How does quantum tunneling occur without an observer?

[Juraj]

I have question that involves quantum tunneling and wave function collapse that occurs when the state of an object is measured.

I will try to explain what I mean. We don't know the exact location of an electron in an atom, because it doesn't have a location, it is in its wave form and we can't determine the location of a wave. We can collapse a wave by observing it (measuring the location of an electron) and then determining the location, right?

Now, the question is: how can quantum tunneling occur if there is no observer or measurment device to collapse its wave function. How does fission in the Sun occur if no one can collapse the wave function? Is the nucleus just randomly teleporting?

Where am I wrong?

 

[rootone]

With regard to the Sun, you mean fusion.
https://en.wikipedia.org/wiki/Solar_core
In the case of the Sun, hydrogen nucleii, go through a chain of reactions with the end result being the emission of a lot of radiation and the production of Helium.
Heavy isotopes of hydrogen (Deuterium and Tritium) are usually produced as intermediate products.
I don't think quantum tunneling has much to do with it, at least I have not come across that idea before.
I think it's more to do with the momentum and the angle at which nuclear particles collide being sufficiently energetic for the fusion to occur, although that is a probabalistic thing, so maybe QM does play a part.
Only a small amount of particle collisions have a sufficiently high energy. (Otherwise the Sun would instantly explode.)

 

[Khashishi]

Depending on your interpretation of quantum mechanics, reality may not exist without an observer. Regardless of interpretation, you can't say quantum tunneling did or did not occur if you never make a measurement afterwards.

 

[Juraj]

With regard to the Sun, you mean fusion.
https://en.wikipedia.org/wiki/Solar_core
In the case of the Sun, hydrogen nucleii, go through a chain of reactions with the end result being the emission of a lot of radiation and the production of Helium.
Heavy isotopes of hydrogen (Deuterium and Tritium) are usually produced as intermediate products.
I don't think quantum tunneling has much to do with it, at least I have not come across that idea before.
I think it's more to do with the momentum and the angle at which nuclear particles collide being sufficiently energetic for the fusion to occur, although that is a probabalistic thing, so maybe QM does play a part.
Only a small amount of particle collisions have a sufficiently high energy. (Otherwise the Sun would instantly explode.)

Quantum tunneling does indeed happen in the Sun, because the temperature (and therefore the movement of the particles causing the collision of the nuclei - fusion) is insufficient.

Depending on your interpretation of quantum mechanics, reality may not exist without an observer. Regardless of interpretation, you can't say quantum tunneling did or did not occur if you never make a measurement afterwards.

But if I wasn't observing or measuring the object when it is approaching the barrier, the probability wave would never collapse and therefore the object would not be on the other side. My understanding of quantum tunneling is like this: if we put the measurement device on the both sides of the barrier we could collapse the probabilty wave by measuring it and there would be a chance that the device on the other side of the barrier will detect that the particle has "teleported" through it without the required energy (object has tunneled). I think that this understanding is wrong because it doesn't explain the occurance of the tunneling during fusion in the Sun.

 

[Juraj]

Anyone? What's wrong with my understanding?

 

[e.bar.goum]

Anyone? What's wrong with my understanding?

Tunnelling doesn't involve a measurement. Have you ever learned quantum mechanics formally? This is easier to see in the mathematics, but broadly, you can take your wave-function for a particle in your potential (i.e. that of the nucleus or a finite square well) and calculate how it changes over time, and you'll find that your probability distribution "spreads out", and there's a bit of the probability distribution that extends out into a region that ordinarily would be forbidden. The case of a finite square well is the canonical example for undergraduates. https://en.wikipedia.org/wiki/Finite_potential_well The curves represent possible wave-functions for a particle in the finite box potential shown in the figure. You can see an exponentially decreasing probability of seeing the particle outside the box - this is quantum tunnelling.

Now, a position measurement, as I'm sure you know, just samples the probability distributions given by ##|\psi(x)|^2## - and there will be a non-zero chance of measuring the location of the particle as outside the box.

Now, in the sun, recall that while nuclear reactions are of course quantum-mechanical, the sun itself is a rather classical object.

 

[ddd123]

Anyone? What's wrong with my understanding?

Tunnelling can be seen from the wave standpoint as well, and it's much less "weird". You should look at the WKB approximation for tunneling, in which you can do a fairly realistic model for an atomic barrier using a Coulomb potential (blue):

The wave (pink) incides on the barrier, and doesn't lose energy or change its nature (see the same frequency of the wave outside and inside) but the probability amplitude outside is less than the inside (see the amplitude of the wave). Though since it's actually the wavefunction of the particle, finding it outside means that the particle has tunneled.

 

[Juraj]

Now, a position measurement, as I'm sure you know, just samples the probability distributions given by |ψ(x)|2|\psi(x)|^2 - and there will be a non-zero chance of measuring the location of the particle as outside the box.

So (this may sound stupid) if I was throwing a tennis ball to the wall repeatedly many many many times, would I ever be able to observe tunneling? Since I'm observing it, I am measuring it's location, so I suppose that I would never be able to see it happen, right? Can I then explain tunneling like this using the previous example:

if I turned my head away from the ball (so I don't see it and can't measure it's position) and threw it repeatedly, there would be a chance that one time when i turn my head, I will find that the tennis ball is on the other side? Is this right?

I have been thinking about the fusion in the Sun: when two nuclei are colliding, both of them are MEASURING if there is another nuclei close to them, and if it is, the fusion will occur - so is it wrong to think that this measurement of position makes tunneling possible?

 

[Nugatory]

if I turned my head away from the ball (so I don't see it and can't measure it's position) and threw it repeatedly, there would be a chance that one time when i turn my head, I will find that the tennis ball is on the other side? Is this right?

The interactions between the ball and the wall are a measurement, whether you're looking or not.

So (this may sound stupid) if I was throwing a tennis ball to the wall repeatedly many many many times, would I ever be able to observe tunneling?

Each particle in the tennis ball has a minute probability of showing up on the far side of the wall (that's the exponential tail in E.Bar.Goum's graph), and if all the particles in the tennis ball were to just happen to do that at the same time... The ball would have tunnelled through the wall. However, if you calculate the actual probability of such an event happening, you will find that it is unimaginably small. Here I mean the word "unimaginably" literally - there are no two things in human experience that can be compared to provide an accurate analogy for how small this probability is. Consider that the trash can beside my house would lauch itself into Earth orbit if every molecule underneath it happened to be vibrating upwards at the same time... compared with the probability of the ball tunnelling through the wall, orbiting trash cans are an everyday occurrence.

It is easy to overstate the weirdness of quantum mechanics here. As my example of the trash can that doesn't go launching itself into Earth orbit suggests, much of what we see in the macroscopic world we live in happens because the statistical fluctuations of large numbers of microscopic particles averages out over time.

You may also find https://www.physicsforums.com/threads/you-will-not-tunnel-through-a-wall.765716/ helpful.

I have been thinking about the fusion in the Sun: when two nuclei are colliding, both of them are MEASURING if there is another nuclei close to them, and if it is, the fusion will occur - so is it wrong to think that this measurement of position makes tunneling possible?

It would be much better to say that they are "interacting" - the probability of the fusion happening can be (and usually is) calculated without ever considering the position of either nucleus.

 

[atyy]

Tunnelling doesn't involve a measurement. Have you ever learned quantum mechanics formally? This is easier to see in the mathematics, but broadly, you can take your wave-function for a particle in your potential (i.e. that of the nucleus or a finite square well) and calculate how it changes over time, and you'll find that your probability distribution "spreads out", and there's a bit of the probability distribution that extends out into a region that ordinarily would be forbidden. The case of a finite square well is the canonical example for undergraduates. https://en.wikipedia.org/wiki/Finite_potential_well The curves represent possible wave-functions for a particle in the finite box potential shown in the figure. You can see an exponentially decreasing probability of seeing the particle outside the box - this is quantum tunnelling.

Now, a position measurement, as I'm sure you know, just samples the probability distributions given by ##|\psi(x)|^2## - and there will be a non-zero chance of measuring the location of the particle as outside the box.

Now, in the sun, recall that while nuclear reactions are of course quantum-mechanical, the sun itself is a rather classical object.

I am skeptical of your claim that tunneling does not involve measurement. You mentioned "probability" in connection with "tunneling". Probability in quantum mechanics enters via the Born rule, which assumes measurement.

 

[Nugatory]

I am skeptical of your claim that tunneling does not involve measurement. You mentioned "probability" in connection with "tunneling". Probability in quantum mechanics enters via the Born rule, which assumes measurement.

I'm not sure whether the disagreement here is about whether you're both using the word "measurement" in the same way, or whether the interaction/measurement that is happening is specifically a position measurement (which is what OP's question is about), or simply an aesthetic disagreement how the fusion is best described in plain English (no right answer IMO, as the primary reason to invoke tunnelling in the description is to reinforce that a correct treatment of the interaction must be quantum mechanical).

But I'm pretty sure it's not helping the OP...

 

[Juraj]

The interactions between the ball and the wall are a measurement, whether you're looking or not

Oh, I don't know how did I miss that.

Thank you all

 

[atyy]

I'm not sure whether the disagreement here is about whether you're both using the word "measurement" in the same way, or whether the interaction/measurement that is happening is specifically a position measurement (which is what OP's question is about), or simply an aesthetic disagreement how the fusion is best described in plain English (no right answer IMO, as the primary reason to invoke tunnelling in the description is to reinforce that a correct treatment of the interaction must be quantum mechanical).

But I'm pretty sure it's not helping the OP...

I thought the OP was asking a different type of question. For example, he writes "Now, the question is: how can quantum tunneling occur if there is no observer or measurment device to collapse its wave function. How does fission in the Sun occur if no one can collapse the wave function? Is the nucleus just randomly teleporting?"

This seemed to me the sort of question like "Is the moon there when no one is looking". Within the standard interpretation, the answer is that the theory is silent on the issue. This is why I stressed where the assumption of a measurement or observer or classical apparatus is entering, when the Born rule is used.

Of course there may be non-standard interpretations in which one can answer, yes the moon is there when no one is looking. But I think one should state the additional assumptions clearly if one is not using the standard interpretation.

 

[atyy]

The interactions between the ball and the wall are a measurement, whether you're looking or not.

Oh, I don't know how did I miss that.

Thank you all

Well, what I would stress here is that a measurement is not an interaction between two quantum objects. A measurement is an interaction between a classical object (or observer or whatever one wants to call it) and a quantum system. So if the ball is quantum and the wall is quantum, then their interaction is not a measurement. One can find interactions between a quantum object and a quantum environment called a "measurement" in the literature, but that is short hand. To distinguish it from a true measurement, in which a classical environment interacts with a quantunm object, the quantum object interacting with a quantum environment is sometimes more carefully called a "pre-measurement".

 

[Juraj]

Well, what I would stress here is that a measurement is not an interaction between two quantum objects. A measurement is an interaction between a classical object (or observer or whatever one wants to call it) and a quantum system. So if the ball is quantum and the wall is quantum, then their interaction is not a measurement. One can find interactions between a quantum object and a quantum environment called a "measurement" in the literature, but that is short hand. To distinguish it from a true measurement, in which a classical environment interacts with a quantunm object, the quantum object interacting with a quantum environment is sometimes more carefully called a "pre-measurement".

But is the interaction between quantum environment and the quantum object causing the wave-function collapse? If not, then how is it possible for object in its wave form to pass through a barrier at all?

EDIT: And is the Born rule at any moment applied in quantum tunneling?

 

[ZapperZ]

Quantum tunneling does indeed happen in the Sun, because the temperature (and therefore the movement of the particles causing the collision of the nuclei - fusion) is insufficient.
But if I wasn't observing or measuring the object when it is approaching the barrier, the probability wave would never collapse and therefore the object would not be on the other side. My understanding of quantum tunneling is like this: if we put the measurement device on the both sides of the barrier we could collapse the probabilty wave by measuring it and there would be a chance that the device on the other side of the barrier will detect that the particle has "teleported" through it without the required energy (object has tunneled). I think that this understanding is wrong because it doesn't explain the occurance of the tunneling during fusion in the Sun.

There is a more fundamental misunderstanding here that will require that you go back to a more basic issue with QM.

If A and B are two observables, then if A and B do not commute, then any measurement of observable represented by A does not collapse the wavefunction for B! I may now know a value measure for A, but the value of B is still undetermined and will in superposition of a number of possible outcomes.

Now, let's go back to the tunneling issue. If I have, say, a metal-insulator-metal junction, then the insulator is a tunnel barrier for the conduction electrons. Due to the QM nature of the conduction electrons, there will be a wavefunction that will "leak" into the barrier region. This means that if I were to make a position measurement, there is a probability that there will be conduction electrons somewhere in the barrier. However, I do not need to detect such position observation to detect the tunneling effect. Instead, I can simply detect the tunnel current when I apply a potential across the barrier. I don't have to "collapse" the wavefunction for the position measurement here at all! All I did was to make a measurement of a different observable (current), and voila! I've shown the presence of this tunneling phenomenon.

Note that this is what is done in many other experiments to show the clear presence of superposition phenomenon. In the Stony Brook/Delft experiment, they show the superposition of the supercurrent by measuring the presence of the coherence gap, i.e. they didn't measure the supercurrent itself (which would have caused it to collapse and hide its superposition), but rather another non-related quantity.

Zz.

 

[Juraj]

Now, let's go back to the tunneling issue. If I have, say, a metal-insulator-metal junction, then the insulator is a tunnel barrier for the conduction electrons. Due to the QM nature of the conduction electrons, there will be a wavefunction that will "leak" into the barrier region. This means that if I were to make a position measurement, there is a probability that there will be conduction electrons somewhere in the barrier. However, I do not need to detect such position observation to detect the tunneling effect. Instead, I can simply detect the tunnel current when I apply a potential across the barrier. I don't have to "collapse" the wavefunction for the position measurement here at all! All I did was to make a measurement of a different observable (current), and voila! I've shown the presence of this tunneling phenomenon.

Doesn't that only prove the presence of tunneling without observing the location directly? I mean, at some point the wave function had to collapse, maybe not directly by our measurement devices but perhaps by interacting with the barrier (as Nugatory stated).

 

[ZapperZ]

Doesn't that only prove the presence of tunneling without observing the location directly? I mean, at some point the wave function had to collapse, maybe not directly by our measurement devices but perhaps by interacting with the barrier (as Nugatory stated).

You seem to have no concept of what is "collapsing", and the significance of commuting and non-commuting observables. A measurement of position DOES NOT collapse the value for the momentum, for example.

So what exactly is meant by "at some point, the wave function had to collapse"? This is a meaningless statement.

Zz.

 

[Juraj]

You seem to have no concept of what is "collapsing", and the significance of commuting and non-commuting observables. A measurement of position DOES NOT collapse the value for the momentum, for example.

So what exactly is meant by "at some point, the wave function had to collapse"? This is a meaningless statement.

Zz.

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]

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?

You are wrong in all of it.

1. Have you done tunneling transmission problem at all? This is done in Intro QM courses.

2. The barrier does not collapse anything. It is not a position measuring device. If it is, then ALL position measurement will be "collapsed", because electrons in solid bumps into the surface barrier of a bulk material all the time! What do you think is a "work function"? And yet, I still have a Bloch wavefuction describing these electrons. Why hasn't it collapsed already since it bumps into these surface barriers?

Zz.

 

[Juraj]

You are wrong in all of it.

1. Have you done tunneling transmission problem at all? This is done in Intro QM courses.

2. The barrier does not collapse anything. It is not a position measuring device. If it is, then ALL position measurement will be "collapsed", because electrons in solid bumps into the surface barrier of a bulk material all the time! What do you think is a "work function"? And yet, I still have a Bloch wavefuction describing these electrons. Why hasn't it collapsed already since it bumps into these surface barriers?

Zz.

How is barrier not a position measuring device? Every interaction involves some kind of measurement. If we don't collapse a wave into a particle by measuring it somehow (or interacting), how can the location of the electron exist? If the wave never collapsed, we cannot say that it's located in the barrier or outside the barrier because it does not have a location.

 

[ZapperZ]

How is barrier not a position measuring device? Every interaction involves some kind of measurement. If we don't collapse a wave into a particle by measuring it somehow (or interacting), how can the location of the electron exist? If the wave never collapsed, we cannot say that it's located in the barrier or outside the barrier because it does not have a location.

Read what I wrote. If the barrier is a position measuring device, then ALL the electrons in the solid have collapsed their wave function, according to you!

Would you stand by this claim?

Zz.

 

[Juraj]

Read what I wrote. If the barrier is a position measuring device, then ALL the electrons in the solid have collapsed their wave function, according to you!

Would you stand by this claim?

Zz.

All the electrons interacting with the barrier have collapsed their position wave functions, although their momentum wave function is still undetermined and by measuring the momentum of the electron, the position wave function will go back to its superposition state. What's wrong with collapsing every electron in a solid?

 

[ZapperZ]

All the electrons interacting with the barrier have collapsed their position wave functions, although their momentum wave function is still undetermined and by measuring the momentum of the electron, the position wave function will go back to its superposition state. What's wrong with collapsing every electron in a solid?

A lot of things wrong with it. First and foremost, it doesn't jive with what we observe!

Secondly, you need to go back and derive the tunneling phenomenon, especially in getting the transmission and reflection amplitudes. Now, using that, tell me where the position has been determined at the barrier.

You are fixated on this issue that the position is measured at the barrier. This is false, and you have not shown the physics to support it. I used to do tunneling spectroscopy measurement in high-to superconductors. I'd love for you to show me that you can pin point the Position of the cooper pairs in my tunneling current.

Otherwise, I'm done with this one. You are welcome to hold on to your belief.

Zz.

 

[Juraj]

A lot of things wrong with it. First and foremost, it doesn't jive with what we observe!

How come? I'm pretty sure we don't observe superposition waves in solids - we observe particles with definite locations which are product of interaction with the barrier.

If that is not true, when does the wave function collapse? It HAS to collapse, otherwise we don't have a location! When does it collapse and what is the cause?

 

[e.bar.goum]

How come? I'm pretty sure we don't observe superposition waves in solids - we observe particles with definite locations which are product of interaction with the barrier.

If that is not true, when does the wave function collapse? It HAS to collapse, otherwise we don't have a location! When does it collapse and what is the cause?

ZZ gave you a pretty great example telling you otherwise - the Stony Brook/Delft experiment. Here's an article about it. https://www3.amherst.edu/~jrfriedman/Leggett Physics World article/PW article.pdf

And I'm going to say it again, you don't need measurement of position for tunnelling to take place. Did you read the wiki article I linked way upthread for the finite square well potential? It's pretty much the second problem an undergraduate will do in quantum mechanics, after the infinite square well. Here's another link. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/pfbox.html, and another one https://farside.ph.utexas.edu/teaching/315/Waveshtml/node96.html all with slightly different approaches.

But the point is, is that tunnelling naturally comes without measurement. You construct your Hamiltonian, wack it through the Schrödinger equation, solve, and bam, tunnelling.

 

[Nugatory]

If that is not true, when does the wave function collapse? It HAS to collapse, otherwise we don't have a location! When does it collapse and what is the cause?

You may be misunderstanding what wave function collapse means. An interaction can collapse the wave function without giving the particle a location (a momentum measurement will do this), and the particle can have a location without collapsing the wave function (the known-position state is an uncollapsed superposition in any other basis). As e.bar.goum has already explained twice, most interactions proceed without ever collapsing the wave function into a known-position state.

 

[atyy]

But is the interaction between quantum environment and the quantum object causing the wave-function collapse? If not, then how is it possible for object in its wave form to pass through a barrier at all?

In tunneling, the barrier is treated as a quantum object, and the interaction of the particle with the barrier does not cause the wave function to collapse. That a wave can pass through the barrier is not purely quantum mechanical. The mathematics of quantum tunneling is analogous to the evanescent wave of classical electromagnetic waves.

http://www.andrew.cmu.edu/user/dcprieve/Evanescent waves.htm

EDIT: And is the Born rule at any moment applied in quantum tunneling?

The Born rule is applied in tunneling when the square of the wave function is interpreted as the probability of finding a particle a a given position when a position measurement is made.

 

[write4u]

Anyone? What's wrong with my understanding?

Perhaps you are interpreting the term"observer" too narrowly. In an abstract sense, all physical objects are observers of each other and exchange and process information of one kind or another.

ITheir behavior transmits information. Other particles receive (observe), process, and react to this information.
When a photon strikes an object, it also collapses the wavefunction. Gravity is the physical result of an observable relationship between two objects. The difference is that humans can translate this relationship, while non-sentient objects can only respond physically and are not consciously "aware" of this relationship, but in the abstract they could still be called observers (receivers)..

 

[Seban87]

Tunnelling indeed involves measurement. If we try to find the position of the electron a large number of times, most of the times it will be found inside the barrier meaning that the state of the quantum mechanical system has collapsed to a state corresponding to the position inside the barrier. Some times the electron will be found outside the barrier also (the number of such measurements depends on the probability given by quantum mechanics.) In this case the state has collapsed to a state corresponding to position outside the barrier. With regard to the sun, we indeed see the sun and experience its effect. This is indeed a measurement. It need not even be direct. For instance, the plants use the energy from the sun and we see the plants growing up. All these are measurements.

 

[Juraj]

ITheir behavior transmits information. Other particles receive (observe), process, and react to this information.
When a photon strikes an object, it also collapses the wavefunction. Gravity is the physical result of an observable relationship between two objects. The difference is that humans can translate this relationship, while non-sentient objects can only respond physically and are not consciously "aware" of this relationship, but in the abstract they could still be called observers (receivers)..

Tunnelling indeed involves measurement. If we try to find the position of the electron a large number of times, most of the times it will be found inside the barrier meaning that the state of the quantum mechanical system has collapsed to a state corresponding to the position inside the barrier. Some times the electron will be found outside the barrier also (the number of such measurements depends on the probability given by quantum mechanics.) In this case the state has collapsed to a state corresponding to position outside the barrier. With regard to the sun, we indeed see the sun and experience its effect. This is indeed a measurement. It need not even be direct. For instance, the plants use the energy from the sun and we see the plants growing up. All these are measurements.

Well, that's what I thought in the first place, but everyone is giving me different answers...

 

[Demystifier]

Tunneling requires something which effectively can be interpreted as "wave function collapse". This means that tunneling requires decoherence, i.e. interaction with a large number of degrees of freedom. Decoherence can also be interpreted as "measurement", but such an interpretation is not essential for understanding of tunneling.

 

[e.bar.goum]

Tunneling requires something which effectively can be interpreted as "wave function collapse". This means that tunneling requires decoherence, i.e. interaction with a large number of degrees of freedom. Decoherence can also be interpreted as "measurement", but such an interpretation is not essential for understanding of tunneling.

Do you have a reference for this linking of decoherence with tunnelling as a requirement? A technical treatment would be good. Thanks!

 

[Demystifier]

Do you have a reference for this linking of decoherence with tunnelling as a requirement? A technical treatment would be good. Thanks!

I don't know a specific reference for tunneling, but there is a lot of technical literature linking decoherence with apparent "wave unction collapse". On the other hand, from general QM textbooks it should be clear than tunneling is linked with wave function collapse.

 

[e.bar.goum]

I don't know a specific reference for tunneling, but there is a lot of technical literature linking decoherence with apparent "wave unction collapse". On the other hand, from general QM textbooks it should be clear than tunneling is linked with wave function collapse.

I'm very familiar with the former, it's the latter I'm struggling with. Naturally, my quantum texts are in my office, where I am not. If you had a specific reference, that'd be great.