3.11.17

What Are The Paradoxes In Quantum Mechanics?

What Are The Paradoxes In Quantum Mechanics?
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What are the paradoxes in quantum mechanics? originally appeared on Quora: the knowledge sharing network where compelling questions are answered by people with unique insights.
Answer by Allan Steinhardt, PhD, Author "Radar in the Quantum Limit", Formerly DARPA's Chief Scientist, on Quora:
What are the paradoxes in quantum mechanics? I can give you five, all of which have been experimentally confirmed. Some are already commercial products, other may be soon. As quantum is rapidly entering commercial markets, it is insightful to approach the question as in "what are the capabilities that quantum mechanics can provide in the real world that most laymen would interpret as startling, or impossible, based on intuition?" I then close with some comments about paradoxes writ large and why they arise in Quantum. In each case I provide links to science literature, usually to original sources.

1) Teleportation: Quantum technology allows us to "beam" an exact replica (down to quantum numbers i.e. superposition state) of one system at point A to another system at point B, arbitrarily far away. This topic is discussed in this paper Experimental quantum teleportation, and also this answer on Quora.
Caveat: We must first send clumps of matter, i.e., ship raw matter to "clone" from point A to point B. We also must learn, and communicate, the desired state of this matter (i.e. the superposition state) through a "standard" (though suitably conditioned) comms channel, at less than or equal the speed of light. This probably will destroy the original system, being, human, whatever. So there is no violation of light speed constraint on information transfer. Read more here. The "paradox" here is that teleportation even of living humans is theoretically feasible, though (likely) technically impossible or impractical.
2) Remote detection of eavesdropping: This is the basis of secure quantum encryption. Using entanglement we can detect whether a (quantum) message between Sender and Receiver has been intercepted in transit. It makes no difference how far away the eavesdropper was, the mere impact of his/her measurement is detected.
Caveat: Sender and Receiver must compare notes, no speed of light violation. See Quantum cryptography without Bell's theorem. The "paradox" here is we can learn if someone somewhere read a private message without knowing who or how, even though we cannot access the reader!
3) "Spooky" calculation: Here we use superposition to obtain more equivalent computations than hardware and clock cycle enumeration would suggest is feasible. This "hack" exploits the fact that quantum states can be in superposition and in so doing can "remotely" interfere with each other. Thus we can store, in a quantum computer, ones and zeros, and do calculations simultaneously on both without duplicating hardware. See Quantum Computing since Democritus.
Caveat: Only some problems can be sped up this way. As of February 2016, we have no quantum computers that are faster than regular computers for any compute problem, but that is expected to change. Protein folding has been shown to be among the class of problems where quantum can help. It would be great if we could actually get there commercially. The "paradox" here is that we can have, in one computer, more calculations in one nanosecond than there are atoms in the universe! See What is a quantum computer?.
4) Interaction free measurement: The best way to explain this is that we can measure something in quantum without measuring it. Of all the animals in the Quantum Zoo this is the most exotic! See: PHYSICS ILLINOIS, and How does the quantum zeno effect work?.
Caveat: We need to get the object "near" the sensor, we just don't actually allow the sensor to disturb the object in any way. This does allow us to measure things that normally would be harmed through measurement, such as cold atoms. The "paradox" here is that we can measure things remotely in ways that, while limited, defy our sense of time and space.
5) Life extension of particles: Because quantum causes particles to interact with each other in weird ways we actually can slow down the decay of particles. Note: this is not special relativity here, the particle remains at rest, it just "feels" time differently, unlike its surroundings. See nist.gov.
Caveat: Unlike time dilation in relativity, this effect is limited to particles that evolve through state superposition. The "paradox" is we can selectively slow down time "simply" by interacting with a (certain type of) dynamic system.
Note for Nerds:  Paradox is an ambiguous word. Unresolved ambiguity in language usage makes quantum impossible to explain satisfactorily without defining terms. (The quantum particles are in a state of superposition, don't let our language follow suit!) Paradox can mean one of three things: (i) we get different contradictory answers using logic, (ii) we appear to get different contradictory answers using logic, and (iii) we observe something that defies common sense. We always use paradox in quantum in this third sense. There is never a logic paradox in quantum. If (i) occurred in any branch of mathematics this would be an epic event. If it were possible to get two different answers in arithmetic using two different solution paths we would need to dismantle and rebuild math from scratch. Item (ii) occurs all the time in "pure" math and math as applied to physics. But as the word "appear" suggests this is a subjective event, unlike (i), which is about math not us. As a child we are puzzled by things we perceive later as "obvious" as an adult. Like (ii), (iiii) is subjective. But unlike (ii), item (iii) is about our sense of the physical realm, not our sense of theory. When laymen say there is a paradox in Quantum they never mean "hey the Hermitian operator in Quantum appears to give contradictory results when I select different basis functions in Hilbert space". If they did we would be at paradox definition (ii) [if resolvable], or (i) [if unresolvable]. In Quantum (sans strong gravity) the paradox is always physical, i.e. case (iii). The fact that we call Quantum paradoxical is a testament to (A) its awesome predictive power and explanatory success, and (B) its deep mathematical basis. No one ever accuses, say, cell biology, or social science, of being paradoxical!
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