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Entanglement – the order of measurements can be important

  1. Aug 17, 2011 #1
    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.
     
  2. jcsd
  3. Aug 17, 2011 #2

    DrChinese

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    Could you give a synopsis of what you are saying? I don't follow this.

    Thanks.
     
  4. Aug 17, 2011 #3
    Re: FTL-gedanken experiment

    but the s and p swapped - I try with formulas to show that it should give a difference.
    --------------------------------------------------------------------------------

    Why I think the order may be important in some types of experiments:

    S-photons encounter a PBS (0) - polarize horizontally / vertically (and the vertically are detected).
    P-photon encounters a PBS (45) - polarization diagonal positive / negative (and both the diagonal positive and negative are detected).
    Both interrupts entanglement and both causes in addition a difference of half a wave between the transmitted and reflected.

    If s first meetings PBS (0): It will transmit Beam with roughly the same wavelength shift as before for all.

    If p first meetings PBS (45): s-beam will be oriented diagonally negative / positive - with a difference of half a wave - and when this beam subsequent meetings PBS (0): half of each type will be transmitted - so this time the resulting beam consists of a fifty-fifty blend with a half wave difference.
     
  5. Aug 17, 2011 #4

    xts

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    Could you say that once again in more ordered way?
    With some drawings of the experimental setup (at least reference to) you say about?
    There are tens of FTL-gedanken experiments, differing in such details, so it is really hard to follow you...

    Anyway, the answer is: no, the order of measurements doesn't matter.
    If you want me to point a flaw in your view (as I understand you believe it matters) - give a clear setup and description.
     
  6. Aug 17, 2011 #5

    DrChinese

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    So we are going to see a series of clicks on each side. Is there some ratio which you assert will change? Perhaps the ratio of p=V to s=+ ?

    Because that will stay constant regardless of the order. Not sure what the "half wave" thing is you are trying to pitch.
     
  7. Aug 17, 2011 #6
    'FTL - gedanken experiment' is a topic in this forum - where this was post # 13

    Argument against was that this kind never gave any difference.
    I think it does in this case - and therefore I have tried to follow the experiment via formulas in the hope of obtaining a concrete discussion of this particular experiment.
     
  8. Aug 17, 2011 #7
    No not the rate of p = V to s = + - but the connection between polarizing and 'half wave' difference.
    The 'half wave' difference are the difference between transmission with the PBS and reflection.
     
  9. Aug 17, 2011 #8

    xts

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    Ouch?
    I can't find such topic using simple search.
    I would really advice you to give easy to follow references, rather than puzzles, and write your math in an ordered, easily readable [itex]\TeX[/itex] way.
     
  10. Aug 17, 2011 #9

    DrChinese

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    I believe you are saying that there are differences in individual cases but that the statistical ratios do not change in the aggregate. Am I close?

    If so, then you acknowledge there is no observable experimental difference. Which is what I am saying. :smile: (Because one can always assert X is important or Y is important for anything when there is no observable difference in outcomes. And this is that case.)
     
  11. Aug 17, 2011 #10
    Last submit at Jul27-11 / p 4 at PFQ or search on UChr.
    OK the math could be more readable - but hopefully understandable with a little patience.
     
  12. Aug 17, 2011 #11
    no statistical difference
     
  13. Aug 18, 2011 #12
    A simpler version:

    The p - photons are measured horizontally / vertically = x/y.

    The sister - photons s are measured at + 45 / - 45 degrees = +/-.

    The measuring state with regard to polarization is describe by base x/y for p and +/- for s.

    I start with the first measured and then change base for the other.

    There are detectors at 0, 90 and -45 degrees, so only s-photons with +45 degrees continue.

    With p first and s second - state of s photons that continue:

    1) k*( lp1,x> ls2,+> + lp1,y> ls2,+>)

    , - where k = scale factor - or more simple without p1, s2 and k just:

    2) lx> l+> + ly> l+>

    With p second and s first - ie s measured but p not measured yet :

    3) lx> l+> - ly> l+>

    A difference (+ / -), but not measurable.


    Using entanglement with respect to time:

    When the photon passes a PBS changed the reflected photons a half wave = 1/2. No significant change = 0/2.

    With p first and s second:

    4) lx> l+> + ly> l+>

    p measured ==>

    5) lx, 0/2 > l+> + ly, 1/2> l+>

    time entanglement ==>

    6) lx, 0/2 > l+,0/2> + ly, 1/2> l+,1/2>

    s measured ==>

    7) lx, 0/2 > l+,0/2 +0/2> + ly, 1/2> l+,1/2 +0/2>

    So half = the measured 'vertical' - is shifted half-wave


    With s first measured:

    8) lx> l+,0/2 > - ly> l+,0/2> time entanglement ==>

    9) lx,0/2> l+,0/2 > - ly,0/2> l+,0/2>

    If the s+ is detected before p it should change anything for s+.

    When later measuring p:

    10) lx,0/2+0/2> l+,0/2 > - ly,0/2+1/2> l+,0/2>

    The difference between ‘p first’ or ‘s first and detected before p’ should be measurable with a double slit or maybe better a suitable interferometer.
     
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