# Entanglement – the order of measurements can be important

1. Aug 17, 2011

### UChr

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. Aug 17, 2011

### DrChinese

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

Thanks.

3. Aug 17, 2011

### UChr

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.

4. Aug 17, 2011

### xts

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.

5. Aug 17, 2011

### DrChinese

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.

6. Aug 17, 2011

### UChr

'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.

7. Aug 17, 2011

### UChr

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.

8. Aug 17, 2011

### xts

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 $\TeX$ way.

9. Aug 17, 2011

### DrChinese

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. (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.)

10. Aug 17, 2011

### UChr

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.

11. Aug 17, 2011

### UChr

no statistical difference

12. Aug 18, 2011

### UChr

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.