I'm sorry I thought you understood the point of the machine -- you don't.
There is no "point of the machine", rocketdodger. (Unless you're assuming your conclusions.)
You're simply asking questions about what would happen to a body's awareness under 2 different physical conditions.
When you agreed to the first part, I assumed it meant you understood that the machine was capable of magically "patching up" the fact that some particles were farther from each other than they should be, so that the new interactions between all the particles were effectively the same as the old ones even though the distances are completely different.
Of course I understood that. Still do.
The only reason I kept the head intact is because I knew it would be less extreme than some other possibilities, case in point you agreed with that scenario but disagree with this one yet they are actually the same from a technical standpoint.
They are not at all the same from a technical standpoint.
In one condition, you separate the body from the head which has no effect on the brain (given the effect of the machine) which is the organ that makes consciousness start and stop.
In another condition, you vaporize the brain itself and spread it across the galaxy... but you keep the particles moving in the same manner that they all would be if they were all together, including the ways in which they would be affected by other particles.
The vaporization of the brain is significant here, although you seem to believe it is not. And the relative behaviors of the now distant particles is of much less importance than you obviously appreciate.
The difference is like asking what if I cut my truck in two between the cab and the bed, and magically kept the particles going back and forth... and what if I vaporized it and spread it across the galaxy and kept the particles responding to each other.
Only in the first scenario could my truck still do the work it does now, including small-scale stuff like firing the spark plugs and moving exhaust. Ditto for the brain.
Your "semantics don't matter" approach leads you to absurdity upon absurdity, but this apparently only makes the hypothesis that much more awesome in your estimation.
The problem is, when Planck introduced his shocking work, he noted that he was forced to accept it because of the hard evidence. And when Einstein introduced his shocking work, he could demonstrate concretely how our currently accepted science implied that these shocking things must be true.
Your philosophy, however, has no such basis. Which means you should take its absurdities more as red flags than green lights.
So lets go back to an even simpler example and make sure we agree to it. Instead of you and the space you are in, lets just look at two particles. Not even two atoms, just two particles.
If, by definition, the machine's action is this:
1) Applying some spatial/temporal transformation to one of the particles ( any of the 4 or more dimensions we know of )
2) "Patching up" the interactions between the two particles such that if behavior A of particle 1 would lead to behavior A of particle 2, 1(A) --> 2(A), in the original "un-transformed" setup, behavior A of particle 1 will lead to behavior A' of particle 2, 1(A)-->2(A'), where the ' denotes that A' is identical to A other than the fact that it has the transformation applied to it.
In other words, if particle 1 would move a little and disturb particle 2 such that it moves a little, the machine would keep this interaction consistent *even if* the transformation applied took particle 2 thousands of lightyears from particle 1. Meaning, the particles would have no idea they were that far from each other -- their causal interactions with each other are effectively the same.
Do you accept this magical action of the machine? Do you accept that after the action of the machine the causal interactions between the two particles are effectively identical?
NOTE that one can view this machine as simply a "modified" laws of nature. We don't know "why" particles act the way they do, we just know "how" they act ( to the extent that we can determine that ). So this machine is simply something that insures the "how" of particle behavior is "locked down" to a given set by drastically changing the "why" of their action.
Dude... I know what you're saying, and it doesn't matter.
You can't vaporize a working physical system, strew it across thousands of light years, and expect that this system can do the same work it did before,
even if you keep the particles responding to each other magically.
