Let’s say I have a machine that can make all the atoms in your body suddenly and permanently* invisible.
However, any new atoms that make their way into your body (after I zap you with my machine) will remain visible. This means when you eat your next meal, I will see it being digested and then excreted.
My question is what else will I see? What will it look like as the nutients make their way around your body? I’m guessing that the first thing to start to become visible would be your blood. What effect would the intake of oxygen have on your appearance? How long until you look quite normal?
*For as long as they are a part of your body.
The problem is that you aren’t posing a question that makes any sense in the real world. You have made up a magical scenario, and the answer to the question depends entirely on how you want the magic to work.
When you are observing living things you aren’t seeing atoms, you are seeing molecules. What you are seeing is the effect of the electron transitions caused by the combination of atoms into molecules and various other atomic interactions.
To illustrate this, look at a bean. That bean was constructed, entirely and literally, from air and water. There’s nothing else in there except air and water, and the water itself came form the air in the form of water vapour. Yet the bean is quite visible despite all the components it was made from being utterly invisible. That transition from the invisible to the visible occurs because way the atoms are arranged affects the way that they emit light.
So even if you could magically make all the atoms in a human invisible, there is no way of knowing how that magic works. It is magic, Your magic. If you say that it works for 12 hours then that is how long it works.
If the magic wears off as soon as any magicked atom becomes chemically bonded to any normal atom, then a person will be visible within seconds, and restored to normal visibility within minutes
All the cells in the body are constantly respiring. They take on oxygen all the time. Normal. non-magicked oxygen from the air. That oxygen binds instantly to the haemoglobin in the blood, then to the enzymes within the mitochondria. It also becomes dissolved in the water within the body, both directly and as carbonic acid.
So the instant you magically turn a person invisible, the lungs will become visible, and then the blood that is flowing through the lungs, and from their the heart, the larger blood vessels and then then the rest of the body. Within seconds the full outline of the person will be visible as the haemoglobin, water and ATP all become perfectly visible. Within a few minutes the hydrogen bonds within the water will have interacted with pretty much every atom within the body, and the person will be visible again.
Of course your magic might require that a molecule remains invisible so long as it contains even a single invisible atom. In that case you will need several weeks before the person is more than vaguely visible. The sheer degree of mixing of invisible atoms via reactants and plain old water will ensure that it will be along time before you have an appreciable amount of novel material floating around the system. Full visibility will never be regained in adults, since the teeth will always remain mostly invisible. The surface layers of the teeth may appear as a hazy outline of surface deposits and plaque, but they will never be fully visible ever again and the pulp will always be visible.
Minor nitpick: this is only about 99.5% correct. The bean also includes phosphorus, potassium, sodium, and small amounts of other minerals (all of these probably make up about a tenth percent to a half percent of the total mass of the bean). Grass also includes a lot of silicon. All of these minerals come from the soil.
The main point, though, is correct. Your body is constantly absorbing oxygen and mixing it into every cell of your body. So – assuming a molecule becomes gradually more visible as it gets more unmagicked atoms – pretty much the entire body (except teeth and bones) will slowly start becoming visible immediately after the spell. In an adult, teeth will never really become visible, and bones will much more slowly be replaced (not that you could see them, since the skin will replace itself much quicker).
Isn’t the outer layer of skin dead? The dead layers would not appear until shed and replaced by new skin, so the person would appear flushed. I’m not sure how pronounced this effect would be, because I don’t know the ratio of dead to living skin.
Hair and nails would not appear until re-grown. As noted above, adult teeth would never fully re-appear.
Incidently, the invisible man would have been blind. If light is passing through him it’s not being absorbed and sensed by his eyes.
Now Dopers are admitting that they are nitpicking half percent inaccuracies. I’m not sure if this is an improvement. 
No. Dead does not mean isolated.
Even the outermost layers of the epidermis are constantly bathed with moisture and oils from various glands. The outer layers of the epidermis would actually be one of the first parts of the body to become fully visible.
Ditto for teeth. Inanimate crystal lattice yes, but isolated, not at all. The enamel is constantly absorbing an exchanging materials with the saliva, as smoker or heavy coffee drinker can tell you. And since the enamel of each tooth is essentially a single crystal, surface changes would instantaneously propagate to the entire visible tooth. I’m not sure of the rate of interchange between enamel and saliva, but certainly within half an hour the surface enamel will have exchanged material with the saliva.
Well, no.
Firstly, and most importantly, it’s magic, and the author said it didn’t work that way. Trying to argue that magic works in a manner that the author specifically said it does not work is about as silly and pointless as it gets. Within the universe invisibility was possible and it didn’t affect vision. Trying to argue that invisibility is magically possible, but that vision isn’t magically possible while invisible is just silly.
Secondly I suspect that you don’t realise how little light the human rods and cones absorb. It’s about 10% of the light that passes through the pupil, but spread over an area about four times the size of the iris. So, imagine an area about the size of a small postage stamp, and illuminated to about 1/1000th of ambient light levels. Unless you were looking very carefully from a distance of inches, I doubt you would be able to see it. A person would be effectively invisible even if their eyes were absorbing light perfectly normally.
Not sure about this. In order for all of the dead skin to become visible, magic “invisible” atoms need to be replaced by normal ones. That requires a chemical exchange. I’m pretty sure dead skin is more stable than this, it isn’t constantly reacting. Certainly, any chemical exchange would be slower than oxygen reacting with blood, so any change in appearance would be slower. As per the OP, it would have a visible effect.
Effectively invisible does not equal truely invisible. I included it as an interesting aside. If the whole thing is silly, why are you bothering to respond to this thread? I don’t have a problem with these kind of hypotheticals, as they can be entertaining to read and lead to better understanding. I find your point about just how little light the human eye absorbs to be an interesting one.
Frankly, I think pointing out a half percent inaccuracy, while clearly admitting that it’s only half a percent, is the highest and truest calling of a Doper. 
And if we really wanted to answer the spirit of the OP, we can define the magic thusly: each region of say one-tenth millimeter across or so will be transparent proportional to the amount of mass in the region that’s enchanted (as a ratio of all the mass in the region), but the light that isn’t magically transparented will be reflected and absorbed by the material in the region according to normal physics regardless of what is enchanted.
If the magic worked like that, then I think we’d see the enchanted person immediately start fading in, a bit more at the lungs and whatever body parts are most active, but otherwise fairly evenly across the body, but only slowly fading in and reaching a fairly steady state of say 80% translucency within, I dunno a day or two, as the oxygen reaches close to equilibrium. Then the body slowly fades in over weeks as the rest of the mass is replaced.
If the OP not only enchanted a person, but took care to also enchant a big tank of oxygen or air that the person was breathing from, then we could see the classic ‘food in the stomach’ idea.
In The Invisible Man, Wells made a point about how filthy a city like London was at the time. Especially with all the horse shit covering the streets.
Impossible hypotheticals live up to expectations only when authors work out their own. They know what points they are trying to make, and so know what they can assume and what pieces of reality they can exclude. Other peoples’ impossibles are impossible because no two people will make the same set of assumptions to get to the impossible start. Therefore no two people will be able to give the same coherent account about where the tale goes. It’s not science; it’s a story.
To bring this into the realm of the plausible, let’s say that we replace all of the atoms (or non-hydrogen atoms, if you’re worried about deuteration poisoning) of a person’s body with marker isotopes, and that we have a medical scanner that can pinpoint the location of all the normal-isotope atoms and reconstruct an image from them. Would that satisfy the naysayers?
Of course, the “atom converts/reverts molecule” is the interesting one. By breathing, you are absorbing oxygen at a fairly high rate. huge amounts of the body would include new oxygen within minutes; most of the bloodstream would be visible from hemoglobin in a matter of seconds?
Ditto for drinking water. Between the two inputs, your “invisble man”, I’m guessing, would look like a progressively less transparent bag of blood in a few minutes to a few hours.
There’s lost of “amazingfacts” places (TLTG - too lazy to google) which will tell you how often blood circulates in the human body. Seems to me that within 3 minutes any blood should make a full round trip, right up to just below the surface of the skin.
The plus side is it solves the diet problem - if this happened to me, at least my weight problem would be invisible since that stuff never seems to come off…
For the record this is exactly what I was thinking of, though I could have “fleshed” it out a bit more.
I don’t think I appreciated just how quickly the person would look like a bag of blood until reading the responses though. If you consider just how closely blood vessels are packed together, that’s pretty much all you would be able to see at first.
Nah, the inaccuracy needs to be at least two orders of magnitude more trivial to meet true Doper Standards.
Th problem with this is that there is no normal physics at play. Haemoglobin, for example, absorbs red light in part because of the oxygen/carbon dioxide it is bonded to. So if the light in a region strikes haemobglobin, does the entire molecule absorb because of a single stray oxygen atom?
I don’t see any way that you’d replace 80% mass within a few days. While you’d absorb a fair mass of oxygen over two days, most of it is just circulating within the same pool, entering the mitochondria and being respired again as CO2. So you’d be losing unenchanted atoms almost as fast as you gained them. I doubt there would be significantly more oxygen incorporated after two days than after to hours.
Roughly the same applies to food. Most of it is going to be circulating in a fairly small pool of glycogen/glucose stores. Relatively little is going to be incorporated into new body mass in the short term.
As a WAG I suspect you would need at least a week to exchange 20% of your body mass, and 12 months to exchange 80%.
You didn’t actually read the post that you quoted, did you?
Nobody ever said it was as fats as oxygen reacting with the blood. However it is at least as fast as any other tissue type within the body.
There is no such thing as truly invisible. We are talking about a story here, an event that never happened and never could happen.
Even within the story, the protagonist was never truly invisible, as Exapno Mapcase points out.
It is your objection that is patently silly, not the thread.
If you want a straight answer without all the nitpicking…
clearly the answer is 1 hour.
You are welcome.
What a cool, if impractical, bit of magic.
ewwwww