[math-fun] A polarization puzzle - my solution (Eugene Salamin)
Salamin's proof is stronger than mine in the sense that it works for any linear transformation as the effect of the optics; mine only works for "normal" linear transformations. Both are valid for quantum mechanics. Meeker's objection to our proofs is somewhat scary. Both my & Salamin's impossibility proofs seem valid provided the optical device is "passive" in the sense that it sort of acts like a potential in the Schrodinger equation, rather than being part of the wavefunction -- i.e. the state of the optical device itself is assumed unaltered. Meeker's objection pertains if that state is allowed to alter. I think Meeker is correct if that were allowed.
I don't know if my question is even going to make sense. What about a "demon"-like contraption that has at its disposal an array of photon-sources indexed by polarization state; it receives a photon, measures its polarization, looks up the "opposite", and routes an opposite photon into its output? Is such a device possible? Would it meet Gene's criteria? It's obviously not the same photon -- but it's not clear to me whether a photon reflected off a mirror is the same photon either. On Thu, Jun 4, 2015 at 4:38 PM, Warren D Smith <warren.wds@gmail.com> wrote:
Salamin's proof is stronger than mine in the sense that it works for any linear transformation as the effect of the optics; mine only works for "normal" linear transformations. Both are valid for quantum mechanics.
Meeker's objection to our proofs is somewhat scary. Both my & Salamin's impossibility proofs seem valid provided the optical device is "passive" in the sense that it sort of acts like a potential in the Schrodinger equation, rather than being part of the wavefunction -- i.e. the state of the optical device itself is assumed unaltered. Meeker's objection pertains if that state is allowed to alter. I think Meeker is correct if that were allowed.
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On 6/4/2015 1:44 PM, Allan Wechsler wrote:
I don't know if my question is even going to make sense.
What about a "demon"-like contraption that has at its disposal an array of photon-sources indexed by polarization state; it receives a photon, measures its polarization,
This idea violates the no-cloning theorem. You can't measure a quantum state completely, you can only measure whether it has a certain polarization or not. Roughly speaking you can only ever measure half of the state information, per the uncertainty principle. But that doesn't mean the problem is impossible; there may be a way to reverse the polarization without ever determining what it is. Brent Meeker
looks up the "opposite", and routes an opposite photon into its output? Is such a device possible? Would it meet Gene's criteria? It's obviously not the same photon -- but it's not clear to me whether a photon reflected off a mirror is the same photon either.
On Thu, Jun 4, 2015 at 4:38 PM, Warren D Smith <warren.wds@gmail.com> wrote:
Salamin's proof is stronger than mine in the sense that it works for any linear transformation as the effect of the optics; mine only works for "normal" linear transformations. Both are valid for quantum mechanics.
Meeker's objection to our proofs is somewhat scary. Both my & Salamin's impossibility proofs seem valid provided the optical device is "passive" in the sense that it sort of acts like a potential in the Schrodinger equation, rather than being part of the wavefunction -- i.e. the state of the optical device itself is assumed unaltered. Meeker's objection pertains if that state is allowed to alter. I think Meeker is correct if that were allowed.
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participants (3)
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Allan Wechsler -
meekerdb -
Warren D Smith