Re: [math-fun] Plenty of Room at the Bottom, Part II
Dumb question: Given the rotation of the Earth & revolution around the Sun & so forth, is there a well-defined notion of "up" & "down" ? I guess if a photon is transmitted via a polarization-preserving optical fiber, then this notion may be well-defined, but I seem to recall that it is better if fibers _don't_ attempt to preserve polarization, since I seem to recall that ever-so-small differences in the speeds of various polarization orientations can build up over many miles of fiber length & cause bad problems -- e.g., self-interference. This is probably just an engineering problem, but since I've heard of thought experiments where Alice & Bob are separated by light-years & I didn't know how they planned to organize the coordinate axes in the first place. At 01:00 PM 8/13/2009, Thomas Colthurst wrote:
Here's a candidate scheme: Alice is in Tokyo and Bob is in London and they receive a steady stream of entangled particles.
Alice waits for a very rapid price change in TYO (Toyota) to happen in Tokyo -- a $10/share difference in 10 milliseconds, say.
She then looks at her latest particle and if it matches the direction of the price change, then she takes action: sells if both are up, buys if both are down.
Meanwhile, Bob observes all of his particles and trades on each one, buying if his measurement is down and selling if his measurement is up.
If we neglect transaction costs, and assume that news about Toyota breaks in Tokyo more often than it does in London, then whenever Alice doesn't take action, then Bob is just randomly buying and selling and whenever Alice does take action, then Bob's trade locks in Alice's profit.
-Thomas C
On Thu, Aug 13, 2009 at 3:33 PM, Michael Kleber <michael.kleber@gmail.com>wrote:
My idea was specifically about Bell's Inequality violations, in which two measurements of an entangled pair of particles can have a higher correlation than is possible with any "hidden-variables" interpretation of QM (2/3 vs 5/9).
--Michael
On Thu, Aug 13, 2009 at 3:27 PM, Dave Dyer <ddyer@real-me.net> wrote:
My layman's understanding is this:
Suppose you have a supply of entangled particles and manage to ship half of each pair to New York and London. You know that if you observe one and find it in "up" state, the other would instantaneously be observable in "down" state. You can verify this later (after light speed delay) by comparing notes.
The problem is that you can't use this to communicate,
(1) You can't set the state of the particle, only observe (so you can't set the New York particles to "up" or "down" so London can see the effect.
(2) You also can't tell if a particle has already been observed, so you can't signal by selectively not observing.
In the math used to describe these processes, there is no state until you make an observation, so there is no loophole by which you can tease more information out of the system. It remains to be seen if the math, which has withstood 100 years of practical tests, is absolutely correct.
The directions of up and down, or X,Y,Z, are arbitrary; you may choose them in any convenient manner. An optical fiber cannot be fabricated to be totally polarization independent. Impurities and inhomogeneities in the glass, lack of perfect circularity of the fiber core, strains (either frozen in when the glass was annealed or from fiber bends), stray electric and magnetic fields, and thermal gradients are some of the causes of parasitic birefringence. After a few meters of such fiber, the output cannot be trusted to have any particular polarization, and since these causes can be time dependent, so is the output polarization. Polarization preserving fiber is fabricated by introducing intentional birefrigence, typically a refractive index difference of 0.0001. This is the mode index, not the material index. Commonly, the preform (the glass cylinder that is pulled to make fiber) contains a pair of stress rods surrounding the core; these will set up an internal stress in the annealed fiber. Other designs use noncircular cores. The two polarization eigenstates are at right angles, and if the input light is launched into an eigenstate, it will stay there. The large consistent imposed birefringence dominates the small random parasitic ones. The core of such a fiber must be sufficiently small as to guide only a single mode (or a pair of modes differing only in polarization). There are also fibers that guide only a single polarization mode, the opposite polarization leaking into the cladding. There are two disadvantages to polarization preserving fibers: the cost is higher, and when the fiber ends are spliced or connectorized, fiber orientational alignment is essential. I'm not sure how one handles entangled photons. The fibers must preserve at the very least more than just two polarization states, or if not preserve, then alter in a predictable manner. When I find out what they do, I will report back. -- Gene ________________________________ From: Henry Baker <hbaker1@pipeline.com> To: Thomas Colthurst <thomaswc@gmail.com> Cc: math-fun <math-fun@mailman.xmission.com> Sent: Thursday, August 13, 2009 2:06:02 PM Subject: Re: [math-fun] Plenty of Room at the Bottom, Part II Dumb question: Given the rotation of the Earth & revolution around the Sun & so forth, is there a well-defined notion of "up" & "down" ? I guess if a photon is transmitted via a polarization-preserving optical fiber, then this notion may be well-defined, but I seem to recall that it is better if fibers _don't_ attempt to preserve polarization, since I seem to recall that ever-so-small differences in the speeds of various polarization orientations can build up over many miles of fiber length & cause bad problems -- e.g., self-interference. This is probably just an engineering problem, but since I've heard of thought experiments where Alice & Bob are separated by light-years & I didn't know how they planned to organize the coordinate axes in the first place. At 01:00 PM 8/13/2009, Thomas Colthurst wrote:
Here's a candidate scheme: Alice is in Tokyo and Bob is in London and they receive a steady stream of entangled particles.
Alice waits for a very rapid price change in TYO (Toyota) to happen in Tokyo -- a $10/share difference in 10 milliseconds, say.
She then looks at her latest particle and if it matches the direction of the price change, then she takes action: sells if both are up, buys if both are down.
Meanwhile, Bob observes all of his particles and trades on each one, buying if his measurement is down and selling if his measurement is up.
If we neglect transaction costs, and assume that news about Toyota breaks in Tokyo more often than it does in London, then whenever Alice doesn't take action, then Bob is just randomly buying and selling and whenever Alice does take action, then Bob's trade locks in Alice's profit.
-Thomas C
On Thu, Aug 13, 2009 at 3:33 PM, Michael Kleber <michael.kleber@gmail.com>wrote:
My idea was specifically about Bell's Inequality violations, in which two measurements of an entangled pair of particles can have a higher correlation than is possible with any "hidden-variables" interpretation of QM (2/3 vs 5/9).
--Michael
On Thu, Aug 13, 2009 at 3:27 PM, Dave Dyer <ddyer@real-me.net> wrote:
My layman's understanding is this:
Suppose you have a supply of entangled particles and manage to ship half of each pair to New York and London. You know that if you observe one and find it in "up" state, the other would instantaneously be observable in "down" state. You can verify this later (after light speed delay) by comparing notes.
The problem is that you can't use this to communicate,
(1) You can't set the state of the particle, only observe (so you can't set the New York particles to "up" or "down" so London can see the effect.
(2) You also can't tell if a particle has already been observed, so you can't signal by selectively not observing.
In the math used to describe these processes, there is no state until you make an observation, so there is no loophole by which you can tease more information out of the system. It remains to be seen if the math, which has withstood 100 years of practical tests, is absolutely correct.
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participants (2)
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