How small can something be and still have a shadow?

photo by asilverthorne - public domain

My five-year-old daughter asked this question.  There must be some lower size limit at which you just can’t cast a shadow, right? 

Not necessarily.  As it turns out, you can be really any size and still have a shadow.

All it takes to make a shadow is to block light, and since light is made of photons (basically, consider them the particles that make light waves,) I figure all you technically have to do is keep photons from going through you and – ta-da! – shadow!

Photons?

For my shadow-making purposes, I’m just dealing with whether at least one photon gets knocked off course.  But, it should be noted that light, among other quantum entities, is a particle and a wave at the same time, as was figured out with the classroom-famous double-slit experiment.  Recently, some intrepid scientists at a Swiss university photographed light in both its forms simultaneously.  An article and animated video of how they did it can be found here.

Using the naked eye…

The smallest shadow that you can see would be made by whatever object is so small that you can barely see it, so if you’re, say, me, the smallest visible shadow would be from maybe a grain of sand about the size of this period here.

Using some serious tech…

Some scientists at an Australian university made a bit of a splash when they photographed the shadow made by an atom using only visible light and an extremely powerful optical microscope.  

Says Professor Dave Kielpinski of Griffith University's Centre for Quantum Dynamics:  "We wanted to investigate how few atoms are required to cast a shadow and we proved it takes just one. We have reached the extreme limit of microscopy; you can not see anything smaller than an atom using visible light.”

Check out the atom shadow right here.

Using my basic definition…

And coming at it from the particle physics realm, you could actually be no size and still block a photon and therefore have a one-photon-sized shadow.  That is, if you’re something like an electron.

Electrons are so teeny that physicists consider them to just have no size.  Basically, they’re a one-dimensional point for all intents and purposes, and mathematics involving electrons work out just fine if electrons are sizeless and referred to as a “point particle.”

Handily, photons are similarly teeny, all energy and no mass (like the toddlers of the quantum world perhaps?), which means they go and go at the speed of, well, light, until something stops them.

But point-like as electrons may be, they still don’t usually let photons pass right through.  It's hard to tell because of the wave nature of all parties involved, but we're quite certain that photons can collide with electrons enough that diagrams are made to commemorate the moments. 

When photon meets electron, they can collide with a variety of results, including the creation of totally different particles, but always with some change in energy and trajectory.  Regardless of what exactly happens, it would be rare indeed for you to find the photon continuing on its initial path once a collision has occurred, so technically, the photon didn’t land behind the electron, and therefore – ta da! – shadow!

If this all sounds a little too far-fetched and you need some better insight, ask the Shadow.  He knows.  J

What would happen if you cooled a Skittle down to absolute zero and hit it with a hammer?

photo by StockSnap  - public domain 

Because inquiring eight-year-olds want to know!

Before we proceed, a few definitions –

A Skittle is an M&M-looking candy-coated chewy sugar rush, for which you may have heard the ad campaign, Taste the Rainbow, or the more evocative Experience the Rainbow. 

(By the way, put a Skittle or M&M in water and watch the coating dissolve except for the “S” or “M” which floats to the top.  Yum!)

The hammer we mean is just the basic clawed type you have in your toolbox for bashing nails, thumbs and absolute zero Skittles.

Absolute zero is presumably as cold as something can be, and warrants a little further explanation than the former two ingredients.

Dude, that is cold.

photo by moritz320 - public domain

Zero degrees Celsius is where water freezes, zero degrees Fahrenheit is where I don’t let my kids go outside for very long, and zero degrees Kelvin is absolute zero -- where molecules stop moving around.  (Quick review – under normal circumstances, molecules are always moving around.  Faster in gases, slower in solids, but we haven’t seen ‘em actually hold still yet.)

Now, absolute zero is not the complete absence of all movement.  The super-frozen molecules don’t move, but the particles within the atoms that make up the molecules are still moving around in their usual way, just in their ground state.  An atom’s ground state is its lowest-possible energy state, so basically the electrons are being as chill as they can be, but they’re still zinging around in their dizzying dance of quantum probability (which we’ll mess with later on.)

Scientists have gotten some substances to within spittin’ distance of absolute zero, and when things get that cold, they often exhibit bizarre behaviors, such as becoming superconductors (having no electrical resistance) or superfluids (flowing without viscosity.)  Helium superfluid can flow in an endless fountain, and superconductors’ magnetic fields can cause levitation. 

So could you super-freeze a Skittle?

photo by Heamer - public domain

Getting complex molecules down to nuthin’-Kelvin is very tricky.  So far, gases have been the best candidates. 

Researchers at MIT got some sodium potassium molecules down to almost zero Kelvin, but they had to assemble the molecules from their constituent atoms as they went along.  They found, though, that the super-cold molecules were stable, long-lasting, and showed electric charge imbalances that could produce a magnetic effect between molecules.

Professor Martin Zwierlein of MIT says that “with ultracold molecules, you can get a huge variety of different states of matter, like superfluid crystals, which are crystalline, yet feel no friction, which is totally bizarre. This has not been observed so far, but predicted.”

Perhaps a Skittle would be a candidate for a superfluid crystal, if the crystalline structure of sucrose would play any part.  Figuring that a Skittle is mostly sugar, we’re looking at a bunch of these molecules:

12 atoms of carbon, 22 atoms of hydrogen, and 11 atoms of oxygen (C12H22O11)

-- a far cry from the two-atom item (NaK) put on deep freeze at MIT.

Another group of scientists from the University of Colorado found that their ultra-cold potassium rubidium (KRb) molecules flew apart upon collision, so perhaps our Skittle would need some sort of containment to keep it intact until the hammer hit.

So it’s hard to say for sure if our absolute zero Skittle would just fall apart, become some superfluid soup of sugar components, or be hard as a rock.

So hit it with a hammer, already!

photo by jackmac34 – public domain

We did put a Skittle through a test run with a household freezer and a household hammer, and in that case, it shattered admirably into many non-uniform shards.

Our best guess at this point is that if a Skittle maintained its cohesion through the cooling process, the hammer hit would raise the temperature at the moment of impact by making the molecules move, and would probably result in a very pulverized Skittle.

Unless said Skittle became an exotic state of matter first and ascended to a realm beyond the mundane friction a hammer would produce.  You could have superfluid crystal Skittle, or ether-Skittle or plasma-Skittle or pile-of-atoms-that-used-to-be-a-Skittle -- just as elusive to experience as an actual rainbow.

…Fade to black.  “That concludes the regular physics version of the answer.  Thank you for reading.  Feel free to go home and freeze a Skittle.  Or…read on…”

Absolute Zero Skittle: the Quantum Theory Fun Part

photo by geralt – public domain

MIT’s Professor Zwierlein also said, “We are very close to the temperature at which quantum mechanics plays a big role in the motion of molecules, so these molecules would no longer run around like billiard balls, but move as quantum mechanical matter waves."

Now we’re talking!

You see, quantum particles exist under a slightly different set of rules than we big huge visible solid-looking things.  Those teeny pieces move in such a way as to function as both particles and waves, kind of fuzzy in their location, as if occupying many spaces at once while moving too fast to be captured on film – physicists generally determine their “location” by figuring out the probability of where they most likely might be.

So let’s get theoretical with our Skittle. 

As stated before, absolute zero is the state of having chilled-out molecules but their constituent atoms still have energy; the atoms are just in their ground state.  Let’s see what might happen, according to the chalkboard, if we slowed down our Skittle until even the subatomic particles were not moving.*

There’s an odd and seemingly true (as far as we can tell) feature of quantum physics called Heisenberg’s uncertainty principle, brought to us in 1927 by theoretical physicist Werner Heisenberg.

Heisenberg wrote: "It seems to be a general law of nature that we cannot determine position and velocity simultaneously with arbitrary accuracy."

The uncertainty principle is general acknowledgment that we just can’t make a precise statement about the where and where-to of a fundamental particle; it’s exact position and state of motion (momentum) cannot be simultaneously defined.  Kinda goes with the fact that a probability is as close as we get to pinpointing, say, an electron.  And even though it’s meant to be an observation of an apparent limitation, the principle exists as a math formula.

The actual equation for the uncertainty principle is apparently pretty uncertain itself, if you survey the internet, so we’re going to go with Stanford University’s take on it, as explained in the Stanford Encyclopedia of (get this) Philosophy (quantum physics kind of belongs in the philosophy circle, after all) right here!

This is why our Skittle is weird:   δpδq ∼ h

…where δp = indetermination of particle's position, and δq = indetermination of particle's momentum, and h = Planck’s constant, which is 6.626 x 10-34 joule seconds (i.e. a super teeny number.)**

So if just for fun we treat Heisenberg’s relation like a straight-up math equation rather than a general statement about how much we can’t know, we can figure this:

If all motion stopped, that is, if even the subatomic particles held still, then the range in error of momentum (δq) would be zero because its movement (i.e. lack thereof) would be absolutely known, and then the range in error of position (δp) would have to make up for it by becoming infinite.

Or as Heisenberg put it: "In a stationary state of an atom its phase is in principle indeterminate."

Or as physicist Kenneth Ford explains: “Carried to a limit, it even means that if you knew one quantity precisely, with perfect exactitude, there is another quantity about which you would know nothing.”

Or as I put it: a Skittle at absolute-NO-motion-zero could be… anywhere.***

Experience that theoretical rainbow!  Then smash it with a theoretical hammer.

*I care not that this is impossible by all accounts. 

**Planck’s constant is a teeny number that’s proven to be super useful in equations dealing with particle physics.  A semi-related and similarly teeny number is the Planck length (about 10-35m,) which has been described thus:

The number of Planck lengths that could be lined up across a proton is comparable to the number of protons that could line up from Philadelphia to New York!

I just had to share that.

***Yeah, yeah, it wouldn’t really happen that way… even when working with probability within the uncertainty principle, you still have borders of sorts, like the quantum Skittle would be mostly under the hammer and not all hanging out in Morocco and Proxima Centauri…but as we say in particle physics and astrophysics, “the math works out!”