<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>On 19 Aug 2004 10:26:27 -0400, Arnold Neumaier\n<Arnold.Neumaier@univie.ac.at> wrote:\n\n>Picking on the language is not very constructive. But if you like,\n>I can be more precise:\n>\n>\'\'From a stochstic process used to model a system, one can only infer\n>properties about large ensembles of identically prepared systems.\n>(And only in the approximation that this ensemble is representative\n>of the theoretical, infinite ensemble defined by the stochastic model.)\n\nArnold, you will again complain about picking on the language, but what\nyou wrote above makes no sense either. How large an ensemble must be to\nbe "large?". The devil is always in the details. You will not escape it!\n\n\n>>>A random number generator only simulates a stochastic process\n>>>(of identically distributed numbers). If you run a binary random number\n>>>generator once, it just gives you 0 or 1, and not both with a certain\n>>>probability. To say the 1 occured with probability 1/2 makes only sense\n>>>if you consider large ensembles...\n>>\n>> Large ensembles will not help. They need to be infinite.\n>\n>Strictly speaking, yes. But in the approximations physicists are\n>generally working, this amounts to the same. In the limit of arbitrarily\n>large samples, the statistical uncertainty goes to zero, under reasonable\n>assumptions.\n\nArnold, again you are talking about things that make no sense\nwhatsoever. What are "approximations physicists are generally working?"\nPhysicists are working with single atoms! They are working with single\nuniverse! What are "reasonable assumptions?" What does it means "goes to\nzero?" You mean "limit"? What infinite limit has to do with ANY finite\nsample? Don\'t you know that you can skip any finite part of a convergent\nsequence and it will still have the same infinite limit?\n\n\n>> But nothing\n>> infinite is at disposal of an experimentalist. Random generator is\n>> pretty good to simulate real events, like a mathematical line is pretty\n>> good to simulate real particle trajectory.\n>\n>Well, EEQT is supposed to be theoretical physics, explaining things\n>as they _are_. I agree that one can use number generators to simulate\n>trajectories that look like \'typical\' realizations of your stochastic\n>processes. But one can use arbitrary sequences of numbers instead of\n>sequences generated by random number generators, and one still obtains\n>realizations of your stochastic process, though now untypical,\n>less likely ones.\n\nThe same applies to any theory involving probabilities. Are going to get\nrid of probabilities at all? Chase them out of physics, economy,\ngenetics, applied information theory?\n\n>\n>\n>This is why I said that EEQT cannot be the complete answer:\n>What guarantees in your setting that the \'true\', unique trajectory that\n>actually happens is typical rather than atypical? And how typical is it?\n\nI will answer your question with real pleasure, provided you define\nprecisely for me the terms you are using: "typical" vs "atypical"!\n\n\n>>>>>For a single system you cannot apply probabilities,\n>>>>>but you need them in your algorithm.\n>>>>\n>>>>I need a random number generator. That is all I need.\n>>>\n>>>But this is already importing ensembles. Any finite sequence of numbers\n>>>could have been produced by a number generator; if you only have a single\n>>>instance, there is no sure way of telling different sequences apart.\n>>\n>> You can criticize the same way application of ANY mathematical concept\n>> to the real world. We always use models, idealizations and\n>> approximations.\n>\n>Not quite. My criticism would not apply to a Newtonian world and\n>measurements with worst case errors. While one only obtains approximate\n>agreement, one can check whether a prediction is correct, false, or\n>borderline.\n\nAgain you are using terms that have no precise definition, like\n"correct", "borderline" etc. You assume that these are well defined\nnotions, but they are not. You can ignore this fact. Or you can take\ninto account. Like with everything.\n\n>In a stochastic setting, _every_ realization of a stochastic process has\n>probability 0; exactly one of them actually happens - - - the certainty\n>status of a stochastic model for a single history seems comparatively\n>poor.\n\nThere is this magic term: "expectation". It magically adds subjective\nelement to probability. Given a stochastic process, if it is a correct\none, we can compute correct expectations. There is no guarantee that\nexpecting these expectations will be helpful, yet when there is nothing\nbetter than expectations, we do better (as it seems) by expecting\ncorrectly computed expectations rather than incorrectly computed ones.\nWhy is it so is a great mystery, but it is always better, as it seems,\nto base our predictions on knowledge (however incomplete) rather than on\nignorance.\n\nI am proposing a model that can be used to compute expectations, and I\nsuggest that it is a model that simulates REAL events in a real world,\nand that it simulates these events better than other models.\n\nIt allows us (I think) to have an insight into a possible real\nmechanism. Insights are as important as numbers. Because\nwith insight we can find ways of computing new numbers, that we would\nnot even know about without insights.\n\nThus EEQT has a double role: it allows us to compute expectations (and,\nin fact, more expectations than usual QT), and it also allows us to have\ninsights into the possible workings of the Nature. These insights may\nhappen to be wrong - the future will show.\n\n\n>>>>It is well known\n>>>>that chaotic dynamics can produce random sequences practically\n>>>>indistinguishable from random ones.\n>>>\n>>>Once one allows FAPP arguments in the foundations of QM, all problems\n>>>are gone. The question is whether there is a way to avoid the FAPP\n>>>arguments.\n>>\n>> There is no way to avoid FAPP arguments.\n>\n>Such arguments are not needed in classical physics, including relativity.\n>This has the consequence that in these disciplines there is no such\n>continuing debate about the foundations - no longer needing FAPP means\n>having found the foundations.\n\nHere again I disagree. Think of the use of "time" in classical physics.\nYou assume that time "exists" and you model it by a parameter T. But we\nhave no idea what is times, whether it "flows" or whether time that does\nnot yet "exists" can be assumed to "exist". WE have no idea, and we do\nnot want to ask these most important questions, because we think that\nthese questions are not important FAPP!\n\n\n>>>>Do you mean that there is no way to\n>>>>generate a random number? Everybody does it. Probably you will complain\n>>>>about pseudo-random rather than random? Well, pseudo-random exist, and\n>>>>chaotic systems exist. I am happy with them.\n>>>\n>>>They exist only given an underlying deterministic system.\n>>>Where is that in EEQT?\n>>\n>> EEQT is an "event enhanced quantum theory". It does not pretend to be a\n>> "theory of everything". Therefore it makes models. Like in\n>> electrodynamics, we know that electrons are not point particles, that\n>> they have internal structure, but we neglect this structure and take\n>> only as much as we really need to answer certain questions. For instance\n>> we can even classically model "spin" of the electron (Bargman-Telegdi)\n>> without really knowing what is the "real nature of the spin".\n>\n>Ok. So you agree that EEQT is an incomplete theory, even enhanced by\n>quantum fields with quarks and leptons, and that its structure needs to\n>be modified on deeper levels?\n\nOf course it is an incomplete theory! I would say even more: I consider\nit quite possible that there is no complete theory and that there never\nwill be one.\n\n\n>> And applying\n>> this mechanisms allows us to predict more than the standard quantum\n>> theory. Moreover, this mechanism is not in contradiction with\n>> observations - as far as I know.\n>>\n>>>My conjecture is that things in QM need a similar point of view.\n>>>Seen from such an angle, there is little fundamental difference\n>>>between the Copenhagen interpretation and your EEQT - both need some\n>>>classical information and statistical techniques to deduce the most\n>>>likely underlying scenario.\n>>\n>> The difference is in the predictive power: for instance tunneling time,\n>> time of arrival etc.\n>\n>Tunneling times can be computed approximately using standard quantum\n>mechanics - quantum chemistry of reaction rates is about that.\n\nSo, please, compute me time needed for a particle to tunnel through a\npotential barrier, and compute it from first principles! For this, of\ncourse, you must know how to model time in quantum mechanics.\n\nBut before doing so you may like to examine different approaches to\nthe "tunneling times" (Landauer, Bohm, etc. etc.) so that you will be\nable to understand why there is a discussion about this subject, why\nthere are controversies, why there is no one generally accepted\ndefinition.\n\nYou see, the "detection" event can not even be defined within the\nstandard quantum theory. Wigner tried to do it, but his paper has\na mathematical error and is inconclusive. There are theories of\n"continuous monitoring" but they are also based on hidden assumptions.\nEEQT may be wrong and incomplete, but at least the assumptions are made\nclear: 1) a better model is based on an algebra with a nontrivial center\n2) a better model is based on Linblad type evolution\n\nIf you read papers trying to model "quantum measurements" using unitary\nevolution, you will always find that there is some cheating involved,\nsome sweeping the dirt under the rug, so that no one will see it right\naway!\n\nark\n--\n\nArkadiusz Jadczyk\nhttp://quantumfuture.net/quantum_future/jadpub.htm\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>On 19 Aug 2004 10:26:27 -0400, Arnold Neumaier
<Arnold.Neumaier@univie.ac.at> wrote:
>Picking on the language is not very constructive. But if you like,
>I can be more precise:
>
>''From a stochstic process used to model a system, one can only infer
>properties about large ensembles of identically prepared systems.
>(And only in the approximation that this ensemble is representative
>of the theoretical, infinite ensemble defined by the stochastic model.)
Arnold, you will again complain about picking on the language, but what
you wrote above makes no sense either. How large an ensemble must be to
be "large?". The devil is always in the details. You will not escape it!
>>>A random number generator only simulates a stochastic process
>>>(of identically distributed numbers). If you run a binary random number
>>>generator once, it just gives you or 1, and not both with a certain
>>>probability. To say the 1 occured with probability 1/2 makes only sense
>>>if you consider large ensembles...
>>
>> Large ensembles will not help. They need to be infinite.
>
>Strictly speaking, yes. But in the approximations physicists are
>generally working, this amounts to the same. In the limit of arbitrarily
>large samples, the statistical uncertainty goes to zero, under reasonable
>assumptions.
Arnold, again you are talking about things that make no sense
whatsoever. What are "approximations physicists are generally working?"
Physicists are working with single atoms! They are working with single
universe! What are "reasonable assumptions?" What does it means "goes to
zero?" You mean "limit"? What infinite limit has to do with ANY finite
sample? Don't you know that you can skip any finite part of a convergent
sequence and it will still have the same infinite limit?
>> But nothing
>> infinite is at disposal of an experimentalist. Random generator is
>> pretty good to simulate real events, like a mathematical line is pretty
>> good to simulate real particle trajectory.
>
>Well, EEQT is supposed to be theoretical physics, explaining things
>as they _are_. I agree that one can use number generators to simulate
>trajectories that look like 'typical' realizations of your stochastic
>processes. But one can use arbitrary sequences of numbers instead of
>sequences generated by random number generators, and one still obtains
>realizations of your stochastic process, though now untypical,
>less likely ones.
The same applies to any theory involving probabilities. Are going to get
rid of probabilities at all? Chase them out of physics, economy,
genetics, applied information theory?
>
>
>This is why I said that EEQT cannot be the complete answer:
>What guarantees in your setting that the 'true', unique trajectory that
>actually happens is typical rather than atypical? And how typical is it?
I will answer your question with real pleasure, provided you define
precisely for me the terms you are using: "typical" vs "atypical"!
>>>>>For a single system you cannot apply probabilities,
>>>>>but you need them in your algorithm.
>>>>
>>>>I need a random number generator. That is all I need.
>>>
>>>But this is already importing ensembles. Any finite sequence of numbers
>>>could have been produced by a number generator; if you only have a single
>>>instance, there is no sure way of telling different sequences apart.
>>
>> You can criticize the same way application of ANY mathematical concept
>> to the real world. We always use models, idealizations and
>> approximations.
>
>Not quite. My criticism would not apply to a Newtonian world and
>measurements with worst case errors. While one only obtains approximate
>agreement, one can check whether a prediction is correct, false, or
>borderline.
Again you are using terms that have no precise definition, like
"correct", "borderline" etc. You assume that these are well defined
notions, but they are not. You can ignore this fact. Or you can take
into account. Like with everything.
>In a stochastic setting, _every_ realization of a stochastic process has
>probability 0; exactly one of them actually happens - - - the certainty
>status of a stochastic model for a single history seems comparatively
>poor.
There is this magic term: "expectation". It magically adds subjective
element to probability. Given a stochastic process, if it is a correct
one, we can compute correct expectations. There is no guarantee that
expecting these expectations will be helpful, yet when there is nothing
better than expectations, we do better (as it seems) by expecting
correctly computed expectations rather than incorrectly computed ones.
Why is it so is a great mystery, but it is always better, as it seems,
to base our predictions on knowledge (however incomplete) rather than on
ignorance.
I am proposing a model that can be used to compute expectations, and I
suggest that it is a model that simulates REAL events in a real world,
and that it simulates these events better than other models.
It allows us (I think) to have an insight into a possible real
mechanism. Insights are as important as numbers. Because
with insight we can find ways of computing new numbers, that we would
not even know about without insights.
Thus EEQT has a double role: it allows us to compute expectations (and,
in fact, more expectations than usual QT), and it also allows us to have
insights into the possible workings of the Nature. These insights may
happen to be wrong - the future will show.
>>>>It is well known
>>>>that chaotic dynamics can produce random sequences practically
>>>>indistinguishable from random ones.
>>>
>>>Once one allows FAPP arguments in the foundations of QM, all problems
>>>are gone. The question is whether there is a way to avoid the FAPP
>>>arguments.
>>
>> There is no way to avoid FAPP arguments.
>
>Such arguments are not needed in classical physics, including relativity.
>This has the consequence that in these disciplines there is no such
>continuing debate about the foundations - no longer needing FAPP means
>having found the foundations.
Here again I disagree. Think of the use of "time" in classical physics.
You assume that time "exists" and you model it by a parameter T. But we
have no idea what is times, whether it "flows" or whether time that does
not yet "exists" can be assumed to "exist". WE have no idea, and we do
not want to ask these most important questions, because we think that
these questions are not important FAPP!
>>>>Do you mean that there is no way to
>>>>generate a random number? Everybody does it. Probably you will complain
>>>>about pseudo-random rather than random? Well, pseudo-random exist, and
>>>>chaotic systems exist. I am happy with them.
>>>
>>>They exist only given an underlying deterministic system.
>>>Where is that in EEQT?
>>
>> EEQT is an "event enhanced quantum theory". It does not pretend to be a
>> "theory of everything". Therefore it makes models. Like in
>> electrodynamics, we know that electrons are not point particles, that
>> they have internal structure, but we neglect this structure and take
>> only as much as we really need to answer certain questions. For instance
>> we can even classically model "spin" of the electron (Bargman-Telegdi)
>> without really knowing what is the "real nature of the spin".
>
>Ok. So you agree that EEQT is an incomplete theory, even enhanced by
>quantum fields with quarks and leptons, and that its structure needs to
>be modified on deeper levels?
Of course it is an incomplete theory! I would say even more: I consider
it quite possible that there is no complete theory and that there never
will be one.
>> And applying
>> this mechanisms allows us to predict more than the standard quantum
>> theory. Moreover, this mechanism is not in contradiction with
>> observations - as far as I know.
>>
>>>My conjecture is that things in QM need a similar point of view.
>>>Seen from such an angle, there is little fundamental difference
>>>between the Copenhagen interpretation and your EEQT - both need some
>>>classical information and statistical techniques to deduce the most
>>>likely underlying scenario.
>>
>> The difference is in the predictive power: for instance tunneling time,
>> time of arrival etc.
>
>Tunneling times can be computed approximately using standard quantum
>mechanics - quantum chemistry of reaction rates is about that.
So, please, compute me time needed for a particle to tunnel through a
potential barrier, and compute it from first principles! For this, of
course, you must know how to model time in quantum mechanics.
But before doing so you may like to examine different approaches to
the "tunneling times" (Landauer, Bohm, etc. etc.) so that you will be
able to understand why there is a discussion about this subject, why
there are controversies, why there is no one generally accepted
definition.
You see, the "detection" event can not even be defined within the
standard quantum theory. Wigner tried to do it, but his paper has
a mathematical error and is inconclusive. There are theories of
"continuous monitoring" but they are also based on hidden assumptions.
EEQT may be wrong and incomplete, but at least the assumptions are made
clear: 1) a better model is based on an algebra with a nontrivial center
2) a better model is based on Linblad type evolution
If you read papers trying to model "quantum measurements" using unitary
evolution, you will always find that there is some cheating involved,
some sweeping the dirt under the rug, so that no one will see it right
away!
ark
--
Arkadiusz Jadczyk
http://quantumfuture.net/quantum_future/jadpub.htm
--