First of all, I want to unsatisfactorily dispense with two sub-items that keep popping up: (a) the subluminal transfer of information and (b) the coordination of quantum mechanics with special relativity.
In the first instance, we are simply assuming that information may be transmitted via quantum entanglement regardless of whether that is ever proven true in actuality. If we simply declare that quantum entanglement cannot convey a signal then we may very well be correct but we are evading the actual topic at hand: causality. The questions of information transfer raise significant problems with the no-cloning theorem and with the uncertainty principle, but those are separate issues (which though very intriguing are nonetheless tangential). The very existence of quantum entanglement invokes those and all we can say is: that’s just how it works & we don’t yet know why!
Now as for the second issue, I simply want to reiterate that quantum mechanics and special relativity are not a unified theory; the two cannot be encompassed within a single known mathematical framework. The very phenomenon of quantum entanglement underscores that discrepancy and indeed its conjectured existence first made that clear. We cannot use the discordance between quantum mechanics and special relativity to controvert either nor can we transport the principles of one to the other. This is a rather crucial aspect because we are here discussing precisely those circumstances in which the two are brought into greatest conflict within our current models.
OK, so moving right along, I think I’ve identified what appears to be the central impediment to which I was alerted in contemplating this post from PatrickHenry:
If the hypotheticallly instantaneous transmission system makes them both into a single frame of reference, then you'll never have a 3d reference frame, because it too will be in instantaneous communications with the others.
OK, in order to address this issue I want to begin by posting two links regarding wormholes (which I would’ve found much quicker had they been in the correct folder..) that feature the most relevant points. While Traversable Wormholes covers a lot of pertinent topics, the key parts begin with the following excerpt under Time Travel:
Wormholes are constrained by relativity to travel at sublight speeds and are time-dilated as per normal. Clocks placed at the mouths of a wormhole always remain in synchronisation with each other. If I look through one end of a wormhole and compare the near clock with the far clock they always agree. Even if one end of the wormhole is travelling at relativistic speeds many light years away. Einstein says moving clocks run slow. There would appear to be a paradox here. We observe the two clocks keeping time with each other, yet relativity says the 'distant', travelling clock is running slowly. How do we reconcile this? Only by concluding that the distant clock has been displaced in space and time.
Now, here is the crux I think of why we’ve been talking past one another, surely due in no small part to my often poor articulation skills. Our quantumly entangled communication channel (henceforth “ansible”) is always operating on the same inertial frame. This is why I keep emphasizing the point that nothing is ‘moving’ anywhere in the course of the transmission: even if one terminal is being carried along at a relativistic speed on our starship, its clock will always remained synchronized with the terminal at the other end. In effect, our understanding of quantum entanglement dictates that the entangled particles are not subject to relativistic time dilation; indeed, they can be said to coexist in the same point in time-space regardless of our external perception of them. That is the basic essence of the phenomenon.
The apparent paradox arises because the starship’s clock is in the course of, let’s say, 86.6% luminal velocity running at half the rate as the clock on Earth, and vice versa due to time dilation. However, as far as our ansible is concerned, the two terminals are perfectly synchronized with one another and this synchronization is fixed in that inertial frame in which they originated. So, before I get to the implications of that and the (possibly unwise) mental leaps I was making in reconciling this discordance, I want to introduce another piece of the puzzle excerpted from Wormholes and Time Machines:
Most physicists will find this result [wormhole instability] very satisfying, for it avoids a sumultaneity paradox. Einstein's special theory of relativity treats space-time in a very even-handed and symmetric way. It requires a complete equivalence of "inertial reference frames", space-time coordinate systems moving through space with any constant speed (including zero). These must be equivalent by any internal measurement that would single out one such frame as special. For example, no measurements made inside a spaceship traveling at near light-speed can show different results from similar measurements made when the ship was at rest in space. In special relativity "at rest in space" is a meaningless concept, since that condition is undetectable.
Thus, a semi-permanent wormhole would present a problem for special relativity not only because it would breach the light-speed barrier but also because the reference-frame symmetry would be broken. If a wormhole connection between separated regions of space existed only long enough to permit a message to be sent, it would seem that a reference-frame test could be made that would single out one reference frame as "preferred". Absolute space would be detected and defined.
Our basic disagreement, I now suspect, revolves about the reconciliation of our starship reference frame with our ansible reference frame which is also the Earth’s reference frame. Our quantum-entanglement ansible is indifferent to the time-dilated reference frame of our communicators, but nonetheless all the communications are taking place on the inertial frame of the ansible, which is the same at both ends. This is a severe violation of special relativity but then that is simply an apparent fact of the phenomenon of quantum entanglement itself. It is in the course of the interaction of our traveller and his ansible that the two separate spheres of quantum theory and special relativity are bridged (much to our dismay..)
How, where, why does the bridge exist? Who knows – that’s what physicists are trying to figure out. My guess would be it’s on some Superstring in the Tenth Dimension =) – but that’s something well beyond my understanding (or anyone else’s at this moment).
OK, so in the course of my previous comments I made two dreadful errors of my own (hanging head in shame), and here they are. First, when I kept reiterating that our communiques were traversing a single inertial frame I did not properly define what that was and when I would segue back and forth between that and the two reference frames of our communicators and then alluding to a necessary third observer (reference frame) to create a second inertial frame I did not specify what the hell I was talking about.. This was evidently the source of much confusion.
Anyhow, to make things as clear as I’m able, the one inertial frame of our transmission is that of our quantumly entangled ansible which happens to coincide with the reference frame of our Earthbound terminal even when it is being operated from the reference frame of our starship terminal. The third reference frame necessary to create a second intertial frame must be some other ansible operating on a ‘frequency’ different than that of our first ansible and then somehow interacting with both of our first two communicators – thereby introducing our causality issues.
When I said that you were ‘incorrectly’ privileging first one reference frame and then the other, I meant that by coordinating the times of each transmission as if they were taking place on the reference frame of the respective terminals, you were in effect treating them as if they were operating along two different ‘wormholes’ in each direction, rather than traversing one two-way wormhole. In effect, our entangled particles were forcibly subjected to the relativistic time dilation experienced by their surroundings, but that is not the current understanding of the phenomenon! We cannot treat our ansible transmissions strictly as if our two speakers are speaking to one another, but rather must treat them as if our two particles are ‘communing’ with one another and that this “spooky action at a distance” is then interpreted into the respective reference frames of their observers.
It is a bridge between quantum mechanics and special relativity – galavanting through the ether. =)
Now, that leaves unresolved the fact that our communicators are nonetheless operating in their own respective reference frames and must somehow interpret the ordering of the transmissions, which must be chronically linear if we are to avoid causality loops and the implosion of the universe.. It was in my conjectural reconciling of this phase that I made my second dreadful error, because I performed some mental acrobatics moving our transmission from the classical level to the quantum level to the relativistic level and back to the classical level without bothering to explain what I was doing, in part because I was not altogether clear myself what I was doing until alerted to it while pondering this post and this post by Physicist.
OK, so what did I do? When I was trying to draw a ‘verbal picture’ in my first lengthy post, and what I was trying to convey when invoking the graphics in sharpblue’s article, can perhaps be better depicted in the following solution to the apparent Twin Paradox.
Please check out the link to see a Flash animation of the transmits in action. This is a much better graphical layout of that which my parallel and perpendicular lines with variable time frames were attempting to capture (and why I later said that I know the lines were not in fact parallel). My previous formulation was a pallid, pathetic imitation of one side of this exchange.. :(
So, in effect, what I am doing from a mathematical standpoint is correcting for the ‘twin paradox’ over and over again each time a transmission is sent in order to represent the time dilation effect. Stated differently, I am effectively dropping the starship into a stationary position every time it transmits even though in actuality the starship remains in near-luminal motion. Since the ansible is operating as if it never left earth, which on whatever level quantum entanglement operates might as well be the case, I am basically performing the same correction that the twins must perform to reconcile their age discrepancy upon the star travelling twin’s return home.
Now, this little mental trick is open to significant objection! The first and foremost which occurred to me much earlier but which I didn’t raise because I figured we had enough issues to deal with is that although the communications may be instantaneous as far as the ansible is concerned, they would probably not be perceived as such by the communicators due to the time dilation factor. Hmm.. Better yet, let me take the possibilities as I see them in order:
1) It may well be the case that our ansible simply refuses to function when moving at relativistic speeds (or more precisely that we cannot detect its functioning due to our motion). In that case, we could communicate instantly at will over interstellar distances but only when we occupy the same inertial frame as does the ansible - when in motion the starship’s transmitter would be deaf and mute.
2) More likely the case (I think), and what I’m referring to above, it may be that our time-dilated perception of the communiques while in motion leads us to perceive those as if they are stretched out interminably at one end but a mere unintelligible blip at the other. Again, we can communicate just fine when dropping out of motion, but while in motion everything would be uselessly garbled (actually, this implies the possibility of certain modulations to correct for the time-dilation effect, but let’s not go there either!)
3) Finally, it may just be the case that the entangled quanta somehow compensate for our own experience of relativity, and thereby the ansible works just fine even when the ship is in motion. That’s basically the scenario we’ve been discussing all along since the alternatives are a much different or a much shorter (it doesn’t work – get over it!) kind of debate.
In whatever case, the simple two-way use of this same ansible and presumably any other ansible operating on the same inertial frame cannot violate causality! That’s because the communication itself is occurring on the same inertial frame no matter what the relative inertial frames of the persons communicating! Again, to return to my earlier notation, that does not ultimately resolve our problem at hand because there will always be at least some other inertial frames which can at least hypothetically interact with that inertial frame thereby raising the prospect of causality loops. Short of that, so long as the starship itself does not travel at superluminal velocity, then we cannot cross the time travel boundary because the communication itself is not travelling at any velocity. Heck, as far as the entangled quantum is concerned, it may as well have never left the Earth at all!
There’s also the conundrum of what happens when we turn the far ansible terminal around and bring it back to Earth, but that’s a whole ‘nother can o’ worms! I’ve already devoted enough hours to this one!! =)
I hope I’ve finally made myself clear! Now please tear it apart so I can withdraw back into my orderly intuitive little cave where I belong! :p