View Full Version : [SOLVED] I don't understand EPR
<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>I want to make it clear that I\'m *not* pushing any alternate\ntheories here. I simply don\'t get it and would appreciate\nsome hints. I\'m not denying Aspect\'s experiments, or Bell\'s\nanalysis or anything. I\'m begging for help.\n\nAs the subject says, I don\'t understand the EPR paradox.\nAnd so, I\'m pretty much stumbling when it comes to Bell\'s\ntheorm and the Aspect experiment and so on.\n\nMy problem is this. Let\'s take the Aspect expt. to start.\nThe idea is, there is a pair of photons, each circularly\npolarized, and traveling roughly 180 degrees from eachother.\nThey are supposed to be in a definite total angular momentum,\nso as to agree with the fact that the single atom that\nemitted both has indeed finished up with the same angular\nmomentum as it started.\n\nThe explanation goes, if the polarizer on one side detects\na photon as vertical, then a vertical polarizer on the other\nside *must* detect the other photon as vertical.\n\nOk, it\'s that "must" that stumps me. Why "must?" As near\nas I can tell, you\'ve got a circularly polarized photon,\nit has an amplitude to be detected as vertical by a\npolarizer. The photon that goes through the polarizer\nis not in the same state as it was before. Now it is\nlinearly polarized, oriented vertical.\n\nSo what I don\'t get is, where in QM does it say the other\nphoton *must* now be in a linear vertical state? Its partner\nis not in the same state any more, so why should the two\nphotons "add up" to the same angular momentum they did?\nDon\'t we need to include in the sum the effects on the\npolarizer? Isn\'t it now the (as yet undetected) photon,\nthe working-bits of the polarizer, and the post-polarizer-\nphoton that sum to the correct total angular momentum?\n\nI\'m so clueless. Help?\ngrelbr\n\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>I want to make it clear that I'm *not* pushing any alternate
theories here. I simply don't get it and would appreciate
some hints. I'm not denying Aspect's experiments, or Bell's
analysis or anything. I'm begging for help.
As the subject says, I don't understand the EPR paradox.
And so, I'm pretty much stumbling when it comes to Bell's
theorm and the Aspect experiment and so on.
My problem is this. Let's take the Aspect expt. to start.
The idea is, there is a pair of photons, each circularly
polarized, and traveling roughly 180 degrees from eachother.
They are supposed to be in a definite total angular momentum,
so as to agree with the fact that the single atom that
emitted both has indeed finished up with the same angular
momentum as it started.
The explanation goes, if the polarizer on one side detects
a photon as vertical, then a vertical polarizer on the other
side *must* detect the other photon as vertical.
Ok, it's that "must" that stumps me. Why "must?" As near
as I can tell, you've got a circularly polarized photon,
it has an amplitude to be detected as vertical by a
polarizer. The photon that goes through the polarizer
is not in the same state as it was before. Now it is
linearly polarized, oriented vertical.
So what I don't get is, where in QM does it say the other
photon *must* now be in a linear vertical state? Its partner
is not in the same state any more, so why should the two
photons "add up" to the same angular momentum they did?
Don't we need to include in the sum the effects on the
polarizer? Isn't it now the (as yet undetected) photon,
the working-bits of the polarizer, and the post-polarizer-
photon that sum to the correct total angular momentum?
I'm so clueless. Help?
grelbr
Phillip Helbig---remove CLOTHES to reply
Jul2-04, 04:31 AM
<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>\nIn article <1a325379.0406300628.6d138b4@posting.google.com>,\ ngrelbr@hotmail.com (grelbr) writes:\n\n> The idea is, there is a pair of photons, each circularly\n> polarized, and traveling roughly 180 degrees from eachother.\n> They are supposed to be in a definite total angular momentum,\n> so as to agree with the fact that the single atom that\n> emitted both has indeed finished up with the same angular\n> momentum as it started.\n>\n> The explanation goes, if the polarizer on one side detects\n> a photon as vertical, then a vertical polarizer on the other\n> side *must* detect the other photon as vertical.\n\nNot so much vertical as opposite. If photon A is up, then we know that\nphoton B must be down. How is this different from a red ball and a blue\nball, instead of two photons, so that if we measure one ball to be red\nwe know that the other must be blue? The point is, we can CHOOSE if we\nwant to measure. Instead of measuring up and down, we could measure\nleft and right. If photon A is left, then photon B is right. OK, still\nno mystery. The strange bit is that we can choose what to measure at A\nand know what will be measured at B, even though there is no way causal\ninformation can propagate from A to B in time.\n\nLet\'s do this experiment a hundred times. We measure whether A is left\nor right and whether B is up or down. There won\'t be any correlation.\nBut if we measure whether B is left or right as well, the measurements\nwill always be opposite.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1a325379.0406300628.6d138b4@posting.google.com>,
grelbr@hotmail.com (grelbr) writes:
> The idea is, there is a pair of photons, each circularly
> polarized, and traveling roughly 180 degrees from eachother.
> They are supposed to be in a definite total angular momentum,
> so as to agree with the fact that the single atom that
> emitted both has indeed finished up with the same angular
> momentum as it started.
>
> The explanation goes, if the polarizer on one side detects
> a photon as vertical, then a vertical polarizer on the other
> side *must* detect the other photon as vertical.
Not so much vertical as opposite. If photon A is up, then we know that
photon B must be down. How is this different from a red ball and a blue
ball, instead of two photons, so that if we measure one ball to be red
we know that the other must be blue? The point is, we can CHOOSE if we
want to measure. Instead of measuring up and down, we could measure
left and right. If photon A is left, then photon B is right. OK, still
no mystery. The strange bit is that we can choose what to measure at A
and know what will be measured at B, even though there is no way causal
information can propagate from A to B in time.
Let's do this experiment a hundred times. We measure whether A is left
or right and whether B is up or down. There won't be any correlation.
But if we measure whether B is left or right as well, the measurements
will always be opposite.
Frank Hellmann
Jul2-04, 04:32 AM
<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>\nThat \'must\' is precisely the spooky action at a distance. you are\ndealing with entanglement, means: The two photons are NOT independent\nof each other.\nLet\'s see if I can do this from the top of my head:\n\nA circular polarization can be written as |R> = |x> + i|y> and |L> =\n|x> - i|y> in the basis in which the polarizer meassures.\nNow due to conversation of angular momentum AND parity it turns out\nyour decayed state should look like this (note that this is a\nsuperposition, and it\'s nonlocal as photons |1> and |2> can be far\napart by now):\n|1,L>|2,R> - |1,R>|2,L> = |1,x>|2,x> + i|1,x>|2,y> - i|1,y>|2,x> +\n|1,y>|2,y> - |1,x>|2,x> + i|1,x>|2,y> - i|1,y>|2,x> - |1,y>|2,y> =\n2i(|1,x>|2,y> + |1,y>|2,x>)\n\nNow if we meassure photon |1> in the x direction we are left with a\npure |2,y> state which means we \'must\' meassure the second photon\nperpendicular to the first.\n\nThe key point is that both of them are described by one wave function,\nthey are not independent photons but entangled.\n\nIt comes down to the fact that the product state of the decay is not\ntwo individual photons with definite states which together satisfy\nangular momentum conservation but a superposition.\n\n---\n\nfrank\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>That 'must' is precisely the spooky action at a distance. you are
dealing with entanglement, means: The two photons are NOT independent
of each other.
Let's see if I can do this from the top of my head:
A circular polarization can be written as |R> = |x> + i|y> and |L> =|x> - i|y> in the basis in which the polarizer meassures.
Now due to conversation of angular momentum AND parity it turns out
your decayed state should look like this (note that this is a
superposition, and it's nonlocal as photons |1> and |2> can be far
apart by now):
|1,L>|2,R> - |1,R>|2,L> = |1,x>|2,x> + i|1,x>|2,y> - i|1,y>|2,x> +|1,y>|2,y> - |1,x>|2,x> + i|1,x>|2,y> - i|1,y>|2,x> - |1,y>|2,y> =2i(|1,x>|2,y> + |1,y>|2,x>)
Now if we meassure photon |1> in the x direction we are left with a
pure |2,y> state which means we 'must' meassure the second photon
perpendicular to the first.
The key point is that both of them are described by one wave function,
they are not independent photons but entangled.
It comes down to the fact that the product state of the decay is not
two individual photons with definite states which together satisfy
angular momentum conservation but a superposition.
---
frank
<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\nCerthas@gmail.com (Frank Hellmann) wrote in message news:<e2b39847.0407010725.79b58207@posting.google. com>...\n> A circular polarization can be written as |R> = |x> + i|y> and |L> =\n> |x> - i|y> in the basis in which the polarizer meassures.\n> Now due to conversation of angular momentum AND parity it turns out\n> your decayed state should look like this (note that this is a\n> superposition, and it\'s nonlocal as photons |1> and |2> can be far\n> apart by now):\n> |1,L>|2,R> - |1,R>|2,L> = |1,x>|2,x> + i|1,x>|2,y> - i|1,y>|2,x> +\n> |1,y>|2,y> - |1,x>|2,x> + i|1,x>|2,y> - i|1,y>|2,x> - |1,y>|2,y> =\n> 2i(|1,x>|2,y> + |1,y>|2,x>)\n\nIn his preprint here\n\nhttp://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf\n\nAspect uses |1,L>|2,R> + |1,R>|2,L> rather than - as you say.\nSo it should be |1,x>|2,x> + |1,y>|2,y>, meaning the photons\nhave to be parallel, not perpendicular.\n\nBut it does not change the overall thrust of your post. The state\ncan\'t be factored into a product of two states, one for each photon.\nThey are entangled.\n\nSadly, I\'m still confused, only now it\'s about different things.\nI will have to go study up on some of the books and articles that\nhave been suggested in this newsgroup. Thanks muchly.\ngrelbr\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Certhas@gmail.com (Frank Hellmann) wrote in message news:<e2b39847.0407010725.79b58207@posting.google.com>...
> A circular polarization can be written as |R> = |x> + i|y> and |L> =
> |x> - i|y> in the basis in which the polarizer meassures.
> Now due to conversation of angular momentum AND parity it turns out
> your decayed state should look like this (note that this is a
> superposition, and it's nonlocal as photons |1> and |2> can be far
> apart by now):
> |1,L>|2,R> - |1,R>|2,L> = |1,x>|2,x> + i|1,x>|2,y> - i|1,y>|2,x> +
> |1,y>|2,y> - |1,x>|2,x> + i|1,x>|2,y> - i|1,y>|2,x> - |1,y>|2,y> =
> 2i(|1,x>|2,y> + |1,y>|2,x>)
In his preprint here
http://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf
Aspect uses |1,L>|2,R> + |1,R>|2,L> rather than - as you say.
So it should be |1,x>|2,x> + |1,y>|2,y>, meaning the photons
have to be parallel, not perpendicular.
But it does not change the overall thrust of your post. The state
can't be factored into a product of two states, one for each photon.
They are entangled.
Sadly, I'm still confused, only now it's about different things.
I will have to go study up on some of the books and articles that
have been suggested in this newsgroup. Thanks muchly.
grelbr
<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>\nFrank Hellmann <Certhas@gmail.com> writes\n\n>The key point is that both of them are described by one wave function,\n>they are not independent photons but entangled.\n\nSo it would be valid for a naive to consider \'them\' as a single\nparticle?\n\nCan I now consider what might happen when a measurement of one is\nconsidered?\n\nI asked this before, and basically got told \'no: see bell\'.\nUnfortunately nobody has come up with a brief and clear description of\nwhat bell is about.\n\nWhy can we not see the particle as a single unit, which communicated\n\'internally\' at infinite velocity? That is, along the axis joining the\n\'two halves\' space is contracted to zero distance (internally). That is\n(put horribly crudely) the particle sees itself as stationary and\ncompact but sees space travelling past at the appropriate velocity, but\ninstead of being in one direction it sees (in effect) \'external\' space\ncoming towards it "from two directions". I hope, but rather doubt, that\nthis makes sense to anybody. I can visualise it easily.\n\nThat way the conceptual problem where other observers see measurements\ntaken at different times, and even reversing which observer made the\n\'first\' measurement, simply vanish.\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com (whitelist check on first posting)<<\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Frank Hellmann <Certhas@gmail.com> writes
>The key point is that both of them are described by one wave function,
>they are not independent photons but entangled.
So it would be valid for a naive to consider 'them' as a single
particle?
Can I now consider what might happen when a measurement of one is
considered?
I asked this before, and basically got told 'no: see bell'.
Unfortunately nobody has come up with a brief and clear description of
what bell is about.
Why can we not see the particle as a single unit, which communicated
'internally' at infinite velocity? That is, along the axis joining the
'two halves' space is contracted to zero distance (internally). That is
(put horribly crudely) the particle sees itself as stationary and
compact but sees space travelling past at the appropriate velocity, but
instead of being in one direction it sees (in effect) 'external' space
coming towards it "from two directions". I hope, but rather doubt, that
this makes sense to anybody. I can visualise it easily.
That way the conceptual problem where other observers see measurements
taken at different times, and even reversing which observer made the
'first' measurement, simply vanish.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com (whitelist check on first posting)<<
Frank Hellmann
Jul9-04, 10:32 AM
<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>\nOz <oz@farmeroz.port995.com> wrote in message news:<ZU0JtmE2Sm7AFwBZ@farmeroz.port995.com>...\n> Frank Hellmann <Certhas@gmail.com> writes\n>\n> >The key point is that both of them are described by one wave function,\n> >they are not independent photons but entangled.\n>\n> So it would be valid for a naive to consider \'them\' as a single\n> particle?\n>\nIt\'s a good question which I personally can not anwser completely\nsatisfactory since I\'m just learning myself.\n\nSingle particle states are defined to be states that transform under\ncertain representations of the Lorentz Group (Gallileo Group).\n\nIn other words (using Gallileo group): This wave function we are\ntalking about here lives in the tensor product of the Hilbert space of\nfunctions on 3 Dimensional Euclidean geometry.\nH(x)H\nIf it were seperable it would live on\nH(+)H\nA rotation acts as Rv on v element H\nThen it acts as R(x)R on v element H(x)H\nThus you can tell what a single particle state is by considering it\'s\ntransformation properties under Gallileo.\n\nAt the end of the day the mathematical structure is what is important\nif you find a different way to look at it with two spaces and a single\nparticle it\'s just as well but might not be particularly usefull.\nIt will give the same predictions.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Oz <oz@farmeroz.port995.com> wrote in message news:<ZU0JtmE2Sm7AFwBZ@farmeroz.port995.com>...
> Frank Hellmann <Certhas@gmail.com> writes
>
> >The key point is that both of them are described by one wave function,
> >they are not independent photons but entangled.
>
> So it would be valid for a naive to consider 'them' as a single
> particle?
>
It's a good question which I personally can not anwser completely
satisfactory since I'm just learning myself.
Single particle states are defined to be states that transform under
certain representations of the Lorentz Group (Gallileo Group).
In other words (using Gallileo group): This wave function we are
talking about here lives in the tensor product of the Hilbert space of
functions on 3 Dimensional Euclidean geometry.
H(x)H
If it were seperable it would live on
H(+)H
A rotation acts as Rv on v element H
Then it acts as R(x)R on v element H(x)H
Thus you can tell what a single particle state is by considering it's
transformation properties under Gallileo.
At the end of the day the mathematical structure is what is important
if you find a different way to look at it with two spaces and a single
particle it's just as well but might not be particularly usefull.
It will give the same predictions.
Arnold Neumaier
Jul9-04, 11:09 AM
<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>\nFrank Hellmann wrote:\n> Oz <oz@farmeroz.port995.com> wrote in message news:<ZU0JtmE2Sm7AFwBZ@farmeroz.port995.com>...\n> \n>>Frank Hellmann <Certhas@gmail.com> writes\n>>\n>>\n>>>The key point is that both of them are described by one wave function,\n>>>they are not independent photons but entangled.\n>>\n>>So it would be valid for a naive to consider \'them\' as a single\n>>particle?\n>>\n>\n> It\'s a good question which I personally can not anwser completely\n> satisfactory since I\'m just learning myself.\n>\n> Single particle states are defined to be states that transform under\n> certain representations of the Lorentz Group (Gallileo Group).\n\nTo qualify as a _single_ (elementary) particle they must correspond to\nirreducible representations.\n\nThis means that a state of two entangled photons will not be a single\nparticle state. Entanglement is specific to reducible representations,\nsince it is a statement about states in a tensor product of representations.\n\nArnold Neumaier\n\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Frank Hellmann wrote:
> Oz <oz@farmeroz.port995.com> wrote in message news:<ZU0JtmE2Sm7AFwBZ@farmeroz.port995.com>...
>
>>Frank Hellmann <Certhas@gmail.com> writes
>>
>>
>>>The key point is that both of them are described by one wave function,
>>>they are not independent photons but entangled.
>>
>>So it would be valid for a naive to consider 'them' as a single
>>particle?
>>
>
> It's a good question which I personally can not anwser completely
> satisfactory since I'm just learning myself.
>
> Single particle states are defined to be states that transform under
> certain representations of the Lorentz Group (Gallileo Group).
To qualify as a _single_ (elementary) particle they must correspond to
irreducible representations.
This means that a state of two entangled photons will not be a single
particle state. Entanglement is specific to reducible representations,
since it is a statement about states in a tensor product of representations.
Arnold Neumaier
Tom Trotter
Jul9-04, 12:03 PM
<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>\ngrelbr@hotmail.com (grelbr) wrote in message news:<1a325379.0406300628.6d138b4@posting.google.c om>...\n> I want to make it clear that I\'m *not* pushing any alternate\n> theories here. I simply don\'t get it and would appreciate\n> some hints. I\'m not denying Aspect\'s experiments, or Bell\'s\n> analysis or anything. I\'m begging for help.\n>\n> As the subject says, I don\'t understand the EPR paradox.\n> And so, I\'m pretty much stumbling when it comes to Bell\'s\n> theorm and the Aspect experiment and so on.\n>\n> My problem is this. Let\'s take the Aspect expt. to start.\n> The idea is, there is a pair of photons, each circularly\n> polarized, and traveling roughly 180 degrees from eachother.\n> They are supposed to be in a definite total angular momentum,\n> so as to agree with the fact that the single atom that\n> emitted both has indeed finished up with the same angular\n> momentum as it started.\n>\n> The explanation goes, if the polarizer on one side detects\n> a photon as vertical, then a vertical polarizer on the other\n> side *must* detect the other photon as vertical.\n>\n> Ok, it\'s that "must" that stumps me. Why "must?" As near\n> as I can tell, you\'ve got a circularly polarized photon,\n> it has an amplitude to be detected as vertical by a\n> polarizer. The photon that goes through the polarizer\n> is not in the same state as it was before. Now it is\n> linearly polarized, oriented vertical.\n\nThe light (opposite moving photons) emitted by a single\natom\'s electron decay process (via the laser excitation\nof atomic calcium cascades in Aspect) is polarized\nidentically. The photons are "correlated in polarization"\nvia the emission process.\n\nIf the polarizers are oriented at the same angle, then\nif the polarizer on one side transmits enough light (ie.,\na photon\'s worth) during a given coincidence window to\nregister a detection, then the polarizer on the other\nside will (in the ideal) also transmit enough light\nduring that coincidence window to register a detection.\n\n>\n> So what I don\'t get is, where in QM does it say the other\n> photon *must* now be in a linear vertical state? Its partner\n> is not in the same state any more, so why should the two\n> photons "add up" to the same angular momentum they did?\n> Don\'t we need to include in the sum the effects on the\n> polarizer? Isn\'t it now the (as yet undetected) photon,\n> the working-bits of the polarizer, and the post-polarizer-\n> photon that sum to the correct total angular momentum?\n\nIt\'s the spins of the paired photons between emission and\npolarization that sum to conserve the angular momentum of\nthe atom that emitted them, and that\'s responsible for their\nentanglement. The light transmitted by the polarizers is no\nlonger entangled.\n\nIt\'s the "sameness" of polarization via emission that\'s\nbeing measured (filtered through the separated polarizers).\n\nThis is why LHV formulations (such as Bell\'s) where Lambda\nis the "angle" of polarization of the photons following\nemission and prior to polarization/detection don\'t work --\nthat is, they produce inequalities that will be experimentally\nviolated.\n\nThe angle of polarization of paired photons via emission is\nirrelevant wrt determining *coincidental* detection. It\'s only\nthe sameness of polarization of paired photons via emission\nthat matters in the combined context.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>grelbr@hotmail.com (grelbr) wrote in message news:<1a325379.0406300628.6d138b4@posting.google.com>...
> I want to make it clear that I'm *not* pushing any alternate
> theories here. I simply don't get it and would appreciate
> some hints. I'm not denying Aspect's experiments, or Bell's
> analysis or anything. I'm begging for help.
>
> As the subject says, I don't understand the EPR paradox.
> And so, I'm pretty much stumbling when it comes to Bell's
> theorm and the Aspect experiment and so on.
>
> My problem is this. Let's take the Aspect expt. to start.
> The idea is, there is a pair of photons, each circularly
> polarized, and traveling roughly 180 degrees from eachother.
> They are supposed to be in a definite total angular momentum,
> so as to agree with the fact that the single atom that
> emitted both has indeed finished up with the same angular
> momentum as it started.
>
> The explanation goes, if the polarizer on one side detects
> a photon as vertical, then a vertical polarizer on the other
> side *must* detect the other photon as vertical.
>
> Ok, it's that "must" that stumps me. Why "must?" As near
> as I can tell, you've got a circularly polarized photon,
> it has an amplitude to be detected as vertical by a
> polarizer. The photon that goes through the polarizer
> is not in the same state as it was before. Now it is
> linearly polarized, oriented vertical.
The light (opposite moving photons) emitted by a single
atom's electron decay process (via the laser excitation
of atomic calcium cascades in Aspect) is polarized
identically. The photons are "correlated in polarization"
via the emission process.
If the polarizers are oriented at the same angle, then
if the polarizer on one side transmits enough light (ie.,
a photon's worth) during a given coincidence window to
register a detection, then the polarizer on the other
side will (in the ideal) also transmit enough light
during that coincidence window to register a detection.
>
> So what I don't get is, where in QM does it say the other
> photon *must* now be in a linear vertical state? Its partner
> is not in the same state any more, so why should the two
> photons "add up" to the same angular momentum they did?
> Don't we need to include in the sum the effects on the
> polarizer? Isn't it now the (as yet undetected) photon,
> the working-bits of the polarizer, and the post-polarizer-
> photon that sum to the correct total angular momentum?
It's the spins of the paired photons between emission and
polarization that sum to conserve the angular momentum of
the atom that emitted them, and that's responsible for their
entanglement. The light transmitted by the polarizers is no
longer entangled.
It's the "sameness" of polarization via emission that's
being measured (filtered through the separated polarizers).
This is why LHV formulations (such as Bell's) where \Lambda
is the "angle" of polarization of the photons following
emission and prior to polarization/detection don't work --
that is, they produce inequalities that will be experimentally
violated.
The angle of polarization of paired photons via emission is
irrelevant wrt determining *coincidental* detection. It's only
the sameness of polarization of paired photons via emission
that matters in the combined context.
<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"Oz":\n> So it would be valid for a naive to consider \'them\'\n> as a single particle? Can I now consider what might\n> happen when a measurement of one is considered?\n\nThis (the bi-photon issue) is what Sir Karl Raimund\nPopper asked [\'Zur Kritik der Ungenauigkeitsrelationen\',\nin \'Die Naturwissenschaften\', 22, 807-808,(1934)]\nshortly before EPR paper. In this paper Popper\ninvented an interesting gedanken experiment, involving\ntwo entangled particles (or, say, a bi-particle).\n\nEinstein did not think (1934) that Popper\'s gedanken\nexperiment could be carried out, since to predict\nposition and momentum of the A-entangled-particle,\nboth time and energy of the B-entangled-particle have\nto be measured simultaneously, which appeared to be\nimpossible (a sort of Bohrian line of reasoning, contra\nEPR!).\n\nAccording to Nathan Rosen (the \'R\' in EPR) it might\nhave been possible that Popper\'s gedanken experiment\ninfluenced Einstein and EPR. According to Max Jammer\n(and Popper himself) Popper\'s gedanken experiment is\nan \'overdetermined\' EPR argument.\n\nKim and Shih, at last, performed the experiment\nhttp://www.arxiv.org/abs/quant-ph/9905039 ,\nand Asher Peres wrote something else ...\nhttp://www.arxiv.org/abs/quant-ph/9910078\n\nRegards,\ns.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Oz":
> So it would be valid for a naive to consider 'them'
> as a single particle? Can I now consider what might
> happen when a measurement of one is considered?
This (the bi-photon issue) is what Sir Karl Raimund
Popper asked ['Zur Kritik der Ungenauigkeitsrelationen',
in 'Die Naturwissenschaften', 22, 807-808,(1934)]
shortly before EPR paper. In this paper Popper
invented an interesting gedanken experiment, involving
two entangled particles (or, say, a bi-particle).
Einstein did not think (1934) that Popper's gedanken
experiment could be carried out, since to predict
position and momentum of the A-entangled-particle,
both time and energy of the B-entangled-particle have
to be measured simultaneously, which appeared to be
impossible (a sort of Bohrian line of reasoning, contra
EPR!).
According to Nathan Rosen (the 'R' in EPR) it might
have been possible that Popper's gedanken experiment
influenced Einstein and EPR. According to Max Jammer
(and Popper himself) Popper's gedanken experiment is
an 'overdetermined' EPR argument.
Kim and Shih, at last, performed the experiment
http://www.arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/9905039 ,
and Asher Peres wrote something else ...
http://www.arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/9910078
Regards,
s.
<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>\nTom Trotter <tom129@juno.com> writes\n\n>It\'s the "sameness" of polarization via emission that\'s\n>being measured (filtered through the separated polarizers).\n>\n>This is why LHV formulations (such as Bell\'s) where Lambda\n>is the "angle" of polarization of the photons following\n>emission and prior to polarization/detection don\'t work --\n>that is, they produce inequalities that will be experimentally\n>violated.\n\nOK. You are getting near to explaining bells inequalities, which nobody\nhas done here (simply) before.\n\nAre you saying that bell assumed two particles leaving with a set angle\nlambda. That is one at lambda+pi/2 and one lambda-pi/2?\n\n>From this he derived the appropriate statistics,\nwhich turned out *not* to agree with experiment?\n\n>The angle of polarization of paired photons via emission is\n>irrelevant wrt determining *coincidental* detection. It\'s only\n>the sameness of polarization of paired photons via emission\n>that matters in the combined context.\n\nWhat experiment showed was that if one was up, the other must be down.\n\nJust out of interest I imagine this has also been done for entangled\nelectrons, to give the same result? Nuclear decay, perhaps?\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com (whitelist check on first posting)<<\nozacoohdb@despammed.com still functions.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Tom Trotter <tom129@juno.com> writes
>It's the "sameness" of polarization via emission that's
>being measured (filtered through the separated polarizers).
>
>This is why LHV formulations (such as Bell's) where \Lambda
>is the "angle" of polarization of the photons following
>emission and prior to polarization/detection don't work --
>that is, they produce inequalities that will be experimentally
>violated.
OK. You are getting near to explaining bells inequalities, which nobody
has done here (simply) before.
Are you saying that bell assumed two particles leaving with a set angle
\lambda. That is one at \lambda+\pi/2 and one \lambda-\pi/2?
>From this he derived the appropriate statistics,
which turned out *not* to agree with experiment?
>The angle of polarization of paired photons via emission is
>irrelevant wrt determining *coincidental* detection. It's only
>the sameness of polarization of paired photons via emission
>that matters in the combined context.
What experiment showed was that if one was up, the other must be down.
Just out of interest I imagine this has also been done for entangled
electrons, to give the same result? Nuclear decay, perhaps?
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com (whitelist check on first posting)<<
ozacoohdb@despammed.com still functions.
<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>\nFrank Hellmann <Certhas@gmail.com> writes\n\n>>Oz\n>> So it would be valid for a naive to consider \'them\' as a single\n>> particle?\n>>\n>It\'s a good question which I personally can not anwser completely\n>satisfactory since I\'m just learning myself.\n>\n>Single particle states are defined to be states that transform under\n>certain representations of the Lorentz Group (Gallileo Group).\n\nI would imagine this not to be so of a \'widely separated\' entangled\npair. This means that in this context my concept of \'single\' is not that\nused in QM. That\'s fine.\n\n>In other words (using Gallileo group): This wave function we are\n>talking about here lives in the tensor product of the Hilbert space of\n>functions on 3 Dimensional Euclidean geometry.\n>H(x)H\n>If it were seperable it would live on\n>H(+)H\n\nHang on though. Haven\'t you just implied its \'not separable\' since it\ndoesn\'t live on H(+)H? That is, its neither \'single\' nor \'double\'?\n\nOr, put another way the pair is neither (using the normal definitions) a\nsingle nor a double particle? So, one can say its not a double particle,\neven if its not a single particle? Does this make me half right?\n\n>A rotation acts as Rv on v element H\n>Then it acts as R(x)R on v element H(x)H\n>Thus you can tell what a single particle state is by considering it\'s\n>transformation properties under Gallileo.\n\nThank you for your very clear illustrations. I\'m very much clearer about\nthe whole thing (which doesn\'t mean I really understand it of course).\n\nNow I imagine that I could pick a special basis of rotations R, such\nthat on some axes it looks like one/two single particles but in others\nit does not. I am doing this visually, so plenty of scope for error. I\nguess that rotations with an axis along the centreline of the \'two\nparticles\' look like single particles, whilst the others do not. That\'s\nprobably very unclear. Perhaps I should try and ape your kets in the\nfull and certain knowledge that I will have all the key details wrong,\njust try to look at what I am trying to say rather than what I am\nactually saying!\n\n(RxR HxH) ->\n(R_1xR_1 H_1xH_1) + (R_2xR_2 H_2xH_2) + (R_3 H_3) +(R_3 H_3)\n\nThat is on axes perpendicular to the axis joining the \'two particle\npaths\' you see *both* an up and a down rotated, but on the other axes\nyou see a single particle rotated. That is the particle is in some sense\nboth single and double.\n\nOf course it is totally beyond my capability to show this is so.\n\n>At the end of the day the mathematical structure is what is important\n>if you find a different way to look at it with two spaces and a single\n>particle it\'s just as well but might not be particularly usefull.\n\nConceptually it makes a big difference. One can imagine a particle\ncommunicating (or appearing to) \'internally\' at ftl, using a variety of\nplausible arguments. I am uncomfortable about two separate particles\ndoing so.\n\n>It will give the same predictions.\n\nI sincerely hope so, else it would be wrong!\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\n\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Frank Hellmann <Certhas@gmail.com> writes
>>Oz
>> So it would be valid for a naive to consider 'them' as a single
>> particle?
>>
>It's a good question which I personally can not anwser completely
>satisfactory since I'm just learning myself.
>
>Single particle states are defined to be states that transform under
>certain representations of the Lorentz Group (Gallileo Group).
I would imagine this not to be so of a 'widely separated' entangled
pair. This means that in this context my concept of 'single' is not that
used in QM. That's fine.
>In other words (using Gallileo group): This wave function we are
>talking about here lives in the tensor product of the Hilbert space of
>functions on 3 Dimensional Euclidean geometry.
>H(x)H
>If it were seperable it would live on
>H(+)H
Hang on though. Haven't you just implied its 'not separable' since it
doesn't live on H(+)H? That is, its neither 'single' nor 'double'?
Or, put another way the pair is neither (using the normal definitions) a
single nor a double particle? So, one can say its not a double particle,
even if its not a single particle? Does this make me half right?
>A rotation acts as Rv on v element H
>Then it acts as R(x)R on v element H(x)H
>Thus you can tell what a single particle state is by considering it's
>transformation properties under Gallileo.
Thank you for your very clear illustrations. I'm very much clearer about
the whole thing (which doesn't mean I really understand it of course).
Now I imagine that I could pick a special basis of rotations R, such
that on some axes it looks like one/two single particles but in others
it does not. I am doing this visually, so plenty of scope for error. I
guess that rotations with an axis along the centreline of the 'two
particles' look like single particles, whilst the others do not. That's
probably very unclear. Perhaps I should try and ape your kets in the
full and certain knowledge that I will have all the key details wrong,
just try to look at what I am trying to say rather than what I am
actually saying!
(RxR HxH) ->
(R_{1xR_1} H_{1xH_1}) + (R_{2xR_2} H_{2xH_2}) + (R_3 H_3) +(R_3 H_3)
That is on axes perpendicular to the axis joining the 'two particle
paths' you see *both* an up and a down rotated, but on the other axes
you see a single particle rotated. That is the particle is in some sense
both single and double.
Of course it is totally beyond my capability to show this is so.
>At the end of the day the mathematical structure is what is important
>if you find a different way to look at it with two spaces and a single
>particle it's just as well but might not be particularly usefull.
Conceptually it makes a big difference. One can imagine a particle
communicating (or appearing to) 'internally' at ftl, using a variety of
plausible arguments. I am uncomfortable about two separate particles
doing so.
>It will give the same predictions.
I sincerely hope so, else it would be wrong!
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
Tom Trotter
Jul15-04, 03:57 AM
<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>\nOz <oz@farmeroz.port995.com> wrote in message news:<8Kpg65ICw77AFwUX@farmeroz.port995.com>...\n> Tom Trotter <tom129@juno.com> writes\n>\n> >It\'s the "sameness" of polarization via emission that\'s\n> >being measured (filtered through the separated polarizers).\n> >\n> >This is why LHV formulations (such as Bell\'s) where Lambda\n> >is the "angle" of polarization of the photons following\n> >emission and prior to polarization/detection don\'t work --\n> >that is, they produce inequalities that will be experimentally\n> >violated.\n>\n> OK. You are getting near to explaining bells inequalities, which nobody\n> has done here (simply) before.\n\nThere\'s really nothing to explain wrt Bell inequalities.\nThey\'re just arithmetic relationships wrt quantities\nof groups of things.\n\n>\n> Are you saying that bell assumed two particles leaving with a set angle\n> lambda. That is one at lambda+pi/2 and one lambda-pi/2?\n\nIn terms of light and photons, Bell\'s lambda is the property\nof the light coming from the emitter, and incident on the\npolarizers, a (at A) and b (at B), that, if it were known,\nwould allow more accurate predictions of individual results.\n\nSo, lambda effectively refers to the *polarization* of the\noppositely directed beams of light (in, say, the\nAspect experiment) via emission.\n\n>\n> From this he derived the appropriate statistics,\n> which turned out *not* to agree with experiment?\n\nBell\'s theorem is an arithmetic relationship which\nmust be satisfied if the relationship between lambda\nand a and lambda and b is relevant to the determination\nof coincidental detection. Experiment shows that\nit isn\'t. (But this can be deduced without\nreferring to experiments.) It\'s the relationship\nbetween the emitted photons (that is, it\'s their\ncombined orientation, not their individual orientations)\nwrt the polarizers that matters in determining\ncoincidental detection. This *relationship* is\na global or nonlocal parameter pertaining to\npaired photons. It doesn\'t vary. The relationship\nis that paired photons are polarized identically.\n\nIn other words, the correlations in the combined\ncontext don\'t depend on the same thing that\nmore accurate predictions of results of individual\nmeasurements would depend on.\n\nThe things that are happening to produce individual\nresults are still happening in the combined context.\nThey just aren\'t relevent when talking about the\ncombined context.\n\n>\n> >The angle of polarization of paired photons via emission is\n> >irrelevant wrt determining *coincidental* detection. It\'s only\n> >the sameness of polarization of paired photons via emission\n> >that matters in the combined context.\n>\n> What experiment showed was that if one was up, the other must be down.\n\nExperiment has shown that paired photons\n(ie., photons emitted from the same atom)\nare polarized identically -- which is\nwhat the emission model pertaining to the\nway Aspect produced photon pairs says.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Oz <oz@farmeroz.port995.com> wrote in message news:<8Kpg65ICw77AFwUX@farmeroz.port995.com>...
> Tom Trotter <tom129@juno.com> writes
>
> >It's the "sameness" of polarization via emission that's
> >being measured (filtered through the separated polarizers).
> >
> >This is why LHV formulations (such as Bell's) where \Lambda
> >is the "angle" of polarization of the photons following
> >emission and prior to polarization/detection don't work --
> >that is, they produce inequalities that will be experimentally
> >violated.
>
> OK. You are getting near to explaining bells inequalities, which nobody
> has done here (simply) before.
There's really nothing to explain wrt Bell inequalities.
They're just arithmetic relationships wrt quantities
of groups of things.
>
> Are you saying that bell assumed two particles leaving with a set angle
> \lambda. That is one at \lambda+\pi/2 and one \lambda-\pi/2?
In terms of light and photons, Bell's \lambda is the property
of the light coming from the emitter, and incident on the
polarizers, a (at A) and b (at B), that, if it were known,
would allow more accurate predictions of individual results.
So, \lambda effectively refers to the *polarization* of the
oppositely directed beams of light (in, say, the
Aspect experiment) via emission.
>
> From this he derived the appropriate statistics,
> which turned out *not* to agree with experiment?
Bell's theorem is an arithmetic relationship which
must be satisfied if the relationship between \lambda
and a and \lambda and b is relevant to the determination
of coincidental detection. Experiment shows that
it isn't. (But this can be deduced without
referring to experiments.) It's the relationship
between the emitted photons (that is, it's their
combined orientation, not their individual orientations)
wrt the polarizers that matters in determining
coincidental detection. This *relationship* is
a global or nonlocal parameter pertaining to
paired photons. It doesn't vary. The relationship
is that paired photons are polarized identically.
In other words, the correlations in the combined
context don't depend on the same thing that
more accurate predictions of results of individual
measurements would depend on.
The things that are happening to produce individual
results are still happening in the combined context.
They just aren't relevent when talking about the
combined context.
>
> >The angle of polarization of paired photons via emission is
> >irrelevant wrt determining *coincidental* detection. It's only
> >the sameness of polarization of paired photons via emission
> >that matters in the combined context.
>
> What experiment showed was that if one was up, the other must be down.
Experiment has shown that paired photons
(ie., photons emitted from the same atom)
are polarized identically -- which is
what the emission model pertaining to the
way Aspect produced photon pairs says.
<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>\nOz <oz@farmeroz.port995.com> wrote in message news:<8Kpg65ICw77AFwUX@farmeroz.port995.com>...\n[snips]\n> What experiment showed was that if one was up, the other must be down.\n\nWell, actually they showed quite a bit more than that. They showed\nthat the angular dependance, at any angle, of the rate of coincidence\nis just what QM predicts. At least within the experimental error\nbars.\n\nIn other words, if you have a polarizer on the left that is vertical,\nthen a polarizer on the right that is at some angle theta to the\nvertical, then the coincident detection rate is a function of theta.\nThe measured behaviour of this function is as predicted by QM.\nThe preprint by Aspect I mentioned up thread shows this function.\n\nFor photons, you don\'t really get up or down, but vertical\nor horizontal or circular or like. That is, if a photon is\nlinearly polarized, then it can be detected to be up-and-down\npolarized, or left-and-right, or some angle in between.\n\n> Just out of interest I imagine this has also been done for entangled\n> electrons, to give the same result? Nuclear decay, perhaps?\n\nPeople have done some experiments with other decays. I saw one\nin the arxiv about production of quarks and subsequent decay\nof a resonance. As expected, it followed QM and violated\nBell\'s inequality for certain ranges. I could not really\nfollow the paper in any detail though, other than the conclusion\nthat they did observe a violation of Bell\'s inequality.\n\nThis type of experiment presents more challenges for charged particles.\nDetection equipment is more cumbersome (Stern Gerlach type equipment),\nyou need to have vacuum to allow the electrons (or whatever) to move,\ndecays producing electron pairs are higher energy, and so on. With\nphotons, you can much more easily produce the test photons, you can\nlet the photons move through nearly any transparent material (air,\nglass, etc.), poloarizers and detectors are easy to obtain, easy to\nconfigure, easy to test. ("Easy" in the relative sense.) And you\ndon\'t have to worry about energies that involve ionizing radiation,\nso it\'s easier to convince your institution let you do the experiment.\ngrelbr\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Oz <oz@farmeroz.port995.com> wrote in message news:<8Kpg65ICw77AFwUX@farmeroz.port995.com>...
[snips]
> What experiment showed was that if one was up, the other must be down.
Well, actually they showed quite a bit more than that. They showed
that the angular dependance, at any angle, of the rate of coincidence
is just what QM predicts. At least within the experimental error
bars.
In other words, if you have a polarizer on the left that is vertical,
then a polarizer on the right that is at some angle \theta to the
vertical, then the coincident detection rate is a function of \theta.
The measured behaviour of this function is as predicted by QM.
The preprint by Aspect I mentioned up thread shows this function.
For photons, you don't really get up or down, but vertical
or horizontal or circular or like. That is, if a photon is
linearly polarized, then it can be detected to be up-and-down
polarized, or left-and-right, or some angle in between.
> Just out of interest I imagine this has also been done for entangled
> electrons, to give the same result? Nuclear decay, perhaps?
People have done some experiments with other decays. I saw one
in the arxiv about production of quarks and subsequent decay
of a resonance. As expected, it followed QM and violated
Bell's inequality for certain ranges. I could not really
follow the paper in any detail though, other than the conclusion
that they did observe a violation of Bell's inequality.
This type of experiment presents more challenges for charged particles.
Detection equipment is more cumbersome (Stern Gerlach type equipment),
you need to have vacuum to allow the electrons (or whatever) to move,
decays producing electron pairs are higher energy, and so on. With
photons, you can much more easily produce the test photons, you can
let the photons move through nearly any transparent material (air,
glass, etc.), poloarizers and detectors are easy to obtain, easy to
configure, easy to test. ("Easy" in the relative sense.) And you
don't have to worry about energies that involve ionizing radiation,
so it's easier to convince your institution let you do the experiment.
grelbr
<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>\ngrelbr <grelbr@hotmail.com> writes\n>\n>Oz <oz@farmeroz.port995.com> wrote in message news:<8Kpg65ICw77AFwUX@farmeroz.po\n>rt995.com>... \n>[snips]\n>> What experiment showed was that if one was up, the other must be down.\n>\n>Well, actually they showed quite a bit more than that. They showed\n>that the angular dependance, at any angle, of the rate of coincidence\n>is just what QM predicts. At least within the experimental error\n>bars.\n>\n>In other words, if you have a polarizer on the left that is vertical,\n>then a polarizer on the right that is at some angle theta to the\n>vertical, then the coincident detection rate is a function of theta.\n>The measured behaviour of this function is as predicted by QM.\n>The preprint by Aspect I mentioned up thread shows this function.\n\nHmm. I am intrigued. How would one work this out? Lets think.\nI haven\'t done this sort of thing for years, no, decades.\n\nIf particle one arrived at the vertical polariser (A) and passed through\nthen we could say the probability of it getting through for an incident\nangle of L(ambda) would be sin(L) (=l) (from a very *very* old memory).\nAt polariser B, set at some angle theta (T) to A, it would be hmm, let\nme think, sin(T+pi/2+L) (=t)?\nHmm, yes, that feels about right. So the probability of getting two\ndetections would be sin(L)sin(T+L+pi/2), and similarly for one at A and\nnone at B, and vice versa (and no detections).\nHmmm. I\'m not at all sure that sums to unity, better check.\nlt + l(1-t) + t(1-l) + (1-l)(1-t) = 1\n\nOh, it does, so perhaps I\'m right.\nMore likely I have exposed a terrible and embarrassing ignorance.\n\nCan we use this to give a simple example of bells inequality. For\nexample perhaps the above is NOT the correct way to model it. My\nassumption of an \'incoming angle of L\', may well be suspect. I\'m not\nvery happy about it myself. It doesn\'t feel quite right because its\neffectively assuming two (separate) particles leaving in antiphase.\n\nI would ideally want to put the particles through some more polarisers\nbecause I think I could separate out a \'double-particle\' from two single\nones that way. For two single particles, sent through a series of\npolarisers, I ought to be able to get their polarisation the same, but I\ncould *never* do that for an entangled pair that would always end up in\nantiphase.\n\n>For photons, you don\'t really get up or down, but vertical\n>or horizontal or circular or like.\n\nOf course you are right.\n\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>grelbr <grelbr@hotmail.com> writes
>
>Oz <oz@farmeroz.port995.com> wrote in message news:<8Kpg65ICw77AFwUX@farmeroz.po
>rt995.com>...
>[snips]
>> What experiment showed was that if one was up, the other must be down.
>
>Well, actually they showed quite a bit more than that. They showed
>that the angular dependance, at any angle, of the rate of coincidence
>is just what QM predicts. At least within the experimental error
>bars.
>
>In other words, if you have a polarizer on the left that is vertical,
>then a polarizer on the right that is at some angle \theta to the
>vertical, then the coincident detection rate is a function of \theta.
>The measured behaviour of this function is as predicted by QM.
>The preprint by Aspect I mentioned up thread shows this function.
Hmm. I am intrigued. How would one work this out? Lets think.
I haven't done this sort of thing for years, no, decades.
If particle one arrived at the vertical polariser (A) and passed through
then we could say the probability of it getting through for an incident
angle of L(ambda) would be sin(L) (=l) (from a very *very* old memory).
At polariser B, set at some angle \theta (T) to A, it would be hmm, let
me think, sin(T+\pi/2+L) (=t)?
Hmm, yes, that feels about right. So the probability of getting two
detections would be sin(L)sin(T+L+\pi/2), and similarly for one at A and
none at B, and vice versa (and no detections).
Hmmm. I'm not at all sure that sums to unity, better check.
lt + l(1-t) + t(1-l) + (1-l)(1-t) = 1
Oh, it does, so perhaps I'm right.
More likely I have exposed a terrible and embarrassing ignorance.
Can we use this to give a simple example of bells inequality. For
example perhaps the above is NOT the correct way to model it. My
assumption of an 'incoming angle of L', may well be suspect. I'm not
very happy about it myself. It doesn't feel quite right because its
effectively assuming two (separate) particles leaving in antiphase.
I would ideally want to put the particles through some more polarisers
because I think I could separate out a 'double-particle' from two single
ones that way. For two single particles, sent through a series of
polarisers, I ought to be able to get their polarisation the same, but I
could *never* do that for an entangled pair that would always end up in
antiphase.
>For photons, you don't really get up or down, but vertical
>or horizontal or circular or like.
Of course you are right.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
Tom Trotter
Jul15-04, 02:23 PM
<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\ngrelbr@hotmail.com (grelbr) wrote in message news:<1a325379.0407140959.5d3df304@posting.google. com>...\n> Oz <oz@farmeroz.port995.com> wrote in message news:<8Kpg65ICw77AFwUX@farmeroz.port995.com>...\n> [snips]\n> > What experiment showed was that if one was up, the other must be down.\n>\n> Well, actually they showed quite a bit more than that. They showed\n> that the angular dependance, at any angle, of the rate of coincidence\n> is just what QM predicts. At least within the experimental error\n> bars.\n>\n> In other words, if you have a polarizer on the left that is vertical,\n> then a polarizer on the right that is at some angle theta to the\n> vertical, then the coincident detection rate is a function of theta.\n\nI\'m not disagreeing with anything you\'ve said,\n(it seems like you understand EPR ok),\nbut there might be a clearer, way\nto phrase/illustrate some of the pertinent\nconsiderations.\n\nTheta is the angular difference between the\norientation of the polarizers, a and b, as you\nlook through the transmission line from one\npolarizer to the other.\n\nNow consider one pair of photons, correlated\nin linear polarization via emission. (Because,\ncircular polarization can be expressed\nin terms of linear polarization).\n\nAs you look through the transmission line,\nwith a line of sight from one polarizer to the\nother, and with the polarizers in alignment\n(identically oriented), then this alignment\ncan be represented by a single line (ie., the\nline representing the orientation of a is\ncongruent with the line representing the\norientation of b when the polarizers are\naligned) bisecting the circle that represents\nthe transmission line.\n\nNow let another bisecting line represent\nthe identical plane of polarization of\na pair of opposite moving photons.\n\nIt\'s easy to see that as you rotate the\nline representing the plane of polarization\nof the light incident on the polarizers,\nthen the probability of detection (pertaining\nto the amplitude/intensity of the light\ntransmitted by the polarizers) will change\naccordingly, and this probability will\nbe the same at both ends when the polarizers\nare in alignment. So, when the polarizers\nare aligned, the probability of coincidental\ndetection is (in the ideal) 1.\n\nNow have the line representing the polarization\nof the light incident on the polarizers remain\nstationary, and rotate one of the polarizer\nsetting lines. As Theta increases, then\nthe rate of coincidental detection decreases,\nand vice versa, as a circular function of\nTheta -- and this relationship holds\nno matter what the polarization of the\nlight is, so long as photons emitted by the\nsame atom are correlated in polarization\nvia emission.\n\n> The measured behaviour of this function is as predicted by QM.\n> The preprint by Aspect I mentioned up thread shows this function.\n\nIt\'s also perhaps helpful to note that this is\nrelated to classical optics via polariscopes and Malus\' Law.\n\n>\n> For photons, you don\'t really get up or down, but vertical\n> or horizontal or circular or like. That is, if a photon is\n> linearly polarized, then it can be detected to be up-and-down\n> polarized, or left-and-right, or some angle in between.\n\nNote also that the photons that are detected (transmitted\nby the polarizers) are not the same photons that are coming\nfrom the emitter.\n\nWhat\'s being measured in the combined context isn\'t the\npolarization of individual photons at a or b, but rather\nthe relationship of paired photons wrt Theta. This\nis what makes the context a nonlocal one -- in the sense\nthat nonlocal does *not* connote instantaneous\ntransmission of anything.\n\nThis is sort of the archetypal quantum mechanical\nscenario -- ie., entanglement -- correlating the behavior\nof two entities that have a common source, or have\ninteracted, or are separate parts of a larger entity.\n\n>\n> > Just out of interest I imagine this has also been done for entangled\n> > electrons, to give the same result? Nuclear decay, perhaps?\n>\n> People have done some experiments with other decays. I saw one\n> in the arxiv about production of quarks and subsequent decay\n> of a resonance. As expected, it followed QM and violated\n> Bell\'s inequality for certain ranges.\n\n[... snip]\n\nThe violations of Bell inequalities are superfluous, since\nthe inequalities are based on formulations that include\na parameter, lambda, that\'s irrelevant wrt the combined\ncontext.\n\nSo, I\'m not sure -- do we understand EPR? Do we understand\nBell?\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>grelbr@hotmail.com (grelbr) wrote in message news:<1a325379.0407140959.5d3df304@posting.google.com>...
> Oz <oz@farmeroz.port995.com> wrote in message news:<8Kpg65ICw77AFwUX@farmeroz.port995.com>...
> [snips]
> > What experiment showed was that if one was up, the other must be down.
>
> Well, actually they showed quite a bit more than that. They showed
> that the angular dependance, at any angle, of the rate of coincidence
> is just what QM predicts. At least within the experimental error
> bars.
>
> In other words, if you have a polarizer on the left that is vertical,
> then a polarizer on the right that is at some angle \theta to the
> vertical, then the coincident detection rate is a function of \theta.
I'm not disagreeing with anything you've said,
(it seems like you understand EPR ok),
but there might be a clearer, way
to phrase/illustrate some of the pertinent
considerations.
\Theta is the angular difference between the
orientation of the polarizers, a and b, as you
look through the transmission line from one
polarizer to the other.
Now consider one pair of photons, correlated
in linear polarization via emission. (Because,
circular polarization can be expressed
in terms of linear polarization).
As you look through the transmission line,
with a line of sight from one polarizer to the
other, and with the polarizers in alignment
(identically oriented), then this alignment
can be represented by a single line (ie., the
line representing the orientation of a is
congruent with the line representing the
orientation of b when the polarizers are
aligned) bisecting the circle that represents
the transmission line.
Now let another bisecting line represent
the identical plane of polarization of
a pair of opposite moving photons.
It's easy to see that as you rotate the
line representing the plane of polarization
of the light incident on the polarizers,
then the probability of detection (pertaining
to the amplitude/intensity of the light
transmitted by the polarizers) will change
accordingly, and this probability will
be the same at both ends when the polarizers
are in alignment. So, when the polarizers
are aligned, the probability of coincidental
detection is (in the ideal) 1.
Now have the line representing the polarization
of the light incident on the polarizers remain
stationary, and rotate one of the polarizer
setting lines. As \Theta increases, then
the rate of coincidental detection decreases,
and vice versa, as a circular function of
\Theta -- and this relationship holds
no matter what the polarization of the
light is, so long as photons emitted by the
same atom are correlated in polarization
via emission.
> The measured behaviour of this function is as predicted by QM.
> The preprint by Aspect I mentioned up thread shows this function.
It's also perhaps helpful to note that this is
related to classical optics via polariscopes and Malus' Law.
>
> For photons, you don't really get up or down, but vertical
> or horizontal or circular or like. That is, if a photon is
> linearly polarized, then it can be detected to be up-and-down
> polarized, or left-and-right, or some angle in between.
Note also that the photons that are detected (transmitted
by the polarizers) are not the same photons that are coming
from the emitter.
What's being measured in the combined context isn't the
polarization of individual photons at a or b, but rather
the relationship of paired photons wrt \Theta. This
is what makes the context a nonlocal one -- in the sense
that nonlocal does *not* connote instantaneous
transmission of anything.
This is sort of the archetypal quantum mechanical
scenario -- ie., entanglement -- correlating the behavior
of two entities that have a common source, or have
interacted, or are separate parts of a larger entity.
>
> > Just out of interest I imagine this has also been done for entangled
> > electrons, to give the same result? Nuclear decay, perhaps?
>
> People have done some experiments with other decays. I saw one
> in the arxiv about production of quarks and subsequent decay
> of a resonance. As expected, it followed QM and violated
> Bell's inequality for certain ranges.
[... snip]
The violations of Bell inequalities are superfluous, since
the inequalities are based on formulations that include
a parameter, \lambda, that's irrelevant wrt the combined
context.
So, I'm not sure -- do we understand EPR? Do we understand
Bell?
Frank Hellmann
Jul15-04, 02:23 PM
<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> >In other words (using Gallileo group): This wave function we are\n> >talking about here lives in the tensor product of the Hilbert space of\n> >functions on 3 Dimensional Euclidean geometry.\n> >H(x)H\n> >If it were seperable it would live on\n> >H(+)H\n>\n> Hang on though. Haven\'t you just implied its \'not separable\' since it\n> doesn\'t live on H(+)H? That is, its neither \'single\' nor \'double\'?\n>\n\nYes it\'s double. Two particles live on the tensor product space, and\ntransform under the (reducible) tensor product of the irreducible\nrepresentation of the relevant group.\nTensor products is how you group degrees of freedom together in QM.\n\n> Or, put another way the pair is neither (using the normal definitions) a\n> single nor a double particle? So, one can say its not a double particle,\n> even if its not a single particle? Does this make me half right?\n>\n\nAs mentioned before you are somewhat on the right track since what is\nimportant here is that you need to consider them as one wavefunction,\nhowever this one wave function does properly represent two particles\nsince it transforms under R(x)R.\n\n(snip)\n> (RxR HxH) ->\n> (R_1xR_1 H_1xH_1) + (R_2xR_2 H_2xH_2) + (R_3 H_3) +(R_3 H_3)\n>\n\nHmmm....\n\nI can kind of see what you mean but it\'s not how tensor products work.\nFirst of all let\'s keep things simple, take the tensor product of two\nthree dimensional Hilbert spaces.\nThe basis of this 9 dimensional tensor space is:\n(x1,x2)(x1,y2)(x1,z2)(y1,x2)(y1,y2)(y1,z2)(z1 ,x2)(z1,y2)(z1,z2)\nThe basis of the H(+)H space is\n(x1)(x2)(y1)(y2)(z1)(z2)\n\nNow keep in mind that this is not your physical 3D space but a 3\ndimensional Hilbert space (we can\'t use 2D since 2+2=2*2, think a Spin\n1 particle with the states 1,0,-1).\n\nA General rotation that leaves the z axis invariant will leave only\n(z1,z2) invariant in the tensor space, but both (z1) and (z2) in the\nsum space.\nI\'m somewhat out of my experience here, it would take me a while to\nwritedown the actual formulae. And I don\'t quite see what you were\ndoing there except that you seemed to have a slightly skewed\ngeometrical intuition of the tensor product.\n\nThe problem is that we are really talking about infinite dimensional\nHilbert spaces of functions on low/three dimensional vector spaces.\nSomehow it is the case that the tensor product of two such hilbert\nspaces looks like a Hilbert space on a six dimensional vector space. I\ncan\'t see how this comes about. But it\'s what gives us the niceties of\nthinking about this stuff in terms of wavefunctions on the classical\nconfiguration space.\n\nIf somebody else want\'s to illuminate this, please feel free!!\n\n> >At the end of the day the mathematical structure is what is important\n> >if you find a different way to look at it with two spaces and a single\n> >particle it\'s just as well but might not be particularly usefull.\n>\n> Conceptually it makes a big difference. One can imagine a particle\n> communicating (or appearing to) \'internally\' at ftl, using a variety of\n> plausible arguments. I am uncomfortable about two separate particles\n> doing so.\n>\n\nWell a particle is a point really classically. Elementary particles\nare not supposed to have any internal structure at all.\nAnd if you are feeliung uncomfortable about it you\'re on the right\nway, remember:\n\n"Anyone who is not shocked by quantum theory has not understood it."\n-Niels Bohr\n;)\n\n---\nfrank\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>>In other words (using Gallileo group): This wave function we are
> >talking about here lives in the tensor product of the Hilbert space of
> >functions on 3 Dimensional Euclidean geometry.
> >H(x)H
> >If it were seperable it would live on
> >H(+)H
>
> Hang on though. Haven't you just implied its 'not separable' since it
> doesn't live on H(+)H? That is, its neither 'single' nor 'double'?
>
Yes it's double. Two particles live on the tensor product space, and
transform under the (reducible) tensor product of the irreducible
representation of the relevant group.
Tensor products is how you group degrees of freedom together in QM.
> Or, put another way the pair is neither (using the normal definitions) a
> single nor a double particle? So, one can say its not a double particle,
> even if its not a single particle? Does this make me half right?
>
As mentioned before you are somewhat on the right track since what is
important here is that you need to consider them as one wavefunction,
however this one wave function does properly represent two particles
since it transforms under R(x)R.
(snip)
> (RxR HxH) ->
> (R_{1xR_1} H_{1xH_1}) + (R_{2xR_2} H_{2xH_2}) + (R_3 H_3) +(R_3 H_3)
>
Hmmm....
I can kind of see what you mean but it's not how tensor products work.
First of all let's keep things simple, take the tensor product of two
three dimensional Hilbert spaces.
The basis of this 9 dimensional tensor space is:
(x1,x2)(x1,y2)(x1,z2)(y1,x2)(y1,y2)(y1,z2)(z1,x2)( z1,y2)(z1,z2)
The basis of the H(+)H space is
(x1)(x2)(y1)(y2)(z1)(z2)
Now keep in mind that this is not your physical 3D space but a 3
dimensional Hilbert space (we can't use 2D since 2+2=2*2, think a Spin
1 particle with the states 1,0,-1).
A General rotation that leaves the z axis invariant will leave only
(z1,z2) invariant in the tensor space, but both (z1) and (z2) in the
sum space.
I'm somewhat out of my experience here, it would take me a while to
writedown the actual formulae. And I don't quite see what you were
doing there except that you seemed to have a slightly skewed
geometrical intuition of the tensor product.
The problem is that we are really talking about infinite dimensional
Hilbert spaces of functions on low/three dimensional vector spaces.
Somehow it is the case that the tensor product of two such hilbert
spaces looks like a Hilbert space on a six dimensional vector space. I
can't see how this comes about. But it's what gives us the niceties of
thinking about this stuff in terms of wavefunctions on the classical
configuration space.
If somebody else want's to illuminate this, please feel free!!
> >At the end of the day the mathematical structure is what is important
> >if you find a different way to look at it with two spaces and a single
> >particle it's just as well but might not be particularly usefull.
>
> Conceptually it makes a big difference. One can imagine a particle
> communicating (or appearing to) 'internally' at ftl, using a variety of
> plausible arguments. I am uncomfortable about two separate particles
> doing so.
>
Well a particle is a point really classically. Elementary particles
are not supposed to have any internal structure at all.
And if you are feeliung uncomfortable about it you're on the right
way, remember:
"Anyone who is not shocked by quantum theory has not understood it."
-Niels Bohr
;)
---
frank
Tom Trotter
Jul16-04, 08:19 AM
<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\nOz <oz@farmeroz.port995.com> wrote in message news:<XEaKJ1BSI38AFwoi@farmeroz.port995.com>...\n> Frank Hellmann <Certhas@gmail.com> writes\n\n[... snip]\n\n> >At the end of the day the mathematical structure is what is important\n> >if you find a different way to look at it with two spaces and a single\n> >particle it\'s just as well but might not be particularly usefull.\n>\n> Conceptually it makes a big difference. One can imagine a particle\n> communicating (or appearing to) \'internally\' at ftl, using a variety of\n> plausible arguments. I am uncomfortable about two separate particles\n> doing so.\n\nThe paired photons produced by Aspect via\natomic calcium cascades are moving in opposite\ndirections, have different wavelengths, and\nopposite angular momenta. They\'re two different,\nand separate, \'particles\'.\n\nAnd, it\'s not necessary to be contemplating\nhow they can be \'communicating\' with each\nother. They aren\'t.\n\nThe correlations in the combined context\nare due to the photons of any given\npair being identically polarized via\nthe emission process.\n\n>From Greenstein and Zajonc (The Quantum\nChallange, 1997, p. 133):\n"... the spin angular momentum of a photon\nis related to its polarization state. The\nspin of a photon can only be aligned parallel\nor antiparallel to its direction of motion;\nparallel alignment corresponds to right-handed\ncircular polarization, antiparallel to left-\nhanded circular polarization. The two photons\nneed not be emitted in opposite directions,\nbut if we select those that are, conservation\nof angular momentum now requires that their\nhandedness be the same. Therefore, they must\nhave the same polarization: both right- or\nboth left-circularly polarized."\n\nNow, if you want to make a local hidden\nvariable theory work wrt the combined\ncontext, then, as Bell noted, you\'ll need\nsome sort of mechanism whereby the two\nends of the experimental setup can\ninstantaneously communicate. But, that\nwould be a silly construction, since it\'s\nalready been shown that lambda (the\npolarization of the photons) is irrelevant\nto the determination of coincidental\ndetection.\n\nIn the individual measurement context,\nthe emission-produced *polarization* of\na photon is (along with the orientation\nof the polarizer that it is interacting\nwith) the determining factor.\n\nIn the combined measurement context, the\nemission-produced *relationship* between\npaired photons is (along with the combined\norientations of the polarizers) the\ndetermining factor.\n\nIn the combined context, since the\n*relationship* between paired photons\ndoesn\'t vary from pair to pair (only\nthe polarization does), the only variable\nleft to consider in determining rates\nof coincidental detection is Theta, the\nangular difference in polarizer settings.\n\nDoes any of this make sense, or do you\nthink we should continue to talk about\nftl or instantaneous communication between\nparticles or filters and/or detectors in\nEPRBell experiments?\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Oz <oz@farmeroz.port995.com> wrote in message news:<XEaKJ1BSI38AFwoi@farmeroz.port995.com>...
> Frank Hellmann <Certhas@gmail.com> writes
[... snip]
> >At the end of the day the mathematical structure is what is important
> >if you find a different way to look at it with two spaces and a single
> >particle it's just as well but might not be particularly usefull.
>
> Conceptually it makes a big difference. One can imagine a particle
> communicating (or appearing to) 'internally' at ftl, using a variety of
> plausible arguments. I am uncomfortable about two separate particles
> doing so.
The paired photons produced by Aspect via
atomic calcium cascades are moving in opposite
directions, have different wavelengths, and
opposite angular momenta. They're two different,
and separate, 'particles'.
And, it's not necessary to be contemplating
how they can be 'communicating' with each
other. They aren't.
The correlations in the combined context
are due to the photons of any given
pair being identically polarized via
the emission process.
>From Greenstein and Zajonc (The Quantum
Challange, 1997, p. 133):
"... the spin angular momentum of a photon
is related to its polarization state. The
spin of a photon can only be aligned parallel
or antiparallel to its direction of motion;
parallel alignment corresponds to right-handed
circular polarization, antiparallel to left-
handed circular polarization. The two photons
need not be emitted in opposite directions,
but if we select those that are, conservation
of angular momentum now requires that their
handedness be the same. Therefore, they must
have the same polarization: both right- or
both left-circularly polarized."
Now, if you want to make a local hidden
variable theory work wrt the combined
context, then, as Bell noted, you'll need
some sort of mechanism whereby the two
ends of the experimental setup can
instantaneously communicate. But, that
would be a silly construction, since it's
already been shown that \lambda (the
polarization of the photons) is irrelevant
to the determination of coincidental
detection.
In the individual measurement context,
the emission-produced *polarization* of
a photon is (along with the orientation
of the polarizer that it is interacting
with) the determining factor.
In the combined measurement context, the
emission-produced *relationship* between
paired photons is (along with the combined
orientations of the polarizers) the
determining factor.
In the combined context, since the
*relationship* between paired photons
doesn't vary from pair to pair (only
the polarization does), the only variable
left to consider in determining rates
of coincidental detection is \Theta, the
angular difference in polarizer settings.
Does any of this make sense, or do you
think we should continue to talk about
ftl or instantaneous communication between
particles or filters and/or detectors in
EPRBell experiments?
<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\nTom Trotter <tom129@juno.com> writes\n>\n>Oz <oz@farmeroz.port995.com> wrote in message news:<8Kpg65ICw77AFwUX@farmeroz.p\n>o\n>rt995.com> ...\n>> Tom Trotter <tom129@juno.com> writes\n>>\n>> >It\'s the "sameness" of polarization via emission that\'s\n>> >being measured (filtered through the separated polarizers).\n>> >\n>> >This is why LHV formulations (such as Bell\'s) where Lambda\n>> >is the "angle" of polarization of the photons following\n>> >emission and prior to polarization/detection don\'t work --\n>> >that is, they produce inequalities that will be experimentally\n>> >violated.\n>>\n>> OK. You are getting near to explaining bells inequalities, which nobody\n>> has done here (simply) before.\n>\n>There\'s really nothing to explain wrt Bell inequalities.\n>They\'re just arithmetic relationships wrt quantities\n>of groups of things.\n\n<sigh>\n\nBut which things and what does experiment show under what circumstances?\nPerhaps I should say \'what effect does the experimental results that\ntest bells inequalities imply\'.\n\nSomething to do with \'hidden variables\', but that\'s too broad a brush to\ngain any insight.\n\n>> Are you saying that bell assumed two particles leaving with a set angle\n>> lambda. That is one at lambda+pi/2 and one lambda-pi/2?\n>\n>In terms of light and photons, Bell\'s lambda is the property\n>of the light coming from the emitter, and incident on the\n>polarizers, a (at A) and b (at B), that, if it were known,\n>would allow more accurate predictions of individual results.\n\nRight. So in this example bell assumed that he did (in theory) know\nlambda and found this did NOT agree with experiment?\n\n>So, lambda effectively refers to the *polarization* of the\n>oppositely directed beams of light (in, say, the\n>Aspect experiment) via emission.\n\nSo the assumption (falsely made) was that each particle left with a set\nlambda?\n\n>> From this he derived the appropriate statistics,\n>> which turned out *not* to agree with experiment?\n>\n>Bell\'s theorem is an arithmetic relationship which\n>must be satisfied if the relationship between lambda\n>and a and lambda and b is relevant to the determination\n>of coincidental detection.\n\nIs there such a thing as \'coincidental detection\', given the many frames\nobservers can be in?\n\n>Experiment shows that\n>it isn\'t. (But this can be deduced without\n>referring to experiments.) It\'s the relationship\n>between the emitted photons (that is, it\'s their\n>combined orientation, not their individual orientations)\n>wrt the polarizers that matters in determining\n>coincidental detection.\n\nOK. That\'s how I always read it.\n\n>This *relationship* is\n>a global or nonlocal parameter pertaining to\n>paired photons. It doesn\'t vary. The relationship\n>is that paired photons are polarized identically.\n>\n>In other words, the correlations in the combined\n>context don\'t depend on the same thing that\n>more accurate predictions of results of individual\n>measurements would depend on.\n>\n>The things that are happening to produce individual\n>results are still happening in the combined context.\n>They just aren\'t relevent when talking about the\n>combined context.\n\nOk. So if we consider the pair as a single particle it must be\ninevitable that if (on \'decay\' - ie detection of one) one is detected,\nthen the other has defined characteristics.\n\nThat\'s it. Nothing else to it.\n\nSo what\'s wrong with the following argument:\n\n1) The particles are one particle until detected.\n2) Because they are separated (to the outside world) only one particle\nwill be detected at any point in global (flat space, right) spacetime.\n3) We cannot force the properties of the detected particle, just measure\nif its up or down.\n4) The waveform of the emitted (double) particle co-evolves. That is it\nconstantly varies its lambda, with \'one half\' being in antiphase with\nthe other. This must be enforced, it seems to me.\n5) We force a detection. We can only detect one particle of the\n\'combined pair\' so the very detection process must break the\nentanglement. Note that the detector interacts with the \'combined pair\'.\n\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Tom Trotter <tom129@juno.com> writes
>
>Oz <oz@farmeroz.port995.com> wrote in message news:<8Kpg65ICw77AFwUX@farmeroz.p
>o
>rt995.com>...
>> Tom Trotter <tom129@juno.com> writes
>>
>> >It's the "sameness" of polarization via emission that's
>> >being measured (filtered through the separated polarizers).
>> >
>> >This is why LHV formulations (such as Bell's) where \Lambda
>> >is the "angle" of polarization of the photons following
>> >emission and prior to polarization/detection don't work --
>> >that is, they produce inequalities that will be experimentally
>> >violated.
>>
>> OK. You are getting near to explaining bells inequalities, which nobody
>> has done here (simply) before.
>
>There's really nothing to explain wrt Bell inequalities.
>They're just arithmetic relationships wrt quantities
>of groups of things.
<sigh>
But which things and what does experiment show under what circumstances?
Perhaps I should say 'what effect does the experimental results that
test bells inequalities imply'.
Something to do with 'hidden variables', but that's too broad a brush to
gain any insight.
>> Are you saying that bell assumed two particles leaving with a set angle
>> \lambda. That is one at \lambda+\pi/2 and one \lambda-\pi/2?
>
>In terms of light and photons, Bell's \lambda is the property
>of the light coming from the emitter, and incident on the
>polarizers, a (at A) and b (at B), that, if it were known,
>would allow more accurate predictions of individual results.
Right. So in this example bell assumed that he did (in theory) know
\lambda and found this did NOT agree with experiment?
>So, \lambda effectively refers to the *polarization* of the
>oppositely directed beams of light (in, say, the
>Aspect experiment) via emission.
So the assumption (falsely made) was that each particle left with a set
\lambda?
>> From this he derived the appropriate statistics,
>> which turned out *not* to agree with experiment?
>
>Bell's theorem is an arithmetic relationship which
>must be satisfied if the relationship between \lambda
>and a and \lambda and b is relevant to the determination
>of coincidental detection.
Is there such a thing as 'coincidental detection', given the many frames
observers can be in?
>Experiment shows that
>it isn't. (But this can be deduced without
>referring to experiments.) It's the relationship
>between the emitted photons (that is, it's their
>combined orientation, not their individual orientations)
>wrt the polarizers that matters in determining
>coincidental detection.
OK. That's how I always read it.
>This *relationship* is
>a global or nonlocal parameter pertaining to
>paired photons. It doesn't vary. The relationship
>is that paired photons are polarized identically.
>
>In other words, the correlations in the combined
>context don't depend on the same thing that
>more accurate predictions of results of individual
>measurements would depend on.
>
>The things that are happening to produce individual
>results are still happening in the combined context.
>They just aren't relevent when talking about the
>combined context.
Ok. So if we consider the pair as a single particle it must be
inevitable that if (on 'decay' - ie detection of one) one is detected,
then the other has defined characteristics.
That's it. Nothing else to it.
So what's wrong with the following argument:
1) The particles are one particle until detected.
2) Because they are separated (to the outside world) only one particle
will be detected at any point in global (flat space, right) spacetime.
3) We cannot force the properties of the detected particle, just measure
if its up or down.
4) The waveform of the emitted (double) particle co-evolves. That is it
constantly varies its \lambda, with 'one half' being in antiphase with
the other. This must be enforced, it seems to me.
5) We force a detection. We can only detect one particle of the
'combined pair' so the very detection process must break the
entanglement. Note that the detector interacts with the 'combined pair'.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
Joe Rongen
Jul19-04, 03:08 AM
<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\nBRIGHT AND PURE SOURCE OF HIGH-FIDELITY ENTANGLED\nPHOTONS FOR QUANTUM COMPUTATION AND TELEPORTATION,\nJuly 15 Like virtuosos tuning their violins, researchers at the University\nof Illinois at Urbana-Champaign have tuned their instruments and harmonized\nthe production of entangled photons, pushing rates to more than 1 million\npairs per second. The brighter and purer entangled states could assist\nresearchers in applications involving quantum information processing -\nsuch as quantum computation, teleportation and cryptography and help\nscientists better understand the mysterious transition from quantum\nmechanics to classical physics.\nFull story at http://www.physorg.com/news398.html\n\n== End ======================================\n\nAmazingl y enough but now entangled photons are\nset up in a "high fidelity" mode... what will be next ?\n\n\n---\nOutgoing mail is certified Virus Free.\nChecked by AVG anti-virus system (http://www.grisoft.com).\nVersion: 6.0.720 / Virus Database: 476 - Release Date: 7/14/04\n\n\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>BRIGHT AND PURE SOURCE OF HIGH-FIDELITY ENTANGLED
PHOTONS FOR QUANTUM COMPUTATION AND TELEPORTATION,
July 15 Like virtuosos tuning their violins, researchers at the University
of Illinois at Urbana-Champaign have tuned their instruments and harmonized
the production of entangled photons, pushing rates to more than 1 million
pairs per second. The brighter and purer entangled states could assist
researchers in applications involving quantum information processing -
such as quantum computation, teleportation and cryptography and help
scientists better understand the mysterious transition from quantum
mechanics to classical physics.
Full story at http://www.physorg.com/news398.html
== End ======================================
Amazingly enough but now entangled photons are
set up in a "high fidelity" mode... what will be next ?
---
Outgoing mail is certified Virus Free.
Checked by AVG anti-virus system (http://www.grisoft.com).
Version: 6..720 / Virus Database: 476 - Release Date: 7/14/04
Tom Trotter
Jul19-04, 03:08 AM
<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\nOz <oz@farmeroz.port995.com> wrote in message news:<L1Rd1nA5A29AFww3@farmeroz.port995.com>...\n> Tom Trotter <tom129@juno.com> writes\n> >\n> >Oz <oz@farmeroz.port995.com> wrote in message news:<8Kpg65ICw77AFwUX@farmeroz.p\n> >o\n> >rt995.com>...\n> >> Tom Trotter <tom129@juno.com> writes\n> >>\n> >> >It\'s the "sameness" of polarization via emission that\'s\n> >> >being measured (filtered through the separated polarizers).\n> >> >\n> >> >This is why LHV formulations (such as Bell\'s) where Lambda\n> >> >is the "angle" of polarization of the photons following\n> >> >emission and prior to polarization/detection don\'t work --\n> >> >that is, they produce inequalities that will be experimentally\n> >> >violated.\n> >>\n> >> OK. You are getting near to explaining bells inequalities, which nobody\n> >> has done here (simply) before.\n> >\n> >There\'s really nothing to explain wrt Bell inequalities.\n> >They\'re just arithmetic relationships wrt quantities\n> >of groups of things.\n>\n> <sigh>\n>\n> But which things ...\n\nAny things. Let\'s say you have a number objects\nthat, among them, have three different, discernable\ncharacteristics, or properties, or parameters,\nA, B, and C.\n\nBell\'s inequality says that the number of objects\nthat have A but not B plus the number of objects\nthat have B but not C is greater than or equal\nto the number of objects that have A but not C.\n\n> ... and what does experiment show under what circumstances?\n> Perhaps I should say \'what effect does the experimental results that\n> test bells inequalities imply\'.\n\nThe experimental results support the qm formulation,\nand the emission model, which says that paired photons\nare entangled via the emission process\n\nA violation of a Bell inequality tells you that the\ninequality is based on a formulation (lhv) that isn\'t\napplicable to the experimental context.\n\nThe lhv formulation is inapplicable because the\nthing (lambda) that determines the results in individual\nmeasurements isn\'t what determines the results in\ncombined contexts. Lambda refers to the angle of\npolarization of the photons incident on the polarizers\nat A and B. This angle of polarization is irrelevant\nin the combined context. What is relevant is that\npaired photons be polarized identically.\n\n>\n> Something to do with \'hidden variables\', but that\'s\n> too broad a brush to gain any insight.\n>\n\nThe EPRBell tests reveal nothing about local hidden variables\nexcept that formulations including them aren\'t applicable\nto these experimental contexts.\n\nThe EPRBell tests don\'t reveal anything about \'reality\',\nor \'nonlocality\' (in the sense that A and B are communicating\nftl or instantaneously), or determinism vs. indeterminism, or\nwhether lhv theories are, in general, possible.\n\nCertainly, lhv formulations are *inapplicable* to certain\ncontexts.\n\n> >> Are you saying that bell assumed two particles leaving with a set angle\n> >> lambda. That is one at lambda+pi/2 and one lambda-pi/2?\n> >\n> >In terms of light and photons, Bell\'s lambda is the property\n> >of the light coming from the emitter, and incident on the\n> >polarizers, a (at A) and b (at B), that, if it were known,\n> >would allow more accurate predictions of individual results.\n>\n> Right. So in this example bell assumed that he did (in theory) know\n> lambda and found this did NOT agree with experiment?\n>\n\nThe subtle but most relevant assumption associated\nwith the inclusion of the lambda term in the formulation\nand combining it with polarizer orientations at a and b,\nis that knowing the polarization of the photons of\na pair would allow for more accurate predictions of\nrates of coincidental detection, ie., that lambda is\nrelevant in the combined context.\n\nBut lambda has nothing to do with determining rates\nof coincidental detection.\n\nSo, violations of Bell inequalities don\'t tell you\nthat there\'s no lambda, but simply that the specific\npolarization of the photons is not the property\nof the photons that you need to know to accurately\npredict rates of coincidental detection.\n\nThe essential knowledge is that the photons\nof any given pair are polarized identically\nvia emission. Since this *relationship* doesn\'t\nvary from pair to pair, then, effectively,\nyou don\'t need to consider anything about\nthe photons in calculating expectation values\nfor rates of coincidental detection wrt\nvarying mutual polarizer orientations.\n\nYou only need to consider the angular difference\nof mutual polarizer settings.\n\n\n> >So, lambda effectively refers to the *polarization* of the\n> >oppositely directed beams of light (in, say, the\n> >Aspect experiment) via emission.\n>\n> So the assumption (falsely made) was that each particle left with a set\n> lambda?\n\nNo, the problematic assumption is that lambda has\nsomething to do with determining rates of\n*coincidental* detection.\n\n>\n> >> From this he derived the appropriate statistics,\n> >> which turned out *not* to agree with experiment?\n> >\n> >Bell\'s theorem is an arithmetic relationship which\n> >must be satisfied if the relationship between lambda\n> >and a and lambda and b is relevant to the determination\n> >of coincidental detection.\n>\n> Is there such a thing as \'coincidental detection\', given the many frames\n> observers can be in?\n\nYes, as I\'ve mentioned before, experimenters expend\ngreat effort in trying to ensure that they\'re dealing\nwith photons emitted from the same atom in their\ncoincidence counting hardware.\n\n>\n> >Experiment shows that\n> >it isn\'t. (But this can be deduced without\n> >referring to experiments.) It\'s the relationship\n> >between the emitted photons (that is, it\'s their\n> >combined orientation, not their individual orientations)\n> >wrt the polarizers that matters in determining\n> >coincidental detection.\n>\n> OK. That\'s how I always read it.\n>\n> >This *relationship* is\n> >a global or nonlocal parameter pertaining to\n> >paired photons. It doesn\'t vary. The relationship\n> >is that paired photons are polarized identically.\n> >\n> >In other words, the correlations in the combined\n> >context don\'t depend on the same thing that\n> >more accurate predictions of results of individual\n> >measurements would depend on.\n> >\n> >The things that are happening to produce individual\n> >results are still happening in the combined context.\n> >They just aren\'t relevent when talking about the\n> >combined context.\n>\n> Ok. So if we consider the pair as a single particle it must be\n> inevitable that if (on \'decay\' - ie detection of one) one is detected,\n> then the other has defined characteristics.\n\nI don\'t think it\'s a good approach to consider the pair\nas a single particle. Photon 1 and photon 2 of any given pair\nemitted by the same atom are distinctly separate photons.\nThey\'re of different wavelengths, travelling in different\ndirections, and not communicating in any way. They\'re\nentangled because they\'re identically polarized due to\ntheir common origins in the intermediate decay stages,\nback to the ground state, of the electrons of the atom\nfrom which they\'re emitted.\n\n>\n> That\'s it. Nothing else to it.\n>\n> So what\'s wrong with the following argument:\n>\n> 1) The particles are one particle until detected.\n\nNo, they\'re two, separate photons, entangled via an atomic\nemission process.\n\n> 2) Because they are separated (to the outside world) only one particle\n> will be detected at any point in global (flat space, right) spacetime.\n\nNo, sometimes both photons from the same emission\nprocess are detected.\n\n> 3) We cannot force the properties of the detected particle, just measure\n> if its up or down.\n\nAll you know is , in a detection/coincidence interval, whether\nA registered a detection or not, and whether B registered\na detection or not. The emission polarization of photons\nof a pair remains, effectively, unknown. But, because the\nphotons are polarized identically via emission, then you can\nsay something about the probability of coincidental detection\nif you know the orientation of the polarizers wrt each other.\n\n> 4) The waveform of the emitted (double) particle co-evolves. That is it\n> constantly varies its lambda, with \'one half\' being in antiphase with\n> the other. This must be enforced, it seems to me.\n\nI don\'t think this would be a good way of talking about\nit. I don\'t have any really firm opinions about it.\nMaybe lambda does vary between the emitter and the\npolarizer. But, for the purposes of making accurate\npredictions of rates of coincidental detection, it doesn\'t\nmatter. In any case, how would you go about finding\nout?\n\n> 5) We force a detection. We can only detect one particle of the\n> \'combined pair\' so the very detection process must break the\n> entanglement. Note that the detector interacts with the \'combined pair\'.\n\nThe detection process does break the entanglement, but sometimes\nboth photons of a pair are detected.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Oz <oz@farmeroz.port995.com> wrote in message news:<L1Rd1nA5A29AFww3@farmeroz.port995.com>...
> Tom Trotter <tom129@juno.com> writes
> >
> >Oz <oz@farmeroz.port995.com> wrote in message news:<8Kpg65ICw77AFwUX@farmeroz.p
> >o
> >rt995.com>...
> >> Tom Trotter <tom129@juno.com> writes
> >>
> >> >It's the "sameness" of polarization via emission that's
> >> >being measured (filtered through the separated polarizers).
> >> >
> >> >This is why LHV formulations (such as Bell's) where \Lambda
> >> >is the "angle" of polarization of the photons following
> >> >emission and prior to polarization/detection don't work --
> >> >that is, they produce inequalities that will be experimentally
> >> >violated.
> >>
> >> OK. You are getting near to explaining bells inequalities, which nobody
> >> has done here (simply) before.
> >
> >There's really nothing to explain wrt Bell inequalities.
> >They're just arithmetic relationships wrt quantities
> >of groups of things.
>
> <sigh>
>
> But which things ...
Any things. Let's say you have a number objects
that, among them, have three different, discernable
characteristics, or properties, or parameters,
A, B, and C.
Bell's inequality says that the number of objects
that have A but not B plus the number of objects
that have B but not C is greater than or equal
to the number of objects that have A but not C.
> ... and what does experiment show under what circumstances?
> Perhaps I should say 'what effect does the experimental results that
> test bells inequalities imply'.
The experimental results support the qm formulation,
and the emission model, which says that paired photons
are entangled via the emission process
A violation of a Bell inequality tells you that the
inequality is based on a formulation (lhv) that isn't
applicable to the experimental context.
The lhv formulation is inapplicable because the
thing (\lambda) that determines the results in individual
measurements isn't what determines the results in
combined contexts. \Lambda refers to the angle of
polarization of the photons incident on the polarizers
at A and B. This angle of polarization is irrelevant
in the combined context. What is relevant is that
paired photons be polarized identically.
>
> Something to do with 'hidden variables', but that's
> too broad a brush to gain any insight.
>
The EPRBell tests reveal nothing about local hidden variables
except that formulations including them aren't applicable
to these experimental contexts.
The EPRBell tests don't reveal anything about 'reality',
or 'nonlocality' (in the sense that A and B are communicating
ftl or instantaneously), or determinism vs. indeterminism, or
whether lhv theories are, in general, possible.
Certainly, lhv formulations are *inapplicable* to certain
contexts.
> >> Are you saying that bell assumed two particles leaving with a set angle
> >> \lambda. That is one at \lambda+\pi/2 and one \lambda-\pi/2?
> >
> >In terms of light and photons, Bell's \lambda is the property
> >of the light coming from the emitter, and incident on the
> >polarizers, a (at A) and b (at B), that, if it were known,
> >would allow more accurate predictions of individual results.
>
> Right. So in this example bell assumed that he did (in theory) know
> \lambda and found this did NOT agree with experiment?
>
The subtle but most relevant assumption associated
with the inclusion of the \lambda term in the formulation
and combining it with polarizer orientations at a and b,
is that knowing the polarization of the photons of
a pair would allow for more accurate predictions of
rates of coincidental detection, ie., that \lambda is
relevant in the combined context.
But \lambda has nothing to do with determining rates
of coincidental detection.
So, violations of Bell inequalities don't tell you
that there's no \lambda, but simply that the specific
polarization of the photons is not the property
of the photons that you need to know to accurately
predict rates of coincidental detection.
The essential knowledge is that the photons
of any given pair are polarized identically
via emission. Since this *relationship* doesn't
vary from pair to pair, then, effectively,
you don't need to consider anything about
the photons in calculating expectation values
for rates of coincidental detection wrt
varying mutual polarizer orientations.
You only need to consider the angular difference
of mutual polarizer settings.
> >So, \lambda effectively refers to the *polarization* of the
> >oppositely directed beams of light (in, say, the
> >Aspect experiment) via emission.
>
> So the assumption (falsely made) was that each particle left with a set
> \lambda?
No, the problematic assumption is that \lambda has
something to do with determining rates of
*coincidental* detection.
>
> >> From this he derived the appropriate statistics,
> >> which turned out *not* to agree with experiment?
> >
> >Bell's theorem is an arithmetic relationship which
> >must be satisfied if the relationship between \lambda
> >and a and \lambda and b is relevant to the determination
> >of coincidental detection.
>
> Is there such a thing as 'coincidental detection', given the many frames
> observers can be in?
Yes, as I've mentioned before, experimenters expend
great effort in trying to ensure that they're dealing
with photons emitted from the same atom in their
coincidence counting hardware.
>
> >Experiment shows that
> >it isn't. (But this can be deduced without
> >referring to experiments.) It's the relationship
> >between the emitted photons (that is, it's their
> >combined orientation, not their individual orientations)
> >wrt the polarizers that matters in determining
> >coincidental detection.
>
> OK. That's how I always read it.
>
> >This *relationship* is
> >a global or nonlocal parameter pertaining to
> >paired photons. It doesn't vary. The relationship
> >is that paired photons are polarized identically.
> >
> >In other words, the correlations in the combined
> >context don't depend on the same thing that
> >more accurate predictions of results of individual
> >measurements would depend on.
> >
> >The things that are happening to produce individual
> >results are still happening in the combined context.
> >They just aren't relevent when talking about the
> >combined context.
>
> Ok. So if we consider the pair as a single particle it must be
> inevitable that if (on 'decay' - ie detection of one) one is detected,
> then the other has defined characteristics.
I don't think it's a good approach to consider the pair
as a single particle. Photon 1 and photon 2 of any given pair
emitted by the same atom are distinctly separate photons.
They're of different wavelengths, travelling in different
directions, and not communicating in any way. They're
entangled because they're identically polarized due to
their common origins in the intermediate decay stages,
back to the ground state, of the electrons of the atom
from which they're emitted.
>
> That's it. Nothing else to it.
>
> So what's wrong with the following argument:
>
> 1) The particles are one particle until detected.
No, they're two, separate photons, entangled via an atomic
emission process.
> 2) Because they are separated (to the outside world) only one particle
> will be detected at any point in global (flat space, right) spacetime.
No, sometimes both photons from the same emission
process are detected.
> 3) We cannot force the properties of the detected particle, just measure
> if its up or down.
All you know is , in a detection/coincidence interval, whether
A registered a detection or not, and whether B registered
a detection or not. The emission polarization of photons
of a pair remains, effectively, unknown. But, because the
photons are polarized identically via emission, then you can
say something about the probability of coincidental detection
if you know the orientation of the polarizers wrt each other.
> 4) The waveform of the emitted (double) particle co-evolves. That is it
> constantly varies its \lambda, with 'one half' being in antiphase with
> the other. This must be enforced, it seems to me.
I don't think this would be a good way of talking about
it. I don't have any really firm opinions about it.
Maybe \lambda does vary between the emitter and the
polarizer. But, for the purposes of making accurate
predictions of rates of coincidental detection, it doesn't
matter. In any case, how would you go about finding
out?
> 5) We force a detection. We can only detect one particle of the
> 'combined pair' so the very detection process must break the
> entanglement. Note that the detector interacts with the 'combined pair'.
The detection process does break the entanglement, but sometimes
both photons of a pair are detected.
Bruce Bowen
Jul19-04, 03:08 AM
<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\ngrelbr@hotmail.com (grelbr) wrote in message news:<1a325379.0406300628.6d138b4@posting.google.c om>...\n>\n> As the subject says, I don\'t understand the EPR paradox.\n> And so, I\'m pretty much stumbling when it comes to Bell\'s\n> theorm and the Aspect experiment and so on.\n\n> The explanation goes, if the polarizer on one side detects\n> a photon as vertical, then a vertical polarizer on the other\n> side *must* detect the other photon as vertical.\n>\n> Ok, it\'s that "must" that stumps me. Why "must?" As near\n> as I can tell, you\'ve got a circularly polarized photon,\n> it has an amplitude to be detected as vertical by a\n> polarizer. The photon that goes through the polarizer\n> is not in the same state as it was before. Now it is\n> linearly polarized, oriented vertical.\n\n"Why \'must?\'"\n\nThe "must" you refer to is an empirical reality! In the same way\nthat "The speed of light in a vacuum is constant in all inertial\nreference frames." Our job is to come up with a theory that (at least\nmathematically if nothing else) models it correctly. There is no\nlogical way to model this reality other than to assume they are not\nindependent, but this assumption (non-local dependencies) violates (at\nleast the spirit of) GTR. This is the whole reason why it is\n"spooky", and not understood at a visceral level.\n\n-Bruce\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>grelbr@hotmail.com (grelbr) wrote in message news:<1a325379.0406300628.6d138b4@posting.google.com>...
>
> As the subject says, I don't understand the EPR paradox.
> And so, I'm pretty much stumbling when it comes to Bell's
> theorm and the Aspect experiment and so on.
> The explanation goes, if the polarizer on one side detects
> a photon as vertical, then a vertical polarizer on the other
> side *must* detect the other photon as vertical.
>
> Ok, it's that "must" that stumps me. Why "must?" As near
> as I can tell, you've got a circularly polarized photon,
> it has an amplitude to be detected as vertical by a
> polarizer. The photon that goes through the polarizer
> is not in the same state as it was before. Now it is
> linearly polarized, oriented vertical.
"Why 'must?'"
The "must" you refer to is an empirical reality! In the same way
that "The speed of light in a vacuum is constant in all inertial
reference frames." Our job is to come up with a theory that (at least
mathematically if nothing else) models it correctly. There is no
logical way to model this reality other than to assume they are not
independent, but this assumption (non-local dependencies) violates (at
least the spirit of) GTR. This is the whole reason why it is
"spooky", and not understood at a visceral level.
-Bruce
Joe Rongen
Jul19-04, 03:09 AM
<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"Oz" <oz@farmeroz.port995.com> wrote in message\nnews:L1Rd1nA5A29AFww3@farmeroz.port995.co m...\n\n[snip]\n\n> <sigh>\n>\n> But which things and what does experiment show under what circumstances?\n> Perhaps I should say \'what effect does the experimental results that\n> test bells inequalities imply\'.\n>\n> Something to do with \'hidden variables\', but that\'s too broad a brush to\n> gain any insight.\n\n>From the book "ENtanglement"\n"The greatest mystery in physics" (2002)\nAuthor Amir D. Aczel, ISBN 1-55192-540-4\n\nPage: 121: EPR say: "If without in any way disturbing a system,\nwe can predict with certainty (i.e., with probability equal to unity)\nthe value of a physical quantity, then there exist an element of\nphysical reality corresponding to this physical quantity"\n\nPage 152: What Bell showed was that even if all the premises\nof EPR were correct, with the consequence that QM would\nhave to be completed with hidden variables, no theory using -local-\nhidden variables (which, of course was what EPR desired) would\nagree with all of the statistical predictions of QM.\n\nPage 181: These hidden variables are like instruction sheets: and\nthe particles following the instructions, with no -direct- correlations\nbetween the particles, ensure that their behavior is correlated.\nIf the universe is -local- in its nature (that is, there is no possibility\nfor super-luminal communication or effect, i.e., the world as Einstein\nviewed it) then the information that is needed to complete the\nquantum theory must be conveyed through some pre-programmed\nhidden variables.\n\n[ Aspect\'s three experiments explained]\n\nPage 189: Aspect\'s third set of experiments was also successful\nand again locality and hidden-variables were defeated in favor of QM.\n\n.... it contained an immensely important dynamic component, which\nadded to the power of his entire set of positive results for QM and\nhelped establish non-local entanglement as a real phenomenon.\n====================\n\nRegards Joe - 17 July 2004\n\n--\nEvery blade of grass has its Angel that bends over it and whispers,\n"Grow, grow." The Talmud\n\n\n---\nOutgoing mail is certified Virus Free.\nChecked by AVG anti-virus system (http://www.grisoft.com).\nVersion: 6.0.720 / Virus Database: 476 - Release Date: 7/14/04\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Oz" <oz@farmeroz.port995.com> wrote in message
news:L1Rd1nA5A29AFww3@farmeroz.port995.com...
[snip]
> <sigh>
>
> But which things and what does experiment show under what circumstances?
> Perhaps I should say 'what effect does the experimental results that
> test bells inequalities imply'.
>
> Something to do with 'hidden variables', but that's too broad a brush to
> gain any insight.
>From the book "ENtanglement"
"The greatest mystery in physics" (2002)
Author Amir D. Aczel, ISBN 1-55192-540-4
Page: 121: EPR say: "If without in any way disturbing a system,
we can predict with certainty (i.e., with probability equal to unity)
the value of a physical quantity, then there exist an element of
physical reality corresponding to this physical quantity"
Page 152: What Bell showed was that even if all the premises
of EPR were correct, with the consequence that QM would
have to be completed with hidden variables, no theory using -local-
hidden variables (which, of course was what EPR desired) would
agree with all of the statistical predictions of QM.
Page 181: These hidden variables are like instruction sheets: and
the particles following the instructions, with no -direct- correlations
between the particles, ensure that their behavior is correlated.
If the universe is -local- in its nature (that is, there is no possibility
for super-luminal communication or effect, i.e., the world as Einstein
viewed it) then the information that is needed to complete the
quantum theory must be conveyed through some pre-programmed
hidden variables.
[ Aspect's three experiments explained]
Page 189: Aspect's third set of experiments was also successful
and again locality and hidden-variables were defeated in favor of QM.
.... it contained an immensely important dynamic component, which
added to the power of his entire set of positive results for QM and
helped establish non-local entanglement as a real phenomenon.
====================
Regards Joe - 17 July 2004
--
Every blade of grass has its Angel that bends over it and whispers,
"Grow, grow." The Talmud
---
Outgoing mail is certified Virus Free.
Checked by AVG anti-virus system (http://www.grisoft.com).
Version: 6..720 / Virus Database: 476 - Release Date: 7/14/04
Tom Trotter
Jul25-04, 08:16 AM
<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\nbrucebo@my-deja.com (Bruce Bowen) wrote in message news:<b824a8a0.0407161200.4ce6329d@posting.google. com>...\n> grelbr@hotmail.com (grelbr) wrote in message news:<1a325379.0406300628.6d138b4@posting.google.c om>...\n> >\n> > As the subject says, I don\'t understand the EPR paradox.\n> > And so, I\'m pretty much stumbling when it comes to Bell\'s\n> > theorm and the Aspect experiment and so on.\n>\n> > The explanation goes, if the polarizer on one side detects\n> > a photon as vertical, then a vertical polarizer on the other\n> > side *must* detect the other photon as vertical.\n> >\n> > Ok, it\'s that "must" that stumps me. Why "must?" As near\n> > as I can tell, you\'ve got a circularly polarized photon,\n> > it has an amplitude to be detected as vertical by a\n> > polarizer. The photon that goes through the polarizer\n> > is not in the same state as it was before. Now it is\n> > linearly polarized, oriented vertical.\n>\n> "Why \'must?\'"\n>\n> The "must" you refer to is an empirical reality! In the same way\n> that "The speed of light in a vacuum is constant in all inertial\n> reference frames." Our job is to come up with a theory that (at least\n> mathematically if nothing else) models it correctly. There is no\n> logical way to model this reality other than to assume they are not\n> independent, but this assumption (non-local dependencies) violates (at\n> least the spirit of) GTR. This is the whole reason why it is\n> "spooky", and not understood at a visceral level.\n\nI think your assessment might be a little misleading.\n\nThe data streams at A and B aren\'t independent in the observational\ncontext that analyzes a property they have in common. In other\nobservational contexts, including individual contexts, they\nare independent.\n\nCorrelated events separated by spacelike intervals (nonlocal dependencies)\ndo not violate standard physics (even in spirit). The nonlocal\ncorrelations do not indicate that the correlated events depend on\neach other. Rather, nonlocal correlations are revealed in observational\ncontexts that measure some non-varying relationship between the\nquanta that are interacting with the hardware to produce the observed correlations.\n\nWhat\'s happening in the nonlocal contexts isn\'t spooky. It can\nbe understood "at a visceral level", ie., in terms of classical\nanalogs.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>brucebo@my-deja.com (Bruce Bowen) wrote in message news:<b824a8a0.0407161200.4ce6329d@posting.google.com>...
> grelbr@hotmail.com (grelbr) wrote in message news:<1a325379.0406300628.6d138b4@posting.google.com>...
> >
> > As the subject says, I don't understand the EPR paradox.
> > And so, I'm pretty much stumbling when it comes to Bell's
> > theorm and the Aspect experiment and so on.
>
> > The explanation goes, if the polarizer on one side detects
> > a photon as vertical, then a vertical polarizer on the other
> > side *must* detect the other photon as vertical.
> >
> > Ok, it's that "must" that stumps me. Why "must?" As near
> > as I can tell, you've got a circularly polarized photon,
> > it has an amplitude to be detected as vertical by a
> > polarizer. The photon that goes through the polarizer
> > is not in the same state as it was before. Now it is
> > linearly polarized, oriented vertical.
>
> "Why 'must?'"
>
> The "must" you refer to is an empirical reality! In the same way
> that "The speed of light in a vacuum is constant in all inertial
> reference frames." Our job is to come up with a theory that (at least
> mathematically if nothing else) models it correctly. There is no
> logical way to model this reality other than to assume they are not
> independent, but this assumption (non-local dependencies) violates (at
> least the spirit of) GTR. This is the whole reason why it is
> "spooky", and not understood at a visceral level.
I think your assessment might be a little misleading.
The data streams at A and B aren't independent in the observational
context that analyzes a property they have in common. In other
observational contexts, including individual contexts, they
are independent.
Correlated events separated by spacelike intervals (nonlocal dependencies)
do not violate standard physics (even in spirit). The nonlocal
correlations do not indicate that the correlated events depend on
each other. Rather, nonlocal correlations are revealed in observational
contexts that measure some non-varying relationship between the
quanta that are interacting with the hardware to produce the observed correlations.
What's happening in the nonlocal contexts isn't spooky. It can
be understood "at a visceral level", ie., in terms of classical
analogs.
<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\nFrank Hellmann <Certhas@gmail.com> writes\n\n>I can kind of see what you mean but it\'s not how tensor products work.\n>First of all let\'s keep things simple, take the tensor product of two\n>three dimensional Hilbert spaces.\n>The basis of this 9 dimensional tensor space is:\n>(x1,x2)(x1,y2)(x1,z2)(y1,x2)(y1,y2)(y1,z2)(z 1,x2)(z1,y2)(z1,z2)\n>The basis of the H(+)H space is\n>(x1)(x2)(y1)(y2)(z1)(z2)\n\nRight.\nThat\'s what charles implied, but your explanation is utterly clear.\nOf course I now see why it has to be like that.\n\n>Now keep in mind that this is not your physical 3D space but a 3\n>dimensional Hilbert space (we can\'t use 2D since 2+2=2*2, think a Spin\n>1 particle with the states 1,0,-1).\n\nHilbert spaces keep getting bandied about but I\'ve never been very clear\nabout them. I read the 9D tensor product space as something along the\nlines of probability of finding particle 1 at x1 AND particle 2 at x2 (x\nhere = (x,y,z)). That makes sense since x1 spans 3D independently of x2\nspanning 3D.\n\nHmm.\nNo, that\'s perhaps not quite right as this would be 6D, or would it?\n\n>A General rotation that leaves the z axis invariant will leave only\n>(z1,z2) invariant in the tensor space, but both (z1) and (z2) in the\n>sum space.\n\nOK. That makes sense. It would only be invariant if both particles were\n(speaking loosely) on the z-axis, not just either one. That said, I\'ve\nclearly not quite grokked this.\n\n>The problem is that we are really talking about infinite dimensional\n>Hilbert spaces of functions on low/three dimensional vector spaces.\n\nOk. So we have an infinite set of functions, presumably related to all\npossible combinations of all possible states. Each of which is a\nfunction of (x,y,z). Is this related to the fact that there is only one\nparticle (or finite particles) so if we have one <here> then it isn\'t\n<there>.\n\n>Somehow it is the case that the tensor product of two such hilbert\n>spaces looks like a Hilbert space on a six dimensional vector space.\n\nNow I am confused.....\n\n>I\n>can\'t see how this comes about. But it\'s what gives us the niceties of\n>thinking about this stuff in terms of wavefunctions on the classical\n>configuration space.\n\n<whoosh...>\n\n>> Conceptually it makes a big difference. One can imagine a particle\n>> communicating (or appearing to) \'internally\' at ftl, using a variety of\n>> plausible arguments. I am uncomfortable about two separate particles\n>> doing so.\n>>\n>\n>Well a particle is a point really classically. Elementary particles\n>are not supposed to have any internal structure at all.\n\nWell, that\'s where I have a problem. Clearly electrons do, or they\nwouldn\'t diffract. Further a point particle should have infinite\nmomentum (if at a precise point), which is a tad unphysical.\n\n>And if you are feeliung uncomfortable about it you\'re on the right\n>way, remember:\n>\n>"Anyone who is not shocked by quantum theory has not understood it."\n>-Niels Bohr\n>;)\n\nI have no problem with qm (so far) just seeing the particles as waves.\nI\'m trying to find out where this breaks down and entanglement is the\nnext area I must start to grok.\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Frank Hellmann <Certhas@gmail.com> writes
>I can kind of see what you mean but it's not how tensor products work.
>First of all let's keep things simple, take the tensor product of two
>three dimensional Hilbert spaces.
>The basis of this 9 dimensional tensor space is:
>(x1,x2)(x1,y2)(x1,z2)(y1,x2)(y1,y2)(y1,z2)(z1,x2)( z1,y2)(z1,z2)
>The basis of the H(+)H space is
>(x1)(x2)(y1)(y2)(z1)(z2)
Right.
That's what charles implied, but your explanation is utterly clear.
Of course I now see why it has to be like that.
>Now keep in mind that this is not your physical 3D space but a 3
>dimensional Hilbert space (we can't use 2D since 2+2=2*2, think a Spin
>1 particle with the states 1,0,-1).
Hilbert spaces keep getting bandied about but I've never been very clear
about them. I read the 9D tensor product space as something along the
lines of probability of finding particle 1 at x1 AND particle 2 at x2 (x
here = (x,y,z)). That makes sense since x1 spans 3D independently of x2
spanning 3D.
Hmm.
No, that's perhaps not quite right as this would be 6D, or would it?
>A General rotation that leaves the z axis invariant will leave only
>(z1,z2) invariant in the tensor space, but both (z1) and (z2) in the
>sum space.
OK. That makes sense. It would only be invariant if both particles were
(speaking loosely) on the z-axis, not just either one. That said, I've
clearly not quite grokked this.
>The problem is that we are really talking about infinite dimensional
>Hilbert spaces of functions on low/three dimensional vector spaces.
Ok. So we have an infinite set of functions, presumably related to all
possible combinations of all possible states. Each of which is a
function of (x,y,z). Is this related to the fact that there is only one
particle (or finite particles) so if we have one <here> then it isn't
<there>.
>Somehow it is the case that the tensor product of two such hilbert
>spaces looks like a Hilbert space on a six dimensional vector space.
Now I am confused.....
>I
>can't see how this comes about. But it's what gives us the niceties of
>thinking about this stuff in terms of wavefunctions on the classical
>configuration space.
<whoosh...>
>> Conceptually it makes a big difference. One can imagine a particle
>> communicating (or appearing to) 'internally' at ftl, using a variety of
>> plausible arguments. I am uncomfortable about two separate particles
>> doing so.
>>
>
>Well a particle is a point really classically. Elementary particles
>are not supposed to have any internal structure at all.
Well, that's where I have a problem. Clearly electrons do, or they
wouldn't diffract. Further a point particle should have infinite
momentum (if at a precise point), which is a tad unphysical.
>And if you are feeliung uncomfortable about it you're on the right
>way, remember:
>
>"Anyone who is not shocked by quantum theory has not understood it."
>-Niels Bohr
>;)
I have no problem with qm (so far) just seeing the particles as waves.
I'm trying to find out where this breaks down and entanglement is the
next area I must start to grok.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
<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\nTom Trotter <tom129@juno.com> writes\n\n>The paired photons produced by Aspect via\n>atomic calcium cascades are moving in opposite\n>directions, have different wavelengths, and\n>opposite angular momenta. They\'re two different,\n>and separate, \'particles\'.\n\nOh. That makes it more complicated.\nMuch more.\n\n>And, it\'s not necessary to be contemplating\n>how they can be \'communicating\' with each\n>other. They aren\'t.\n\nGood. Everyone else says they are....\nWell, some do, anyway.\n\n>The correlations in the combined context\n>are due to the photons of any given\n>pair being identically polarized via\n>the emission process.\n\nThat seems simple enough, so why the fuss?\n\n>The two photons\n>need not be emitted in opposite directions,\n>but if we select those that are, conservation\n>of angular momentum now requires that their\n>handedness be the same. Therefore, they must\n>have the same polarization: both right- or\n>both left-circularly polarized."\n\nOk, seems simple enough...\n\n>Now, if you want to make a local hidden\n>variable theory work wrt the combined\n>context, then, as Bell noted, you\'ll need\n>some sort of mechanism whereby the two\n>ends of the experimental setup can\n>instantaneously communicate. But, that\n>would be a silly construction, since it\'s\n>already been shown that lambda (the\n>polarization of the photons) is irrelevant\n>to the determination of coincidental\n>detection.\n\nI\'ve lost it there.\nAs I read this its obvious.\nIt can\'t be obvious or there wouldn\'t be a fuss.\n\n>In the individual measurement context,\n>the emission-produced *polarization* of\n>a photon is (along with the orientation\n>of the polarizer that it is interacting\n>with) the determining factor.\n>\n>In the combined measurement context, the\n>emission-produced *relationship* between\n>paired photons is (along with the combined\n>orientations of the polarizers) the\n>determining factor.\n>\n>In the combined context, since the\n>*relationship* between paired photons\n>doesn\'t vary from pair to pair (only\n>the polarization does), the only variable\n>left to consider in determining rates\n>of coincidental detection is Theta, the\n>angular difference in polarizer settings.\n>\n>Does any of this make sense,\n\nMakes my head spin because it seems to say that the two particles are\nemitted in a certain relationship. Say with parallel spin.\n\nThis means that if you detect one with a particular spin then you must\ndetect the other with that particular spin. That\'s because they always\nhad that spin from the start.\n\nThis doesn\'t gell terribly well though. If the particles are photons I\ncan rotate (one of) the polarisations by a stepwise path through a\nseries of polarisers. I was under the impression that if you did this\nthen you still maintained the parallel spin on final detection. There\nare a variety of caveats one could bring to bear to overcome this, but I\nam in fact unclear of the expected result.\n\nI am also not 100% clear about spin, never having studied it.\nI currently crudely classify it as I would polarisation, although I know\nits a 3D thingy really.\n\n>or do you\n>think we should continue to talk about\n>ftl or instantaneous communication between\n>particles or filters and/or detectors in\n>EPRBell experiments?\n\nIf you wouldn\'t mind, I would appreciate it.\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Tom Trotter <tom129@juno.com> writes
>The paired photons produced by Aspect via
>atomic calcium cascades are moving in opposite
>directions, have different wavelengths, and
>opposite angular momenta. They're two different,
>and separate, 'particles'.
Oh. That makes it more complicated.
Much more.
>And, it's not necessary to be contemplating
>how they can be 'communicating' with each
>other. They aren't.
Good. Everyone else says they are....
Well, some do, anyway.
>The correlations in the combined context
>are due to the photons of any given
>pair being identically polarized via
>the emission process.
That seems simple enough, so why the fuss?
>The two photons
>need not be emitted in opposite directions,
>but if we select those that are, conservation
>of angular momentum now requires that their
>handedness be the same. Therefore, they must
>have the same polarization: both right- or
>both left-circularly polarized."
Ok, seems simple enough...
>Now, if you want to make a local hidden
>variable theory work wrt the combined
>context, then, as Bell noted, you'll need
>some sort of mechanism whereby the two
>ends of the experimental setup can
>instantaneously communicate. But, that
>would be a silly construction, since it's
>already been shown that \lambda (the
>polarization of the photons) is irrelevant
>to the determination of coincidental
>detection.
I've lost it there.
As I read this its obvious.
It can't be obvious or there wouldn't be a fuss.
>In the individual measurement context,
>the emission-produced *polarization* of
>a photon is (along with the orientation
>of the polarizer that it is interacting
>with) the determining factor.
>
>In the combined measurement context, the
>emission-produced *relationship* between
>paired photons is (along with the combined
>orientations of the polarizers) the
>determining factor.
>
>In the combined context, since the
>*relationship* between paired photons
>doesn't vary from pair to pair (only
>the polarization does), the only variable
>left to consider in determining rates
>of coincidental detection is \Theta, the
>angular difference in polarizer settings.
>
>Does any of this make sense,
Makes my head spin because it seems to say that the two particles are
emitted in a certain relationship. Say with parallel spin.
This means that if you detect one with a particular spin then you must
detect the other with that particular spin. That's because they always
had that spin from the start.
This doesn't gell terribly well though. If the particles are photons I
can rotate (one of) the polarisations by a stepwise path through a
series of polarisers. I was under the impression that if you did this
then you still maintained the parallel spin on final detection. There
are a variety of caveats one could bring to bear to overcome this, but I
am in fact unclear of the expected result.
I am also not 100% clear about spin, never having studied it.
I currently crudely classify it as I would polarisation, although I know
its a 3D thingy really.
>or do you
>think we should continue to talk about
>ftl or instantaneous communication between
>particles or filters and/or detectors in
>EPRBell experiments?
If you wouldn't mind, I would appreciate it.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
<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\nTom Trotter <tom129@juno.com> writes\n\n>Any things. Let\'s say you have a number objects\n>that, among them, have three different, discernable\n>characteristics, or properties, or parameters,\n>A, B, and C.\n\nOK.\n\n>Bell\'s inequality says that the number of objects\n>that have A but not B plus the number of objects\n>that have B but not C is greater than or equal\n>to the number of objects that have A but not C.\n\n<nnngth>\n\nNine possibilities, if I read you right.\n(0,0,0), (1,0,0), (0,1,0), (0,0,1),\n(1,1,1), (1,1,0), (0,1,1), (1,0,1)\nno, eight.\n\nSo A but not B would be\n(1,0,0), (1,0,1)\n\nand B not C\n(1,1,0), (0,1,0)\n\nand A not C\n(1,0,0), (1,1,0)\n\nleaving\n(0,0,0) and (1,1,1).\n\nIf we take (x,y,z) to be the proportion of the total in the appropriate\nstate then bell LHS states:\n\n[A not B] + [B not C]\n\n= (1,0,0) + (1,0,1) + (1,1,0) + (0,1,0)\n\n= [(1,0,0) + (1,1,0)] + [(1,0,1) + (0,1,0)]\n\n= [A not C] + [something >=0]\n\nI\'m sure I\'ve seen that in boolean math somewhere....\n\nOK. I really don\'t comprehend why nobody has mentioned this before...\nIts not exactly rocket science.\n\n>> ... and what does experiment show under what circumstances?\n>> Perhaps I should say \'what effect does the experimental results that\n>> test bells inequalities imply\'.\n>\n>The experimental results support the qm formulation,\n>and the emission model, which says that paired photons\n>are entangled via the emission process\n\nCan you explain this in the context of bells inequality,\nnow that\'s been explained. That way I will be able to see what the fuss\nis about?\n\nI have deleted the rest of your long posting because it will cause\nthread bloat and confusion when I am clearly not yet ready to appreciate\nit. Hopefully you will be able to cut&paste it back in at the\nappropriate stage as we progress.\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Tom Trotter <tom129@juno.com> writes
>Any things. Let's say you have a number objects
>that, among them, have three different, discernable
>characteristics, or properties, or parameters,
>A, B, and C.
OK.
>Bell's inequality says that the number of objects
>that have A but not B plus the number of objects
>that have B but not C is greater than or equal
>to the number of objects that have A but not C.
<nnngth>
Nine possibilities, if I read you right.
(0,0,0), (1,0,0), (0,1,0), (0,0,1),
(1,1,1), (1,1,0), (0,1,1), (1,0,1)
no, eight.
So A but not B would be
(1,0,0), (1,0,1)
and B not C
(1,1,0), (0,1,0)
and A not C
(1,0,0), (1,1,0)
leaving
(0,0,0) and (1,1,1).
If we take (x,y,z) to be the proportion of the total in the appropriate
state then bell LHS states:
[A not B] + [B not C]
= (1,0,0) + (1,0,1) + (1,1,0) + (0,1,0)= [(1,0,0) + (1,1,0)] + [(1,0,1) + (0,1,0)]= [A[/itex] not C] + [something [itex]>=0]
I'm sure I've seen that in boolean math somewhere....
OK. I really don't comprehend why nobody has mentioned this before...
Its not exactly rocket science.
>> ... and what does experiment show under what circumstances?
>> Perhaps I should say 'what effect does the experimental results that
>> test bells inequalities imply'.
>
>The experimental results support the qm formulation,
>and the emission model, which says that paired photons
>are entangled via the emission process
Can you explain this in the context of bells inequality,
now that's been explained. That way I will be able to see what the fuss
is about?
I have deleted the rest of your long posting because it will cause
thread bloat and confusion when I am clearly not yet ready to appreciate
it. Hopefully you will be able to cut&paste it back in at the
appropriate stage as we progress.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
Tom Trotter
Jul28-04, 03:58 AM
<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\nOz <oz@farmeroz.port995.com> wrote in message news:<j1QXlDYMhgBBFwRw@farmeroz.port995.com>...\n> Tom Trotter <tom129@juno.com> writes\n>\n> >The paired photons produced by Aspect via\n> >atomic calcium cascades are moving in opposite\n> >directions, have different wavelengths, and\n> >opposite angular momenta. They\'re two different,\n> >and separate, \'particles\'.\n>\n> Oh. That makes it more complicated.\n> Much more.\n\nNot really. The polarizers are just analyzing\na property that photon 1 and photon 2 have in\ncommon, because according to the emission model\nthat common property is polarization. Whatever\nthe *emission-produced* polarization might be\n(and it remains an unknown), it\'s the same\nfor photon 1 and photon 2.\n\n>\n> >And, it\'s not necessary to be contemplating\n> >how they can be \'communicating\' with each\n> >other. They aren\'t.\n>\n> Good. Everyone else says they are....\n> Well, some do, anyway.\n\nIf there is communication happening, then\nit has to be instantaneous, and it\'s up to\nthose who hold that this instantaneous\ncommunication is happening to demonstrate it.\nThis would entail being able to predict the\neffect that changing the setting at polarizer\na would have on the detection attribute\nrecorded at detector B, and vice versa.\n\nIn the combined context, which includes\njoint polarizer settings for paired photons,\nthe data streams at A and B aren\'t\nindependent. But, this doesn\'t mean\nthat A and B are \'communicating\'. The\npolarizers are simply analyzing a shared\nproperty, an emission-produced relationship\nbetween photon 1 and photon 2.\n\n> That seems simple enough, so why the fuss?\n>\n\nIt\'s just an interpretational issue. Why do\nsome people like the MWI of qm? I don\'t know\nexactly. But I would suppose that a lot of\nthe fuss is due to misinterpretations of\nBell\'s 1964 paper. Experimental violations\nof Bell inequalities really don\'t tell you\nanything about the *existence*, or not,\nof hidden variables, nor do they necessitate\nthe invention of unknown ftl \'signals\' or\n\'influences\', or instantaneous,\nEinstein-causality-violating \'mechanisms\'\nin order to understand the results.\n\nExperimental violations of Bell inequalities,\nand Bell\'s pre-experiment analysis, *do* tell\nyou that, minimally, something is wrong\nwith the formulation on which such inequalities\nare based -- that it includes terms and/or\noperations that aren\'t *applicable* to the\nexperimental context.\n\n> >Now, if you want to make a local hidden\n> >variable theory work wrt the combined\n> >context, then, as Bell noted, you\'ll need\n> >some sort of mechanism whereby the two\n> >ends of the experimental setup can\n> >instantaneously communicate. But, that\n> >would be a silly construction, since it\'s\n> >already been shown that lambda (the\n> >polarization of the photons) is irrelevant\n> >to the determination of coincidental\n> >detection.\n>\n> I\'ve lost it there.\n> As I read this its obvious.\n> It can\'t be obvious or there wouldn\'t be a fuss.\n\nWhy not? The world is full of people who\nbelieve all sorts of weird things. Bell\'s\nstuff has been incorrectly talked about in\na certain way for so long that most people\njust take it for granted that it has to do\nwith the existence of hidden variables and\nthe necessity of instantaneous \'influences\'.\n\nHere\'s a quote from Greenstein and Zajonc\'s,\nThe Quantum Challenge - Modern Research on the\nFoundations of Quantum Mechanics (1997, p. 149).\n\n"Turn now to an EPR experiment of the type we\nhave been describing. Two photons are emitted\nat the outset; one travels toward Alice, the\nother toward Bob. If their polarization analyzers\nare oriented along the same direction, then every\ntime Alice and Bob perform measurements, they\nget identical results. They never get opposite\npolarizations. This is an \'EPR correlation\' --\nand how are we to explain it?\n\n"Prior to Bell\'s theorem and the experiments we\nhave just recounted, the explanation would have\nbeen equally trivial. We simply would have\npostulated that the photons heading toward\nAlice and Bob had identical polarizations. If\nthey had started off with angular momentum zero,\nand if angular momentum was conserved, then in\nthe absence of external torques we would find\nthe final angular momentum to be zero as well,\nguaranteeing their polarizations to be identical.\nBut the polarizations of the two individual\nphotons are precisely what we mean by local\nhidden variables -- and we know now that these\ncannot exist."\n\nMe again. In an otherwise really good book,\nGreenstein and Zajonc have bought into the\nmistaken idea that Bell\'s analysis has something\nto do with the *existence* of hidden variables.\n\nAFAIK, it\'s not disputed by anyone that hidden variables\nexist in the context of individual measurements.\nSo, are we to suppose that these variables that\nare relevant wrt determining individual data\nstreams simply cease to exist in the context\nof considering both data streams.\n\nOf course not. It\'s simply that, in the\ncombined context, a different parameter or\nproperty of the unknown variable is relevant\nwrt the determination of coincidental detection\nthan is relevant wrt the determination of\nthe individual results of a single data\nstream. In the combined context, it\'s not\nthe polarization, per se, that determines\ncoincidental detection, but rather it has\nto do with how photon 1 and photon 2 are\nrelated wrt their emission-produced\npolarizations.\n\nCan \'supplementary parameters\' exist and\nstill not be applicable wrt a certain\nexperimental context? Does the moon\nexist when you\'re not looking at it? :-)\n\n>\n> >In the individual measurement context,\n> >the emission-produced *polarization* of\n> >a photon is (along with the orientation\n> >of the polarizer that it is interacting\n> >with) the determining factor.\n> >\n> >In the combined measurement context, the\n> >emission-produced *relationship* between\n> >paired photons is (along with the combined\n> >orientations of the polarizers) the\n> >determining factor.\n> >\n> >In the combined context, since the\n> >*relationship* between paired photons\n> >doesn\'t vary from pair to pair (only\n> >the polarization does), the only variable\n> >left to consider in determining rates\n> >of coincidental detection is Theta, the\n> >angular difference in polarizer settings.\n> >\n> >Does any of this make sense,\n>\n> Makes my head spin because it seems to say\n> that the two particles are emitted in a certain\n> relationship. Say with parallel spin.\n\nSay with identical polarization.\n\n>\n> This means that if you detect one with a particular spin then you must\n> detect the other with that particular spin. That\'s because they always\n> had that spin from the start.\n\nIt means that if the separated polarizers are\naligned, then if you register a detection at\nA you\'ll also register a detection at B -- and\nif you don\'t register a detection at A, then\nyou also won\'t register a detection at B.\nThe probability of recording coincidental\n(identical) detection attributes for paired\nphotons, with the polarizers aligned is, in the\nideal, 1.\n\nAs you rotate the polarizers to increase\nthe angle (Theta) between them, then the\nprobability of coincidental detection\ndecreases as a circular function of Theta.\n\n>\n> This doesn\'t gell terribly well though. If the particles are photons I\n> can rotate (one of) the polarisations by a stepwise path through a\n> series of polarisers. I was under the impression that if you did this\n> then you still maintained the parallel spin on final detection. There\n> are a variety of caveats one could bring to bear to overcome this, but I\n> am in fact unclear of the expected result.\n\nIf you mean that the entanglement (ie., the emission\nproduced relationship between the polarizations\nof photon 1 and photon 2) can be preserved, via\nseparated polarizers, I don\'t think so.\n\nI\'m not sure I understand what doesn\'t gell for you.\n\n>\n> I am also not 100% clear about spin, never having studied it.\n> I currently crudely classify it as I would polarisation, although I know\n> its a 3D thingy really.\n\nI\'m not sure I \'understand\' spin either. But I don\'t\nthink of it as a 3D thingy. Polarization, which is\nrelated to spin, is of course a 3D thingy really. At\nleast that\'s how I think of it (until corrected, if\nnecessary).\n\n>\n> >or do you\n> >think we should continue to talk about\n> >ftl or instantaneous communication between\n> >particles or filters and/or detectors in\n> >EPRBell experiments?\n>\n> If you wouldn\'t mind, I would appreciate it.\n\nOk. What?\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Oz <oz@farmeroz.port995.com> wrote in message news:<j1QXlDYMhgBBFwRw@farmeroz.port995.com>...
> Tom Trotter <tom129@juno.com> writes
>
> >The paired photons produced by Aspect via
> >atomic calcium cascades are moving in opposite
> >directions, have different wavelengths, and
> >opposite angular momenta. They're two different,
> >and separate, 'particles'.
>
> Oh. That makes it more complicated.
> Much more.
Not really. The polarizers are just analyzing
a property that photon 1 and photon 2 have in
common, because according to the emission model
that common property is polarization. Whatever
the *emission-produced* polarization might be
(and it remains an unknown), it's the same
for photon 1 and photon 2.
>
> >And, it's not necessary to be contemplating
> >how they can be 'communicating' with each
> >other. They aren't.
>
> Good. Everyone else says they are....
> Well, some do, anyway.
If there is communication happening, then
it has to be instantaneous, and it's up to
those who hold that this instantaneous
communication is happening to demonstrate it.
This would entail being able to predict the
effect that changing the setting at polarizer
a would have on the detection attribute
recorded at detector B, and vice versa.
In the combined context, which includes
joint polarizer settings for paired photons,
the data streams at A and B aren't
independent. But, this doesn't mean
that A and B are 'communicating'. The
polarizers are simply analyzing a shared
property, an emission-produced relationship
between photon 1 and photon 2.
> That seems simple enough, so why the fuss?
>
It's just an interpretational issue. Why do
some people like the MWI of qm? I don't know
exactly. But I would suppose that a lot of
the fuss is due to misinterpretations of
Bell's 1964 paper. Experimental violations
of Bell inequalities really don't tell you
anything about the *existence*, or not,
of hidden variables, nor do they necessitate
the invention of unknown ftl 'signals' or
'influences', or instantaneous,
Einstein-causality-violating 'mechanisms'
in order to understand the results.
Experimental violations of Bell inequalities,
and Bell's pre-experiment analysis, *do* tell
you that, minimally, something is wrong
with the formulation on which such inequalities
are based -- that it includes terms and/or
operations that aren't *applicable* to the
experimental context.
> >Now, if you want to make a local hidden
> >variable theory work wrt the combined
> >context, then, as Bell noted, you'll need
> >some sort of mechanism whereby the two
> >ends of the experimental setup can
> >instantaneously communicate. But, that
> >would be a silly construction, since it's
> >already been shown that \lambda (the
> >polarization of the photons) is irrelevant
> >to the determination of coincidental
> >detection.
>
> I've lost it there.
> As I read this its obvious.
> It can't be obvious or there wouldn't be a fuss.
Why not? The world is full of people who
believe all sorts of weird things. Bell's
stuff has been incorrectly talked about in
a certain way for so long that most people
just take it for granted that it has to do
with the existence of hidden variables and
the necessity of instantaneous 'influences'.
Here's a quote from Greenstein and Zajonc's,
The Quantum Challenge - Modern Research on the
Foundations of Quantum Mechanics (1997, p. 149).
"Turn now to an EPR experiment of the type we
have been describing. Two photons are emitted
at the outset; one travels toward Alice, the
other toward Bob. If their polarization analyzers
are oriented along the same direction, then every
time Alice and Bob perform measurements, they
get identical results. They never get opposite
polarizations. This is an 'EPR correlation' --
and how are we to explain it?
"Prior to Bell's theorem and the experiments we
have just recounted, the explanation would have
been equally trivial. We simply would have
postulated that the photons heading toward
Alice and Bob had identical polarizations. If
they had started off with angular momentum zero,
and if angular momentum was conserved, then in
the absence of external torques we would find
the final angular momentum to be zero as well,
guaranteeing their polarizations to be identical.
But the polarizations of the two individual
photons are precisely what we mean by local
hidden variables -- and we know now that these
cannot exist."
Me again. In an otherwise really good book,
Greenstein and Zajonc have bought into the
mistaken idea that Bell's analysis has something
to do with the *existence* of hidden variables.
AFAIK, it's not disputed by anyone that hidden variables
exist in the context of individual measurements.
So, are we to suppose that these variables that
are relevant wrt determining individual data
streams simply cease to exist in the context
of considering both data streams.
Of course not. It's simply that, in the
combined context, a different parameter or
property of the unknown variable is relevant
wrt the determination of coincidental detection
than is relevant wrt the determination of
the individual results of a single data
stream. In the combined context, it's not
the polarization, per se, that determines
coincidental detection, but rather it has
to do with how photon 1 and photon 2 are
related wrt their emission-produced
polarizations.
Can 'supplementary parameters' exist and
still not be applicable wrt a certain
experimental context? Does the moon
exist when you're not looking at it? :-)
>
> >In the individual measurement context,
> >the emission-produced *polarization* of
> >a photon is (along with the orientation
> >of the polarizer that it is interacting
> >with) the determining factor.
> >
> >In the combined measurement context, the
> >emission-produced *relationship* between
> >paired photons is (along with the combined
> >orientations of the polarizers) the
> >determining factor.
> >
> >In the combined context, since the
> >*relationship* between paired photons
> >doesn't vary from pair to pair (only
> >the polarization does), the only variable
> >left to consider in determining rates
> >of coincidental detection is \Theta, the
> >angular difference in polarizer settings.
> >
> >Does any of this make sense,
>
> Makes my head spin because it seems to say
> that the two particles are emitted in a certain
> relationship. Say with parallel spin.
Say with identical polarization.
>
> This means that if you detect one with a particular spin then you must
> detect the other with that particular spin. That's because they always
> had that spin from the start.
It means that if the separated polarizers are
aligned, then if you register a detection at
A you'll also register a detection at B -- and
if you don't register a detection at A, then
you also won't register a detection at B.
The probability of recording coincidental
(identical) detection attributes for paired
photons, with the polarizers aligned is, in the
ideal, 1.
As you rotate the polarizers to increase
the angle (\Theta) between them, then the
probability of coincidental detection
decreases as a circular function of \Theta.
>
> This doesn't gell terribly well though. If the particles are photons I
> can rotate (one of) the polarisations by a stepwise path through a
> series of polarisers. I was under the impression that if you did this
> then you still maintained the parallel spin on final detection. There
> are a variety of caveats one could bring to bear to overcome this, but I
> am in fact unclear of the expected result.
If you mean that the entanglement (ie., the emission
produced relationship between the polarizations
of photon 1 and photon 2) can be preserved, via
separated polarizers, I don't think so.
I'm not sure I understand what doesn't gell for you.
>
> I am also not 100% clear about spin, never having studied it.
> I currently crudely classify it as I would polarisation, although I know
> its a 3D thingy really.
I'm not sure I 'understand' spin either. But I don't
think of it as a 3D thingy. Polarization, which is
related to spin, is of course a 3D thingy really. At
least that's how I think of it (until corrected, if
necessary).
>
> >or do you
> >think we should continue to talk about
> >ftl or instantaneous communication between
> >particles or filters and/or detectors in
> >EPRBell experiments?
>
> If you wouldn't mind, I would appreciate it.
Ok. What?
Creighton Hogg
Jul28-04, 03:58 AM
<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\nOn 27 Jul 2004, Oz wrote:\n>\n> Frank Hellmann <Certhas@gmail.com> writes\n> >\n> >Well a particle is a point really classically. Elementary particles\n> >are not supposed to have any internal structure at all.\n>\n> Well, that\'s where I have a problem. Clearly electrons do, or they\n> wouldn\'t diffract.\n\nAs far as we know, electrons don\'t have internal structure. Why do you\nthink diffraction would show otherwise?\n\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On 27 Jul 2004, Oz wrote:
>
> Frank Hellmann <Certhas@gmail.com> writes
> >
> >Well a particle is a point really classically. Elementary particles
> >are not supposed to have any internal structure at all.
>
> Well, that's where I have a problem. Clearly electrons do, or they
> wouldn't diffract.
As far as we know, electrons don't have internal structure. Why do you
think diffraction would show otherwise?
<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\nCreighton Hogg <wchogg@hep.wisc.edu> writes\n>\n>On 27 Jul 2004, Oz wrote:\n>>\n>> Frank Hellmann <Certhas@gmail.com> writes\n>> >\n>> >Well a particle is a point really classically. Elementary particles\n>> >are not supposed to have any internal structure at all.\n>>\n>> Well, that\'s where I have a problem. Clearly electrons do, or they\n>> wouldn\'t diffract.\n>\n>As far as we know, electrons don\'t have internal structure. Why do you\n>think diffraction would show otherwise?\n\nOf course it depends on what you mean by \'internal\' structure.\nIf you mean its a composite particle, then no.\n\nIf you mean its a soliton-like structure in several dimensions, then\nyes. Then, as a wave, it can be diffracted. This calls for a soliton-\nlike object that **isn\'t** of constant amplitude and extent, quite the\ncontrary.\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\n\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Creighton Hogg <wchogg@hep.wisc.edu> writes
>
>On 27 Jul 2004, Oz wrote:
>>
>> Frank Hellmann <Certhas@gmail.com> writes
>> >
>> >Well a particle is a point really classically. Elementary particles
>> >are not supposed to have any internal structure at all.
>>
>> Well, that's where I have a problem. Clearly electrons do, or they
>> wouldn't diffract.
>
>As far as we know, electrons don't have internal structure. Why do you
>think diffraction would show otherwise?
Of course it depends on what you mean by 'internal' structure.
If you mean its a composite particle, then no.
If you mean its a soliton-like structure in several dimensions, then
yes. Then, as a wave, it can be diffracted. This calls for a soliton-
like object that **isn't** of constant amplitude and extent, quite the
contrary.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
Creighton Hogg
Jul28-04, 10:11 AM
<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\n\n\n\nOn 28 Jul 2004, Oz wrote:\n\n>\n>\n> Creighton Hogg <wchogg@hep.wisc.edu> writes\n> >\n> >On 27 Jul 2004, Oz wrote:\n> >>\n> >> Frank Hellmann <Certhas@gmail.com> writes\n> >> >\n> >> >Well a particle is a point really classically. Elementary particles\n> >> >are not supposed to have any internal structure at all.\n> >>\n> >> Well, that\'s where I have a problem. Clearly electrons do, or they\n> >> wouldn\'t diffract.\n> >\n> >As far as we know, electrons don\'t have internal structure. Why do you\n> >think diffraction would show otherwise?\n>\n> Of course it depends on what you mean by \'internal\' structure.\n> If you mean its a composite particle, then no.\n>\n> If you mean its a soliton-like structure in several dimensions, then\n> yes. Then, as a wave, it can be diffracted. This calls for a soliton-\n> like object that **isn\'t** of constant amplitude and extent, quite the\n> contrary.\n\nPerhaps we mean different things by diffraction. I mean diffraction in\nthe sense of the double-slit experiment, where you see a diffraction\npattern from the scattering of a beam of electrons off of something. This\nwouldn\'t imply that electrons are solitons at all.\nI assume you mean diffraction in a different way?\n\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On 28 Jul 2004, Oz wrote:
>
>
> Creighton Hogg <wchogg@hep.wisc.edu> writes
> >
> >On 27 Jul 2004, Oz wrote:
> >>
> >> Frank Hellmann <Certhas@gmail.com> writes
> >> >
> >> >Well a particle is a point really classically. Elementary particles
> >> >are not supposed to have any internal structure at all.
> >>
> >> Well, that's where I have a problem. Clearly electrons do, or they
> >> wouldn't diffract.
> >
> >As far as we know, electrons don't have internal structure. Why do you
> >think diffraction would show otherwise?
>
> Of course it depends on what you mean by 'internal' structure.
> If you mean its a composite particle, then no.
>
> If you mean its a soliton-like structure in several dimensions, then
> yes. Then, as a wave, it can be diffracted. This calls for a soliton-
> like object that **isn't** of constant amplitude and extent, quite the
> contrary.
Perhaps we mean different things by diffraction. I mean diffraction in
the sense of the double-slit experiment, where you see a diffraction
pattern from the scattering of a beam of electrons off of something. This
wouldn't imply that electrons are solitons at all.
I assume you mean diffraction in a different way?
Tom Trotter
Jul30-04, 11:43 AM
<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\nOz <oz@farmeroz.port995.com> wrote in message news:<PEcMpMY\\$OhBBFwn4@farmeroz.port995.com>...\ n\n[snip discussion of Bell\'s inequality]\n\nOk, so much for the inequalities. Their\nsymbolic truth is indisputable. What *is* being\ndisputed is whether or not their violation (via\nplugging in either qm expectation values or experimental\nresults) tells you anything about locality\n(Einstein causality), or reality, or instantaneous\nsignals or \'influences\'. Imho, the answer is\nno, with qualifications.\n\nThere is *something* wrong with the\nformulations on which the inequalities are\nbased -- that much we can be sure of.\n\nI\'m also pretty sure that contemplating the\ninequalities themselves will confuse (and\npossibly drive you batty, at least it did me\nfor a while) the important issue wrt the\nphysics involved -- which concerns the\nrecipe for producing the experimental\nviolations (ie., what, exactly, is causing\nthe observed coincidence patterns).\n\n> >> ... and what does experiment show under what circumstances?\n> >> Perhaps I should say \'what effect does the experimental results that\n> >> test bells inequalities imply\'.\n> >\n> >The experimental results support the qm formulation,\n> >and the emission model, which says that paired photons\n> >are entangled via the emission process\n>\n> Can you explain this in the context of bells inequality,\n> now that\'s been explained. That way I will be able to see\n> what the fuss is about?\n\nNo. I can\'t explain it in the context of Bell\'s inequality.\nNeither can anybody else, afaik. That\'s what all the fuss\nis about. :-)\n\nThis requires some elaboration. The problem\nis that it\'s assumed that if the photons produced\nvia the emission process have some definite but\nunknown polarization prior to hitting the polarizers,\nand the individual data streams at A and B are\n*causally* independent of each other, then the\nexperimental context dealing with coincidental\ndetection must be modeled as Bell modeled it.\n\nBut we\'re forgetting something if we do it that\nway. In the combined context the relevant\nparameter related to the hidden variable\ndoesn\'t vary. So, even though we\'re assuming\nthat the hidden variable, and relevant hidden\nparamenter, *exist*, it wouldn\'t be included\nin the formula for predicting variable rates\nof coincidental detection.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Oz <oz@farmeroz.port995.com> wrote in message news:<PEcMpMY$OhBBFwn4@farmeroz.port995.com>...
[snip discussion of Bell's inequality]
Ok, so much for the inequalities. Their
symbolic truth is indisputable. What *is* being
disputed is whether or not their violation (via
plugging in either qm expectation values or experimental
results) tells you anything about locality
(Einstein causality), or reality, or instantaneous
signals or 'influences'. Imho, the answer is
no, with qualifications.
There is *something* wrong with the
formulations on which the inequalities are
based -- that much we can be sure of.
I'm also pretty sure that contemplating the
inequalities themselves will confuse (and
possibly drive you batty, at least it did me
for a while) the important issue wrt the
physics involved -- which concerns the
recipe for producing the experimental
violations (ie., what, exactly, is causing
the observed coincidence patterns).
> >> ... and what does experiment show under what circumstances?
> >> Perhaps I should say 'what effect does the experimental results that
> >> test bells inequalities imply'.
> >
> >The experimental results support the qm formulation,
> >and the emission model, which says that paired photons
> >are entangled via the emission process
>
> Can you explain this in the context of bells inequality,
> now that's been explained. That way I will be able to see
> what the fuss is about?
No. I can't explain it in the context of Bell's inequality.
Neither can anybody else, afaik. That's what all the fuss
is about. :-)
This requires some elaboration. The problem
is that it's assumed that if the photons produced
via the emission process have some definite but
unknown polarization prior to hitting the polarizers,
and the individual data streams at A and B are
*causally* independent of each other, then the
experimental context dealing with coincidental
detection must be modeled as Bell modeled it.
But we're forgetting something if we do it that
way. In the combined context the relevant
parameter related to the hidden variable
doesn't vary. So, even though we're assuming
that the hidden variable, and relevant hidden
paramenter, *exist*, it wouldn't be included
in the formula for predicting variable rates
of coincidental detection.
<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>\nTom Trotter <tom129@juno.com> writes\n>\n>\n>\n>\n>Oz <oz@farmeroz.port995.com> wrote in message news:<PEcMpMY\\$OhBBFwn4@farmeroz.po\n>rt995.com>. ..\n>\n[A not B] + [B not C]= [A not C] + [something >=0]\n\n>Ok, so much for the inequalities. Their\n>symbolic truth is indisputable. What *is* being\n>disputed is whether or not their violation (via\n>plugging in either qm expectation values or experimental\n>results) tells you anything about locality\n>(Einstein causality), or reality, or instantaneous\n>signals or \'influences\'. Imho, the answer is\n>no, with qualifications.\n\nWell, obviously a lot of people think otherwise.\nThe question is "what is their view".\n\nAn example experiment and the results relating to bell\'s inequality is\nappropriate at this point.\n\n>There is *something* wrong with the\n>formulations on which the inequalities are\n>based -- that much we can be sure of.\n\nUntil I see and experiment and results I have an open mind.\n\n>I\'m also pretty sure that contemplating the\n>inequalities themselves will confuse (and\n>possibly drive you batty,\n\nHopefully, but I\'m generally considered pretty batty anyway.\n\n>This requires some elaboration. The problem\n>is that it\'s assumed that if the photons produced\n>via the emission process have some definite but\n>unknown polarization prior to hitting the polarizers,\n\nOK. Now, are we saying EACH has a definite but unknown polarisation or\nthat \'the pair\' has definite but unknown polarisation?\n\n>and the individual data streams at A and B are\n>*causally* independent of each other, then the\n>experimental context dealing with coincidental\n>detection must be modeled as Bell modeled it.\n\nSo, simply, how DID he model it?\n\n>But we\'re forgetting something if we do it that\n>way. In the combined context the relevant\n>parameter related to the hidden variable\n>doesn\'t vary. So, even though we\'re assuming\n>that the hidden variable, and relevant hidden\n>paramenter, *exist*, it wouldn\'t be included\n>in the formula for predicting variable rates\n>of coincidental detection.\n\nThis doesn\'t make sense unless I know more about the setup and the\nanalysis.\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Tom Trotter <tom129@juno.com> writes
>
>
>
>
>Oz <oz@farmeroz.port995.com> wrote in message news:<PEcMpMY$OhBBFwn4@farmeroz.po
>rt995.com>...
>
[A not B] + [B not C]= [A not C] + [something >=0]
>Ok, so much for the inequalities. Their
>symbolic truth is indisputable. What *is* being
>disputed is whether or not their violation (via
>plugging in either qm expectation values or experimental
>results) tells you anything about locality
>(Einstein causality), or reality, or instantaneous
>signals or 'influences'. Imho, the answer is
>no, with qualifications.
Well, obviously a lot of people think otherwise.
The question is "what is their view".
An example experiment and the results relating to bell's inequality is
appropriate at this point.
>There is *something* wrong with the
>formulations on which the inequalities are
>based -- that much we can be sure of.
Until I see and experiment and results I have an open mind.
>I'm also pretty sure that contemplating the
>inequalities themselves will confuse (and
>possibly drive you batty,
Hopefully, but I'm generally considered pretty batty anyway.
>This requires some elaboration. The problem
>is that it's assumed that if the photons produced
>via the emission process have some definite but
>unknown polarization prior to hitting the polarizers,
OK. Now, are we saying EACH has a definite but unknown polarisation or
that 'the pair' has definite but unknown polarisation?
>and the individual data streams at A and B are
>*causally* independent of each other, then the
>experimental context dealing with coincidental
>detection must be modeled as Bell modeled it.
So, simply, how DID he model it?
>But we're forgetting something if we do it that
>way. In the combined context the relevant
>parameter related to the hidden variable
>doesn't vary. So, even though we're assuming
>that the hidden variable, and relevant hidden
>paramenter, *exist*, it wouldn't be included
>in the formula for predicting variable rates
>of coincidental detection.
This doesn't make sense unless I know more about the setup and the
analysis.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
<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\nTom Trotter <tom129@juno.com> writes\n>\n>\n>\n>\n>Oz <oz@farmeroz.port995.com> wrote in message news:<PEcMpMY\\$OhBBFwn4@farmeroz.po\n>rt995.com>. ..\n>\n[A not B] + [B not C]= [A not C] + [something >=0]\n\n>Ok, so much for the inequalities. Their\n>symbolic truth is indisputable. What *is* being\n>disputed is whether or not their violation (via\n>plugging in either qm expectation values or experimental\n>results) tells you anything about locality\n>(Einstein causality), or reality, or instantaneous\n>signals or \'influences\'. Imho, the answer is\n>no, with qualifications.\n\nWell, obviously a lot of people think otherwise.\nThe question is "what is their view".\n\nAn example experiment and the results relating to bell\'s inequality is\nappropriate at this point.\n\n>There is *something* wrong with the\n>formulations on which the inequalities are\n>based -- that much we can be sure of.\n\nUntil I see and experiment and results I have an open mind.\n\n>I\'m also pretty sure that contemplating the\n>inequalities themselves will confuse (and\n>possibly drive you batty,\n\nHopefully, but I\'m generally considered pretty batty anyway.\n\n>This requires some elaboration. The problem\n>is that it\'s assumed that if the photons produced\n>via the emission process have some definite but\n>unknown polarization prior to hitting the polarizers,\n\nOK. Now, are we saying EACH has a definite but unknown polarisation or\nthat \'the pair\' has definite but unknown polarisation?\n\n>and the individual data streams at A and B are\n>*causally* independent of each other, then the\n>experimental context dealing with coincidental\n>detection must be modeled as Bell modeled it.\n\nSo, simply, how DID he model it?\n\n>But we\'re forgetting something if we do it that\n>way. In the combined context the relevant\n>parameter related to the hidden variable\n>doesn\'t vary. So, even though we\'re assuming\n>that the hidden variable, and relevant hidden\n>paramenter, *exist*, it wouldn\'t be included\n>in the formula for predicting variable rates\n>of coincidental detection.\n\nThis doesn\'t make sense unless I know more about the setup and the\nanalysis.\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Tom Trotter <tom129@juno.com> writes
>
>
>
>
>Oz <oz@farmeroz.port995.com> wrote in message news:<PEcMpMY$OhBBFwn4@farmeroz.po
>rt995.com>...
>
[A not B] + [B not C]= [A not C] + [something >=0]
>Ok, so much for the inequalities. Their
>symbolic truth is indisputable. What *is* being
>disputed is whether or not their violation (via
>plugging in either qm expectation values or experimental
>results) tells you anything about locality
>(Einstein causality), or reality, or instantaneous
>signals or 'influences'. Imho, the answer is
>no, with qualifications.
Well, obviously a lot of people think otherwise.
The question is "what is their view".
An example experiment and the results relating to bell's inequality is
appropriate at this point.
>There is *something* wrong with the
>formulations on which the inequalities are
>based -- that much we can be sure of.
Until I see and experiment and results I have an open mind.
>I'm also pretty sure that contemplating the
>inequalities themselves will confuse (and
>possibly drive you batty,
Hopefully, but I'm generally considered pretty batty anyway.
>This requires some elaboration. The problem
>is that it's assumed that if the photons produced
>via the emission process have some definite but
>unknown polarization prior to hitting the polarizers,
OK. Now, are we saying EACH has a definite but unknown polarisation or
that 'the pair' has definite but unknown polarisation?
>and the individual data streams at A and B are
>*causally* independent of each other, then the
>experimental context dealing with coincidental
>detection must be modeled as Bell modeled it.
So, simply, how DID he model it?
>But we're forgetting something if we do it that
>way. In the combined context the relevant
>parameter related to the hidden variable
>doesn't vary. So, even though we're assuming
>that the hidden variable, and relevant hidden
>paramenter, *exist*, it wouldn't be included
>in the formula for predicting variable rates
>of coincidental detection.
This doesn't make sense unless I know more about the setup and the
analysis.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
<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> As it happens, two of Aspect\'s experiments and the first Geneva experiment\n> are among those that are severely affected by the data adjustment. Look\n> at\n> the raw data and you find that the natural local realist explanation fits\n> it\n> almost perfectly -- which is surprising really, in view of the various\n> other\n> factors that one would expect to reduce the visibility of the coincidence\n> curves.\n>\n> Most Bell test experiments use tests that are only valid if the "fair\n> sampling" assumption is valid. It is now well known that, in general, it\n> is\n> not. In many cases a test that could have shown that the sample is *not*\n> fair is, as far as I can tell, conducted using an inappropriate choice of\n> detector settings. Local realist models as well as quantum theory\n> predict\n> that the total coincidence counts for the "Bell test angles" will all be\n> equal. The ones that need to be tested are the ones in between. [See\n> quant-ph/0210150 and various other papers on the Chaotic Ball model on my\n> web site.]\n>\n> Cheers\n> Caroline\n>\n> Caroline H Thompson\n>\n> ch.thompson1@virgin.net\n> http://freespace.virgin.net/ch.thompson1/\n\nSure that local theories are not ruled out and can explain the quantum\nresults. However, EPR affirms it "should not come from philosophical a\npriori". (locality is a philosphical a priori.)\n\nInstead of an priori, a mathematical definition : The correlation is\ndefined as a superposition of non-locality and locality : Indeed in every\nbasic handbook, one finds :\n\nC(A,B)=<AB> - <A><B> (correlation with variance 1)\n\nThe first term is showed to be not local (Bell), the second is by definition\nlocal, and contains a hidden variable, since the eigenvector of the I\noperator is degenerate (a local measurement in A is given by AxI) : this\ngives rise to the local probabilities :\n\np(+_A)=1/4*(1-cos(theta_A-2phi))\n......\n\nphi is a hidden variable parametrizing the eigenvector of the I (identity)\noperator which "does not disturb system B".\n\n<A>=p(+_A)-p(-_A)....hence <A> depends on cos(phi), and is 0 on average over\nphi.\n\nSince the correlation is of second order in cos(phi) this decreases the\nlatter to -7/8*cos(theta) and :\n\n<CHSH>=7/8*Sqrt(2)=2.47\n\nwhich is almost in agreement with experimental data with efficient detection\nform Boulder NIST, i.e. 2.37.\n\nSo it is an improvement to explain the experimental value out of the basic\ntheory, withtout further hypotheses on the experimental setup.\n\nSincerely.\n\n\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>As it happens, two of Aspect's experiments and the first Geneva experiment
> are among those that are severely affected by the data adjustment. Look
> at
> the raw data and you find that the natural local realist explanation fits
> it
> almost perfectly -- which is surprising really, in view of the various
> other
> factors that one would expect to reduce the visibility of the coincidence
> curves.
>
> Most Bell test experiments use tests that are only valid if the "fair
> sampling" assumption is valid. It is now well known that, in general, it
> is
> not. In many cases a test that could have shown that the sample is *not*
> fair is, as far as I can tell, conducted using an inappropriate choice of
> detector settings. Local realist models as well as quantum theory
> predict
> that the total coincidence counts for the "Bell test angles" will all be
> equal. The ones that need to be tested are the ones in between. [See
> http://www.arxiv.org/abs/quant-ph/0210150 and various other papers on the Chaotic Ball model on my
> web site.]
>
> Cheers
> Caroline
>
> Caroline H Thompson
>
> ch.thompson1@virgin.net
> http://freespace.virgin.net/ch.thompson1/
Sure that local theories are not ruled out and can explain the quantum
results. However, EPR affirms it "should not come from philosophical a
priori". (locality is a philosphical a priori.)
Instead of an priori, a mathematical definition : The correlation is
defined as a superposition of non-locality and locality : Indeed in every
basic handbook, one finds :
C(A,B)=<AB> -[/itex] <A><B> (correlation with variance 1)
The first term is showed to be not local (Bell), the second is by definition
local, and contains a hidden variable, since the eigenvector of the I
operator is degenerate (a local measurement in A is given by AxI) : this
gives rise to the local probabilities :
p(+_A)=1/4*(1-cos(\theta_A-2phi))
......
\phi is a hidden variable parametrizing the eigenvector of the I (identity)
operator which "does not disturb system B".
<A>=p(+_A)-p(-_A)....hence <A> depends on cos(\phi), and is on average over
[itex]\phi.
Since the correlation is of second order in cos(\phi) this decreases the
latter to -7/8*cos(\theta) and :
<CHSH>=7/8*\Sqrt(2)=2.47
which is almost in agreement with experimental data with efficient detection
form Boulder NIST, i.e. 2.37.
So it is an improvement to explain the experimental value out of the basic
theory, withtout further hypotheses on the experimental setup.
Sincerely.
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