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Quantum Test Found For Mathematical Undecidability
KentuckyFC writes "Philosophers have long wondered at the profound link between mathematics and physics, but how deep does this connection go? Pretty deep according to the results of a quantum experiment exploring the nature of mathematical undecidability. Here's how: any logical system must be based on axioms, which are propositions that are defined to be true. A proposition is logically independent from these axioms if it can neither be proved nor disproved from them; mathematicians say it is undecidable. In the experiment, researchers encoded a set of axioms as quantum states. A particular measurement on this system can then be thought of as a proposition which, if undecidable, yields a random result — which is what they found. 'This sheds new light on the (mathematical) origin of quantum randomness in these measurements,' say the researchers (abstract)."
Can someone please explain in layman's terms how this results in a decision, for those of us who aren't quantum mathematicians? I somewhat get the whole "indecision results in a decision" thing but seems to be a hard idea to wrap my brain around so to speak.
They're saying that no one orders lobster at McDonald's -- not because people don't like lobster, but because it's not on the menu. You can't base how the general population feels about lobster by asking McDonald's how many lobsters they sell compared to how many hamburgers.
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So instead of looking to see what people feel about lobster, they're asking restaurants how many lobsters they sell in order to determine if lobster is even on the menu. Once that's set in stone, THEN they can start testing the demographics of how many people prefer lobster to what.
At least that's how I interpreted what they're doing...
I am the richest astronaut ever to win the superbowl.
Interesting. I think you are onto something here. We can think of a universe as an encoding of a particular axiomatic system, and then there are "facts" in that universe which come up to surface with high probability. To an observer they look like "laws". Moreover, there may be some undecidable propositions which, to an observer, appear like sheer randomness. Also, if the number of qubits in the universe is infinite, it is quite possible that the universe "knows" everything.
Does this also mean we could also prove theorems by physical experiment?