What is puzzling here is that this is BASIC, intro QM stuff!

Zz.

 

[Demystifier]

Evolution of Ψ, no collapse required.

In your beautiful simulation, the wave function is present at both sides. If no collapse is required, then why the particle is observed at only one side? If that needs no collapse, then what does need a collapse?

 

[Demystifier]

How about you actually prove you are right?

For that purpose I would suggest you to read some theoretical textbook on decoherence and its relation to the theory of quantum measurements. For instance, the book by M. Schlosshauer.

 

[ZapperZ]

In your beautiful simulation, the wave function is present at both sides. If no collapse is required, then why the particle is observed at only one side? If that needs no collapse, then what does need a collapse?

This is silly. A reflection of a barrier isn't a "collapse". It measured nothing because you still don't know the position of the particle at any given time. You don't detect the particle when it hits the barrier!

You want to know what will detect its position? Wrap a loop of wire right at the barrier so that when an electron hits it, it will induce a current there to indicate the electron was there! THAT is how you do a detection!

Zz.

 

[ZapperZ]

For that purpose I would suggest you to read some theoretical textbook on decoherence and its relation to the theory of quantum measurements. For instance, the book by M. Schlosshauer.

This is a cop-out. I asked you to show this in this particular SIMPLE tunneling scenario that all physics undergraduates have done, and you point me to a book on decoherence?

In other words, you can't do what I asked you to show.

Zz.

 

[Demystifier]

So where is the "collapse"?

Do you know any example in QM where the collapse is needed?

 

[ZapperZ]

Do you know any example in QM where the collapse is needed?

I'm going to cut this off here, because you have a very devious, sneaky way of carrying this discussion. Instead of directly addressing what you were asked, you throw off distracting items and avoid answering the questions completely. I don't know what you're trying to pull off here, but I don't have the time to entertain you anymore.

Zz.

 

[Demystifier]

You want to know what will detect its position? Wrap a loop of wire right at the barrier so that when an electron hits it, it will induce a current there to indicate the electron was there! THAT is how you do a detection!

I agree. And I add: that's how you do a collapse. And that's how the particle, according to the standard theoretical interpretation of QM, attains a definite position.

 

[Demystifier]

I'm going to cut this off here, because you have a very devious, sneaky way of carrying this discussion. Instead of directly addressing what you were asked, you throw off distracting items and avoid answering the questions completely. I don't know what you're trying to pull off here, but I don't have the time to entertain you anymore.

Sorry, but I cannot explain why collapse is needed in this special case before explaining why the collapse is need in the general case. Since I don't know how much about the collapse in general you already know, I asked you to give an example of a phenomenon where the collapse is definitely needed. In that way I would better understand your way of thinking about the collapse, so I could adjust my answer to your way of thinking. Such adjustment is definitely needed, because clearly there is a lot of mutual misunderstanding here.

 

[atyy]

In very few words- tunnelling is a phenomenon associated with $\Psi$, not with <$x$>.

That's fine as a matter of definition. However, you did define it as being associated with <$x$> in your first description in post #6 where you said "You can see an exponentially decreasing probability of seeing the particle outside the box - this is quantum tunnelling."

The difficulty is that these are so close, especially if you read the OP's question it is closer to your first definition of tunneling where <$x$> is used.

 

[Demystifier]

After cooling my brain a little bit, I think I understood what was the source of mutual misunderstanding. It seems that two closely related but still different things are both called "tunelling":
1. The split of wave function into two parts, one of which is on the other side of the barrier.
2. The phenomenon that the particle happens to be on the other side of the barrier.

The 1. of course does not need any collapse, observer, decoherence, measurement, Bohmian trajectories, or anything else of that sort.
The 2. does need something (not necessarily everything) of that sort.

E.bar.goum and ZZ, is it clearer now?

 

[DrChinese]

Isn't electron before a measurement just a probability wave? It doesn't have a particular location, since we can't determine the location of a wave. But when interacting with the barrier, the wave collapses (reduction of multiple states to just one state, with the probability of finding it on the other side of the barrier, and inside the barrier). Where am I wrong?

ZapperZ has explained this, but I will add some different words in case that helps.

All electrons are in a state of superposition (and a state of uncertainty) at ALL times. It is IMPOSSIBLE to collapse any quantum particles' non-commuting properties simultaneously. Think about these statements and you will see the assumption you are making.

When any observation is made, you are potentially changing the basis of what is known - ie position or momentum, or potentially even a partial mix of both. Ditto for other non-commuting pairs. But there is always uncertainty. So when you mention collapse, you are really referring to collapse on some basis. And you are either talking about a collapse that changes the basis or one that does not. But you are never talking about "total" collapse because there is not such thing.

 

[Juraj]

ZapperZ has explained this, but I will add some different words in case that helps.

All electrons are in a state of superposition (and a state of uncertainty) at ALL times. It is IMPOSSIBLE to collapse any quantum particles' non-commuting properties simultaneously. Think about these statements and you will see the assumption you are making.

When any observation is made, you are potentially changing the basis of what is known - ie position or momentum, or potentially even a partial mix of both. Ditto for other non-commuting pairs. But there is always uncertainty. So when you mention collapse, you are really referring to collapse on some basis. And you are either talking about a collapse that changes the basis or one that does not. But you are never talking about "total" collapse because there is not such thing.

I am aware that momentum and position both have their separate superposition states and by knowing one, we don't know the other. In my assumption I was specifically referring to position wave-function for which I stated that it collapses when it interacts with the barrier. And also, I'm familiar with the fact that electons are constantly in the superposition states for the reasons I noted above.

After cooling my brain a little bit, I think I understood what was the source of mutual misunderstanding. It seems that two closely related but still different things are both called "tunelling":
1. The split of wave function into two parts, one of which is on the other side of the barrier.
2. The phenomenon that the particle happens to be on the other side of the barrier.

The 1. of course does not need any collapse, observer, decoherence, measurement, Bohmian trajectories, or anything else of that sort.
The 2. does need something (not necessarily everything) of that sort.

Can someone confirm this?

 

[e.bar.goum]

After cooling my brain a little bit, I think I understood what was the source of mutual misunderstanding. It seems that two closely related but still different things are both called "tunelling":
1. The split of wave function into two parts, one of which is on the other side of the barrier.
2. The phenomenon that the particle happens to be on the other side of the barrier.

The 1. of course does not need any collapse, observer, decoherence, measurement, Bohmian trajectories, or anything else of that sort.
The 2. does need something (not necessarily everything) of that sort.

E.bar.goum and ZZ, is it clearer now?

Yes. Finally! That's what we were arguing about.

 

[e.bar.goum]

That's fine as a matter of definition. However, you did define it as being associated with <$x$> in your first description in post #6 where you said "You can see an exponentially decreasing probability of seeing the particle outside the box - this is quantum tunnelling."

The difficulty is that these are so close, especially if you read the OP's question it is closer to your first definition of tunneling where <$x$> is used.

Not really. I was using imprecise language, but I still was talking about $\Psi$(x) - "probability amplitude" would have been more precise.

Anyway, the issue for pages now has been one of terminology, which is the least interesting kind of physics issue.

 

[Nugatory]

In my assumption I was specifically referring to position wave-function for which I stated that it collapses when it interacts with the barrier.

It does not. It collapses (if you're going to use a collapse interpretation at all, and this thread is shaping up to be pretty good evidence that collapse interpretations do not help understanding tunneling) when and if some interaction localizes it to one side or the other of the barrier.

I keep on finding myself returning to the first post in this thread, where you asked about fusion between two nuclei separated by the Coulomb force barrier so that classically they can never collide. I prepare my two nuclei in a state such that the amplitude for them fusing is non-zero; I blink my eyes; and the next time I look they might be fused. There's nothing here that says that we had to have both nuclei located on the same side of the barrier at any point, or that the interaction with the barrier caused any collapse.

 

[DrChinese]

I am aware that momentum and position both have their separate superposition states and by knowing one, we don't know the other. In my assumption I was specifically referring to position wave-function for which I stated that it collapses when it interacts with the barrier.

As Nugatory points out, this is not correct (actually you don't know on what basis there is collapse).

But assuming it was: placing a particle in a more definite position causes its momentum to become progressively more uncertain. That gives it progressively more values it could possibly have... and some of those will take it through the potential barrier. QED.

 

[e.bar.goum]

I am aware that momentum and position both have their separate superposition states and by knowing one, we don't know the other. In my assumption I was specifically referring to position wave-function for which I stated that it collapses when it interacts with the barrier. And also, I'm familiar with the fact that electons are constantly in the superposition states for the reasons I noted above.

In any case, the measurement/collapse that Demystifier was talking about wasn't due to interactions with the barrier.

Can someone confirm this?

Yes, that's what we were arguing about. I would still say that 1. is a more appropriate use of the term, because 2. is just 1+measurement, which doesn't actually help understand tunneling, or elucidate any more physics. But I'm happy at this stage to agree to disagree with Demystifier on this issue . However, again, that is not what your OP referred to in terms of "collapse due to interactions with a barrier".

 

[atyy]

Yes, that's what we were arguing about. I would still say that 1. is a more appropriate use of the term, because 2. is just 1+measurement, which doesn't actually help understand tunneling, or elucidate any more physics. But I'm happy at this stage to agree to disagree with Demystifier on this issue . However, again, that is not what your OP referred to in terms of "collapse due to interactions with a barrier".

To argue about what "is" is, you used the term "phenomenon", so we should also be happy to disagree on which the more appropriate definition of "phenomenon" is

"No phenomenon is a real phenomenon until it is an observed phenomenon." http://izquotes.com/quote/196799

I've become pretty sure that Bohmians are the purest Copenhagenists.

 

[Nugatory]

Oh man... Just when I thought this thread was back on track and responding to the OP...
OK, as long as everyone is using plenty of smileys, I guess it's still OK.

 

[Swamp Thing]

However, again, that is not what your OP referred to in terms of "collapse due to interactions with a barrier".

Maybe a better description of tunnelling would be, "collapse due to interaction, 'beyond' the barrier and despite the existence of a barrier"

 

[e.bar.goum]

Maybe the right description of tunnelling is, "collapse due to interaction, 'beyond' the barrier and despite the existence of a barrier"

I don't really think that sentence makes sense unless you say "measurement of the location of a particle due to interaction, 'beyond' the barrier and despite the existence of a barrier"

But I'd still describe that as "a measurement of tunnelling" rather than "tunnelling" itself. But, as I think we've established, it's all a little moot, and to be honest, I care a little less every time we go around in a circle about this. But perhaps we should stop using the word "tunnelling" at all, since it clearly causes a lot of angst. (The smiley is for Nugatory ).

But I think most agree in this thread that whether or not you require measurement to say that tunnelling has occurred, that measurement has not occurred due to interactions with the barrier, per the OP.

(As an aside: this thread has been an interesting exercise for me: In nuclear physics, we often picture tunnelling very classically. For alpha decay, say, you picture an alpha particle sitting in the potential vibrating around, hitting the barrier, mostly reflecting off, but each time there's some probability for it to get through, and for the parent nucleus to "decay". But to know whether or not that decay has occurred, some de-coherence/measurement needs to occur. So, presumably, a toy universe that contains only one ²⁴¹Am atom would never actually see it decay. Rather, you'd be in a superposition of ²³⁷Np+$\alpha$ and ²⁴¹Am. Which I suppose is always true anyway. And this is different to fusion again, too, since fusion involves coupling to many internal degrees of freedom, so in some sense, there is an interaction (near) the barrier there.)

 

[Demystifier]

But I think most agree in this thread that whether or not you require measurement to say that tunnelling has occurred, that measurement has not occurred due to interactions with the barrier

I definitely agree with that.

 

[Demystifier]

I've become pretty sure that Bohmians are the purest Copenhagenists.

Not in the sense that they accept the Copenhagen interpretation, but yes in the sense that they take it literally in order to clearly distinguish it from the other (especially Bohmian) interpretations.

 

[Jano L.]

After cooling my brain a little bit, I think I understood what was the source of mutual misunderstanding. It seems that two closely related but still different things are both called "tunelling":
1. The split of wave function into two parts, one of which is on the other side of the barrier.
2. The phenomenon that the particle happens to be on the other side of the barrier.

The 1. of course does not need any collapse, observer, decoherence, measurement, Bohmian trajectories, or anything else of that sort.
The 2. does need something (not necessarily everything) of that sort.

E.bar.goum and ZZ, is it clearer now?

I do not thing this is the root of the disagreement. What I see as important is that ZapperZ considers tunneling to be a physical phenomenon which can be described with Schroedinger equation and wave function that gives probabilities, but no measurement of position is done and no idea of collapse is ever needed to describe this phenomenon. This is how quantum theory is often applied successfully; no measurement of positions of electrons are done, natural autonomous processes are being described and calculations are made that compare well with macroscopic measurements (current, ...)

What you were suggesting is another view, less standard, where we want to continue to describe electrons with wave function and the Schroedinger equation even after the phenomenon of interest has happened, i.e. in the ammeter. I think ZapperZ is right that this has nothing to do with description of tunneling. It has everything to do with description of a measurement of current in the ammeter, but that is a different issue. The tunneling can happen even if no current is being measured.

 

[Demystifier]

I do not thing this is the root of the disagreement. What I see as important is that ZapperZ considers tunneling to be a physical phenomenon which can be described with Schroedinger equation and wave function that gives probabilities, but no measurement of position is done and no idea of collapse is ever needed to describe this phenomenon. This is how quantum theory is often applied successfully; no measurement of positions of electrons are done, natural autonomous processes are being described and calculations are made that compare well with macroscopic measurements (current, ...)

What you were suggesting is another view, less standard, where we want to continue to describe electrons with wave function and the Schroedinger equation even after the phenomenon of interest has happened, i.e. in the ammeter. I think ZapperZ is right that this has nothing to do with description of tunneling. It has everything to do with description of a measurement of current in the ammeter, but that is a different issue. The tunneling can happen even if no current is being measured.

The view which you described (which might coincide with the view of ZZ) perhaps makes sense in the case when a large number of electrons tunnels. This, indeed, corresponds to the tunneling phenomena usually seen in laboratories.

But in principle, it is possible to have a situation in which only one electron tunnels. In such a case, the view which you described would not make much sense. I am convinced that, in the one-electron case, my view is quite standard.

 

[Jano L.]

The view which you described (which might coincide with the view of ZZ) perhaps makes sense in the case when a large number of electrons tunnels. This, indeed, corresponds to the tunneling phenomena usually seen in laboratories.

Yes, I believe this is the case considered in textbooks and by ZapperZ.

But in principle, it is possible to have a situation in which only one electron tunnels. In such a case, the view which you described would not make much sense. I am convinced that, in the one-electron case, my view is quite standard.

I do not see why the view that I described would not make much sense. The equation is the same, the interpretation is the same - it gives probability for position of the electron that is non-zero behind the potential wall. We place a detector (screen, photo-multiplier) behind the potential wall and if it registers, we know the electron has tunneled. We can then compare the frequency of clicks to results based on the Schroedinger equation.

It is possible that the measurements will deviate from the equation - after all, it is quite different experimental setup - but there is no collapse required anywhere in the analysis.

 

[ZapperZ]

The view which you described (which might coincide with the view of ZZ) perhaps makes sense in the case when a large number of electrons tunnels. This, indeed, corresponds to the tunneling phenomena usually seen in laboratories.

But in principle, it is possible to have a situation in which only one electron tunnels. In such a case, the view which you described would not make much sense. I am convinced that, in the one-electron case, my view is quite standard.

No, it isn't. The STANDARD tunneling treatment in textbooks is done on ONE electron, because electron-electron interaction is neglected. So you have a many one-body treatment of tunneling.

Why would the detection of a current due to one electron would somehow allows you to (i) claim that the tunneling must occur only when it is detected and (ii) that the barrier allows you to make a determination of the position of the electron. These are, after all, the two issues that the OP has claimed, and which he had used YOUR posts to justify his view.

The problem here, and why I've given up on this thread, is that you never bothered to offer any physics at all to back up your claim. When I directly asked for it, you pointed me to a book, or avoided my question by offering one-line statement or another question. You will note that I've addressed every single point that you've made, even pointed out to you how I would detect the longitudinal position of an electron.

So before I abandon this thread completely and stop following it, here it is once again.

1. The barrier makes NO positional measurement, be it on one electron, or on many electrons.

2. Tunneling can occur without observation of the tunneling process itself (i.e. at the tunnel junction). What is observed is the effect after the fact, i.e AFTER the tunneling process occurred. If you don't know that what you detected was tunneling current, there's nothing that distinguish this from any ordinary current.

And with that, I am done!

Zz.