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The Megaphragma mymaripenne is the smallest animal with eyes, brain, wings, muscles, guts and genitals.

Wasp

If by some miracle it could be still shrinked, how much smaller could it get before it starts to become largely aware of quantum mechanical effects such as tunneling?

Explanations:

By shrinking I mean wasp being made of less atoms but with similar "organs".

By affected I mean, if that wasp was by some miracle smart as humans, it would have understanding of quantum mechanical effects same as humans have understanding of naive physics.

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    $\begingroup$ According to a guy named "Schrödinger", a cat should be small enough to be affected by quantum mechanics. $\endgroup$ – Nolonar Nov 3 '16 at 14:39
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    $\begingroup$ One of the theories of olfaction (smell) includes pretty significant quantum effects. If that is true, humans (and most other animals) would fit as well. $\endgroup$ – Alice Nov 3 '16 at 15:37
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    $\begingroup$ @Nolonar I don't know who you're talking about, but according to the physicist named Schrödinger, a cat definitely shouldn't be small enough. $\endgroup$ – JiK Nov 3 '16 at 15:58
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    $\begingroup$ As it turns out, photosynthesis uses quantum tunneling to move electrons from the surface, deeper into the leaf without generating heat on the way. So some of the biggest living things on the planet are using "quantum mechanics" outside of chemistry. $\endgroup$ – Chris Becke Nov 4 '16 at 6:05
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    $\begingroup$ Huh... as for Schrödinger... a lion is a cat... a 250kg cat. And now suddenly, it becomes obvious why sabertooths are extinct and we find their bones in limestone. They got stuck trying to tunnel through walls and starved. $\endgroup$ – Damon Nov 4 '16 at 11:17

12 Answers 12

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It is hard to put an exact number on this, but it seems like the answer would be maybe 1000 atoms at most. From Wikipedia,

The [double slit] experiment can be done with entities much larger than electrons and photons, although it becomes more difficult as size increases. The largest entities for which the double-slit experiment has been performed were molecules that each comprised 810 atoms (whose total mass was over 10,000 atomic mass units)

And that is just for superposition in location, not even getting to quantum tunneling like you mention in your question. Observing QM effects in anything larger than that has been notoriously difficult. However, some scientists have been trying to observe a small microbe in a superposition. I can't find anything indicating that the experiment was actually done, just lots of stuff about people trying to do it and thinking it will be done in the next few years. So maybe we will get small bacterium and viruses to experience QM effects relatively soon. That would probably set the upper limit on the size you are asking for. This source claims that even a 100nm microbe would be seriously difficult to observe in a superposition:

A recent proposal suggested “piggybacking” a tiny microbe (100 nanometres) on to a slightly less tiny (15 micrometres) aluminium drum, whose motion has been brought to the quantum level. While this experiment is feasible, the separation between the “two places at once” that the bacteria would find itself in is 100m times smaller than the bacterium itself.

Edit: Just to clarify my wording, everything always experiences quantum effects, they just become unobservably small as the object gets larger and larger (with rare exceptions, like the black body spectrum of the sun, but that is another matter entirely).

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    $\begingroup$ I estimate about 2nm for diffraction effects, as a very rough analysis. Superposition is a slippery concept, but it's nice to see we're on about the same scale. $\endgroup$ – spraff Nov 4 '16 at 18:33
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    $\begingroup$ The problem for superposition is to keep the system coherent. That typically mean a very cold system near the vacuum, definitely not physiological conditions. $\endgroup$ – Davidmh Nov 5 '16 at 15:13
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You appear to have a misunderstanding of how physics works. Classical physics (i.e., the thing we generally refer to when discussing how things interact) is merely an approximation of quantum mechanics. There is no boundary that says "Only past this point are you affected by quantum mechanics."

But, if you are concerned with how this creature would behave, you would need to make it smaller than an atom, as only then does quantum mechanics predict different behavior than Newtonian physics.

Of course, one could simply look up quantum tunneling to see that it applies to particles, and not organisms, which are comprised of lots of particles.


There appears to be some concern about my third citation, and I completely agree. The user on Physics has no linked research, low reputation, and low votes. However, I don't pretend to be an expert in the field of quantum mechanics; I rely entirely on some basic ideas of what it is and the expertise of others. To sum up the above (and comments below): quantum mechanics dominates in the smallest scales, while Newtonian physics dominates in the largest scales, and no one knows why or what the tipping point is.

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    $\begingroup$ Yay! No boundary to QM. My first thought seeing this question. Glad to see your answer. Macroscopic systems don't show quantum behaviour -- usually. Bose-Einstein condensates are one of the exceptions. Although modern electronics runs on QM properties the spooky effects don't flow into our everyday world. $\endgroup$ – a4android Nov 3 '16 at 13:00
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    $\begingroup$ You need a tighter definition of "affected". Chemistry happens because of quantum mechanics. Deuterium is an imperfect substitute for hydrogen in biochemistry because of QM. We don't spontaneously ignite because of QM (triplet vs. singlet Oxygen energy levels). Differently, when our eyes are startlight-adapted we see a "grainy" low-resolution image. Your eyes are detecting individual light quanta. $\endgroup$ – nigel222 Nov 3 '16 at 15:25
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    $\begingroup$ QM predicts different behavior even at macroscopic scales. See the Ultraviolet Catastrophe. True, statistical approximations could be used instead of raw QM, but the statistical approximation relies on quantization of photons... $\endgroup$ – Yakk Nov 3 '16 at 18:32
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    $\begingroup$ Interference has been shown for molecules made of up to 430 atoms, so quite obviously quantum effects don't stop at the atomic scale. $\endgroup$ – celtschk Nov 3 '16 at 18:57
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    $\begingroup$ This answer is incorrect. Just because using quantum mechanics on atoms is more correct than Newtonian doesn't make it the limit. Newtonian mechanics start not working on a larger scale, as @celtschk's example shows. Your "source" Isn't a source at all $\endgroup$ – Zach Saucier Nov 3 '16 at 19:36
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In the world of processors 5nm was assumed as smallest size before quantum tunneling starts to be a problem. If you shrink your wasp 1000 times it will become 200nm long, since its legs are much smaller they will probably be affected by tunneling.

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    $\begingroup$ You are misunderstanding this effect. The quantum tunneling becomes more prominent at 5nm because the gate oxide must shrink (but not because the linewidth is 5nm). As this reduces quantum effects will have significantly more effects (on the gate oxide). But this is not what the 5nm refers to (minimum printable linewidth, or minimum drain->source difference). $\endgroup$ – jbord39 Nov 3 '16 at 16:03
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    $\begingroup$ Not to mention that quantum tunnelling is required for semiconductors to work. The charges simply don't have enough energy to cross the potential boundary - they need to tunnel through. The problem you're talking about is related to unwanted quantum tunnelling - the charges tunnelling through places we don't want them to tunnel through. $\endgroup$ – Luaan Nov 4 '16 at 12:58
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My day job is (currently) designing the software/firmware/electronics for nanopositioning systems. With our current best kit, we can reliably and repeatably move something to 70pm accuracy over a 15um range.

This is a classical-mechanics chunk of metalwork moving. At that range we have significant challenges with material stiffness and other interesting mechanical effects, but the physics is still very much in the classical domain. So the basic chemistry of the wasp's body isn't something it needs to worry about just yet.

Of course quantum tunnelling could be an issue for the wasp's nervous system. Since that relies on electrical signals, it'll have the same issues as shrinking a processor die.

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    $\begingroup$ My day job is (currently) designing the software/firmware/electronics for nanopositioning systems. Wow... I mean wow. :jaw drops: (Sorry for the comment spam.) $\endgroup$ – mg30rg Nov 4 '16 at 9:33
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    $\begingroup$ @mg30rg Someone has to do it :) $\endgroup$ – Roman Nov 4 '16 at 11:50
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    $\begingroup$ Of course, the semiconductors used in those electronics only work thanks to quantum electrodynamics, but that's kind of begging the question - classical physics is just an approximation, a model of the underlying reality. Quantum physics is a more accurate model of the underlying reality (and possibly actual reality - but how could we tell? :)). Things don't "start" or "stop" behaving classically - it's just that under different conditions, classical physics can be a better or worse approximation of reality as far as we care. Quantumness doesn't disappear when things get big. $\endgroup$ – Luaan Nov 4 '16 at 12:56
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    $\begingroup$ Just to be clear it's not a typo, you can accurately position things to roughly the covalent bonding diameter of a hydrogen atom? $\endgroup$ – BenRW Nov 5 '16 at 21:20
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    $\begingroup$ @BenRW With a best specimen of our top-line kit we can measure and position to around 70 picometres resolution. We aim for around 100pm, and we'd reject it if it's worse than about 150pm. Yes, this is insane stuff! There are caveats to this, of course. Temperature and pressure will affect the system if they're not insanely tightly controlled. Also hysteresis is a problem for run-to-run variation - you can't do that kind of fine movement in both directions. $\endgroup$ – Graham Nov 7 '16 at 11:30
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Quite large animals are "affected" by quantum mechanics, because even large animals consist of small parts and many mechanisms at the smallest scales of animal bodies rely on quantum mechanics.

For example: the reason that geckos' feet stick to glass is because of quantum mechanics (Van der Waals forces to be precise: see here). For other examples see this Wikipedia article about quantum biology.

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Your question is rather vague, in that you don't specify what you mean by "affected". Quantum mechanics can affect everything at the molecular level. By that logic, even blue whales are affected by quantum mechanics.

For example:

Vision relies on quantized energy in order to convert light signals to an action potential in a process called phototransduction. In phototransduction, a photon interacts with a chromophore in a light receptor. The chromophore absorbs the photon and undergoes photoisomerization. This change in structure induces a change in the structure of the photo receptor and resulting signal transduction pathways lead to a visual signal. However, the photoisomerization reaction occurs at a rapid rate, <200 fs, with high yield. Models suggest the use of quantum effects in shaping the ground state and excited state potentials in order to achieve this efficiency.

Other examples on that Wikipedia page include:

  • Studies show that long distance electron transfers between redox centers through quantum tunneling plays important roles in enzymatic activity of photosynthesis and cellular respiration.

  • Magnetoreception refers to the ability of animals to navigate using the magnetic field of the earth. A possible explanation for magnetoreception is the radical pair mechanism.

  • Other examples of quantum phenomena in biological systems include olfaction, the conversion of chemical energy into motion, DNA mutation and brownian motors in many cellular processes.

Regarding DNA mutation:

DNA’s twisted ladder structure requires rungs of hydrogen bonds to hold it together; each bond is essentially made up of a single hydrogen atom that unites two molecules. This means sometimes a single atom can determine whether a gene mutates. And single atoms are vulnerable to quantum weirdness. Usually the single atom sits closer to a molecule on one side of the DNA ladder than the other. Al-Khalili and McFadden dug out a long-forgotten proposal made back in 1963 that suggested DNA mutates when this hydrogen atom tunnels, quantum-mechanically, to the “wrong” half of its rung. The pair built on this by arguing that, thanks to the property of superposition, before it is observed, the atom will simultaneously exist in both a mutated and non-mutated state — that is, it would sit on both sides of the rung at the same time.

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  • $\begingroup$ Well that's a 200: success answer! +1! $\endgroup$ – RudolfJelin Nov 4 '16 at 19:05
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The world we know, macroscopically, would not be without quantum mechanics. Even solid matter wouldn't stay in cohesion without it. The sun wouldn't shine, chemical reactions wouldn't exist etc.

You might say: "yeah, but these are things we are used to. They make sense." Exactly. That's the point. We see these things all the time, so they don't sound "quantum", but they are.

Quantum mechanics are everywhere, and if some people say they appear only at some microscopic size, that's only because some "unusual" stuff happens then. Of course it is unusual! We are not that small to see them with our own eyes.

So the answer to the question: "how small should an animal be to show unusual quantum behaviour" would be:. Smaller than you can see (even with a microscope), because that's the definition of "unusual". It turns out to be of the order of hundreds of atoms.

Note that some systems, prepared in "coherent states" can exhibit similar properties because all atoms "beat" at the same rate. Their contributions add up to macroscopic scale.

Now, interesting studies suggest the quantum randomness of the world, one of the most amazing things in quantum mechanics, may be the cause of usual randomness (like flipping a coin). This is a big deal in my opinion:

https://www.sciencenews.org/article/rules-computing-classical-probabilities-might-depend-quantum-randomness

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    $\begingroup$ Best answer so far IMO. Of that randomness article I think not much though – you don't need to resort to quantum effects to explain e.g. fluctuations in gases, such fluctuations can even be observed in purely classical CFD simulations. Basically, any sufficiently chaotic system looks random if you don't have access to the full parameter space, even if the dynamics are actually completely deterministic. In fact this is even the case for quantum mechanics – the Schrödinger equation is perfectly deterministic and only if you introduce decoherence/measurements does it “cause randomness”. $\endgroup$ – leftaroundabout Nov 3 '16 at 20:53
  • $\begingroup$ I don't have a definite opinion about that article. There are effects which are not fully explained through classical thermodynamics, like irreversibility, which might rely fundamentally on quantum randomness. But that's not very clear to me how much we don't know here, and I find the article interesting at least. Anyway, this is not really the point of the answer, but just a note. $\endgroup$ – fffred Nov 4 '16 at 14:16
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Although it's correct to answer "QM happens at macroscopic scales and it affects humans", I'll try to answer in the spirit of the question.

What is a "quantum mechanical effect"? I'll pick one: matter diffraction. How big an animal can be and still diffract through a grating?

Larger particles (including composite particles) have smaller de Broglie wavelengths, and diffraction is most evident when the gap is about the same size as the wavelength. So to get the largest admissible animal, use the smallest admissible diffraction gate.

The de Broglie wavelength depends on momentum $mv=\frac{h}{\lambda}$ and as a coarse simplification, since we're dealing with small animals, pick $v=1~\mathrm{ms^{-1}}$ so $m=\frac{h}{\lambda}$.

Model the "particle" animal as a uniform sphere of "typical" density of $\rho\approx 10~\mathrm{ kg\cdot m^{-3}}$ so $m=\frac{4}{3}\rho\pi r^3\approx 4\rho r^3$ and as we said above, we are looking for $r=\lambda$ so $\frac{h}{r}\approx 4 \rho r^3$ and so...

$r \approx 2\times 10^{-9}~\mathrm m$

Animals significantly bigger than this can't produce diffraction patterns at normal animal speeds. This would be a difficult experiment to perform, since animals are not uniform spheres. You would get chaotic effects when legs broke off and such like, adding somewhat a lot of noise to the results.

You might be able to get larger animals to diffract successfully if they were moving on a tightly curved section of spacetime (they take up less space if they're stretched into the time direction somewhat) e.g. if their trajectory was the orbit of a small black hole, although I don't know enough GR to analyse this and relativistic velocities would shrink the limiting wavelength/radius further.

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  • $\begingroup$ I think animals the size of buckyball would move at speeds similar to velocities of particles in a gas (whether they want to or not), not “typical animal speeds”. $\endgroup$ – JDługosz Nov 5 '16 at 6:09
  • $\begingroup$ Fair enough, but that factor doesn't change it much as an estimate when you take fourth-roots: $v=500ms^{-1}$ gives $4\rho r^3=\frac{h}{500\lambda}$, or $r^4\approx\frac{h}{100}$, $r\approx10^{-9}m$ $\endgroup$ – spraff Nov 6 '16 at 13:14
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When I read "If by some miracle it could be still shrinked [sic]..." in the question, I wonder whether you really want to try to conform to "known" physics, especially if you're telling a story.

But that said, I haven't noticed the phrase "thermodynamic limit" being used in any answers yet. The reason human-sized object don't suddenly teleport is because along these lines:

(1) There's a probability of any given particle "suddenly showing up" anywhere in the known universe, as far as Shrodinger's equation can tell you.

(2) When you put multiple particles together, they behave as a "conjunctive event," in probability-speak. The short version is this: imagine you flip a coin. There's a 50% of either side landing, so neither outcome is a surprise. Now suppose you flip 6*10^23 coins and try to predict the outcome. (ex. "All heads!") Your probability of being right is the product of the probabilities of all the events that would make it up. That probability is minuscule enough that the entire lifespan of the universe (by current estimations) could easily elapse before you successfully guessed the outcome of such an event.

To get "teleportation," you'd need to probabilistic analogue of guessing such an outcome correctly. In other words, we don't see such things happen because the chemistry of the objects that we encounter in daily life (which is a consequence of quantum mechanics) makes is really unlikely for such things to happen during a time-span short enough for a human to observe it. (You'll note that this doesn't rule out such things...it's just says "don't spend your life waiting for it...you'll be bored.")

As an example of a a "thermodynamic limit as a conjunctive even of probabilistic events occurring as determined by quantum mechanics," imagine you have 6*10^23 particles, each with a 1% chance of showing up 1 meter away from where you last observed them, then as a "clump" they'll have a 0.01^(6*10^23) probability of appearing there. I don't think your calculator will be able to tell you what that number is....it's way, way too small of a probability.

This is the "first semester of quantum mechanics" answer, by the way. The afterword of your quantum mechanics textbook may then say, "So...entanglement plays a role in how this actually works, but that's beyond the scope of this book, and not entirely understood yet anyhow." (I guess my point is, don't expect to get the complete answer to this question without devoting your life to physics.)

By the way, if the number 6*10^23 doesn't ring any bells, check out Avogadro's number. (You'll also then have to consider how many multiples of Avogadro's number of molecules make up your lifeform in question.)

Let's point one more thing: A standard example in an introductory class on quantum mechanics (called "modern physics" when I took it) is that of radioactivity (in particular, that of alpha particles, I believe it was), and how quantum mechanics gives an explanation for why it can happen at all. (The answer is tunneling, although let's give it the definition of "a particle having a non-zero probability of suddenly existing away from the chemistry of its usual material, so it then continues its existence without being 'held in place' by all the other particles around it.") But radioactivity doesn't happen because your sample of uranium (for example) is small; it's just the chemistry of the material is such that the probability of a tunneling even is high enough that you can observe it over a time-frame that that people would consider pretty short.

Switching gears, let's get back to your story (or whatever prompted you to ask about this). Miniaturization, as it sounds like you're describing it, isn't really a real-world thing. The objects we encounter in a day-to-day lives are defined by their chemistry, and chemistry can't simply be 'shrunk.' (As an analogy: Build your dream house with Legos, then say "now I want to shrink this down to doll-house sized." To make that happen, you'd need the individual Legos to shrink. But the protons, neutrons and electrons that make up chemistry don't shrink. In fact, they don't vary in any way. Every electron is flawlessly identical to every other electron in the universe. (A physicists, I think John Wheeler, once made a probably-tongue-in-cheek quip about there only being one electron in the universe, doing the job of every electron we ever think exists. If you've every done object-oriented programming, you may find this reminiscent of defining an "electron" class, then instantiation it once every time for each electron that appears to exist in the universe. From the perspective, you might see why some content that the universe's construction seems oddly akin to a computer program.)

So, to actually miniaturize something, you construct something that behaves identically to the original object, but with fewer particles. Whether you can actually do this with a biological entity is probably not a question for the physicists anymore, unless they're physicists who do biological modeling. (As an aside, universities that have a medical school may have some biology-oriented classes in the physics department, probably oriented toward pre-med students that do their undergrad degree in physics. You may also find mathematicians doing things like neurological modeling at such universities.)

If it's sci-fi you're thinking about, you may want to look towards a couple possibilities:

(1) The 'miniaturization' process that you're describing could be more like "nanomachine recreations of biological organisms," which again would means that someone builds a device to try to duplicate the behavior of a given organism. Then you just have to find out a bit more about nanomachines, if you want to try to be accurate within its constraints.

(2) Look to the poorly-understand parts of physics for places where you can get creative. Regarding this...keep in mind that someone with a background in a a little chemistry and no physics may only think of three fundamental particles: protons, neutrons and electrons. (I suppose lots of people know about photons, but they overlook the fact that electrons are the "force mediators" for electrons.) That leads us to the place to dig deeper: If you crack open a particle physics textbook (or flip to the 'particle physics' chapter of a modern physics textbook), you'll see that there's a bunch more of these fundamental particles, some of which have been observed, some of which haven't. The "as of yet not understood" is a fertile place to find things you can make some 'informed speculation' for use in science fiction. (And if you're wondering about why the rest of the particles even exist....my not-particularly-informed response is "stars, stuff that comes from stars, 'mediation of physical effects' and then whatever machinery of the universe that we understood well enough to even suppose that it exists, but not well enough to explain it with any clarity.") Granted, I'm not suggesting that you try to make heads or tails of a particle physics textbook without having studied all the pre-requisites (eg. the usual year of calculus-based physics, intro to modern physics, intro to thermodynamics, undergrad Electricity and Magnetism, undergrad Quantum Mechanics; the in the preface to Griffith's Intro the Elementary Particles he suggests that 'most students in such a class' will have taken everything in that last, but he suggests that the last two don't need to be considered a strict prerequisite.) But unless you do, you'll probably have to fall back on 'informed speculation' ....but, of course, the less you know, the less informed your speculation will inevitably be.

Final note: If story-telling is your aim, don't forget that the primary device for not getting bogged down in "accuracy" is to simply not bring it up. (How much you can get away with that will depend on the story you're trying to tell, of course.)

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  • $\begingroup$ Sorry in advance for what I'm sure are copious typos. That answer wound up pretty long. (^^; $\endgroup$ – steve_0804 Nov 4 '16 at 18:00
  • $\begingroup$ As it stands, it seems to me this is the best answer. $\endgroup$ – RudolfJelin Nov 4 '16 at 19:06
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Humans are affected by quantum mechanics: some human eyes are able to detect a single quantum of light (a photon).

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  • $\begingroup$ Some human eyes? All human eyes can detect singular photons, since the wavelength of a photon is exactly what we have evolved to process/interpret. $\endgroup$ – Harry David Nov 4 '16 at 1:27
  • $\begingroup$ @HarryDavid not native speaker here, lets say it other way - rods are capable to detect single photon at frequencies of visible light. from wiki: A photon is an elementary particle, the quantum of all forms of electromagnetic radiation including light. $\endgroup$ – MolbOrg Nov 4 '16 at 4:21
  • $\begingroup$ @MolbOrg That would be "quantum" as "smallest unit", not necessarily as in "quantum physics". $\endgroup$ – a CVn Nov 5 '16 at 13:40
  • $\begingroup$ @MichaelKjörling can't claim I understand you sentence in full, is that about quantum mechanics in answer - we(a human body) working because that quantum mechanics exists, and one of the reasons why it (CM) is interesting. $\endgroup$ – MolbOrg Nov 5 '16 at 14:19
  • $\begingroup$ @MolbOrg A quantum is a smallest unit of something. Quantum physics is physics as it applies to those smallest units. When Wikipedia states that "a photon is ... the quantum of EM radiation", the claim made is that a photon is the smallest, non-divisible portion of EM radiation. See for example merriam-webster.com/dictionary/quantum. $\endgroup$ – a CVn Nov 5 '16 at 14:31
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Proteins are the smallest machines of the cell that can do anything interesting (for some definition of interesting, but I work with proteins and I am biased). They are long chains of hundreds of aminoacids (thousands of atoms) do things like pumping water, nutrients, and waste in and out of the cells, guide chemical reactions, send signals, etc.

One of the tools to study them are molecular dynamics simulations. They pretty much use classical mechanics (replacing the atoms with a fancy version of soft balls) with minor numerical tweaks to reproduce quantum behaviour to a very accurate degree. The tweaks are mostly to avoid having to solve the full electrostatic problem of where are the electrons at each time step; but nothing of that would seem strange to a microscopical individual.

So, to get generally quantum-weird behaviour you have to go smaller than the basic functional unit of the life as we know it.

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The actual question is : how big can a system be and still be quantic ?

Some theories say that if enough particles are entangled, then the wave function may spontaneously collapse, which means that for example it is not possible to entangle Shrödinger's cat to a decaying atom.

The limit for this would be also the size of this animal.

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