Quantum-Classical Boundary [Archive]

Kanwarpreet Grewal

Aug17-04, 11:26 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\nHi,\n\nWhat theories explain the emergence of a classical world from\nquantum\nmechanics? I know that decoherence theory and Bohr\'s correspondence\nprinciple\ntry to explain this. Are decoherence theory and correspondence\nprinciple\ncompatible with each other? Are there any other theories that explain\nthis?\nAre there people who disagree with decoherence theory?\n\nKanwar\n\n--\n|=============================================== =======|\nGo, wondrous creature! mount where Science guides:\nGo, measure earth, weigh air, and state the tides:\nInstruct the planets in what orbs to run,\nCorrect old time and regulate the Sun;\n|=========================================== ===========|\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>Hi,

What theories explain the emergence of a classical world from
quantum
mechanics? I know that decoherence theory and Bohr's correspondence
principle
try to explain this. Are decoherence theory and correspondence
principle
compatible with each other? Are there any other theories that explain
this?
Are there people who disagree with decoherence theory?

Kanwar

--
|================================================= =====|
Go, wondrous creature! mount where Science guides:
Go, measure earth, weigh air, and state the tides:
Instruct the planets in what orbs to run,
Correct old time and regulate the Sun;
|================================================= =====|

Frank Hellmann

Aug18-04, 04:08 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\nKanwarpreet Grewal <kanwar@cadence.com> wrote in message news:<4121E6EB.566CBB0B@cadence.com>...\n> Hi,\n>\n> What theories explain the emergence of a classical world from\n> quantum\n> mechanics? I know that decoherence theory and Bohr\'s correspondence\n> principle\n\n(Also look up the Ehrenfest theorems)\n\n> try to explain this. Are decoherence theory and correspondence\n> principle\n> compatible with each other? Are there any other theories that explain\n> this?\n> Are there people who disagree with decoherence theory?\n>\n> Kanwar\n\nDecoherence is simply a consequence of unitary evolution. It also\nappears to be nonunitary, though of course it isn\'t (just like\nstatistical physics seem to be statistical though they are really\ndeterministic).\nIn so far decoherence is physical fact, experimentally observed and no\nphysicist can disagree with it.\nHowever, there is disagreement on what it can and can not do. As far\nas I am aware people generally agree that it does not solve the\nmeassurement problem, the central problem of the emergence of a\nclassical world.\nThere are claims that many world interpretations of decoherence can\ngive a classical limit without puting in probabilities by hand, but I\ndon\'t understand the central papers yet, there seems to be non\nconsensus on that.\n\nThe bottom line is, decoherence explains why QM systems are eventually\ngoverned by (nearly) classical statistics if meassured, but can\'t\nexplain the existence of the meassurement apparatus, and the\nassosciated classical world itself.\n\nThe correspondence principle is thus a requirement which is not met by\nQM in the whole. (Though the terms of it\'s noncompliance are so subtle\nthat they hide themself from experimental detection via decoherence.\nWhich has to be a deep result IMHO!)\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>Kanwarpreet Grewal <kanwar@cadence.com> wrote in message news:<4121E6EB.566CBB0B@cadence.com>...
> Hi,
>
> What theories explain the emergence of a classical world from
> quantum
> mechanics? I know that decoherence theory and Bohr's correspondence
> principle

(Also look up the Ehrenfest theorems)

> try to explain this. Are decoherence theory and correspondence
> principle
> compatible with each other? Are there any other theories that explain
> this?
> Are there people who disagree with decoherence theory?
>
> Kanwar

Decoherence is simply a consequence of unitary evolution. It also
appears to be nonunitary, though of course it isn't (just like
statistical physics seem to be statistical though they are really
deterministic).
In so far decoherence is physical fact, experimentally observed and no
physicist can disagree with it.
However, there is disagreement on what it can and can not do. As far
as I am aware people generally agree that it does not solve the
meassurement problem, the central problem of the emergence of a
classical world.
There are claims that many world interpretations of decoherence can
give a classical limit without puting in probabilities by hand, but I
don't understand the central papers yet, there seems to be non
consensus on that.

The bottom line is, decoherence explains why QM systems are eventually
governed by (nearly) classical statistics if meassured, but can't
explain the existence of the meassurement apparatus, and the
assosciated classical world itself.

The correspondence principle is thus a requirement which is not met by
QM in the whole. (Though the terms of it's noncompliance are so subtle
that they hide themself from experimental detection via decoherence.
Which has to be a deep result IMHO!)

---
frank

Aaron Denney

Aug18-04, 04:08 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\n(reformatted, as line breaks were in odd places.)\nOn 2004-08-17, Kanwarpreet Grewal <kanwar@cadence.com> wrote:\n> What theories explain the emergence of a classical world\n> from quantum mechanics? I know that decoherence theory and Bohr\'s\n> correspondence principle try to explain this. Are decoherence theory\n> and correspondence principle compatible with each other? Are there any\n> other theories that explain this? Are there people who disagree with\n> decoherence theory?\n\nBohr\'s correspondence principle isn\'t a theory, just a guiding line\nthat "in some suitable limit" quantum theories should make the same\npredictions as a classical analog. It provides no mechanism, it\'s\njust a heuristic.\n\nDecoherence theory is an attempt to provide a mechanism. Different\nphysicists will say different things about whether it fully succeeds,\nthough I believe there is a wide consensus that it does explain many\nthings.\n\nThe somewhat controversial question is whether decoherence can explain\nthe "measurement problem".\n\nFor a good overview of the decoherence program, I\'d suggest reading\n_Decoherence and the Appearance of a Classical World in Quantum Theory_,\nby D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, and\nH.D. Zeh. (Springer-Verlag, 1996, ISBN 3-540-61394-3)\n\nMany simple models do have easily found "semi-classical" states that\nshare many classical properties, and are close analogs to classical\nstates in the same Hamilitonian -- e.g. high N orbitals, coherent states\nof the harmonic oscillator. The questions are what distinguishes these\nstates, do they show up in appropriate limits, and why and how, if they\ndo.\n\n--\nAaron Denney\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>(reformatted, as line breaks were in odd places.)
On 2004-08-17, Kanwarpreet Grewal <kanwar@cadence.com> wrote:
> What theories explain the emergence of a classical world
> from quantum mechanics? I know that decoherence theory and Bohr's
> correspondence principle try to explain this. Are decoherence theory
> and correspondence principle compatible with each other? Are there any
> other theories that explain this? Are there people who disagree with
> decoherence theory?

Bohr's correspondence principle isn't a theory, just a guiding line
that "in some suitable limit" quantum theories should make the same
predictions as a classical analog. It provides no mechanism, it's
just a heuristic.

Decoherence theory is an attempt to provide a mechanism. Different
physicists will say different things about whether it fully succeeds,
though I believe there is a wide consensus that it does explain many
things.

The somewhat controversial question is whether decoherence can explain
the "measurement problem".

For a good overview of the decoherence program, I'd suggest reading
_Decoherence and the Appearance of a Classical World in Quantum Theory_,
by D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, and
H.D. Zeh. (Springer-Verlag, 1996, ISBN 3-540-61394-3)

Many simple models do have easily found "semi-classical" states that
share many classical properties, and are close analogs to classical
states in the same Hamilitonian -- e.g. high N orbitals, coherent states
of the harmonic oscillator. The questions are what distinguishes these
states, do they show up in appropriate limits, and why and how, if they
do.

--
Aaron Denney
-><-

Arnold Neumaier

Aug19-04, 12:36 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>Kanwarpreet Grewal wrote:\n>\n> What theories explain the emergence of a classical world from\n> quantum\n> mechanics? I know that decoherence theory and Bohr\'s correspondence\n> principle\n> try to explain this. Are decoherence theory and correspondence\n> principle\n> compatible with each other? Are there any other theories that explain\n> this?\n> Are there people who disagree with decoherence theory?\n\nDecoherence in the narrow sense is not disputed. But some adherents\nof it make claims that are far too strong. Maximilian Schlosshauer\nprovides in quant-ph/0312059 an excellent survey of decoherence with\na discussion of the state of affairs of the measurement problem and the\nquantum-classical boundary.\n\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>Kanwarpreet Grewal wrote:
>
> What theories explain the emergence of a classical world from
> quantum
> mechanics? I know that decoherence theory and Bohr's correspondence
> principle
> try to explain this. Are decoherence theory and correspondence
> principle
> compatible with each other? Are there any other theories that explain
> this?
> Are there people who disagree with decoherence theory?

Decoherence in the narrow sense is not disputed. But some adherents
of it make claims that are far too strong. Maximilian Schlosshauer
provides in http://www.arxiv.org/abs/quant-ph/0312059 an excellent survey of decoherence with
a discussion of the state of affairs of the measurement problem and the
quantum-classical boundary.

Arnold Neumaier

Kanwarpreet Grewal

Sep2-04, 02:27 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>Hi,\n\nThanks to everyone who replied to my orignal questions.\n\nSo it seems that decoherence theory\'s basic "selling point" is that it\nremoves the non-diagonal terms from the density matrix. So it does not\nexplain why quantum mechanics is probabilistic. Instead it shows that\nclassical mechanics the intereferences of quantum mechanics are lost.\nBut probability is involved here as well: because only one of the\npossibilities is realized in classical mechanics. So it seems that the\nmeasurment problem is still not solved: I still do not understand what\ncollapse is. If it is a physical "phenomenon" then how to we measure it.\nHow much time does it take, what does it depend on.... etc.\n\nI dont know how others feel about this but classical and quantum world\nstill seem like two different worlds.\n\nI know that some people stay away from interpretation of QM considering\nit a topic for Philosophers. But the problem is far more severe than\npure Philosophy. It is Physics! there are two different world of ideas\nand we must have only one theory.\n\nWhat are the views of others on this.\n\nPS: I dont want my grandkids to come and tell me 50 years later:\n"Granddad, you lived in a world in which you did not even know how\nprobabilities enter into the picture. And you did not think WHY and\ninstead you used that dumb theory to study phenomenon related to light.!\nand even wrote papers!!!!"\n\nI dont want to be laughed at, but I have a feeling that I will be laughed\nat!\n\n\nKanwar\n\n\nArnold Neumaier wrote:\n\n> Kanwarpreet Grewal wrote:\n> >\n> > What theories explain the emergence of a classical world from\n> > quantum\n> > mechanics? I know that decoherence theory and Bohr\'s correspondence\n> > principle\n> > try to explain this. Are decoherence theory and correspondence\n> > principle\n> > compatible with each other? Are there any other theories that explain\n> > this?\n> > Are there people who disagree with decoherence theory?\n>\n> Decoherence in the narrow sense is not disputed. But some adherents\n> of it make claims that are far too strong. Maximilian Schlosshauer\n> provides in quant-ph/0312059 an excellent survey of decoherence with\n> a discussion of the state of affairs of the measurement problem and the\n> quantum-classical boundary.\n>\n> Arnold 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>Hi,

Thanks to everyone who replied to my orignal questions.

So it seems that decoherence theory's basic "selling point" is that it
removes the non-diagonal terms from the density matrix. So it does not
explain why quantum mechanics is probabilistic. Instead it shows that
classical mechanics the intereferences of quantum mechanics are lost.
But probability is involved here as well: because only one of the
possibilities is realized in classical mechanics. So it seems that the
measurment problem is still not solved: I still do not understand what
collapse is. If it is a physical "phenomenon" then how to we measure it.
How much time does it take, what does it depend on.... etc.

I dont know how others feel about this but classical and quantum world
still seem like two different worlds.

I know that some people stay away from interpretation of QM considering
it a topic for Philosophers. But the problem is far more severe than
pure Philosophy. It is Physics! there are two different world of ideas
and we must have only one theory.

What are the views of others on this.

PS: I dont want my grandkids to come and tell me 50 years later:
"Granddad, you lived in a world in which you did not even know how
probabilities enter into the picture. And you did not think WHY and
instead you used that dumb theory to study phenomenon related to light.!
and even wrote papers!!!!"

I dont want to be laughed at, but I have a feeling that I will be laughed
at!

Kanwar

Arnold Neumaier wrote:

> Kanwarpreet Grewal wrote:
> >
> > What theories explain the emergence of a classical world from
> > quantum
> > mechanics? I know that decoherence theory and Bohr's correspondence
> > principle
> > try to explain this. Are decoherence theory and correspondence
> > principle
> > compatible with each other? Are there any other theories that explain
> > this?
> > Are there people who disagree with decoherence theory?
>
> Decoherence in the narrow sense is not disputed. But some adherents
> of it make claims that are far too strong. Maximilian Schlosshauer
> provides in http://www.arxiv.org/abs/quant-ph/0312059 an excellent survey of decoherence with
> a discussion of the state of affairs of the measurement problem and the
> quantum-classical boundary.
>
> Arnold Neumaier

Arnold Neumaier

Sep4-04, 02:04 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>Kanwarpreet Grewal wrote:\n\n> So it seems that decoherence theory\'s basic "selling point" is that it\n> removes the non-diagonal terms from the density matrix.\n\nYes\n\n\n> So it does not explain why quantum mechanics is probabilistic.\n\nYes; but it shows how classical behavior arises out of quantum behavior.\n\n\n> So it seems that the measurement problem is still not solved:\n> I still do not understand what collapse is.\n\nIndeed.\n\n\n> If it is a physical "phenomenon" then how to we measure it.\n\nIt is a physical phenomenon. We see it because we see single traces\nparticles leave in a bubble chamber, and not their superpositions.\n\n\n> How much time does it take, what does it depend on.... etc.\n\nThis is an ill-posed question, since the models where it is applied to\nis inaccurate anyway. In the orthodox theory, the collapse happens\ninstantaneously upon an ideal (von Neumann) measurement.\nBut real measurements are not ideal, and the collapse is neither\ninstantaneous nor in fact complete.\n\n\n> I dont know how others feel about this but classical and quantum world\n> still seem like two different worlds.\n\nAs different as the world under a microscope and the world above\nthe skies. It is a difference of space and time scales.\nClassical just means slowly changing in space and time,\nand hence accessible to our eyes. Being slow, one can average over\nall fast oscillations - this is what decoherence is all about.\nAnd then a classical world emerges. Get the book advertised under\nhttp://www.decoherence.de/ to learn the details.\n\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>Kanwarpreet Grewal wrote:

> So it seems that decoherence theory's basic "selling point" is that it
> removes the non-diagonal terms from the density matrix.

Yes

> So it does not explain why quantum mechanics is probabilistic.

Yes; but it shows how classical behavior arises out of quantum behavior.

> So it seems that the measurement problem is still not solved:
> I still do not understand what collapse is.

Indeed.

> If it is a physical "phenomenon" then how to we measure it.

It is a physical phenomenon. We see it because we see single traces
particles leave in a bubble chamber, and not their superpositions.

> How much time does it take, what does it depend on.... etc.

This is an ill-posed question, since the models where it is applied to
is inaccurate anyway. In the orthodox theory, the collapse happens
instantaneously upon an ideal (von Neumann) measurement.
But real measurements are not ideal, and the collapse is neither
instantaneous nor in fact complete.

> I dont know how others feel about this but classical and quantum world
> still seem like two different worlds.

As different as the world under a microscope and the world above
the skies. It is a difference of space and time scales.
Classical just means slowly changing in space and time,
and hence accessible to our eyes. Being slow, one can average over
all fast oscillations - this is what decoherence is all about.
And then a classical world emerges. Get the book advertised under
http://www.decoherence.de/ to learn the details.

Arnold Neumaier

Joe Rongen

Sep4-04, 02:06 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>"Kanwarpreet Grewal" <kanwar@cadence.com> wrote in\nmessage news:4137085D.B9BA76CA@cadence.com...\n[snip]\n\n> So it seems that the measurment problem is still not solved:\n> I still do not understand what collapse is.\n\nIn short form; a collapse happens for instance, in a cathode ray\ntube when an electron is leaving the cathode and is electronically\ndirected at your TV screen. When the electron hits the phosphor\ninside the tube that is the actual collapse. The indirect results of the\ncollapse are usually displayed as tiny parts of the visible TV picture.\n\n[snip]\n\n> But the problem is far more severe than\n> pure Philosophy. It is Physics! there are two different world of ideas\n> and we must have only one theory.\n>\n> What are the views of others on this.\n\nWell, Lakatos (1970) view was that " the way we interpret\nthe results of our experiments is rarely (perhaps never) so\nas to contradict some accepted theory.\n\n> PS: I dont want my grandkids to come and tell me 50 years later:\n> "Granddad, you lived in a world in which you did not even know how\n> probabilities enter into the picture.\n\nShould one not rather worry about producing faster\nponies, this since all the oil will have ran out by then?\n\n> And you did not think WHY and instead you used that\n> dumb theory to study phenomenon related to light.!\n> and even wrote papers!!!!"\n\nNo one is stopping you to do better, after all the only way\nto be absolutely sure something gets done right is to do it\nyourself.\n\nRegards Joe\n\n\n---\nOutgoing mail is certified Virus Free.\nChecked by AVG anti-virus system (http://www.grisoft.com).\nVersion: 6.0.749 / Virus Database: 501 - Release Date: 9/1/04\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>"Kanwarpreet Grewal" <kanwar@cadence.com> wrote in
message news:4137085D.B9BA76CA@cadence.com...
[snip]

> So it seems that the measurment problem is still not solved:
> I still do not understand what collapse is.

In short form; a collapse happens for instance, in a cathode ray
tube when an electron is leaving the cathode and is electronically
directed at your TV screen. When the electron hits the phosphor
inside the tube that is the actual collapse. The indirect results of the
collapse are usually displayed as tiny parts of the visible TV picture.

[snip]

> But the problem is far more severe than
> pure Philosophy. It is Physics! there are two different world of ideas
> and we must have only one theory.
>
> What are the views of others on this.

Well, Lakatos (1970) view was that " the way we interpret
the results of our experiments is rarely (perhaps never) so
as to contradict some accepted theory.

> PS: I dont want my grandkids to come and tell me 50 years later:
> "Granddad, you lived in a world in which you did not even know how
> probabilities enter into the picture.

Should one not rather worry about producing faster
ponies, this since all the oil will have ran out by then?

> And you did not think WHY and instead you used that
> dumb theory to study phenomenon related to light.!
> and even wrote papers!!!!"

No one is stopping you to do better, after all the only way
to be absolutely sure something gets done right is to do it
yourself.

Regards Joe

---
Outgoing mail is certified Virus Free.
Checked by AVG anti-virus system (http://www.grisoft.com).
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