If we wait infinitely long, will macroscopic objects undergo quantum tunneling?

[PeroK]

On an Earth that has a trillion year history of flipping coins, it should surprise no one when heads has come up a thousand times in a row sometime in their trillion year history.

Actually, if you tossed a coin every second for a trillion years, the expected maximum number of consecutive heads would be less than 100.

The probability of tossing 100 heads in a row is approximately $10^{-30}$. Which puts into perspective the probability of $10^{25}$ atoms all simultaneously doing something that by itself has an almost negligibly small probability.

Electrons can only tunnel short distances, relative to their size. The idea that a macroscopic object like a chair must tunnel an equivalent distance relative to its size is misguided. Each individual atom has almost zero probability of tunneling several metres.

 

[Quantum Waver]

All we have is your interpretation of they say and think. We had an interview with David Griffiths, and he made this very point:

"I think there are two villains here: (1) Physicists, who are (rightly) desperate to explain to the world the extraordinary, fascinating, and profound implications of quantum mechanics. But they are afraid of intimidating an audience that gags at the sight of an equation; they want to convey the excitement without the substance. So they resort to forced similes and grossly misleading metaphors (quantum tunneling means you can walk through walls

https://www.physicsforums.com/insights/interview-physicist-david-j-griffiths/

I'm with Griffiths on this one.

In Sean Carrol's paper, Why Boltzmann Brains are Bad, he shows how the best current cosmological model predicts an overwhelming number of BBs, which in his view would undermine science, since it would be likely we are some kind of Boltzmann fluctuation. Therefore, it's an important issue to resolve for cosmology.

This creates a somewhat surprising situation. While classically a universe dominated by a
positive cosmological constant simply empties out and evolves to zero temperature, quantum mechanically it asymptotes to a fixed nonzero temperature. Such a universe resembles quite closely Boltzmann’s original idea: an eternal thermal system with statistical fluctuations. It is therefore reasonable to worry that BBs will be produced in the eventual future, and dominate the number of intelligent observers in the universe. Note that this conclusion
doesn’t involve speculative ideas such as eternal inflation, the cosmological multiverse, or the string theory landscape – it refers to ordinary ΛCDM, the best-fit model constructed by cosmologists to describe the universe we live in today. We therefore face the prospect that our best modern cosmological model is internally incoherent. - page 12

In the second section, Carroll discusses Boltzmann's view of the Second Law leading to equilibrium, and Poincare's objection that eventually the system will fluctuate back to it's original state over enough time, which is the recurrence theorem.

It was Zermelo who turned Poincare’s mischievous remark about recurrence into a full blown objection to Boltzmann’s understanding of the Second Law [10, 11]. His argument was simple: the recurrence theorem implies that a graph of entropy vs. time must be a periodic function, while the Second Law states that the entropy must monotonically increase, and both cannot be simultaneously true. Zermelo believed that the Second Law was absolute, not merely statistical, and concluded that the mechanistic underpinning to thermodynamics offered by kinetic theory could not be valid. - page 4

Sean also mentions how Feynman thought the issue was important enough to include in his lectures.

Such a universe would be extremely different from our current one. Richard Feynman thought that these points – the puzzle of the low-entropy conditions near the Big Bang, and the inadequacy of Boltzmann’s fluctuation scenario at addressing the problem – were sufficiently important that they should be familiar to first-year undergraduates at Caltech - page 6

But Carrol does conclude that it's potentially not that hard to avoid such scenarios:

Fortunately, the criterion that random fluctuations dominate the fraction of observers in a given cosmological model might not be as difficult to evade as might be naively expected, if Hilbert space is infinite-dimensional and local de Sitter phases settle into a truly stationary vacuum state, free of dynamical Boltzmann fluctuations.

If so, then that would rule out the extremely unlikely future events occurring in the eternal vacuum state. It's at least of interest to try and rule out given the implications as Sean Carroll sees it.

 

[Quantum Waver]

No, that does not follow.

In some given part of the cosmos, some incredibly improbable event (singular, not plural) occurs.
In some other incredibly distant part of the cosmos, some other incredibly improbable event occurs.

The paper, The measure problem in no-collapse (many worlds) quantum
mechanics by Stephen D. H. Hsu, discusses how "maverick branches", as defined by Everett, are a problem for MWI adherents wishing to derive the Born rule.

Everett referred to the branches on which results deviate strongly from Born rule predictions (i.e., exhibit highly improbable results according to the usual probability rule) as maverick branches. By definition, the magnitude of these components under the Hilbert measure vanishes as N becomes large. But there is no sense in which the Hilbert measure is privileged in many worlds. Nor is there even a logical place to introduce it – it must emerge in some way by itself. Everett claimed to derive quantum mechanical probability by taking N to infinity and discarding all zero norm states in this limit, thereby eliminating all maverick outcomes. Most advocates of many worlds regard this reasoning as circular and look elsewhere for a justification of the Born rule. - page 5

And why subjective probability doesn't necessarily resolve the matter:

The question which is not addressed by subjective probability discussions is why we (you and I) ended up on a non-maverick branch of the universal wave function in the first place. It is logically independent of arguments about how we (you and I) should reason, given that our memory records are consistent with the Born rule, decoherence, and a semi-classical reality. In fact, the question to be resolved is similar to the type that arises in any theory of a multiverse (e.g., the string theory landscape): What explains the atypical(relative to other universes) features of our world? - page 8

Also why anthropic reasoning might not either:

Is there, perhaps, an anthropic justification for excluding maverick histories? For example, is it possible that information-processing observers are highly unlikely to arise when any of (A-C) apply? This seems implausible, because significant deviations from the usual quantum probabilities do not seem to preclude complex life. For example, suppose that decoherence were to operate orders of magnitude more slowly than in usual quantum dynamics, because of large (improbable) fluctuations in measuring devices or the environment. But decoherence timescales are many, many orders of magnitude smaller than the relevant timescales for biological processes. So, slower decoherence would not hinder life, despite making this type of branch highly unusual under the Hilbert measure. Also, brain function appears to be essentially classical. Larger deviations from semi-classicality (i.e., additional randomness beyond the usual biophysics) might be a problem that requires additional error correction, but does not seem to be catastrophic to intelligence. In contrast, if there were an anthropic principle excluding maverick branches, we would expect complex life to be very sensitive to deviations from usual quantum dynamics. - page 8

 

[Nugatory]

In MWI it would have to happen in some branch...

Yes, but that just shifts the conversation from "probability it happens" to "probability it happens in the branch that I experience".

 

[Quantum Waver]

It's hard to say from today's perspective what will be possible in 200 years - i can't think of good reason why a perfectly isolated IKEA chair will not produce an excellent interference pattern.

Considering how far physics has come in 200 years, maybe so? Superfluids and Bose-Einstein condensates have been shown to macroscopically tunnel.

 

[PeroK]

The paper, The measure problem in no-collapse (many worlds) quantum
mechanics by Stephen D. H. Hsu, discusses how "maverick branches", as defined by Everett, are a problem for MWI adherents wishing to derive the Born rule.And why subjective probability doesn't necessarily resolve the matter:Also why anthropic reasoning might not either:

Thanks for posting these. My point is that in the absence of experimental evidence, these are largely hypothetical speculations. There is no good reason why an MWI advocate should specify whether the branching is finite, countably infinite or uncountably infinite. They might lean towards uncountably infinite because of the mathematical structure of Hilbert space. But, in the same way that a solid is actually a collection of finitely many atoms, the universal wave-function (if it exists) might be a finite object that is approximately by a continuous wavefunction. There is no experimental evidence one way or another.

What's clear is that once you introduce an uncountably infinite physical process into your model, you are faced with potential paradoxes. Even a countably infinite process. By this I mean that an experiment in a finite time in a finite region of space could produce an infinite amount of information. Of course, it's possible that the universe can do that. But, the root of all these issues about walking through walls stems from this assumption about infinite branching.

The same goes for a literally infinite universe. Again, it's possible that the universe is actually infinite. Then, every second (comoving time) an infinite number of physical processes take place. And, although this is countably infinite (ingoring MWI), you still face the same paradoxes about duplicate Earths or planets where everyone can potentially walk through walls for a year or two.

My point is that it's unreasonable to draw the conclusions that these things happen just because the best current model has no upper limit on the size of the universe. Not least, because the numbers suggest that it is impossible for human observations ever to confirm that the universe is sufficiently large. Even finding a planet where the equivalent of 1000 coin tosses all landing heads is probably impossible ever to find.

In the case of coins,we don't need to have deep knowledge of the laws of the physics to conclude that 1000 heads is possible - we can see 10, 15, 20 heads in a row and extrapolate from there. With the walking though walls, however, we don't understand QM fully enough to declare that this is definitely possible. There's a huge extrapolation involved from the experimental evidence we have about quantum tunneling to potential planets where these things happen all the time.

 

[PeroK]

Just to make a further point, which may be worth making.

In mathematics, we can have a random infinite sequence of heads and tails. This is a well-defined mathematical object. But, we can never toss a coin an infinite number of times. No matter how long we prolong an experiment, we only ever have tossed a coin a finite number of times.

In MWI, if we make a measurement with a countably infinite number of possible outcomes (atomic energy levels, for example), then the resulting wave-function in MWI has a countably infinite number of branches, each with a different energy level. This is a well-defined mathematical object. But, does it correspond to reality? Or, is it, like the infinite sequence of heads and tails, not physically realizable?

There's an elermentary example of this principle in the case of a bouncing ball, dropped from a certain height, which bounces to half the previous height after each bounce. We can model this as an infinite sequence of bounces, which in total sum to a finite time. This works as a model, but it doesn't mean that the ball has bounced an infinite number of times. The model with infinitely many bounces is only an approximation to actually what happens to the ball.

In the same way, we can ask whether the MWI wavefunction is a precise model of reality; or, an idealised mathematical object that approximates natural processes, which themselves lack the infinities of the model.

 

[vanhees71]

Again, how so? A reference for the claims you are making would help.

https://arxiv.org/abs/nucl-th/9708036
https://doi.org/10.1103/RevModPhys.70.77

 

[DaveC426913]

It's more like there would be parts of the cosmos where the incredibly improbably happens on a regular basis. So coins turn up heads a thousand times in a row, dice roll sixes a million times, people walk through walls some of the time, etc. Assuming life can survive in such conditions, the observers would not find such events to be low probability.

Does this count?

 

[PeterDonis]

https://arxiv.org/abs/nucl-th/9708036
https://doi.org/10.1103/RevModPhys.70.77

This is a paper on heavy ion fusion, which is not the kind of fusion that takes place in the Sun.

Also, although the paper does give a schematic formula for the potential barrier, which could be used to analyze fusion in the Sun, it does not give actual formulas for the key terms, the nuclear and coulomb potential. In other words, it does not provide any way of answering the question, why is it the case that quantum tunneling is necessary for fusion in the Sun?

 

[renormalize]

In other words, it does not provide any way of answering the question, why is it the case that quantum tunneling is necessary for fusion in the Sun?

Martin Freer authored a non-technical article about fusion here: https://www.iop.org/about/news/physics-explained/nuclear-fusion#gref

In it, he states:
"The fact that the Sun has managed to burn controllably for 4.5 billion years is related to two key features. First the fusion process proceeds through a quirk of quantum mechanics. Although the Sun is hot, the kinetic energy of the protons is very low compared to the Coulomb repulsion that arises from the two positive proton charges.

Classically, the kinetic energy required to make two protons fuse is about 1000 times greater than they have inside the Sun. There is a repulsive barrier, called the Coulomb barrier. However, in quantum mechanics there is a probability of particles being able to tunnel through this barrier, although classically this would be forbidden. The Sun exploits this small probability.

The second factor is that the first reaction proceeds via the weak interaction, not the strong nuclear force. It is the weak interaction which results in the production of the neutrino and positron. The weak interaction being weak, limits the reaction rate. It is these effects which allows the quiescent burning of nuclear matter inside the Sun."

 

[romsofia]

This is a paper on heavy ion fusion, which is not the kind of fusion that takes place in the Sun.

Also, although the paper does give a schematic formula for the potential barrier, which could be used to analyze fusion in the Sun, it does not give actual formulas for the key terms, the nuclear and coulomb potential. In other words, it does not provide any way of answering the question, why is it the case that quantum tunneling is necessary for fusion in the Sun?

If you'd like to spin this off into another thread, it might be better. I'll do my best to at the end give the steps for OP to estimate it if they're interested (without getting into junk such as the gamow factor), otherwise, not sure if it's the relevant to them.

The details come down to the core density and temperature. In order for the protons to overcome the coulomb barrier, and be in the strong force range, the sun's core needs to be hotter to sustain fusion. Classically, there is none that do that. The only way we can see it occurring is with quantum tunneling, hence the sun needs it. I will post, another I level link, which you can complain isn't "peer-reviewed" (which shouldn't be relevant here, this is standard physics known since the 30s...).

Alas, here are some slides that make the same claim: https://sites.astro.caltech.edu/~george/ay20/Ay20-Lec7x.pdf (page 45/46).

Without going into more details*, the fact is that the sun's core needs to be ~$10^{11} K$. Since your background is in nuclear, open up good ole Krane, start of chapter 14 he gives a similar estimate for thermonuclear fusion for a container of neon gas.

In order to sustain nuclear fusion classically (because that's how much kinetic energy the nuclei need), we need something in that region. It's not that hot, it's ~$10^7 K$, what do we conclude? There is a macroscopic object in our solar system that NEEDS quantum tunneling to sustain it's existence, and even then, it rarely occurs. That's why I thought it'd be a fun exercise for them to see that even in the sun core, only a small amount of THAT tunnels at a given time. This would open their eyes to the concept that it's absurdly rare! If we consider objects, such as chairs, what hope do they have to ever tunnel as a whole?

*If OP would like to learn how to estimate this for the sun, treat the core like an idealized gas, assume that the average kinetic energy is proportional to the temperature in idealized gasses, then use the "equipartition energy equation" ($KE = \frac{3}{2}kT$ where KE is kinetic energy of the needed fusion, k is the boltzmann constant, and T is the temperature needed, which you would solve for algebraically) find the required kinetic energy needed for nuclear fusion to occur for protons, and solve for T. Make sure to convert units if you're not in the habit of doing so yet!

 

[PeterDonis]

There is a repulsive barrier, called the Coulomb barrier.

This at least starts to get at the answer, but it leaves out a key point. If you're just looking at the Coulomb repulsion, that isn't a "barrier", because the repulsive potential energy just keeps rising as the distance gets smaller; it never decreases to provide an attractive potential well. Without such a potential well present at sufficiently short range, quantum tunneling can't take place any more than classical collisions and interactions can.

The previous paper you cited at least mentions the nuclear force, which is attractive at ranges of around 1 femtometer ($10^{-15}$ meters), with a magnitude much larger than the Coulomb repulsive potential energy at that range (for proton-proton interactions, about - 30 MeV vs. about 1 MeV, according to the reference I give below), and so provides the necessary attractive potential well for an incoming particle to tunnel into (or fall into classically if the temperature is high enough). Yes, the 1 MeV is much larger than the average kinetic energy in the Sun's core, which is about 1 keV, so classical barrier penetration is indeed negligible under those conditions.

The following article, while it doesn't give explicit formulas, at least gives a graph of the proton-proton potential:

http://burro.cwru.edu/academics/Astr221/StarPhys/coulomb.html

The Wikipedia article on nuclear force also has some relevant graphs, showing one model for the nuclear potential (the "Reid potential")--which shows it becoming repulsive at shorter ranges--and a comparison between the nuclear attractive force and the Coulomb repulsive force.

https://en.wikipedia.org/wiki/Nuclear_force

 

[vanhees71]

I hope a standard textbook will convince you that for fusion in stars tunneling through the Coulomb barrier is important. It's of course the strong force that's responsible for the binding, but it's short-ranged (range about 1 fm) and the nucleons within the two nuclei must get close to each other to fuse. So here's a textbook source. I don't know a peer reviewed paper about it:

Povh et al. Particles and Nuclei, Springer (2015)

 

[Kinker]

Because macroscopic objects visible to the naked eye cannot be separated from their environment due to quantum decoherence, is it impossible to accidentally experience quantum tunneling even in a universe with infinite time? Is this something that will never happen? Absolutely impossible?

 

[vanhees71]

Quantum tunneling of macroscopic objects is so improbable that FAPP I guess, we'll never observe it. Nowadays it's however possible to observe quantum behavior at pretty large, sometimes macroscopic objects, like entanglement between diamonds

https://physicsworld.com/a/diamonds... like particles,is a hallmark of entanglement.

of "zero-point motion" of the ~10 kg heavy mirrors of the LIGO experiment:

https://physicsworld.com/a/ligo-mirrors-have-been-cooled-to-near-their-quantum-ground-state/

 

[Kinker]

Quantum tunneling of macroscopic objects is so improbable that FAPP I guess, we'll never observe it. Nowadays it's however possible to observe quantum behavior at pretty large, sometimes macroscopic objects, like entanglement between diamonds

https://physicsworld.com/a/diamonds-entangled-at-room-temperature/#:~:text=As phonons behave like particles,is a hallmark of entanglement.

of "zero-point motion" of the ~10 kg heavy mirrors of the LIGO experiment:

https://physicsworld.com/a/ligo-mirrors-have-been-cooled-to-near-their-quantum-ground-state/

Even in a universe with infinite time?

 

[Quantum Waver]

Even in a universe with infinite time?

Based on the current accepted cosmological model, chairs and walls will fluctuate into existence over vast amounts of times until eventually a chair tunnels through a wall.

Then the simulation will mercifully come to an end, and debts will be settled.

 

[Kinker]

Based on the current accepted cosmological model, chairs and walls will fluctuate into existence over vast amounts of times until eventually a chair tunnels through a wall.

Then the simulation will mercifully come to an end, and debts will be settled.

In some ways, that's not too bad. Still, if I were rich in the future, didn't get old, and we solved the entropy problem, wouldn't it be something to think about?

 

[Nugatory]

We now have three threads covering pretty much the same ground. This thread is closed, discussion can continue in https://www.physicsforums.com/threa...-theoretical-possibility-and-reality.1055408/