(Note: Before beginning this post, I would like to remind my readers why I am writing them. It isn’t to educate me or my readers in quantum physics and quantum computing but rather to explore two fundamental questions: What happened to the idea in science fiction? And when did science fiction become fantasy?
Quick synopsis of my argument to date: In science fiction, I like the science to be real and the math to back it up. Too much of SF today is just fantasy science. Star Trek is a leading example of fantasy science in science fiction.)
Trekkies, Trekkers, I have another problem1: the transporter. How exactly does that work? Is it a matter of completely analyzing your quantum state and then using previously shared entangled particles to recreate what you have measured via spooky action? When or how is the perviously entangled particles transported to its destination? Is it sent there magically? The Enterprise away parties beam down to the planet’s surface willy nilly.
The Enterprise transporter appears to me to be a classical transporter and not an entanglement-assisted transporter. This violates all kinds of quantum information theory theorems. We’ll get to that in a bit.
However, first, I need to address a few tangental issues from my last post. (If you have not read it, here it is: “Installment One of Physics in the 24th Century”.)
If one already has warp drive, then why can’t one just warp space allowing, a person to simply step to the desired landing site via a warp bubble that spans the two locations? Remember, this is all short range. 1 Au at the most but, more practically, the distance from synchronous orbit to the planet’s surface. Why bother with all that analysis and figuring out how to transport the quantum state of the thing or person being analyzed to the planet’s surface? Just step across folded Space-Time! Seems to me, one just warps space and puts the passenger in a warped Space-Time bubble and give it a push and Bob’s your uncle. We already have warp technology in the Star Trek universe, right?
Well, the problem with this idea, and with creating an Alcubierre warp bubble to begin with, besides the prohibitive amounts of energy needed to create the bubble, is the extreme temperatures created by the Hawking radiation. (Click here for a layman’s explanation of the Alcubierre warp drive.) Everyone in the bubble would fry and the bubble would destablize. The good news is this only happens at superluminal velocities. At subliminal velocities, the bubble would be stable and no one fries. However, and it is a big however, exotic matter would be needed to create an energy-density field lower than that of vacuum2. That is, with a negative mass.
Even if we solve all these problems and had a Alcubierre warp drive to create a warp slide to the planet’s surface from the Enterprise, what would happen the first time we engaged such a drive near a planet’s surface? We would bend space around that planet. This may very well create a second gravity well. It would be similar to putting a very dense object, like a moon, and positioning it between the ship and the surface of the planet. (Really overlapping the planet and the ship.) This could be catastrophic. It might even move the planet out of its orbit.
Even if this did not happen, when we released the bubble, the particles that the bubble has gathered on this very short trip would destroy anything in front of the bubble, that is, the planet3,4. And thus destroy the ship as well. Perhaps we could simply maintain the warp slide and never let the bubble pop, as it were. The problem then becomes docking with such a distortion in space-time. And don’t forget about the energy costs! They would be, as Pfenning says, “roughly ten orders of magnitude greater than the total mass of the entire visible universe.” So, it seems we are stuck with teleportation or a classical shuttlecraft.
Before continuing on to our main topic, let’s first visit replicators. Replicators and the holosuite are applications of transporter technology. Since we already decided that the transporter would have to work via entanglement, we might run into a problem with replicators. Specifically, the no-cloning theorem.
With an entanglement-assisted transporter, the no-cloning theorem does not apply because we are not creating an identical copy of an arbitrary unknown quantum state. (If you are confused about the two different types of teleportation, classical and quantum entanglement-assisted, click here for a nice article on the topic and the follow up article on entanglement and Eigen states and vectors.) Rather we are entangling one system with another, not copying. As we measure system A, say, in the ship’s transporter, spooky action at a distance is forcing system B, entangled particles on the planet’s surface, into A’s quantum state. In other words, your quantum information state is sent to an entangled set of particles to create a new you. Plus the analysis itself destroys the original state. However, with the replicator, you are actually creating a duplicate quantum state of the item you are replicating. How do we do this? Is this possible? Can we store a back up quantum state to use as a template?
The no-cloning theorem states that it is impossible to create an identical copy of an arbitrary unknown quantum state. Let’s look at an example. (If you believe me about the no-cloning theorem and don’t care about the math, click here.) Say we invented a cloning operator, Ĉ, provided that
Ĉ|φ,ψ> = |φ,φ>
Basically, cloning φ and forcing the second particle into state φ. Let’s take a concrete example. Say we have a particle that is spin-up and another particle that is in an arbitrary state. Applying our operator, it wipes out the second particle’s information and produce a particle in the spin up state.
Ĉ|↑,ψ> = |↑,↑>
Similarly, if you start with two particle that is spin down and the other particle in an arbitrary sate, we get:
Ĉ|↓,ψ> = |↓,↓>
Now, what happens with a particle who’s spin is in another direction? For example, the X direction.
|Ĉ|x+,ψ> =||Ĉ|||↑ + ↓||,ψ>|
Since our cloning operator is a linear operator, if you apply it to a superposition state it is the same as applying it to the first state plus applying it to the second state.
|Ĉ|x+,ψ> =||Ĉ|↑,ψ> + Ĉ|↓,ψ>|
And that is going to turn out to be the state |↑,↑> and |↓,↓> which is not going to be equal to the state |x+,x+>, which is our cloning operator’s target state.
|Ĉ|x+,ψ> =|||↑,↑> + |↓,↓>||≠ |x+,x+>|
Why is that? Well the state |x+,x+> would look like
||x+,x+> = |||↑ + ↓||,||↑ + ↓||>|
|√ 2||√ 2|
And if we multiply that out we get
||x+,x+> =||1||(|↑,↑> + |↑,↓> + |↓,↑>+|↓,↓>)|
However, our cloning operator has not given us the correct state. We are missing the |↑,↓> and |↓,↑> states. The linear operator just won’t permit this.
I know what you’re thinking, the no-cloning only applies in general, this only applies to arbitrary states.
and we can verify that in this special case. So we can clone these specific states7. Please see, the no-cloning theorem for the full proof. (If you are still confused and have read all the material I gave you links for, then go read this last one. Click here.)
Though it is impossible to make perfect copies of an unknown quantum state, we can make imperfect copies. There is hope that we may have replicators one day. Let’s just hope that the imperfections in “Earl Grey, hot” don’t kill you or blow the ship up. (Remember we can’t use classical error correction techniques on quantum states.) Back to the Enterprise’s transporter.
We run into problems with the transporter if it is not entanglement-assisted teleportation but “classical” teleportation because of the no-teleportation theorem, which states that an arbitrary quantum state cannot be measured with complete accuracy. So taking the Heisenberg uncertainty principle and the EPR paradox, this means that the information cannot be converted to classical terms (bits). In other words, teleportation is impossible by first converting quantum state into classical bits, and then moving the bits, and constructing a specific quantum state elsewhere.6
Combined with the no-deletion theorem (given two copies of some arbitrary quantum state, it is impossible to delete one of the copies), this would rule out replication, especially if the patterns were stored on a classical computer and since you could not store a backup of the quantum state anyway, you would have no way to store a pattern for replication. This would also mean no storage of patterns, and no pattern buffer, for the transporter. And probably no pattern filters. Remember, classical error correction won’t work in a quantum system.
Finally, given the no-cloning theorem, our classical transporter would not be able to beam down a exact copy of you. That would not be good. How many flipped quantum states before you die? And, for that matter, how many quantum states will be improperly replicated or transported? I don’t know but I wouldn’t risk it. Leonard McCoy was right to be scared of the transporter and he should have been terrified of the replicators. Even if it is just one quantum state of one quantum particle in your whole body, what about accumulative effects? How many imperfectly copied quantum states can be tolerated before you die? And, as I said in the beginning, if the Star Trek transporter is a entanglement-assisted teleportation device, how in the world are the entangled particles transported to an arbitrary planet’s surface? You might as well just take the shuttlecraft.
Thus, Star Trek warp drive, transporter, replicator and probably the holosuite are all fantasy in science fiction drag. QED. NB: this may not apply to holosuites but it probably does. The way I understand the holodeck, it is a combination of replication and holograms. This violates the no-cloning theorem at the very least. It probably also violates the no-teleportation theorem. (If you’re confused about quantum computing, click here.)
Having said all that, I would like to briefly point point out that there seems to be a real lack of hard science fiction. That is, I have not come across too many stories where the plot turns on a scientific theory or mathematical equations. Even given a rubber science, that is a plausible extension of current scientific theory or even an implausible extension of current science such as the ones I outlined above, most plots rarely turn on the rubber science. Sure, there are Star Trek episodes that do turn on the transporter, but is that science fiction or is that simply thinking of a plot twist and using a magical solution to create that twist? I think the days of hard science fiction are gone. What happened?
“As James Gunn, in the same volume (The Craft of Science Fiction), says: ‘…to understand the problems of characterization in science fiction, we must understand why science fiction has different needs than other fiction.’ He goes on to quote Elizabeth Bowen from Notes on Writing a Novel: ‘Each character is created in order and only in order, that he or she may supply the required action.’ And later C. S. Lewis in ‘On Science Fiction': ‘Every good writer knows that the more unusual the scenes and events of his story are, the slighter, the more ordinary, the more typical his persons should be. Hence Gulliver is a commonplace little man and Alice a commonplace little girl.’
To sum up, if the story turns on the development of the main character as it’s raison d’être, then it is mainstream fiction. If it turns on the idea, the future speculation, then it is science fiction.”
This may explain the glut of alien science fiction stories.
2. Finazzi, Stefano; Liberati, Stefano; Barceló, Carlos (2009). “Semiclassical instability of dynamical warp drives”. Physical Review D 79 (12): 124017. arXiv:0904.0141. Bibcode:2009PhRvD..79l4017F. doi:10.1103/PhysRevD.79.124017.↩
4. Everett, Allen E. (15 June 1996). “Warp drive and causality” (PDF). Physical Review D 53 (12): 7365–7368. Bibcode:1996PhRvD..53.7365E. doi:10.1103/PhysRevD.53.7365. Retrieved 24 July 2013.↩
5. This is my attempt at free hand bra-ket notation. You get the idea.↩
6. However, you can transmit classical information by changing into orthogonal quantum states and then changing it back elsewhere to classical information. Orthoganol quantum states can always be distinguished. Further reading: Herbert, Nick (1982). “FLASH—A superluminal communicator based upon a new kind of quantum measurement”. Foundations of Physics 12 (12): 1171–1179. Bibcode:1982FoPh…12.1171H. doi:10.1007/BF00729622.)↩
7. After doing all the HTML for the math equations and after losing my work at least once because of problems with WordPress, I decided to just include images of the equations I want and go very light on those equations. However, I have provided links throughout this post for those interested in the proofs.↩