I really must get past identical-looking talking head videos. It would also be nice if i could work out how to edit these new high-quality files although the discipline of trying to be smooth and word-perfect is good.
So: Mike Teavee is teleported across a room. Whereas Violet's volume multiplied by a factor of about twenty-four, his is divided by about a thousand. Nonetheless, his mother can pick him up easily and put him in her handbag, so we have to conclude that he lost most of his mass in the process or he would end up about fifty times as dense as the heaviest known metal, osmium. The fact that the teleported chocolate bar was still edible is consistent with this. Something like 0.1% of the matter is reconstituted at the other end, preserving all structures down to the molecular level.
There are in fact plenty of mammals of about this size, so the existence of a human being 15 centimetres tall is not inherently implausible. However, a number of physiological problems arise. One of the most obvious is that Mike's surface area to volume ratio has altered dramatically. Relatively speaking, he now has ten times the surface area to volume ratio he had before, and his insulating layer of subcutaneous fat is only a tenth as thick. Left to himself, he will now quickly die of hypothermia unless the room is close to human body temperature or he is insulated in some other way. It's entirely feasible to suppose that his bunny suit is either artificially heated or a very good insulator. However, it's just as well he's in a chocolate factory as he's going to need a lot of energy-dense food. Some shrews, for example, have to eat five times their own weight in food every day. Most mammals of that size are considerably rounder and have more fat than humans. This applies, for example, to the smaller primates such as tarsiers:
(This animal has a long tail which i have "cut off".)
The second problem i mention is the size of the brain. Mike's brain now has a capacity of around a quarter of a teaspoon. Nonetheless he still seems to be able to behave in a recognisably human manner. I have no idea how this was achieved as that tarsier's brain is probably bigger than his.
There are a couple of other problems, which, as it happens, puzzle me in general. One of these is the problem of narrower tubes. Much of pediatric medicine arises from this. The fluids in a child's body have the same density as an adult's but the passages along which they move are narrower. This means, for example, that whooping cough and asthma are worse for a child than an adult - the passages in the lungs are more easily clogged and they can close more easily. As a matter of fact, this also puzzles me with small mammals, because i imagine the viscosity of murine mucus or blood is similar to ours but they're clearly fine most of the time. I would love to know the answer to this. Mike has this problem too. He has the same blood, lymph, cerebrospinal fluid, mucus, urine and is breathing the same kind of air as us, but all of those have to move through smaller vessels as fast to keep him alive. How is his body doing this?
There is also the problem of the missing mass. Maybe the transporter converts it into exotic dark matter. However, that would not be very useful. I prefer to believe that it's either stored somewhere or converted into energy. Since almost all of Mike's matter has gone somewhere else, since matter cannot be created or destroyed, it may have been converted into energy. According to Einstein's equation of E=mc^2 and assuming he has a mass of about fifty kilogrammes, this is enough energy to keep the whole of human civilisation going for a year at 2010 levels, so the Wonka factory presumably gets very few fuel bills. Alternatively, maybe the mass is stored in another form which can be transmuted into various other types of matter. This might explain where the blueberry juice came from - the gum includes a matter transmitter, or rather receiver, which supplies Violet's body with juice stored from other objects which have been sent through the teleport, or maybe the stick of gum itself is from an earlier version of the transmat device which failed to remove all the matter, in which case it would literally weigh a tonne unless it also contains the gas from the fizzy lifting drinks. So it's all coming together.
Now for the question of bandwidth. In the 1971 film, Mike takes 24 seconds to be transmitted. Since he is "in a million pieces" (and for some reason can still talk), we can assume the average size of each piece is either 50 milligrammes or perhaps 50 microgrammes, depending on when the matter is removed - maybe in transit. I'm still assuming he weighs fifty kilogrammes. A fifty microgramme piece of matter with the same density as water could form a cube about the size of a full stop. I don't particularly have a problem with that except that i'm interested in the composition of these pieces. Are they literally bits of flesh, bone, blood and so forth flying through the air, or are they more like material forms of data packets describing the make-up of tiny bits of his body? It's a fairly neat technique but not one i feel has been fully thought through. Is data compression involved? What is the bandwidth of the signal? It seems to me that many data would be required to encode and reconstruct a human being with intact memories and personality.
Interestingly, this is something which the 1986 remake of the film 'The Fly' addressed by talking about DNA. Jeff Goldblum's character is reconstituted from his DNA, so in a sense the teleport is his mother and he is the result of an extremely rapid pregnancy and childhood. This is a very efficient way of reducing bandwidth and can be further reduced by compressing the data for the human genome and shrunk further still by simply recording the differences between the individual and an average human being. The memories would also need copying of course. This machine is interesting because it is potentially a cure for all possible physical ailments and injuries, although probably one which kills the transportee. The question arises of whether the person at the other end arrives with a sterile colon and no commensal bacteria, or whether it would be safe to transport someone with headlice or a tapeworm. Nonetheless, the idea is somewhat appealing.
There is one final issue with Mike which is quite interesting. He is restored to his normal stature, or rather more than his normal stature, by a taffy-pulling machine. This makes him thinner than before, but unless he was pulled in all directions (or inflated?), he appears to have a negative Poisson ratio: he gets wider as he is pulled. This is interesting also because it might explain what happened to Violet. Maybe her skin is actually getting thicker as she grows and there is less juice than there appears to be.
Therefore, at least two and possibly three of the scenarios are linked here: Mike Teavee and Violet are both highly elastic and their fates involve the unexpected appearance or disappearance of matter, and the fizzy lifting drinks found in the 1971 film may account for the lower than expected mass of the blueberry gum, which was probably created by a teleport device.