- #1
UChr
- 60
- 0
Entanglement – the order of measurements can be important.
I try now with some formulas - hope it's reasonably understandable:
First known substance - unless I am floundering in it:
I imagine that the p - photons is measured first (p1) and meets a PBS (0) (x = horizontal and y = vertical). We can then describe the measuring state with regard to polarization by:
k*( lp1,x> ls2,y> + lp1,y> ls2,x> ) - where k = 1 / sqrt (2) (scale factor).
Next s - photons are measured (s2) with a PBS (+45) (+=+45 degrees and - = - 45 degrees).
Change of base: ls2,x> = k*( ls2,+> + ls2,->) and ls2,y> = k*( ls2,+> - ls2,->) and inserted:
k*k*( lp1,x> ( ls2,+> - ls2,->) + lp1,y> ( ls2,+> + ls2,->))
= k * k * (( lp1,x> ls2,+> - lp1,x> ls2,-> + lp1,y> ls2,+> + lp1,y> ls2,->)
= k*(k*( lp1,x> ls2,+> + lp1,y> ls2,+>) + k*(lp1,y> ls2,-> - lp1,x> ls2,->))
There are detectors at 0, 90 and -45 degrees, so that only photons with +45 degrees continues - equivalent to: k*( lp1,x> ls2,+> + lp1,y> ls2,+>)
which corresponds to the expected: that half of the photons continue on + 45 were measured horizontally and half comes from the vertical (at p).
s measured before p: k*( lp2,-> ls1,+> + lp2,+> ls1,->)
Change of base: lp2,+> = k*( lp2,x> + lp2,y>) and lp2,-> = k*( lp2,x> - lp2,y>) and inserted:
k*( k*( lp2,x> - lp2,y>) ls1,+> + k*( lp2,x> + lp2,y>) ls1,->)
Only photons with +45 degrees continues - equivalent to:
k*( lp2,x>ls1,+> - lp2,y> ls1,+>)
a small difference (+ / -) - but measurable would be that half of those who continue will later be measured 'horizontal' and half 'vertical'
And then finally something perhaps not totally trivial?
When the photon passes a PBS changed the reflected photons a half wave = 1/2. No significant change = 0/2. Used entanglement with respect to time, we get:
k*( lp1,x>lp1, 0/2> ls2,y>ls2, 0/2> + lp1,y>lp1, 1/2> ls2,x>ls2, 1/2> )
and the ‘+45’-photons:
k*( lp1,x> lp1, 0/2> ls2,+> ls2, 0/2> + lp1,y> lp1, 1/2> ls2,+> ls2, 1/2>)
So half = the measured 'vertical' - is shifted half-wave
OR
k*( lp2,-> lp2, 0/2> ls1,+> ls1, 0/2> + lp2,+> lp2, 1/2> ls1,-> ls1, 1/2>)
And the ‘+45’-photons now:
k*( lp2,x> lp2, 0/2> ls1,+> ls1, 0/2> - lp2,y> lp2, 0/2> ls1,+> ls1, 0/2>)
So now they are similar with respect to time.
The difference between p1 and p2-s2-s1 should be measurable with a double slit or a suitable interferometer.
I try now with some formulas - hope it's reasonably understandable:
First known substance - unless I am floundering in it:
I imagine that the p - photons is measured first (p1) and meets a PBS (0) (x = horizontal and y = vertical). We can then describe the measuring state with regard to polarization by:
k*( lp1,x> ls2,y> + lp1,y> ls2,x> ) - where k = 1 / sqrt (2) (scale factor).
Next s - photons are measured (s2) with a PBS (+45) (+=+45 degrees and - = - 45 degrees).
Change of base: ls2,x> = k*( ls2,+> + ls2,->) and ls2,y> = k*( ls2,+> - ls2,->) and inserted:
k*k*( lp1,x> ( ls2,+> - ls2,->) + lp1,y> ( ls2,+> + ls2,->))
= k * k * (( lp1,x> ls2,+> - lp1,x> ls2,-> + lp1,y> ls2,+> + lp1,y> ls2,->)
= k*(k*( lp1,x> ls2,+> + lp1,y> ls2,+>) + k*(lp1,y> ls2,-> - lp1,x> ls2,->))
There are detectors at 0, 90 and -45 degrees, so that only photons with +45 degrees continues - equivalent to: k*( lp1,x> ls2,+> + lp1,y> ls2,+>)
which corresponds to the expected: that half of the photons continue on + 45 were measured horizontally and half comes from the vertical (at p).
s measured before p: k*( lp2,-> ls1,+> + lp2,+> ls1,->)
Change of base: lp2,+> = k*( lp2,x> + lp2,y>) and lp2,-> = k*( lp2,x> - lp2,y>) and inserted:
k*( k*( lp2,x> - lp2,y>) ls1,+> + k*( lp2,x> + lp2,y>) ls1,->)
Only photons with +45 degrees continues - equivalent to:
k*( lp2,x>ls1,+> - lp2,y> ls1,+>)
a small difference (+ / -) - but measurable would be that half of those who continue will later be measured 'horizontal' and half 'vertical'
And then finally something perhaps not totally trivial?
When the photon passes a PBS changed the reflected photons a half wave = 1/2. No significant change = 0/2. Used entanglement with respect to time, we get:
k*( lp1,x>lp1, 0/2> ls2,y>ls2, 0/2> + lp1,y>lp1, 1/2> ls2,x>ls2, 1/2> )
and the ‘+45’-photons:
k*( lp1,x> lp1, 0/2> ls2,+> ls2, 0/2> + lp1,y> lp1, 1/2> ls2,+> ls2, 1/2>)
So half = the measured 'vertical' - is shifted half-wave
OR
k*( lp2,-> lp2, 0/2> ls1,+> ls1, 0/2> + lp2,+> lp2, 1/2> ls1,-> ls1, 1/2>)
And the ‘+45’-photons now:
k*( lp2,x> lp2, 0/2> ls1,+> ls1, 0/2> - lp2,y> lp2, 0/2> ls1,+> ls1, 0/2>)
So now they are similar with respect to time.
The difference between p1 and p2-s2-s1 should be measurable with a double slit or a suitable interferometer.