## Re: Double Slit variant and Popper

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n\nThis is a double-slit version of a thought-experiment dreamed up by\nKarl Popper, and a related experiment was carried out recently by Kim\nand Shih - see http://xxx.lanl.gov/abs/quant-ph/9905039. It is also\nthe subject of (non-granted!) US patent application number\n20020139932.\n\nThere is no problem and no (observable) nonlocality. Suppose Alice\nmeasures which slit the photon passed through on the left (and that if\nshe had not done so that she would have instead seen an interference\npattern on a screen). Bob can choose to measure one of two\nprobability distributions on the right: either which slit the photon\nwent through, or the far-field position on a screen.\n\nIf he measures which slit, then there will be a perfect correlation\nwith Alice\'s result, but this is all it is - no nonlocality. Half the\ntime the photon will pass through the bottom slit, and half the time\nthrough the top slit, and this would have happened even Alice happened\nto have gone home early. So Bob learns nothing about what she has\ndone.\n\nIf instead he measures the far field he will see an interference\ndistribution, rather than an average of two single-slit distributions\n(despite Alice\'s measurement). There are two ways to see this:\nFirst, Alice\'s measured observable clearly commutes with Bob\'s, and\njoint measurements of commuting observables don\'t disturb each others\'\ndistributions. Second, for the double slit to be a double slit, an\nessentially plane wave has to fall on Alice\'s slits, and hence a\nsimilar wave will fall on Bob\'s slits(but quantum-correlated of\ncourse). This wave will pass through both of Bob\'s slits, and hence\nform an interference pattern.\n\nOne cannot think of the left and right photons as separable particles\n(or separable waves) following definite paths; there is a correlation\nsimilar to EPR. In EPR one has the related paradoxical result that by\nmeasuring the position of the left particle and the momentum of the\nright particle, one has determined both the position and the momentum\nof the right particle - a joint measurement of noncommuting\nobservables! But this is not a measurement of the position of the\nright particle in the usual sense, because if a direct measurement of\nthis position is then made immediately afterwards, a totally different\n(and uncorrelated) result will be obtained.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>This is a double-slit version of a thought-experiment dreamed up by
Karl Popper, and a related experiment was carried out recently by Kim
and Shih - see http://xxx.lanl.gov/abs/http://www.a...nt-ph/9905039. It is also
the subject of (non-granted!) US patent application number
20020139932.

There is no problem and no (observable) nonlocality. Suppose Alice
measures which slit the photon passed through on the left (and that if
she had not done so that she would have instead seen an interference
pattern on a screen). Bob can choose to measure one of two
probability distributions on the right: either which slit the photon
went through, or the far-field position on a screen.

If he measures which slit, then there will be a perfect correlation
with Alice's result, but this is all it is $- no$ nonlocality. Half the
time the photon will pass through the bottom slit, and half the time
through the top slit, and this would have happened even Alice happened
to have gone home early. So Bob learns nothing about what she has
done.

If instead he measures the far field he will see an interference
distribution, rather than an average of two single-slit distributions
(despite Alice's measurement). There are two ways to see this:
First, Alice's measured observable clearly commutes with Bob's, and
joint measurements of commuting observables don't disturb each others'
distributions. Second, for the double slit to be a double slit, an
essentially plane wave has to fall on Alice's slits, and hence a
similar wave will fall on Bob's slits(but quantum-correlated of
course). This wave will pass through both of Bob's slits, and hence
form an interference pattern.

One cannot think of the left and right photons as separable particles
(or separable waves) following definite paths; there is a correlation
similar to EPR. In EPR one has the related paradoxical result that by
measuring the position of the left particle and the momentum of the
right particle, one has determined both the position and the momentum
of the right particle - a joint measurement of noncommuting
observables! But this is not a measurement of the position of the
right particle in the usual sense, because if a direct measurement of
this position is then made immediately afterwards, a totally different
(and uncorrelated) result will be obtained.

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Thanks. That was the sort of explanation I was looking for. I'm still a little confused as to how conservation is preserved along with this, however - do you know of any place where the full calculations are worked out? Maybe I'm just being dense at this time of the morning.



> If instead he measures the far field he will see an interference > distribution, rather than an average of two single-slit distributions > (despite Alice's measurement). There are two ways to see this: > First, Alice's measured observable clearly commutes with Bob's, and > joint measurements of commuting observables don't disturb each others' > distributions. Second, for the double slit to be a double slit, an > essentially plane wave has to fall on Alice's slits, and hence a > similar wave will fall on Bob's slits(but quantum-correlated of > course). This wave will pass through both of Bob's slits, and hence > form an interference pattern. > > One cannot think of the left and right photons as separable particles > (or separable waves) following definite paths; there is a correlation > similar to EPR. In EPR one has the related paradoxical result that by > measuring the position of the left particle and the momentum of the > right particle, one has determined both the position and the momentum > of the right particle - a joint measurement of noncommuting > observables! But this is not a measurement of the position of the > right particle in the usual sense, because if a direct measurement of > this position is then made immediately afterwards, a totally different > (and uncorrelated) result will be obtained. Sorry to respond twice so quickly, but I think the thing confusing me is: why, when Alice's particle is projected, isn't Bob's particle projected as well? Or is it? If it is, do you know if there is a place where the calculation is performed to show why it works out? Thanks.

## Re: Double Slit variant and Popper

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nThere is an article by Asher Peres which may be of help, at\nhttp://xxx.lanl.gov/abs/quant-ph?9910078 . It first looks at Popper\'s\noriginal experiment, but(see Figure 2 and pages 9-11), also looks at\nthe situation where one observer has a double slit and the other\nobserver measures position (though the latter uses an array of\ndetectors rather than two slit positions).\n\nPeres emphasises that if the momenta of the particles are well\ncorrelated (so that the total momentum vanishes), then their centre of\nmass position is not well defined from Heisenberg\'s uncertainty\nprinciple, and gives a relevant calculation showing that an\ninterference pattern will be observed.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>There is an article by Asher Peres which may be of help, at
http://xxx.lanl.gov/abs/quant-ph?9910078 . It first looks at Popper's
original experiment, but(see Figure 2 and pages $9-11),$ also looks at
the situation where one observer has a double slit and the other
observer measures position (though the latter uses an array of
detectors rather than two slit positions).

Peres emphasises that if the momenta of the particles are well
correlated (so that the total momentum vanishes), then their centre of
mass position is not well defined from Heisenberg's uncertainty
principle, and gives a relevant calculation showing that an
interference pattern will be observed.



of_1001_nights@hotmail.com (a student) wrote in message news:<3e896289.0411162220.75175db4@p...google.com>... > There is an article by Asher Peres which may be of help, at > http://xxx.lanl.gov/abs/quant-ph?9910078 . It first looks at Popper's > original experiment, but(see Figure 2 and pages $9-11),$ also looks at > the situation where one observer has a double slit and the other > observer measures position (though the latter uses an array of > detectors rather than two slit positions). > Thanks, that helped me understand a lot. Also the Bible verse seemed very appropriate here.