User:Thermochap~enwikibooks/Sandbox/Shrink Me

Atom clusters with blood cell & Andromeda galaxy in background.

This is a sandbox page to explore the justaposition of worlds on two or more size scales.

The image at right is an example of the range of objects that might be seen with a very tiny camera. If we could pan back to see the pico-human who is taking this photograph, then this would be an example of two-world juxtaposition.

Introduction

Modern technology is giving us unprecedented understanding of, and access to, processes on size-scales ranging from that of humans to that of atoms. As a result, thoughts about changing perspective are increasingly both fun and of potentially practical value.

Put another way, now it is not only fun to imagine what it would be like to take a shrinking pill like Alice in Wonderland. The prospect of building a 12" globe with a 3D model of every house visible on Google Earth is moving into technological range, as is the possibility of finding robotic or perhaps even biological inhabitants that might be inclined to take advantage of such emerging real estate.

Examples

Models

The meter ⇔ millimeter model

This takes objects which are a meter in size down to a millimeter. Hence size is divided by a factor of 1000.

Imagine, for example, that your living room floor were covered by a 1/1000 model of a present day city. What would that city look like to you?

If ordinary humans can resolve a tenth of a millimeter with one's naked eye, they might only be able to resolve a tenth of a "milli-world meter" i.e. objects that are about four "milli-world inches" across. That means that you might be able to see a milli-human's hand, but you probably couldn't see what they were doing with their fingers. Thermochap (talk) 18:24, 26 June 2009 (UTC)

Conversely, what would your coffee table look like to the milli-residents of this city? How about a piece of pollen blown in through an open window, or a skin cell shed when you scraped your hand on the edge of the desk?

In a related vein, how would your milli-cars work differently than do normal cars? Would seat belts be as important? Could they be powered by miniature internal combustion engines, or would some other kind of engine make more sense? How would the milli-mileage of these milli-cars compare to that of an ordinary-sized car?

The meter ⇔ micron model

This shrinks objects which are a meter in size down to only a micron in size. Hence distances are multiplied by 10^-6.

The smallest things ordinary folks could see in this model might be 100 "micro-world meters" across. Thermochap (talk) 16:06, 26 June 2009 (UTC)

Imagine for example that your living room floor were shrunk to milli-world size, so that the city-model in your living room now existed on the micro-world scale. What would that micro-world city look like to normal people? How big would the micro-worlder's "micro-planet earth" be?

I guess from below that the micro-planet earth would be about 41.8 feet in diameter. Isn't that about as big as a small house? Thermochap (talk) 22:59, 25 June 2009 (UTC)

Conversely, how would un-shrunk humans look to the micro-humans living in this shrunken town? What would one of their big toes look like? Would one of their fingerprints look like a maze in which you could get lost?

Similarly, how big would atoms look to these micro-humans? Would they be big enough to see with the naked eye? Could modern 3D printers or rapid prototyping devices make physical models for normal-sized people whose atom-scale structure would let us pretend that we were micro-humans too?

Could the micro-cars in this shrunken city similarly run on an internal combustion engine, or would something else be needed? How would their micro-mileage compare? Would speed limits be the same, and how might seatbelts for these micro-cars be redesigned? How about micro-airplanes, and micro-parachutes?

The one-foot-diameter globe

What's it like to live here?

Here the scale factor takes the earth's diameter (4.18×10⁷ feet) down to one foot. This requires multiplication by a factor of 2.39×10^-8, and may be useful e.g. for building scale model solar systems on the size scale of cities.

You probably already know what such a globe would look like to you, as well as what the tiny cities and city streets would look like to the naked eye. Finding the street on which you live might be tough!

The smallest thing ordinary folk might be able to see with their naked eye in this model might be about 0.1 milli-meter or 10^-4×4.18×10⁷ ~ 4180 "globe-world meters" or 4180/1609 ~ 2.6 "globe-world miles" across. Thermochap (talk) 16:11, 26 June 2009 (UTC)

Conversely, however, what would your finger look like to the Nanoworld-2 residents of such a globe? What would the cells in your finger look like? What would the molecules in the cell membrane surfaces of your finger look like? What would the atoms that make up those molecules look like? Would residents of these cities be able to see anything inside the atoms that make up those molecules?

How might residents of those shrunken cities power their automobiles? Would their airplanes have wings, or something else? Would the plumbing in their homes still work, or would that too have to be redesigned?

Media

Fiction

• Gulliver's Travels by Jonathan Swift, 1727
• The Nutcracker and the Mouse King by E. T. Hoffman, 1816 (Amazon)
• Alice's Adventures in Wonderland by Lewis Carroll, 1865
• Mr. Tompkins in Wonderland by George Gamow, 1940 (Amazon)
• Engines of Creation by K. Eric Drexler, 1987 (Amazon)
• Two Bad Ants by Chris Van Allsburg, Houghton Mifflin, Boston, 1988 (Amazon)
• Alice in QuantumLand by Robert Gilmore, 1995 (Amazon)
• The New World of Mr. Tompkins by Gamow and Stammard, 1999 (Amazon)
• Shrinking Mouse by Pat Hutchins, Scholastic, New York, 2000 (Amazon)

Movies and videos

• The Incredible Shrinking Man, 1957 (Amazon)
• Fantastic Voyage, 1966 (Amazon)
• Willie Wonka and the Chocolate Factory, 1971
• The Incredible Shrinking Woman, 1982 (Amazon)
• Inner Space, 1987
• Honey - I Shrunk the Kids, 1989 (Amazon)
• Honey - I Blew Up the Kid, 1992
• Honey - We Shrunk Ourselves, 1997 (Amazon)
• A Bug's Life, 1998 (Amazon)
• The inner life of a cell video.

Effects of Size

Talking about size

Useful numbers for equidimensional (e.g. spherical) solid or liquid objects on selected size scales.

Name of scale	Minimum diameter	Min. volume in [Å3]	Number of atoms at 7×1022 [atoms/cc]	Min. surface area in [Å2]	# surface atoms at 1015 [atoms/cm2]	Max. fraction of atoms on surface	Example
Milliworld-2	1[cm]=108[Å]	(π/6)×1024	30×1021 +	π×1016	3×1015 +	0.0000001	sugar cube
Milliworld-1	1[mm]=107[Å]	(π/6)×1021	30 quintillion +	π×1014	30 trillion +	0.000001	flea
Microworld-3	100[μm]=106[Å]	(π/6)×1018	30 quadrillion +	π×1012	300 billion +	0.00001	sand grain
Microworld-2	10[μm]=105[Å]	(π/6)×1015	30 trillion +	π×1010	3 billion +	0.0001	pollen
Microworld-1	1[μm]=104[Å]	(π/6)×1012	30 billion +	π×108	30 million +	0.001	cell
Nanoworld-3	100[nm]=1000[Å]	(π/6)×109	30 million +	π×106	300 thousand +	0.01	organelle
Nanoworld-2	10[nm]=100[Å]	(π/6)×106	30 thousand +	π×104	3 thousand +	0.1	virus
Nanoworld-1	1[nm]=10[Å]	(π/6)×103	30 +	π×102	30 +	1	buckyball
Picoworld-3	1[Ångström]	(π/6)	1 +	π	1 +	1	atom

How physical interactions change

This table shows how different physical properties take on importance in different ways, according to your size.

The shift in emphasis on various processes depend on the size-scale of one's world.

Effect\Size-Range	MacroWorld	MicroWorld	NanoWorld
Tides & Coriolis	Weak	Negligible	What's that?
Gravity & inertia	Important	Weak	Negligible
Electrostatics	Distracting	Scary	Off the charts
Touch	Extra	Manageable	Extreme
Terminal velocity	High	Slow	Nearly zero
Heat/Brownian motion	Signals random motion	Jostles	Careens & jiggles
Atoms near surface	Few	Many	Most
Energies	Allowed in bands	Odd states are important	Discrete values only
Slow spins	No limit	Slow in steps	Disallowed
Electrons	Shocking	Polarizing	Fuzzy
Measurements	Possible?	Intrusive	Perturbing

How what we find in nature changes

Assuming that you have a way to see as you shrink, how would the world change as you shrunk to the size of an atom while sitting at your desk? How would it change if you were standing on your lawn? How would it change if you were standing in a forest, or sitting on a beach?

How mechanisms for imaging change

Properties of various types of electromagnetic radiation whose speed in vacuo is ~300,000,000 [m/s].

Radiation type	Frequency in [Hz]	Wavelength in [m]	Photon energy in [eV]	Conveyance
AC outlet	60 cycles per second	5000000⇒5000km	0.000000000000248⇒248feV	power cord
Audio signal (C6)	1046.5 Hertz	286000⇒286km	0.00000000000432⇒4.32peV	twisted pair
AM radio	1120000⇒1120kHz	268 meters	0.000000005⇒5neV	shielded wires
FM radio	90700000⇒90.7MHz	3.2 meters	0.000000376⇒376neV	coaxial cable
Microwaves	2450000000⇒2.45GHz	0.120000000⇒120mm	0.000010000⇒10μeV	waveguides
Infrared Light	30000000000000⇒30THz	0.000010000⇒10μm	0.124000000⇒124meV	alkali halide optics
Red light	440000000000000⇒440THz	0.000000680⇒680nm	182 electron Volts	fiber optics
Green light	560000000000000⇒560THz	0.000000540⇒540nm	2.32 electron Volts	fiber optics
Blue light	630000000000000⇒630THz	0.000000470⇒470nm	2.61 electron Volts	fiber optics
Ultraviolet Light	1070000000000000⇒1.07PHz	0.000000280⇒280nm	4.43 electron Volts	quartz optics?
X-rays (Cu-Kα)	1940000000000000000⇒1.94EHz	0.000000000154⇒1.54Å	8030⇒8.03keV	?
Gamma rays	300000000000000000000⇒300EHz	0.000000000001⇒1pm	1240000⇒1.24MeV	?

Kinetic energy vs. reciprocal wavelength.

As you can see from the table above, visible light's wavelength gets a bit large as size scales move below a micron. As object sizes shrink to that of the illumination's wavelength, ray optics goes out the window and only interference effects remain to give us clues about what's there.

The figure at right shows how the wavelength of anything (Planck's constant divided by momentum) relates to that thing's kinetic energy. If we want small wavelengths, therefore, we either have to illuminate with high energy photons (like X-rays and gamma-rays) which are difficult to focus and detect, or to illuminate with charged particles.

Charge makes particles easy to focus and detect with help from electric fields. The particle with the highest charge to mass ratio may turn out to be the electron (shown by the red line in the figure at right). Electrons thus interact most strongly with matter.

On the other hand, higher mass particles have shorter wavelengths for a given amount of kinetic energy. Hence they too come in handy as probes of the very small.

Development platforms and tools

The real world

We refer here to the challenge of building small agents (e.g. nano-robots) equipped with the following:

• a central-processing-unit (CPU),
• some sort of eyes and/or other local sensors,
• some on-board memory,
• an ability to move from point to point,
• a capacity for two-way communication with humans in the larger world,
• a source of ordered energy and
• a way to eliminate waste heat.

What are our prospects for building and integrating each of these components on smaller and smaller size scales?

sensors

Imaging sensors will be limited by the wavelength of the excitations used. For example, the wavelength of light may be a problem for cameras and image resolutions much smaller than the visible wavelength range of 400-700 nanometers.

power considerations

Do we carry our fuel with us, or plan on finding it on the road? Also, how do we dump excess heat? I have a feeling that many biological systems have already figured this stuff out.

See Also

• This scratch space on size-scale awareness.