Seemingly odd quantum tunneling

[DanteKennedy]

Question:
Large objects (say, a sofa) are made of individual atoms, and those atoms are made of subatomic particles. From what I know, smaller particles in principle have higher chance for quantum tunneling than large object and the probability gets exponentially smaller as mass increases. So why don't most object "decay" slowly because the individual particles that made it got tunneled one by one?

Note:
I don't have any advanced knowledge about quantum physics, so it would be good if someone can correct my knowledge if there's any mistakes
(And sorry for bad English)

 

[PeterDonis]

why don't most object "decay" slowly because the individual particles that made it got tunneled one by one?

Because if the particles are bound inside a large object, they're not free particles, and all the stuff you refer to about tunneling and the probability of it assumes free particles. More precisely, it assumes particles that, while they might be "bound" inside a potential barrier (and have some nonzero probability to tunnel through the barrier), they're not bound to other particles of the same type that are also inside the same barrier.

All this is heuristic, btw, because to really discuss all the reasons behind this would mean going well beyond High School level.

 

[DanteKennedy]

while they might be "bound" inside a potential barrier (and have some nonzero probability to tunnel through the barrier), they're not bound to other particles of the same type that are also inside the same barrier.

Does this mean that it can also be applied to molecules (which made of small amounts of atoms) where the bond prevents the molecule to broke up from quantum tunneling?

 

[PeterDonis]

Does this mean that it can also be applied to molecules (which made of small amounts of atoms) where the bond prevents the molecule to broke up from quantum tunneling?

If the scenario is such that you can consider the molecule as a "particle", it has some nonzero probability to tunnel through a barrier, though the probability will be smaller than for, say, a single electron.

 

[Paul Colby]

Tunneling doesn’t (can’t) violate energy conservation. A stable molecule (bound group of atoms) has a lower net energy than the same particles separated into two or more free groups. If this were not the case, the molecule would be unstable and could decay or break apart via tunneling.

 

[DanteKennedy]

A stable molecule (bound group of atoms) has a lower net energy than the same particles separated into two or more free groups. If this were not the case, the molecule would be unstable and could decay or break apart via tunneling.

But what happens during spontaneous molecule breaking? And why particles have lower net energy by forming molecules rather than being separated? Is it always the case?

 

[DanteKennedy]

If the scenario is such that you can consider the molecule as a "particle", it has some nonzero probability to tunnel through a barrier, though the probability will be smaller than for, say, a single electron.

Interesting. So partial tunneling doesn't exist? (Only a fraction/several particles from a larger object initiated tunneling while the rest of the object are intact)

 

[Cthugha]

Interesting. So partial tunneling doesn't exist? (Only a fraction/several particles from a larger object initiated tunneling while the rest of the object are intact)

In a nutshell, that is alpha decay.

 

[DanteKennedy]

In a nutshell, that is alpha decay.

Is the alpha decay on stable elements impossible or just very unlikely?

 

[Cthugha]

Well, as long as there is some lower energy state available in principle, then decay is in principle also possible.
For example, for quite some time bismuth was considered to be the heaviest stable element until some experiment (See this article) demonstrated a very slow decay with a half-life on the order of about $10^{19}$ years.

You can break this down to the question whether lighter particles can be stable. In this respect, the proton is probably one of the lightest ones to consider. Whether it is stable is an open question to the best of my knowledge. Within the standard model it is expected to be stable, but this is not necessarily the case for theories beyond the standard model. People at Super Kamiokande are looking for proton decay (See this article). However, this is not my area of expertise and this is not the forum for physics beyond the standard model.

 

[Demystifier]

Because if the particles are bound inside a large object, they're not free particles, and all the stuff you refer to about tunneling and the probability of it assumes free particles. More precisely, it assumes particles that, while they might be "bound" inside a potential barrier (and have some nonzero probability to tunnel through the barrier), they're not bound to other particles of the same type that are also inside the same barrier.

All this is heuristic, btw, because to really discuss all the reasons behind this would mean going well beyond High School level.

A good example is a neutron. A free neutron is unstable, it decays, but a neutron in an atomic nucleus is stable.

 

[PeterDonis]

what happens during spontaneous molecule breaking?

Can you give an example of what you mean by this?

 

[DanteKennedy]

Can you give an example of what you mean by this?

In the decomposition of hydrogen peroxide, maybe? Is it a process that happened due to energy from outside?

 

[Paul Colby]

And why particles have lower net energy by forming molecules rather than being separated?

There are attractive forces acting between bound particles, right? It takes work (a form of energy) to pull them apart. The act of separating them would give them more energy than they had before. In particle physics spontaneous decays can happen but the total energy of the decay products must always be the same before and after the decay. If the decay products at rest have more energy than the initial particle, the decay just can’t happen.

 

[DanteKennedy]

The act of separating them would give them more energy than they had before.

Can quantum tunneling bypass this? Or maybe an atom can go nowhere that has smaller energy state than the bond state and thus it cannot quantum tunnel, am I correct?

 

[Paul Colby]

Can quantum tunneling bypass this? Or maybe an atom can go nowhere that has smaller energy state than the bond state and thus it cannot quantum tunnel, am I correct?

So, could we all suddenly quantum tunnel into a black hole or into the center of Jupiter? Yes, but it’s very unlikely. Some things are so unlikely that no is a simpler answer to such questions. The point is, tunneling does no work. Work in this context is the action of a force over some distance. Tunneling can’t change the net energy of the system.

 

[DanteKennedy]

So, could we all suddenly quantum tunnel into a black hole or into the center of Jupiter? Yes, but it’s very unlikely.

Does quantum tunneling also allow phenomenon like spontaneous rearrangement? Like a cup morphed into plate (ofc it's an extreme example but the idea is the same), or maybe a much "simpler" phenomenon like DNA mutations? Can tunneling do such thing while conserving energy?

 

[Paul Colby]

Allowed and can happen aren’t the same, right? Just because 5 million in gold bullion could disappear from a vault and reappear in your living room while still conserving energy doesn’t imply this could spontaneously happen. There is more physics involved than the two end states.

 

[DanteKennedy]

There is more physics involved than the two end states.

Hmm, so this is related to the exponentially smaller tunneling probability on the earlier part of this thread? And also related to the law of large numbers?

 

[Paul Colby]

Hmm, so this is related to the exponentially smaller tunneling probability on the earlier part of this thread? And also related to the law of large numbers?

All of physics doesn’t reduce to tunneling. In fact, very little of it does.

 

[DanteKennedy]

Are there other general reasons macroscopic tunneling never happens, besides the exponentially smaller probability as mass increases?

 

[Demystifier]

Yes, decoherence. Macroscopic objects have many degrees of freedom, which interact with many degrees of freedom from the environment, so there is a fast and strong decoherence which makes macroscopic objects essentially classical.

In fact, decoherence can prevent or slow down tunneling even of microscopic objects. One version of this effect is known as the quantum Zeno effect, where frequent measurements slow down the decay.

 

[DanteKennedy]

Yes, decoherence. Macroscopic objects have many degrees of freedom, which interact with many degrees of freedom from the environment

Interesting. Are degrees of freedom a dimensionality for quantum object? Like the x y z of a 3d plane (or roughly like that)?

 

[Demystifier]

Interesting. Are degrees of freedom a dimensionality for quantum object? Like the x y z of a 3d plane (or roughly like that)?

No, the number of degrees of freedom is not directly related to the size of the system. It is more directly related to the number of particles. See also https://en.wikipedia.org/wiki/Degrees_of_freedom_(mechanics)

 

[DanteKennedy]

Yes, decoherence.

But how exactly is the process of collapsing superposition leads to the effective prevention of tunneling for large objects?

 

[Demystifier]

But how exactly is the process of collapsing superposition leads to the effective prevention of tunneling for large objects?

That's because tunneling is a consequence of superposition. For example, suppose that at time $t$ the particle can tunnel from the left to the right, through a barrier in the middle. This means that the wave function at $t$ is nonzero both at the left and at the right, i.e. the wave function is a superposition of a wave function on the left and a wave function on the right. But if the wave function at $t$ collapses to the left part only, then at $t$ it cannot longer tunnel to the right, because the wave function is vanishing on the right so the probability of being on the right vanishes.

 

[DanteKennedy]

But if the wave function at $t$ collapses to the left part only, then at $t$ it cannot longer tunnel to the right, because the wave function is vanishing on the right so the probability of being on the right vanishes.

So for large objects, their wave function is so localized and are constantly being measured by their surroundings, effectively pinning their position? Am I right?

 

[PeroK]

So for large objects, their wave function is so localized and are constantly being measured by their surroundings, effectively pinning their position? Am I right?

A human being (and other life) grows by cell division. Your question would be what stops an entire human being spontaneously cloning itself into two? If a cell can divide, why not an entire large animal?

The biology of a human being is not the same as the biology of a single cell.

A building is not just a large brick. A forest is not just a large tree. A book is not just a big word. And, a sofa is not just a large elementary particle.

You need to find a way to reconcile these differences of scale and how they affect the physics and biology of large things and their constituent parts.

 

[DanteKennedy]

You need to find a way to reconcile these differences of scale and how they affect the physics and biology of large things and their constituent parts.

I wonder if large object can be treated as many independent particles in quantum framework. If a single particle has higher tunneling probability than a whole object, why the object doesn't experience constant "partial tunneling"? Or did it already happen in biology?

I'm changing the subject from the original question but I think this is interesting

 

[PeroK]

I wonder if large object can be treated as many independent particles in quantum framework. If a single particle has higher tunneling probability than a whole object, why the object doesn't experience constant "partial tunneling"? Or did it already happen in biology?

I'm changing the subject from the original question but I think this is interesting

Quantum tunnelling is on a microscopic scale. Not just tunnelling (which you seem to be obsessed by), but QM phenomena are taking place inside a macroscopic object all the time. That does not equate to a macroscopic object itself coherently obeying the laws of molecular physics. A sofa is not just a big molecule.

And, even if all the molecules in a sofa "tunnelled" at the same time by a micron, how would you even notice? You're not going to come into your living room and say "my sofa has spontaneously transported itself $10^{-6} m$ to the left.

This is not interesting. This site had an interview a few years ago with David Griffiths, who wrote one of the most popular undergraduate text books on QM. He said one of things he dislikes is people who only want to talk about objects tunnelling through walls, as this has nothing to do with QM.

If you want to learn QM, learn QM. And, if you want to talk about sofas tunnelling through walls, then you are learning precisely nothing about QM.