Sub Space

In the StarTrek universe:

Subspace is a continuum that exists in conjunction with our own space-time continuum. Every point in our universe has a corresponding point in subspace. Also, at every point in our universe, subspace has a particular frame of reference. One could imagine subspace to be vaguely similar to a huge cloud-like field that pervades the known universe. The particles in one area of such a cloud would be moving at some particular velocity, while the particles in another area may be moving at another particular velocity. Similarly, at every point in our space, subspace has a particular "velocity" or frame of reference.

Subspace physics give rise to WarpDrive technology.

Also a MassiveMultiPlayer? video game that is now called Continuum (guess why).

SubSpace is also needed for communications (as in StarTrek SubspaceTransmission?) otherwise even with WarpDrive you would be limited to sending canisters through a WormHole to deliver messages (like a PneumaticTube? compared to electronic email). There is a phenomenon called QuantumEntanglement? where information is shared instantaneously over distance (albeit only with a few atoms at this point) perhaps this offers aclue?

The television series "Andromeda" (StarshipAndromeda?) has no FTL radio in its universe, and only organic pilots can navigate hyperspace due to some quantum-physics mumbo-jumbo about observables. The practical upshot of this is that long-distance communication is achieved by little courier shuttles, and when two-way travel to an area becomes impossible, so does communication there.

The Stacks and Heaps working behind the scenes in the compiler or interpreter of a typical programming language to store variabes, objects, functions form a kind of SubSpace - they are a TopologicalSpace that implements the DenotationalSemantics of the language. You may have an intuitive MentalModel of where objects are stored in the machine when programming but is this model IsoMorphic? to the SubSpace of the language?

BTW guys, just to make things perfectly clear, SubSpace isn't real. Just in case anyone was confused about it.

Goddamn. There goes my summer trip to Alpha Centauri.

[How about Entanglement? Obviously we don't know enough about it now do make anything practical, but see http://www.gsreport.com/articles/art000136.html

"There is no theoretical limit to the distance over which this could be accomplished, and the small size of individual photons implies that detailed and instant communications could eventually be accomplished."

We should be more humble before making absolute pronouncements. We don't want to live in fantasy either but as the Army Corps of Engineers motto goes: "The difficult, we do immediately. The impossible takes a little longer" :-) ]

According to my physics professor, entanglement still does not break the lightspeed barrier. When we make a measurement of two entangled objects, we break the entanglement between them. The measured one is now entangled with the measuring apparatus. Apparently this works in such a way that the lightspeed barrier is always preserved and one cannot signal faster than through conventional means. I didn't understand the full explanation, but this is his area of research, so I trust him on this.

If you could signal faster than light, we'd be in for some major problems. Because, as Einstein proved, FTL signals mean you can send messages into your past. This allows one to violate causality. The proof of CPT (charge-parity-time) invariance relies on causality. The violation of 3 different conservation laws would have major consequences for the laws of physics. In all likelihood, we wouldn't exist anymore. -- JonathanTang I got it from my nuclear physics textbook. From Eisberg & Resnick, Quantum Physics (2nd ed.), p. 658:
Although testing time-reversal invariance directly to a high degree of accuracy for the weak interaction is difficult, a sensitive indirect test is available by using the so-called CPT Theorem. This is a very general theorem of relativistic quantum mechanics which shows that, for any system governed by any interaction conforming to the relativistic requirement that cause must precede effect, the result of successively carrying out the charge conjugation operation C, the parity operation P, and the time-reversal operation T is to leave the essential description of the behavior of the system unchanged.
I could be misinterpreting this, but I read it to mean that CPT invariance follows from causality. The only other stuff I've read about CPT invariance simply says "mathematical theorem...subject to certain constraints that no physicist seriously doubts", which would fit causality fairly well. -- JonathanTang

Actually the quoted text differs subtly but importantly from your paraphrase. For one thing, it says it the other way around: it says if the system is causal, then it is invariant under CPT conjugation. It doesn't use the term, but this is a Noetherian invariant, a purely mathematical issue, but important in formally defining or deriving conservation laws.

Also, if you think about what special relativity (all by itself, without including other areas of physics) says about causality at all, it only addresses it in the sense of identifying vectors as timelike, lightlike, or spacelike, and if spacelike, are assumed to be non-causal, and otherwise causal. In other words, it pretty much assumes that, for two frames to be causally connected, the frame tagged as the cause must be on or within the light cone of the frame tagged as affected by the cause.

So the quoted text isn't really making an argument about causality of any sort, it actually is just carefully defining the assumptions that it is making.

In particular it is not barring a superluminal causality for any reason except that it explicitly is not what is being discussed. (There are of course arguments against such, they're just not in the quoted text.)

The issue of causality is slippery and deep, in part because of such invariants, so there really are only a few areas of physics we can draw on to actually even define causality, let alone prove things about it. -- DougMerritt

Incidentally I believe the issue of entanglement is identical to that of separability of variables. If separable, at least approximately, then the two systems can be treated with independent wave functions, at least approximately, but if not, then it must be a single wave function for the combined system.

I'm skeptical on that - separation of variables is a general technique for solving partial differential equations, not something that comes out of quantum mechanics specifically. It's often useful in QM because the SchrodingerEquation? is a differential equation. But we also used separation of variables in advanced electromagnetics, to calculate radially symmetrical potentials and such, and there's nothing quantum about that. Classical fields don't exhibit entanglement, but the variables are still (at least approximately) separable. -- jt

I could be completely off-base, it's just a thought. But I didn't mean all inseparable systems are entangled. A necessary condition, not a sufficient one.

I have the book, and for someone who is going 'solely by reviews', that is another example of sweeping pronouncements without looking at all the facts. While I agree John Baez site is useful, the link above points to why: 

  Hot water freezes faster than cold! 
  Why are golf balls dimpled? 
  What is a dippy bird, and how is it used?
  ...
You have to sift through a lot of unrelated material to examine FLT issues. This 200 page book goes into a lot more explanation than the examples above for instance differences between Phase and Group velocities, Stuckelberg-Feynman schemes versus Dirac Sea explanations of electron/positron movements in time. explanations on CPT and COP that would help with the discussion above, Kerr-Newman solutions for black holes etc. For the specific examples of EPR (Einstein-Podolsky-Rosen experiment) he spends almost a chapter examining it, compares Bell's Theorem with Eberhard's proof and Leonard Mandel's analysis. At the end he states:

"This EPR situation seems to show that nature undoubtedly uses superluminal links to accomplish her ends but these deep quantum connections are private lines currently inaccessible - perhaps permanently inaccessible - to humans for communication purposes"

He does not claim it allows for FTL communications, just explores the issues. As for accelerating at 1g again he spends several pages explaining it with a detailed table comparing rocket and earth perspectives and going into the effects of time and length dilation for observers at both ends. Admittedly the book is now a bit dated but as an introduction to the subject, and even to help understand the links above, it is a good start. [What is you opinion on the following:http://omnis.if.ufrj.br/~mbr/warp/etc/cqg16_3973.pdf? Again, it does not solve the problem completely, just reduces impossibly huge requirements to something smaller though still very large. Not for entanglement but warping space, worst case we could send capsules as above. And it still needs negative energy which we don't know how to make though it exists in the form of the CasimirEffect. But each time we reduce the current problems to a smaller set of problems, the completely impossible starts to become maybe, just maybe, somewhat possible. A hundred years ago carrying hundreds of people across continents by air was completely impossible let alone aiming for the moon.]

The research of Nicolas Gisin is already producing practical results in instantaneous communication using Quantum entanglement albeit on the photon/bit level. See http://www.gapoptic.unige.ch/Publications/LookUp.asp?Search=long%20distance It is ongoing now they are up to several miles note in 1997 it was only a few meters. The press focuses more on the "Teleportation" aspect but even if only data can be sent this way, communications on earth would be revolutionized even if it can't be used to talk to Rigel yet :-). It has applications for QuantumComputing and QuantumCryptography? as well as message sending and receiving.

So you dispute that they have been able to "teleport" photons at-a-distance? If that is not in question, can the teleported particles not be used to represent ones and zeros?

It's not really a teleporter, just the HeisenbergCompensator?.

In order to communicate using entanglement at remote distances, trapped ions would have to be entangled then moved apart. However once apart they could indeed be used for remote instantaneous communication and this is an area of active research. For instance it takes 15 minutes to send messages between earth and mars. If trapped ions that were entangled from earth were carried on board a ship there, even though it would take the usual months to get there, once landed, communication could take place instantly. It may be just at the level of "chat" but still, there would be a way to send some information without waiting. See http://www.aip.org/pnu/2004/split/680-2.html

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