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In the 1955 science fiction short story, The Tunnel under the World

a chemical plant explosion kills all the inhabitants of a town, whose consciousnesses are then uploaded into miniature robots living in a replica town on a table top for the purposes of research into advertising techniques.

How would I know if my consciousness had been uploaded into a miniature robot living in a replica town?

What would be the most obvious difference living at the 1 mm scale instead of the 1 m scale? Diffraction effects with my tiny pupils? My experience of the viscosity of the air around me? Regulating my temperature?

[Migrated from physics.stackexchange where it was too broad]

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    $\begingroup$ Note: compare with this story where the effects were explored in detail. And of course Asimov's Fantastic Voyage! $\endgroup$ – JDługosz Apr 25 '16 at 16:51
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    $\begingroup$ I too read and enjoyed this story after someone posted it in the Sci-Fi SE. $\endgroup$ – WorseDoughnut Apr 25 '16 at 18:39
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    $\begingroup$ Reading all the unspoilerized parts of the questions very effectively gives away the spoilerized part (AFAICT not having read the story). If you don't want to spoil the story, don't refer to it. (You can instead say "in a story I'm not naming to avoid spoiling it,..." and include the relevant part of the a synopsis.) $\endgroup$ – msh210 Apr 25 '16 at 20:20
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    $\begingroup$ Giant dust. I doubt they'd be able to make your tiny town 100% dust-free, you'd be seeing dust-specks the size of trees everywhere. $\endgroup$ – Darrel Hoffman Apr 25 '16 at 22:28
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    $\begingroup$ When you meet a fly or an ant you'll know! :P $\endgroup$ – Max Apr 26 '16 at 11:04

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enter image description here

I never read that book, but if there is water in that universe then i would guess it becomes obvious when you try to drink it due its viscosity.

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    $\begingroup$ Welcome to Worldbuilding, Alfred! Despite being short, I think this is a nice and useful answer! $\endgroup$ – T3 H40 Apr 25 '16 at 17:50
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    $\begingroup$ Great answer. Almost nothing would be the same at those scales, but assuming you need to drink water every day, this would be the most obvious. If you don't need to drink water, well then, that's your answer! $\endgroup$ – user1717828 Apr 25 '16 at 17:50
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    $\begingroup$ This is, in fact, the easiest way to check. Open a faucet just a tad so it starts dripping. The size of water drops is almost constant, so you can easily find out not only that your size has changed, but also by how much. $\endgroup$ – Guntram Blohm Apr 25 '16 at 17:54
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    $\begingroup$ The characteristic you are really interested in is surface tension. That is a constant, but you are exactly right, drops from a water faucet would be huge, because of that characteristic. Do note, it's because of the nature of surface tension that makes Giant Ants impossible. (Them!) $\endgroup$ – zipzit Apr 26 '16 at 1:27
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    $\begingroup$ What is this, an answer for ants?! $\endgroup$ – corsiKa Apr 26 '16 at 16:49
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Gravity provides an acceleration of roughly 9.8m/s2.

If you're normal height, something free falling for one second would have to fall about two and a half to three times a person's height. If you're just 1mm tall, the object would fall 4,900 times your height.

Now that ignores drag, etc. But yeah, anything you drop would seem to hit the ground really, really quickly (unless you were somewhere with notably lower gravity than Earth).

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    $\begingroup$ The guys on more technical SE sites seem to have allergies to out-of-the box questions. Here is a pure physics answer to what is really a (imaginative one) pure physics question. $\endgroup$ – Mindwin Apr 25 '16 at 13:08
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    $\begingroup$ Well, actually, with objects small enough that 1mm robots can easily manipulate, minute air currents would really come into play. Your coffee mugs and pencils might wiggle in the air under the influence of wind or even the air particles' Brownian motion, rather than falling. $\endgroup$ – Serban Tanasa Apr 25 '16 at 14:08
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    $\begingroup$ Disparities in this (and other similar effects like speed of light) could be hidden better by running the mind simulation at higher rate than the real thing. $\endgroup$ – Waterlimon Apr 25 '16 at 19:00
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    $\begingroup$ You wouldn't fall very quickly due to the terminal velocity being reached almost instantly. $\endgroup$ – March Ho Apr 25 '16 at 23:04
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    $\begingroup$ Perception of time could be altered. $\endgroup$ – kaay Apr 26 '16 at 10:39
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Natural materials would be the biggest giveaway, the most obvious being wood. The surface textures are quite fixed in size and you're going to be seeing vast sizes on woodgrain where you're expecting fine patterns.

Other materials, like cloth and paper, will be quite hard to work at those sizes, suddenly a fine material becomes a massively thick and heavy one.

You can't just scale down materials with natural fibre thicknesses, these things are going to stand out.

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    $\begingroup$ +1 for materials differences. The tiny little town would look like a half-assed movie set. $\endgroup$ – Ouroborus Apr 26 '16 at 18:42
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    $\begingroup$ This seems kind of weak though, if you have the nanotech to make very humanlike robots of that size then you can probably make artificial wood. $\endgroup$ – Vakus Drake Apr 27 '16 at 3:32
  • $\begingroup$ @VakusDrake, they could equally mix something into the water to reduce its surface tension $\endgroup$ – Separatrix May 4 '16 at 8:06
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You'd notice quite a number of changes pretty fast if you were shrunk to that scale, some of which you have already mentioned, and another big one being the square/cube law - you'd find yourself much faster and stronger relative to your body size.

However, since it isn't really your biological body, some of these differences might be mitigated by the robot's design. The air viscosity could be altered by containing the town in a bubble with a controlled atmosphere (presuming that the robot was made to breathe in that atmosphere). Light would behave differently, but a clever scientist could program your eyes to respond to shorter wavelengths and then paint everything in the ultraviolet. And of course, the robot could be made proportionally weaker so that you wouldn't notice the square/cube effects, as well as generate more heat (or simply function and respond to colder temperatures) than a biological organism of the same size.

If they went that far, it would be hard to notice the difference. But that would be a lot more work than just making a scale replica of a town (although possibly not much more work than uploading brains into tiny functionally human robots in the first place).

Honestly, if they want to research advertising techniques that badly, they should just skip the robots and upload your brain straight into a virtual world.

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    $\begingroup$ I think the story is too old for that. I recall seeing a flight simulator in the 70's that used a real 3D model and flew a camera over it. Full virtual worlds didn't become a common trope 'till The Matrix but started to appear in SF in the 80's. The readers were utterly unaware of computers (in the modern sense) in 1955. $\endgroup$ – JDługosz Apr 25 '16 at 16:48
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    $\begingroup$ Or seriously, skip the robots and the virtual world, and just run their test advertisements with ordinary people in a real town. $\endgroup$ – Jay Apr 27 '16 at 13:32
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    $\begingroup$ While this is true if the robots were proportionate to humans - I don't think we can discount the fact that the nanorobots would have their strength/speed scaled down to be relative to current human strength. $\endgroup$ – Jon Story Apr 27 '16 at 14:07
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    $\begingroup$ @JDługosz Philip K. Dick's Time Out Of Joint is from 1959; Simulacron-3 is from 1964 and was widely translated and made into a movie in 1974. $\endgroup$ – Felix Dombek Apr 29 '16 at 1:10
  • $\begingroup$ Creating a fake reality in his own mind is not using computer-generated VR. Simularicon might be a reboot of the story under discussion, a decade later and a longer format able to explain the new ideas. $\endgroup$ – JDługosz Apr 29 '16 at 17:10
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Brownian motion.

I am surprised this hasn't already been mentioned, but at small scales, the effect of random motion of fluid molecules will play an increasingly large role on the motion of objects.

Instead of staying roughly stationary, you will see moderately-sized objects in the world moving randomly for no apparent reason. Brownian motion is usually observed for micrometer-sized objects, which means anything the size of approximately 1mm in size in your scaled world will start to jump around all the time with no obvious sources of motion.

This is a physical phenomenon which will occur as long as the experimental setup is not evacuated into a vacuum. As such, it will be impossible to prevent except by completely preventing the robot mind from recognising it, but at that point it will probably easier to run a simulation of the world instead.

Diffraction limit of light.

Vision will be restricted by the diffraction limit. Assuming that objects have similar absorption/emission wavelengths and the eye is still interacting with light of similar wavelengths (400-700nm), the diffraction limit will greatly hamper vision.

The human eye has a numerical aperture of 0.23. Since the eye will be scaled appropriately, the NA should not change while being scaled. Using the diffraction limit $d = \frac{\lambda}{2×NA}$, we can find that the maximum resolution of the eye is actually ~2.17 times the wavelength. Therefore, the eye cannot resolve any object roughly 1µm in size (real life) or 1mm in size (scaled), depending on the wavelength. This will cause issues when reading small text that is also scaled.

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    $\begingroup$ Since you brought up optics -- would the 1mm robot be able to see micro creatures normally invisible to our eyes? (They'd definitely need to keep insects out!) $\endgroup$ – rrauenza Apr 26 '16 at 16:06
  • $\begingroup$ @rrauenza You're right, the world would suddenly be full of extremely scary monsters .. shudder $\endgroup$ – Felix Dombek Apr 29 '16 at 1:14
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    $\begingroup$ It's interesting that both of your examples involve strange things happening to objects less than 1mm (scaled). It would seem that if you tried to resolve detail of the world, that you would find it very difficult. Not only would everything this small be out of focus, but it would also be jiggling around randomly. It seems that it would be VERY obvious to tell if one was a 1 mm tall robot. $\endgroup$ – Paddling Ghost Apr 29 '16 at 1:33
  • $\begingroup$ Even bacteria would suddenly be very large probably with you being scaled down approx 1,800 times (Scaling a 1.8m human to 1mm tall) would also be in effect like scaling naturally sized bacteria up by 1,800 times that would make them the equivalent of around 0.36x(3.6-14.4)mm in the scale millimeters you could perhaps adjust the robots eyes and the wavelengths of the light to fix the light issue there but keeping it free of natural bacteria would be real tricky and they would now appear at the scale of a moderately sized insect but trillions of them everywhere probably. $\endgroup$ – MttJocy Apr 30 '16 at 7:15
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    $\begingroup$ @rrauenza no, he said the small eyeball will have worse resolution. They cannot see stuff as small as we can, so reading (scaled down!) text will be a problem. $\endgroup$ – JDługosz May 1 '16 at 4:11
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I've read the story, I think it's a good story, but if you think it through, its plausibility is debatable.

I don't recall if the writer ever said exactly how big the robots were. I was picturing them as maybe 1 foot tall, i.e. much bigger than 1 mm. The closer they are to normal size, the less dramatic any scaling effects.

As others have noted, some things would be fairly obvious, like objects would fall too fast, water puddles would be too thick, the air would seem more viscous. You'd probably notice some square/cube effects, like hot objects would cool off too fast, and you could put more weight on a table or chair without it collapsing. If you had the equipment and expertise and measured the speed of light you could prove it definitively. I don't know how chemists determined the number of atoms in a mole, but if you could reproduce that you could prove it. Etc.

We'd have to ask how far the builders went to deal with such issues. Maybe they didn't give the robots real water but some chemical that behaves in a way that "looks right". (And of course if the robots drink it, they're programmed to think it tastes like water.) Presumably the robots are built so that their strength, speed, etc "feels right". The acceleration of gravity would be tough to work around as long as Tiny Town is on the surface of the Earth. But if you get most things to feel right, maybe nobody notices a few odd things, or if they do, they write it off.

Of course, the whole point of the story was that people just woke up one morning in their robot bodies in this artificial world. Presumably they had no reason to doubt that this was not just another day. So ... how odd would things have to be before you started sayng, "Hey, this is weird"? Sure, someone with scientific expertise who suspected he had been miniaturized like this could think of dozens of experiments to test the theory. But would your everyday experiences be enough to make you ask the question? If you were shrunk to 1 mm, I suspect they would be. But if shrunk to 1 foot? Maybe not. It's really hard to say.

Like if I woke up one day and noticed that, say, a book I dropped fell faster than it should, would my first thought be, "My consciousness must have been uploaded into a miniaturized robot!"? More likely I'd say, "Hey, that's weird. Is that normal? Is there something funny about this book? Oh well, anyway, got to grab some breakfast and get to work ..." Even if there were many things, I'd probably think, "Wow, I'm just really slow today" or "Maybe I should see a doctor" or whatever before I'd think of being turned into a miniature robot. And remember they only had one day to think about it before their brains were reset and they started the day over.

I suppose we could postulate that the robots are all programmed not to notice any discrepancies. They could be programmed to think that the speed at which objects fall is what they've always seen before and this is perfectly normal, etc. In which case the answer would become, It's impossible to tell, because you're programmed not to.

When I read the story I wondered: if the builders of Tiny Town had no moral qualms about uploading people's consciousness into these robots and using them for these experiments, why not just cordon off a real town of real people and do similar experiments? Indeed they wouldn't have to cordon it off, just run their different advertisements and observe what happens. Well, okay, with actual people they couldn't do the daily reset to get a controlled experiment. But it would seem a whole lot cheaper and easier. If they have the political pull that they can requisition the bodies of all the people killed in this explosion and upload their consciousness, surely they have the political pull to get whatever laws they need passed to let them run their advertising campaigns in one little town. Etc.

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    $\begingroup$ Good point about them only having one day to think about it. It takes longer than that to bestir oneself to investigate much more minor oddities in my experience. On the other hand, there are probably a good many people whose first thought on encountering an apparent anomaly in the behaviour of the physical world is something like "My consciousness must have been uploaded into a miniaturized robot"... when it ought to be "maybe I should lay off the drugs". $\endgroup$ – Lostinfrance Apr 25 '16 at 15:14
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    $\begingroup$ @Jay the story doesn't mention exact dimensions, but yes, the town was built on a table top, and when we see the big bad at the end, he was the size of a mountain. $\endgroup$ – Mr Lister Apr 26 '16 at 8:08
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    $\begingroup$ Even at 1ft tall, you're going to notice first thing in the morning - water now has 5X-6X the surface tension/meniscus. The shower droplets will be huge. When you brush your teeth, the water in the sink will act thicker than mercury. You're going to look at your coffee forming a dome in your tiny cup and say "WTF?" $\endgroup$ – Spike0xff Apr 28 '16 at 15:09
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    $\begingroup$ @MttJocy Yes, I was assuming that when they build Tiny Town they use ordinary materials made of ordinary atoms and molecules, just cut to a smaller size. If you assume that they somehow shrink the individual atoms, then many of the tests suggested by me and others here would not distinguish. But that assumes a whole new technology. Nothing like that is hinted at in the story. Though I suppose you could say they don't rule it out, either. As I recall, the story doesn't go into that level of detail about how this town and the robots are built. $\endgroup$ – Jay May 1 '16 at 7:09
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    $\begingroup$ If gravity is multiples "faster", you're going to have a very hard time walking. $\endgroup$ – Veedrac May 1 '16 at 15:34
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In a spin from Separatix's answer, my guess is water (or any other known fluid, but there's none better known than water by most people). Water behaves wildly different at this scale : insects routinely can transport bubbles of water without container by just holding it.

I don't know the physical details, but I doubt you could get a container of 1mm or smaller to hold water in the same way something at our scale does : just due to capilarity, the water will "climb" the walls of any container for a small distance. But at this scale, the distance will be very very big. And puddles of water can very easily be way bigger than a few mm. You will very easily see there's something wrong when you see water holding out in a giant bubble instead of spreading on the floor.

Freezing water also do the trick : snow flakes are of rougly equal size and you would be able to see them way bigger than usual.

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    $\begingroup$ bubbles in boiling water will be huge but the amount of water would be really small too, bubbles would be bigger at this scale? $\endgroup$ – A.L Apr 25 '16 at 12:58
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    $\begingroup$ @A.L Ah. Good point. That's where my insufficient physics background shows up and makes me answer: I don't know. I will remove that part from the answer since after reflection I don't have a clue. $\endgroup$ – Autar Apr 25 '16 at 13:02
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    $\begingroup$ I took the chance of posting a question to Physics about this: Does the size of bubbles in water brought to a boil ever vary as a function of the amount of water? $\endgroup$ – a CVn Apr 25 '16 at 18:19
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    $\begingroup$ I want to become 1mm tall so that I can explore a snowflake bigger than me now. $\endgroup$ – gatherer818 Apr 25 '16 at 21:27
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    $\begingroup$ @realityChemist If you'd be willing to contribute over on Physics, please! In-depth discussion is not what comments are meant for, which is part of the reason why I asked a separate question (which now has one answer, by the way, so if anyone here is curious there is some knowledge to be gleaned over there; I can't really judge its correctness, though). $\endgroup$ – a CVn Apr 26 '16 at 9:48
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Some things you'd notice quickly:

  • The absence of nontranslucent paper. There's only so thin you can make wood pulp so scaling paper down doesn't work. (As a broad physical effect, the color intensity of all diffuse scatterers, like colored glass drops sharply because the light path length in the material is reduced.)
  • Other have danced near this -- you can't escape a swimming pool; when you bathe, you drown. The apparent change in water's viscosity and surface tension causes these effects. Just as you can see insects moving freestanding droplets of water, you can also see them trapped inside droplets by the merciless surface tension. Water "wets" you (meaning it spreads as a thin layer across your surface). This is especially true when you add a surfactant, like soap or detergent. Consequently, when you try to take a bath or shower, you are covered in a smothering layer of water that you can't remove.
  • Diffusion is way too fast (no time correcting in software) or way too slow (with time correction in software). Say you have a grandfather clock so you know the period of a pendulum about $1 \,\text{m}$ long. This goes as $\sqrt{\ell/g}$ where $\ell$ is the length of the pendulum and $g$ is the force due to gravity. If you make me $200$-times smaller, a scaled pendulum runs $\sqrt{200} \approx 14$-times faster. However, diffusions scale as $\Delta x \sim \sqrt{t}$. If my software is modified to make time seem to run $14$-times faster (so my pendulum seems correct), a diffusion will only proceed $\sqrt{14} \approx 3.8$-times as far as it normally would. So either way, diffusion has changed. (Any time you can compare two physical processes that occur with different powers of some parameter, you can detect this sort of scaling.)
  • Things freeze too quickly -- this is square-cubed law again. Likewise, things cook too quickly. "Never thought I'd need a decimal point on the microwave."
  • The texture of meat is too coarse.
  • Radio antennae are now 200-times too short. Ham radio operators have a pretty good idea how long $0.5 \,\text{m}$ is (for a quarter-wave antenna in the $2 \,\text{m}$ band). Regardless of what you do to my internal clock, you can't make the electrons in the antenna resonate as if the antenna were $200$-times longer. Radio transmission to/from radios that have been scaled will work (assuming no obvious sources of powerful interference at the real frequencies, like airport radars, television broadcasts, et al.) but if either the transmitter or the receiver is "in the real world", the wavelengths won't match.
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    $\begingroup$ Thanks to anonymous user, who noticed I had picked up a spurious factor of $3$ in the diffusion argument and fixed it. $\endgroup$ – Eric Towers May 2 '16 at 1:59
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smallest possible flame

A "candle flame" would look disproportionately large (if you manage to light it). Rate at which a material burns or even transfers heat will seem faster (on our normal size a person expects a candle to burn for several hours). A 3mm traditional size flame (which seems to be the smallest possible traditional flame) will look strange to a 1mm size human/robot.

enter image description here

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The problem is that presumably the minature androids could be programmed to not notice such obvious inconsistencies; and any that they do encounter will be corrected for after the regularly scheduled memory reset.

(Indeed the plot of the story was that inconsistencies were only noticed when one deviated from its regular activity schedule and started exploring parts of the model that weren't as accurately rendered.)

One will not notice the surface tension is wrong, or such, when there is no actual water and it is just an hallucination provided by augmented reality filters.   After all, the miniature androids don't need to actually eat and drink; just simulate it.

Still, if someone has the tech to do this, why not just use full on Virtual Reality to run the simulated city?   It would take up a lot less space than maintaining a scale model anyway.

Of course, Tunnel Under the World was written well before the concept of Virtual Reality simulations was developed; in a time when sci-fi writers could envisage miniscule androids capable of emulating human thought, but strangely were still imagining super-computers as needing to occupy an entire city block.

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One should note here that the macroscopic scale is so extremely far away from the atomic scale, that the physical world we experience can to a very good approximation be described by mathematical laws that don't contain an explicit length scale. While they are not invariant under a length rescaling, a change in length scale can instead be implemented by adjusting the parameters that describe the world at the macroscopic scale.

The way you need to change the parameters so that the physics changes in the same way as what you would see had you changed the scale, is called a renormalization group transform. This is a very powerful idea in physics, the application to theory of phase transitions of this earned the Nobel Prize for Kenneth G. Wilson.

So, as pointed out in the other answers, the World will look different like e.g. that the surface tension of water will become far more relevant. However, everything you see will still look like the old World but where the parameters like surface tension, viscosity etc. have been adjusted.

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