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

[Kinker]

TL;DR Summary

If time in the universe is infinite, or if there are infinite universes with the same physical laws as our universe, is it inevitable that macroscopic objects visible to the naked eye will inevitably experience quantum tunneling at some point?

If time in the universe is infinite, or if there are infinite universes with the same physical laws as our universe, is it inevitable that macroscopic objects visible to the naked eye will inevitably experience quantum tunneling at some point?
Or is it an absolutely impossible event because the probability is too low or due to other factors? It can happen at the microscopic level, but is it absolutely impossible at the macroscopic level due to various factors such as quantum decoherence and emergent properties?

 

[PeroK]

TL;DR Summary: If time in the universe is infinite, or if there are infinite universes with the same physical laws as our universe, is it inevitable that macroscopic objects visible to the naked eye will inevitably experience quantum tunneling at some point?

If time in the universe is infinite, or if there are infinite universes with the same physical laws as our universe, is it inevitable that macroscopic objects visible to the naked eye will inevitably experience quantum tunneling at some point?
Or is it an absolutely impossible event because the probability is too low or due to other factors? It can happen at the microscopic level, but is it absolutely impossible at the macroscopic level due to various factors such as quantum decoherence and emergent properties?

Why is this question of any importance?

 

[Nugatory]

Or is it an absolutely impossible event because the probability is too low or due to other factors? It can happen at the microscopic level, but is it absolutely impossible at the macroscopic level due to various factors such as quantum decoherence and emergent properties?

We can calculate the probability of such a thing happening, and we will come up with a small non-zero number. You may, if you choose, attach the words "not absolutely impossible" to this statement - but this tells us more about how you are defining "absolutely impossible" than about how macroscopic objects behave.

Similar questions can be asked even in classical physics. The air pressure underneath my kitchen table is largely balanced by the air pressure above (and both are much greater than the weight of the table) so it stays put. However, the air molecules on both sides are in random thermal motion and there is a non-zero probability (maybe something like $2^{-(10^{25})}$) that they will all just happen to be moving upwards at the same time - the table would blast through the ceiling and roof like an artillery shell. Is there any value in saying that that is not "absolutely" impossible?

As an aside, the quantum mechanical probability of the table tunnelling through the floor is unimaginably smaller than that, maybe $(10^{100})^{-(10^{25})}$.

 

[Vanadium 50]

If I put a chair in a box, the time it takes to be expected to tunnel out exceeds the time it takes for the chair to evaporate.

 

[Kinker]

Why is this question of any importance?

I asked a question because I didn't feel it was accepted intuitively.

 

[DaveC426913]

There's a lot of qualifiers that have to be met before this can be said to be true - one example - as Vanadium points out, is that real objects don't live infinitely long.

Especially when you consider that, long before an entire chair could undergo quantum tunnelling, it is much more likely that small parts of it will undergo tunnelling, leaving a semi-chair, so what is left? (i.e. How many times will an infinite supply of chairs each partially tunnel before you get just one that happens to tunnel in its entirety?)

If you systematically address and eliminate each of these qualifiers, one by one, you may eventually reach the answer that - in principle, given sufficient time and these qualifiers - some macroscopic object could undergo tunnelling, and end up elsewhere in its same configuration.

I think.

It's a similar thought experiment - though not the same - as the idea of random interstellar atoms in the void happening to come together into the shape of a chair (which is classical physics).

If you're interested in extremely unlikely things happening, I think reading up on Boltzmann Brains might yield some fruit.

 

[hutchphd]

TL;DR Summary: If time in the universe is infinite, or if there are infinite universes with the same physical laws as our universe, is it inevitable that macroscopic objects visible to the naked eye will inevitably experience quantum tunneling at some point?

It can happen at the microscopic level, but is it absolutely impossible at the macroscopic level due to various factors such as quantum decoherence and emergent properties

This statement is nonesense (as pointed out previously). Is absolutely impossible more impossible than impossible?? Where is this line between micro and macro? How many angels......

 

[GarberMoisha]

No. Classical objects do not undergo quantum tunneling as they are not known to be in a state of superpositions. It is simply impossible to isolate them from the environment and prevent decoherence and measurement. If you could cool them down and isolate perfectly, they might be able to in a trillion years or more. Theoretically at least. This is a tricky question that is lying in a grey zone of maybe's and shouldbe's.
Choose a smaller object like a virus and it will make sense even with today's capabilities to make a prediction.

 

[romsofia]

It would do you good to see just how little tunneling occurs in macroscopic objects like the Sun. See if you can set up the problem of how much of the core is tunneling at a given instance, and you will quickly see how absurd it would be for a macroscopic object to ever tunnel.

The sun NEEDS quantum tunneling to work, and even then it's ABSURDLY rare for it to happen!

 

[PeterDonis]

The sun NEEDS quantum tunneling to work

How so?

 

[DaveC426913]

they might be able to in a trillion years or more. Theoretically at least

 

[vanhees71]

In fusion the Coulomb barrier is overcome via the tunnel effect.

 

[hutchphd]

simply impossible

So we have impossible, absolutely impossible, and simply impossible? I know I am quibbling but unlikely and impossible mean different things. All things are quantum mechanical (IMHO), often that seems a complication but sometimes it is not salient.

 

[romsofia]

How so?

Sun isn’t massive enough to have nuclear fusion without quantum tunneling. So, our sun would have a different composition and would be dimmer if tunneling couldn’t occur. It would just be some other astrophysical object.

Thus, one must conclude that our sun needs the phenomenon of quantum tunneling in order to be “The Sun” and not “random white dwarf 548”.

 

[PeterDonis]

Sun isn’t massive enough to have nuclear fusion without quantum tunneling.

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

 

[GarberMoisha]

So we have impossible, absolutely impossible, and simply impossible? I know I am quibbling but unlikely and impossible mean different things.

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.

All things are quantum mechanical (IMHO), often that seems a complication but sometimes it is not salient.

Yes, It's weird to me, I already noticed it raises many an eyebrow here talking to quantum physicists about the existence of.... classical objects. They will quantize everything and then go on to use their classical apparati to probe.... the quantum. Because everything is quantum except the very tools... which are also supposed to be quantum but thank God they are not. So they can be used accordingly.

 

[PeterDonis]

I already noticed it raises many an eyebrow here talking to quantum physicists about the existence of.... classical objects.

No, it doesn't. Quantum physicists have no problem at all with classical objects--as limiting cases under particular conditions.

They will quantize everything and then go on to use their classical apparati to probe.... the quantum. Because everything is quantum except the very tools... which are also supposed to be quantum but thank God they are not.

No, we do not know that measuring tools are not quantum. The usual position taken by quantum physicists is that measuring tools are approximated well enough by the classical limit of QM that we can treat them as classical objects for practical purposes. But that is not the same as them being classical objects if "classical" means "not quantum" in some fundamental sense.

 

[PeroK]

It occurs to me that the wall is irrelevant. If you put a chair in an otherwise empty room, then remove the ceiling and knock down all four walls, it still doesn't go anywhere of its own accord. It's not the walls that keep the chair where it is.

If you take the floor away, that's a different matter.

 

[Quantum Waver]

Why is this question of any importance?

It's a potential issue for probability in MWI and infinite universes, since it suggests there will be observers who observe incredibly improbable events, thus messing up their understanding of probability. Sean Carrol has mentioned this as a criticism of MWI. His retort is so much the worse for those observers, but we don't have to worry about them, since it's incredibly unlikely we would end up being them.

I realize this isn't the Interpretation forum, but I replied since it was asked here.

 

[PeterDonis]

I realize this isn't the Interpretation forum, but I replied since it was asked here.

The question wasn't asked of you, it was asked of the OP of this thread, which is not you.

 

[Quantum Waver]

We can calculate the probability of such a thing happening, and we will come up with a small non-zero number. You may, if you choose, attach the words "not absolutely impossible" to this statement - but this tells us more about how you are defining "absolutely impossible" than about how macroscopic objects behave.

Similar questions can be asked even in classical physics. The air pressure underneath my kitchen table is largely balanced by the air pressure above (and both are much greater than the weight of the table) so it stays put. However, the air molecules on both sides are in random thermal motion and there is a non-zero probability (maybe something like $2^{-(10^{25})}$) that they will all just happen to be moving upwards at the same time - the table would blast through the ceiling and roof like an artillery shell. Is there any value in saying that that is not "absolutely" impossible?

Yes, because there is nothing preventing it from happening in the next ten minutes. It's just incredibly unlikely. And in a vast enough universe, it would happen somewhere. That's different from something like perpetual motion. And it's potentially relevant for the cosmos over the long term, since eventually, extremely low probability quantum fluctuations would happen. Thus the Boltzmann brain concern.

 

[Quantum Waver]

The question wasn't asked of you, it was asked of the OP of this thread, which is not you.

Just explaining why I commented in this sub.

 

[romsofia]

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

I guess theoretically it can occur (https://sites.uni.edu/morgans/astro/course/Notes/section2/fusion.html) However, for this level of this thread, I would think this article explains it pretty well: https://bigthink.com/starts-with-a-bang/quantum-reason-sun-shines/

And then for more thought on it (if tunneling didn’t exist): https://astronomy.stackexchange.com...ar-reactions-could-not-proceed-via-quantum-tu

 

[Nugatory]

And in a vast enough universe, it would happen somewhere.

We have to be a bit careful with this claim. The probability of the almost-impossible thing happening is a very small non-zero number, which implies that the probability of it not happening is one minus that very small number - and that number is less than unity for any finite time interval. Thus, there is no certainty that it will happen no matter how long we wait.

 

[Quantum Waver]

We have to be a bit careful with this claim. The probability of the almost-impossible thing happening is a very small non-zero number, which implies that the probability of it not happening is one minus that very small number - and that number is less than unity for any finite time interval. Thus, there is no certainty that it will happen no matter how long we wait.

In MWI it would have to happen in some branch, as the universal wave equation is deterministic, assuming the calculation of non-zero probability is correct. In an infinite universe, everything physically possible also happens. I was assuming a vast enough universe to contain all those low probability events would also do the trick. One where the topology appears flat because it's so big.

 

[PeroK]

And it's potentially relevant for the cosmos over the long term, since eventually, extremely low probability quantum fluctuations would happen. Thus the Boltzmann brain concern.

These are not concerns. The Sun will inevitably die; not with some infinitesimal probablity, but with certainty. It will not burn as a life-supporting star for ever. Even that's hardly a concern, given that climate change (whether human-induced or otherwise), nuclear war, asteroid impact, or deadly global virus are all very likely (if not inevitable) at some stage in human history.

You can't have an international conference on whether the Earth is actually just an instantaneous existence of a Bolzmann brain. It's an irrelevant question, of no consequence. There's nothing you can do with a question like that.

You also seem to labour under the illusion that if an unlikely event happens, then that sets the tone for the future. Even if a chair tunnelled out into the back yard, we'd just assume someone took it out there for some unknown reason and we'd bring it back into the house and carry on with our lives. It's not like we'd have to rewrite the laws of physics. Even if someone saw it, no one would believe them.

Also, it's not what science is about. The medical profession doesn't ponder the question of what happens if - by pure coincidence - every adult on Earth breaks a leg on the same day. That has a likelihood that is at least calculable. Why are you not concerned about that? What would happen to human society if everyone had a near fatal accident on the same day? Without any help from QM, that's inevitably going to happen some day, to some unlucky intelligent species in the Cosmos. But, it's still a total irrelevance. Unlike the almost inevitable asteroid strike.

 

[DaveC426913]

It's a potential issue for probability in MWI and infinite universes, since it suggests there will be observers who observe incredibly improbable events, thus messing up their understanding of probability. Sean Carrol has mentioned this as a criticism of MWI.

This argument makes no sense. It's somewhat analogous to saying because it is incredibly unlikely for a given player to win the lottery, a given player who does win would have his understanding of probability messed up.

 

[Quantum Waver]

This argument makes no sense. It's somewhat analogous to saying because it is incredibly unlikely for a given player to win the lottery, a given player who does win would have his understanding of probability messed up.

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 ot be low probability. DeWitt mentions this in his paper on MWI.

 

[PeroK]

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 ot be low probability. DeWitt mentions this in his paper on MWI.

This is not what physics is about. There's no evidence for any of this stuff. It's chasing a hypothetical fantasy.

 

[Quantum Waver]

This is not what physics is about. There's no evidence for any of this stuff. It's chasing a hypothetical fantasy.

Then take that up with the physicists who worry about that stuff in cosmology and foundations. Physics is about what physicists study.

 

[PeterDonis]

I guess theoretically it can occur (https://sites.uni.edu/morgans/astro/course/Notes/section2/fusion.html)

This site just says the minimum stellar mass for hydrogen fusion is 0.08 solar masses. It says nothing at all about quantum tunnelling or lack thereof in calculating that threshold.

However, for this level of this thread, I would think this article explains it pretty well: https://bigthink.com/starts-with-a-bang/quantum-reason-sun-shines/

This is a pop science article and I cannot find any references in it to actual textbooks or peer-reviewed papers. The article describes calculations, but doesn't actually do them or point to references where they are done.

And then for more thought on it (if tunneling didn’t exist): https://astronomy.stackexchange.com...ar-reactions-could-not-proceed-via-quantum-tu

This is a Stack Exchange thread with, again, no reference to any textbook or peer-reviewed paper that I can find.

 

[PeroK]

Then take that up with the physicists who worry about that stuff in cosmology and foundations.

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.

 

[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.

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.

True, for every incalculable number of improbable events that individually occur in incalculably distant regions of the cosmos, once in a blue moon, two improbable things might occur near each other.

Kind of like a two-time lottery winner. Do two-time lottery winners think they're broken physics?

In a thousand years of lotteries, we will look back and see that two-time lottery winners are, by-and-large not unheard of, so a three-time winner will not be shocking.

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.

 

[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:

Then I'll go find papers in which physicists do discuss unlikely probabilities with both QM and thermodynamics, and why they think it matters. Maybe it doesn't for David Griffiths, but you won't have only my interpretation if you would like the actual sources.

 

[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.

True, for every incalculable number of improbable events that individually occur in incalculably distant regions of the cosmos, once in a blue moon, two improbable things might occur near each other.

Kind of like a two-time lottery winner. Do two-time lottery winners think they're broken physics?

In a thousand years of lotteries, we will look back and see that two-time lottery winners are, by-and-large not unheard of, so a three-time winner will not be shocking.

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.

It does follow, because there's nothing stopping many events happening on a regular basis in some incredibly small part of the cosmos, whether it's branches/worlds or very, very far away. But since posters seem to think I'm misinterpreting what some physicists actually mean when they're not misleading the public, I will go find a paper to be sure.

 

[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?