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An Optical Stern Gerlach experiment

pvt6zh395dqbrj · 2011-05-25 23:25:16

Hello, I wish to design an experiment to demonstrate that when taking the inner product of two vectors, it is neccesary that those vectors be in dual vector spaces with respect to each other. So far, my only idea is to construct an optical stern gerlach apparatus to try and demonstrate this principle. The experiment would…

25-05-2011 11:25pm

#1

pvt6zh395dqbrj

Closed Accounts Posts: 183 ✭✭

Join Date: April 2007

Posts: 152

Hello,

I wish to design an experiment to demonstrate that when taking the inner product of two vectors, it is neccesary that those vectors be in dual vector spaces with respect to each other.

So far, my only idea is to construct an optical stern gerlach apparatus to try and demonstrate this principle. The experiment would consist of a light source, a two channel polariser which would sepearate the light source into its various polarisation states and direct those beams into seperate photomultiplier tubes to perform photon counting statistics on them.

the polarisation state and the coherence time of the initial beam would be then controlled externally by a polariser and a ground glass plate.

I then will place a second two channel polariser after the first and make it rotatable about the beam axis.

My idea then, is that when describing this system by linear algebra, the correct probability amplitudes (determined experimentally by the PMT tubes) will only possible to do by considereing the vectors from the first and second two channel polarisers as being in separate vector spaces.

I think it will work however I think the apparatus may be over complicated. Has anyone ever seen any experimental demonstrations of this principle before?

Thanks

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