<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>touqra@yahoo.com (touqra) wrote in message news:<4a5d59d9.0403310429.355c4744@posting.google. com>...\n> Consider a particle in a box.\n> How can we know its history/past, if QM forbids us to know what is\n> happening inside the box, unless we take measurements? And by\n> measurements, we are trying to find out what is happening at the\n> moment of measurement, not the history of the box.\n> So, does the history of the box exist prior to measurements?\n>\n> What if two observers wanted to measure the property of the particle.\n> Observer A measures first, let say its position. And then, after some\n> time later, observer B measures its position. Before B made any\n> measurements, B has to assume that the particle is in a superposition\n> state. But, A measured the particle already but did not find the\n> particle in any superposition.\n>\n> Isn\'t this a paradox?\n\nHow do we know the history of any physical system? We always have to\napply time evolution, i.e. theory to infer it.\n\nTake the time evolution operator, let\'s call it U(t) giving you the\nevolution of your system by the amount of time t. In classical\nmechanics it\'s easy enough, you know where your particle is after\nmeassurement apply U(-t) to infer where it was. Now in QM things are\ndifferent, a meassurement in general means that you get\nmacroscopically distinct states. We have a system with two states: |a>\nand |b>, and a pointer which has three states |I> for initial, |A> for\nmeasuring position |a> and |B> for |b> now our time evolution looks\nlike this during the meassurement process:\n\nU(T)|a>|I> = |a>|A>\nU(T)|b>|I> = |b>|B>\n\nNow use linearity:\nU(T)(c|a> + d|b>)|I> =\nU(T)(c|a>|I> + d|b>|I>) =\ncU(T)|a>|I> + dU(T)|b>|I> =\nc|a>|A> + d|b>|B>\n\nso the system actually is in a superposition of states here.\n\nThis looks to be rather bad because of course that\'s not what we see,\nwe don\'t see an apparatus in a superposition. However, as |A> and |B>\nare very different microscopically because they are macroscopically\ndistinct we can see that both of these terms evolve individually if we\nlook at the density matrix of things:\n\n<A|B> = 0 because they are so different, they have a different support\nin Hilbert space.\n\nrho = (c|a>|A> + d|b>|B>)(c<a|<A| + d<b|<B|)\n\nto find the evolution of the subsystem trace out the enviroment:\n\ntr_meas=<A|rho|A> + <B|rho|B> = c^2 |a><a| + d^2 |b><b| this reduced\ndensity matrix governs how these subsystems evolve and you see that as\nthere are no diagonal terms this evolution does not correspond to a\nsuperposition in Hilbert space. The sub system has decohered.\n\nIt obeys a classical statistic not a quantum statistic.\n\nNow this is still not classical as we don\'t see classical\nsuperposition of particles either.\n\nHowever there is another thing to remember, we are part of the system.\nWe are part of |I> before the measurement, and evolve into |A> and |B>\nthose are different, different support in Hilbert space, no\ninterference the local subsystems that interact with them (|a> and\n|b>) are no longer in superposition, so the version of us in |A> has\nmeassured |a> the version of us in |B> has meassured |b>.\n\nThis is the origin of many world theories. And pertaining to your\nquestion, the information of the history is now split between the two\nworlds. Each of the physicists can deduce the time evolution U(-t) for\ntheir part of the system but because their systems don\'t interact they\ncan\'t know about the whole history aas they can\'t know about the whole\nsystem.\n\nThis however does not resolve the issue either because if you look at\nthe formulas the probability of finding a particle is encoded in the\nintensity of the system. However we always get two systems, if both\nexist and it\'s just by chance that we are in this one then we would\nexpect a probability of 0.5 for finding both instead of c^2 and d^2\nrespectively.\n\nThe very linearity of the evolution that produces the split makes it\nunaware of the intensities.\n\nSo this does not resolve the problem of meassurement, but it does tell\nus why we have no measurable violations of the superpositiopn\nprinciple. This principle hides itself.\n\nI sketched over many details I did not remember properly, some of the\nstuff here is a matter of opinion as well. Read up on decoherence why\nquantum mechanics can be at the same time practically enormously\nsuccesfull and conceptually so unsatisfying.\n\nThis are BTW features retained in QFT as well. It\'s simply that U is\nmuch more complicated. MUCH more complicated.\n\nHave fun,\nFrank Hellmann\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>touqra@yahoo.com (touqra) wrote in message news:<4a5d59d9.0403310429.355c4744@posting.google.com>...
> Consider a particle in a box.
> How can we know its history/past, if QM forbids us to know what is
> happening inside the box, unless we take measurements? And by
> measurements, we are trying to find out what is happening at the
> moment of measurement, not the history of the box.
> So, does the history of the box exist prior to measurements?
>
> What if two observers wanted to measure the property of the particle.
> Observer A measures first, let say its position. And then, after some
> time later, observer B measures its position. Before B made any
> measurements, B has to assume that the particle is in a superposition
> state. But, A measured the particle already but did not find the
> particle in any superposition.
>
> Isn't this a paradox?
How do we know the history of any physical system? We always have to
apply time evolution, i.e. theory to infer it.
Take the time evolution operator, let's call it U(t) giving you the
evolution of your system by the amount of time t. In classical
mechanics it's easy enough, you know where your particle is after
meassurement apply U(-t) to infer where it was. Now in QM things are
different, a meassurement in general means that you get
macroscopically distinct states. We have a system with two states: |a>
and |b>, and a pointer which has three states |I> for initial, |A> for
measuring position |a> and |B> for |b> now our time evolution looks
like this during the meassurement process:
U(T)|a>|I> = |a>|A>[/itex]
U(T)|b>|I> = |b>|B>
Now use linearity:
U(T)(c|a> + d|b>)|I> =
U(T)(c|a>|I> + d|b>|I>) =
cU(T)|a>|I> + dU(T)|b>|I> =
c|a>|A> + d|b>|B>
so the system actually is in a superposition of states here.
This looks to be rather bad because of course that's not what we see,
we don't see an apparatus in a superposition. However, as |A> and |B>
are very different microscopically because they are macroscopically
distinct we can see that both of these terms evolve individually if we
look at the density matrix of things:
<A|B> = because they are so different, they have a different support
in Hilbert space.
[itex]\rho = (c|a>|A> + d|b>|B>)(c<a|<A| + d<b|<B|)
to find the evolution of the subsystem trace out the enviroment:
tr_meas=<A|\rho|A> + <B|\rho|B> = c^2 |a><a| + d^2 |b><b| this reduced
density matrix governs how these subsystems evolve and you see that as
there are no diagonal terms this evolution does not correspond to a
superposition in Hilbert space. The sub system has decohered.
It obeys a classical statistic not a quantum statistic.
Now this is still not classical as we don't see classical
superposition of particles either.
However there is another thing to remember, we are part of the system.
We are part of |I> before the measurement, and evolve into |A> and |B>
those are different, different support in Hilbert space, no
interference the local subsystems that interact with them (|a> and
|b>) are no longer in superposition, so the version of us in |A> has
meassured |a> the version of us in |B> has meassured |b>.
This is the origin of many world theories. And pertaining to your
question, the information of the history is now split between the two
worlds. Each of the physicists can deduce the time evolution U(-t) for
their part of the system but because their systems don't interact they
can't know about the whole history aas they can't know about the whole
system.
This however does not resolve the issue either because if you look at
the formulas the probability of finding a particle is encoded in the
intensity of the system. However we always get two systems, if both
exist and it's just by chance that we are in this one then we would
expect a probability of .5 for finding both instead of c^2 and d^2
respectively.
The very linearity of the evolution that produces the split makes it
unaware of the intensities.
So this does not resolve the problem of meassurement, but it does tell
us why we have no measurable violations of the superpositiopn
principle. This principle hides itself.
I sketched over many details I did not remember properly, some of the
stuff here is a matter of opinion as well. Read up on decoherence why
quantum mechanics can be at the same time practically enormously
succesfull and conceptually so unsatisfying.
This are BTW features retained in QFT as well. It's simply that U is
much more complicated. MUCH more complicated.
Have fun,
Frank Hellmann