[ExI] a clean well-lighted challenge
anders at aleph.se
Thu Sep 24 13:02:43 UTC 2015
I loved Adrian's stories. Especially the AI one - I did learn something
This is a bit more experimental, but I always seem to end up with dialogue:
The argument was echoing down the hallway.
A: "It is just a convenience. It is not *real*."
B: "What do you mean by *real*? It has effects you can observe, right?"
A: "The effects are real, but then we just make up a convenient
explanation for an unobservable cause."
B: "But you agree there *is* a cause. Something is making them fit
A: "It could just be initial conditions making them correlated or
C: "Are you guys talking about love again?"
They looked away from the whiteboard at the intruder, then quickly
looked back and simultaneously pointed at an equation.
A: "The potential. He thinks it is real..."
B: "...while that postmodernist thinks it is just fiction."
C: "Do you think the electromagnetic field is real?"
A: "Sure, you can measure and interact with it."
B: "It is a tensor field associated with mass-energy."
C: "But you can derive the field equations from the potential, and vice
versa. So the field and potential should be equally real or unreal."
A: "No! The potential is underdetermined: you can add anything that gets
zeroed out when you differentiate it, and you get the same field."
B: "No! If you do any gauge transformation it leaves the field equations
C: "So if potentials are unreal, then their exact form does not matter.
If they are real, they have hidden degrees of freedom."
A: "Always unobservable. So they don't matter. They don't exist. Occham
B: "What about statistical mechanics? There degrees of freedom you
cannot see matter: when you calculate something you count the number of
possible states to make a partition function, and from that you get
entropies and energies..."
A: "A mere convenience!"
C left the room. "Google the Aharonov–Bohm effect." They looked after
him for a moment before whipping up their laptops.
A: "OK, charged particles change phase proportional to the vector
potential they pass through. Great: wave function phase, *another*
unobservable thing, is changed by the unobservable potential. It could
just as well be spirits doing it."
B: "So two particles with the same phase starting from point A and going
to point B will have a phase difference proportional to the magnetic
flux through the area between the paths. That sounds observable."
A: "You can't see phase!"
B: "You can let the particles interfere. Do a standard double slit
experiment, the phase will move the interference fringes. Observable.
Done ages ago."
A: "Wait a moment... look at the diagram. The flux can be hidden inside
a superconducting box. There is no magnetic field where the particles go."
B: "There you go. There is just potential outside the box."
A: "How can there be potential if there is no field?"
B: "He said that if potentials are real they have hidden freedoms. How
come we get *that* interference pattern?"
The two began to hunt through the Wikipedia article for arguments they
hoped would impress the potential of the absent third.
Future of Humanity Institute
Oxford Martin School
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