Remember that temperature is just kinetic energy. At body temperatures, 310 Kelvin or so, atoms move quite a bit, even in solids. You can, coarsely, approximate an atom in a molecule by imagining springs between the atoms; at body temperatures, they're always moving quite a bit with respect to each other.
If you don't position the atom just right -- we're talking about fractions of atomic radius (which are of the order of 10-11 meters) -- it's like tensioning the spring, and then letting it loose. You'll impart a lot of energy to that atom, and it'll likely break the molecule.
In practice, not only do the atoms be pretty much in the correct position (I'd guess something like sub-picometer precision, perhaps femtometers or tens of femtometers (10-15 or 10-14 meters) precision), but also their velocities (including direction) should be roughly retained.
I think so, except for active neurons.
If you construct an animal from known molecules, you can just record the molecule type, position, velocity, temperature (internal kinetic energy), isomeric folding (if metastable molecule like proteins that can "fold" into different shapes), and ionization (if any), and ignore the individual atoms.
(But, like I mentioned earlier, that might not suffice for active neurons; you might have to include atom excitation, to retain the activity in the neurons.
Or you could even go one step higher, and record individual cells.
(Then again, most of the cells in your body -- in your gut, specifically -- are not human; they're bacteria. And without them, you don't live very long.)
Like I said earlier, current ideas about "transport" don't allow examining the data stream at all.
For replication, why not? If you look at the ways the data is best replicated, things like "normalizing" the DNA in all cells and adding a bit to the telomeres (negating the effects of aging in the DNA) would be trivial. To fix other effects of aging, you'd filter out waste compounds inside cells (also related to aging), and e.g. removing fatty materials from the insides of blood vessels.
Let's do some math.
There are about 6×1023 water molecules in 18 grams of water. Using that as a rough guide, and noting that a water molecule contains one oxygen and two hydrogen atoms, we can estimate that a 100 kg (220 pound) human contains roughly 1031 atoms.
One cubic millimeter of water weighs about one milligram, and therefore has about 1022 water molecules; three times as many atoms.
If we need a "filter" that removes unwanted molecules of up to one cubic millimeter in size -- or uses up to one cubic millimeter region to decide what should be removed or changed -- the filter would have to access roughly 1022 atoms to do that.
Sounds terribly daunting, doesn't it? My current workstation has just under 1013 bytes of RAM. That's less than a millionth of what I'd need to "filter" a single cubic millimeter of tissue.
However, this type of filtering is extremely easy to parallelize. Sure, you'd need a massively parallelized machine to do it, but if atom-scale manufacturing was possible (and it'd have to be for any of this to be feasible), such machines would be easy to construct.
In my experience, the biggest bottleneck would be the memory access.
It might be possible to "layer" the memory and processing similar to image mip-mapping: each "layer" describes its contents at a more and more general or abstract level -- the lowest layer describing atoms, the highest layer describing abstract stuff like "part of a blood vessel going thataway", "bone tissue with marrow" --, and the "filtering" causing modification requests to be sent towards the lower layers, and the modifications refined on a layer-by-layer basis.
Heh.. even the idea of getting to program something like that makes my brain perk up
The thing is, it does not branch.
That is, there cannot be any point where a part interacts with another part during the replication. That will cause fatal errors in the transcription.
With regards to the consciousness, even non-fatal experiences can be extremely destructive. Consider surgery: if anasthesia fails, experiencing the surgery is enough to drive a person insane -- even if the surgery goes perfectly, and the body is repaired well enough to heal.
The duplication or transmission has to be instantaneous (at least to the perception of the transportee/duplicee). At one moment you're there, and the next moment you're here. If duplication occurs, there is also another you there too. Both of them share their entire being up to the moment before.
(Note that it does not matter whether time is continuous or quantized, or whether the animal perception is continuous or quantized: the transport or duplication has to be "instantaneous", or the transportee/duplicee will be damaged -- just like you would be if you woke up in the middle of a big surgery.)
When you wake up, can you tell the difference between yourself yesterday and yourself today?
I can't, therefore I must assume all copies of 'me' would think themselves the 'original'. (Unless there was some detectable error in the replication, of course.)
Well, there is still quite a bit of uncertainty about the exact scale at which important stuff in the brain happens. Certainly, computers are still much larger in scale.
On the other hand, I do believe that all the "ineffable" stuff in the brain happens at the quantum level.
In other words, I'd say a quantum computer (not the imaginary kinds, the real kinds that have already been constructed and demonstrated) is a good analogy. If you can transport or duplicate a quantum computer, with its state intact -- I'm assuming quiescent state both in the brain and the quantum computer, not "actively processing"/conscious --, I believe it should work for the brain, too.
That's the Big Question: Does the current state and inputs to the human brain dictate the next state? Or, in other words, does free will exist, or it is simply an illusion?
I suspect it does not really matter, because our sense of "self" is robust enough to deal with a few inconsistencies. In other words, even if the replication was a bit shoddy, I believe we'd still feel continuity. You might have one of our legs the wrong way around or something, and still feel "you" and have perfect continuity.
After all, there are people who've lost a massive part of their brain (due to illness or accident), but still feel perfectly themselves.
The thing that worries me, is how the family and friends react to the transportee/replicate. Would it be easier to accept them as the original, if you considered the technology "magic", not knowing any of the details?
(Knowing what I do about computer security does cause me a lot of grief, knowing how insecure most systems are, and not allowed to do anything about it. I wouldn't be surprised at all if all replicator or transport personnel absolutely refused to use the devices themselves..)