The show has mentioned a "matter stream" being involved in getting you from point A to point B. I believe Christopher was using wormhole as a metaphor, your substance (regardless of it's exact form) is being sent though some kind of conduit to it's destination. Unlike Stargate's rings, the transporter isn't apparently moving you through normal space, there certainly isn't a visual energy beam briefly connecting the ship with the destination.
From Rick Sternbach and Michael Okuda, the technical advisors for TNG and its successors, in the technical notes they created for the production and eventually incorporated into the TNG Technical Manual. It was their attempt to find a more plausible interpretation of the dematerialization-based operation of the transporter. And it is more plausible in terms of raw physics than the old "matter to energy" idea, but it's far more convoluted from a practical standpoint. It would've ideally been preferable to abandon the dematerialization angle altogether, but they were stuck with it because TNG was treated as a continuation of TOS rather than a wholesale continuity reboot. They're analogous because they both involve bypassing normal 3-dimensional space to transmit things through additional dimensions. The reason Sternbach & Okuda established that transporters operate through subspace was to explain how they could beam through solid matter, transporting people inside ships or buildings or into/out of caves underground. Their conclusion was that the beam bypassed normal space by passing through subspace. That's essentially what a wormhole does.
I like your rationalization. I’ve been thinking re quantum superposition, entanglement and consciousness; Heisenberg Compensators to one side for now. Quantum energy described by Schrödinger’s wave function is forced to surf the subspace as a surfer rides an Ocean wave; just as the surfer doesn’t need to take his car and house on the surf board there may be no need to move the fermions and bosons so no massive release of energy their states spring back to a zero point in the Higgs field. Maybe at the right frequencies energy can be extracted and used like replicators. So when materialisation reintroduces the wave function back into the Higgs field at the chosen three dimensional co-ordinates we just ‘pop’ into existence without the need for time delay or the sound effects. There may be no need to disassemble fermions. I think from point of view of Schrödinger’s equation physical continuity in the matter stream for example Copenhagen interpretation (one of many theories to consider) might be reasonable assumption as all possibilities played out in the stream; physical energy interference patterns collapsing to determined state upon materialization means events might have substance. Imho.
I've taken a stab at this on a previous thread: "Realm of Fear contradicts a lot of the pre-existing language relating to transporters but comes closer to explaining how transporters must work to avoid killing transportees IMO. There must be a dimension outside time (per Relics) and space to which the transporter has access. The system scans and quantum links every atom in your body with energy from this dimension and the transporter switches those atoms with their quantum linked counterparts (not exactly quantum linking as we currently know it but some kind of futuristic equivalent). So the transporter's own power keeps the person in a dimensional pocket and the linked energy is kept in our dimension by the confinement beam. The energy then has to be transmitted to the desired location and when the confinement beam is removed the energy and the person snap back to where they should be but in the new location in our dimension. Where I disagree is the allegation that transporting does no DNA damage. It absolutely should. No confinement beam is going to be 100% perfect and some of your information is going to leak away in transit - we have seen this to be a danger in many TNG era episodes. I personally think that replicators cannot replicate living material so no simple cloning machines will exist on starships. The reason for keeping a blueprint of the transportee in the pattern buffer is so that when you beam them back to the ship you can replicate a portion of their DNA that has been lost in the two transports. If the % of the pattern that has leaked away is too high then you end up with a poorly or dead person. It also explains the term, 'Boost your matter gain,' used by Rand, I think in TMP. If the links to the information get scrambled like in TMP you get a dead mess returning when the transportee snaps back in the wrong order. This also covers things like good/evil Kirk or Thomas Riker where the transporter was somehow able to add 50%+ replicated material to the transportee and still have them live through outside intervention. It also means that long distance transport is possible but only if you have a way to maintain a confinement beam to your destination without leaking too much information. My issue with NuTrek transporters is largely that I can't see how the long distance transports are supposed to work using standard 23rd century technology. A new algorithm can tell you mathematically what you need to do, I just don't see how it lets you maintain a confinement beam over such long distances let alone deposit you on a moving target 'safely' in the time it takes the transport to resolve. The degree to which one remains conscious and/or able to interact while in the pocket dimension is open to debate. TWoK and Realm of Fear suggest that there is a threshold at which you can interact while being only partly in our dimension. I don't believe that Saavik was talking to Kirk in the transport beam, she was just continuing her conversation once she materialised sufficiently to allow her brain to continue performing the task it had started while in our dimension prior to dematerialising into the pocket dimension. This system has a few nice story elements that could have kept Trek transporting reasonably elegant. It means one cannot transport too often since you run the risk of DNA damage from too much replicated matter building up in your system. It means you need a localised quantum scanner so no more beaming up without a communication device or locking on to enemies unless you have first 'tagged' them somehow. It means emergency transporters are less accurate and sacrifice a certain level of detail in order to get a lot of people off the ship safely, which has health implications." So in answer to the thread title, a transporter cannot exactly transport itself unless there is a separate device that remains behind to maintain a confinement beam to the destination. The dimension is outside time and space. The issue is sending enough of the quantum-linked energy to the desired destination for enough of them to snap back in the correct order. Of course if energy is being swapped for matter it doesn't really get over the matter to energy conversion ratio. Could halve the amount of energy required by using quantum computing? It's not how transporters were ever really described but it's how I think they should have worked.
Copenhagen’s interpretation every possible universe that can exist does exist and is also fully played out until observed (maybe). On the Subspace carrier wave (the Ocean wave the surfer rides) it is possible for more than one surfer to be on the same wave at the same time even if the waves were initially independent of each other later combining (increasing amplitude) might in some instances cause probability of surfer to tend to be on other board; causing in some instances the surfer to quantum mechanically tunnel to other surf board; non local relative effects from materialization might obey Pauli Exclusion Principle pushing future waves to opposite surf boards. The surfers own wave function’s now exist on opposite surf boards, the wave energies could eventually separate with chance of being stuck on the surf board. This all means the Heisenberg Compensators need an overhaul and subject to proper regular maintenance and the chances of tunnelling on an ‘evil selfie surfboard’ could probably be calculated with uncertainty equations accounting for all variables for there would be many. Imho.
In computer programming there's something known as the metadata, which is commonly defined as "data about data". Thence I'd logically conclude that a transporter can beam itself, since this is explained by the metadata handling lesser units of data.
But that's software. You still need intact hardware to run it on. How the hell can a dissociated cloud of atoms function as a transporter?
Recursion is more aligned with this thread. Becuase the atoms are in a superposition of many possible states and entangled with each other therefore no reason to assume physical laws can't continue in the matter stream in a sense.
I think Gödel's second incompleteness theorem rules out the possibility of a transporter beaming itself. A transporter needs to model and process the complete data about anything it transports, nothing left out, but Godel's theorem proves that no system can completely explain or encompass itself. It can only be completely modeled by a larger system that contains it. And you seem to be saying the matter stream is a Bose-Einstein condensate, but that doesn't mean there's an intact machine in there somewhere. In order for something to function as an intact material object, it needs to have its particles correlated in a macroscopic, "classical" state wherein they're all physically connected into a solid. They need to be in certain positions to work; the particles of the focusing components have to be aligned so that they function as lenses, the particles of the current paths have to be aligned so that they can actually conduct electricity along a path, etc. There needs to be a single definite answer to where the bits go and how they interact in order for them to have a definite effect. Physical laws apply everywhere, but they have to be directed in the right ways to get a desired effect. A huge pile of sawdust is subject to the same physical laws as a catapult made of the same amount of wood, but it's not going to be able to have the same effect, because it's not in a configuration that can exert or take advantage of physical laws in the right way.
Conditions setup wave – wave carries everything including transporter hardware (operational or not) the waves have been entangled at that point and are now ‘in motion’ of a kind riding the subspace wave which was spiked with enough of the right kind of energy to last until wave evaporates (termination event) at designed end point. The subspace pulse energies encoded with the surfer frequencies ride the wave happily on their own to their termination event unless there is a receiving station to catch the wave and fail or the initial subspace pulse wasn’t strong enough resulting in failed termination event the wave dissipates after the surfer hits rocks or miles before beach maybe due to gravitational effect (do gravitons and tachyons affect subspace?) wave energy pops into a door ceiling planet core etc ouch! Assuming the wave is smooth inside the matter stream the transporter does not need to be operational to continue to ride the subspace wave (ocean) it could be re-used to lock onto {self+surfer} again and beam to another wave in the stream beaming within beaming. There may be less energy required to do this since subspace spike already in place maybe just needs a nudge. I think the universe encompasses itself and knows everything about itself in a super self aware state of awesomeness reflecting internally all the time. Classical axioms may not apply in quantum mechanical realms. I think the nature of quantum mechanics is holographic with super internal reflection differing from total in the sense that space and time are connected thus the future and past are reflections of each other. If the wavefunction of the transporter on the surfboard is holographic then I think it should work because it has always been a hologram. We’re just pushing some functions around in a hologram. The technology to set up the correct conditions getting subspace frequencies to match target and push all waves at precise time accounting for relativistic non local effects would have to be ‘bug free’ for sure but once the energies are in motion and stable the hardware could be used again because it is holographic. Maybe subspace pulse at right frequencies is all that’s needed to tinkle with these quantum mechanical forces, of course we would need the right iPhone app to generate correct pulse frequencies accurately and correctly every time. Yes I agree. Thermodynamically speaking when the thrusters go off on the ship it doesn’t stop its inertia keeps it going and requires energy to stop it, a la initial subspace pulse with designed dissipation frequencies. The holographic information remains holographic entangled and in superposition all the time if done correctly. Quantum mechanically speaking the space occupied by the pile of sawdust could just ‘pop’ into a huge Starship there is nothing to prevent this from happening it’s just said to be unlikely.
Judging by what's seen in Voyager's "counterpoint" all the hardware you need to rematerialise people are a couple of projectors you install on the floor. These might as well be holographic? (thus software..)
My understanding of wormholes is that they bend space to allow two distant points to be close together. We've never seen that subspace does this.
You're thinking of a space fold drive. The term "wormhole," coined by John Wheeler, is by analogy with a hole bored through an apple by a worm, connecting one part of the apple's skin with a distant part on the other side through a tunnel passing through the interior. A wormhole, or Einstein-Rosen bridge, is an analogous structure, a sort of spacetime "tunnel" connecting two parts of spacetime by passing through a higher-dimensional realm. And again, I am not saying that a beam through subspace is a wormhole -- any more than John Wheeler was saying that the universe is literally the skin of an apple. It's an analogy. I'm saying they're two different things that have similar effect. They're both ways of sending matter from one part of space to another without passing through the intervening space.