Re: Forms of relativistic dynamics [Archive]

Arnold Neumaier

Dec2-04, 06:15 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>Eugene Stefanovich wrote:\n\n> 1. I don\'t think you can give an operational definition of such things\n> as "timelike 4-vector" or "hyperboloid in the past". Experimentalists\n> do not use these concepts.\n\nI am not talking about operational concepts but about foundations - getting\nthe mathematical concepts right to be able to do correct physics.\nWithout correct concepts operational statements have no meaning.\nThe theory defines what a measurement is. Outside the immediate realm of\neveryday experience, one needs already the conceptual basis to even\ndiscuss what has operational meaning.\n\nI am telling you the conventional way physicists view these things,\nwith some fine points added due to my own understanding.\n(For example, I use a past hyperboloid instead of a future one,\nwhich is mathematically equivalent but gives more intuition to the\nformal construction.)\nPhysicists fared well with this view, hence this needs no further\njustification. Experimentalists working on topics requiring a relativistic\ndescription don\'t have any difficulties understanding my terminology,\nsince it is the standard one.\n\n\n> 2. I think that simultaneous measurements of observables of separated\n> particles are quite possible. At least, there should be no problem\n> to measure positions and momenta of particles in a desktop experiment\n> (the distances are of the order of 1m).\n> with time resolution of 1 picosecond or so. So, notation\n> r_1(t), p_1(t), r_2(t), p_2(t) has perfect meaning with time t being\n> the same (of course, I assume the classical limit here,\n> so there is no quantum "fuzziness").\n\nThis is not a _perfect_ meaning but only an approximate meaning\nif it depends on simultaneity, since then you need to limit\nthe resolution. The view I presented has no resolution limit in the\nclassical setting and can be assumed to be exact (perfect, in your words),\nhence serve as a foundation.\n\n\n> 3. I do not understand your distinction between "instant observer" and\n> "point observer".\n\nI defined it. The instant observer is the fictitious and causally\ninconsistent observer knowing all information on the 3-manifold t=const.\nThe point observer is the still idealized but caussally consistent observer\nknowing all information on the 3-manifold (x-x^*)^2=L^2, x_0<x^*_0,\nwhere for simplicity I took the position to be at x^*=0 (and L can be\ntaken as 1, by picking the right units).\n\n\n> Suppose that we know a full description of the physical system by one\n> observer. (In the quantum case such a description is given by the\n> wave function. In the classical case, such a description is given by\n> values of observables: positions of particles, their momenta, etc.)\n> One of the most important tasks of physics is to find the descriptions\n> of the same system by all other observers.\n\nAgreed.\n\n\n> Usually we are interested\n> only in observers translated in time (dynamics), but other\n> transformations (boosts, rotations, and space translations) are also\n> important.\n\nThis is already the privileged point of view of the instant form,\nwhich you take for inherently given although it isn\'t.\n\nFor the point form, one is primarily interested in all translation\nin space or time, since these appear on equal footing, and one needs\nto be able to translate the views of an observer at point x^* to an\nobserver at another point x^**. This is impossible without general\ntranslations.\n\n\n> 4. This problem is solved by the Dirac\'s formalism.\n> [...] According to Dirac, consider two simplest choices\n>\n> P = P_0\n> J = J_0\n> K = K_0 + Z\n> H = H_0 + V\n>\n> which is the instant form dynamics and\n>\n> P\' = P_0 + Y\n> J\' = J_0\n> K\' = K_0\n> H\' = H_0 + V\n>\n> which is the point form dynamics.\n> Now, there is a theorem (Sokolov) stating that if we have description\n> of the system in the instant form dynamics (P,J,K,H), then one can\n> find an unitary operator U which transforms this description to the\n> point form dynamics, so that the S-matrix caluclated in both cases is\n> the same. Your claim is that these two forms are physically completely\n> equivalent.\n\nYes. Equivalence means that one can translate any physical statement in\none scheme into one in the other scheme and vice versa, and always remain\nconsistent. This is clearly the case, and more is not required.\n\n\n> I disagree. Let us consider how observables of particle 1 transform\n> with\n> respect to space translations in different forms. We will use general\n> equation (1). In the instant form [...]\n> We obtain the familiar result that independent of the interaction in\n> the system, space translations act kinematically.\n>\n> In the point form [...]\n> the transformation results are interaction-dependent\n> (dynamical).\n\nOf course, by definition of the point form. In the point form, the\nLorentz transformations are kinematical. Your argument is circular.\n\nIn general, those transformations are kinematical which are also\nsymmetries of the surface one treats as kinematical reference surface.\nBy choosing a surface without symmetries (which Dirac did not consider\nexplicitly, but which is also a possible form of dynamics), _all_\ntransformations become dynamical. But these weird descriptions are\nalso equivalent to the nice ones.\n\nDo you think Dirac did _not_ realize your simple observation??\nHe understood the problem well enough. In any case, this trivial fact\nyou take as the basis of your disagreement with tradition has been\nwell known for a long time. But no one felt compelled to draw your\nradical conclusions. You may convince yourself of this by entering\nthe key words\nkinematical point-form\nor\nkinematic point-form\ninto Google\'s new academic search engine\nhttp://scholar.google.com/\n\nYou simply _postulate_ a particular 3-dimensional surface as\na priori reference surface, while any 3-dimensional surface in Minkowski\nspace does the job if it meets every world line with time like tangents\nexactly once. (Dirac mentions this on p. 396 of his paper.)\n\nBy limiting yourself in this way and by demanding that others should\nset themselves the same limits, you isolate yourself from the mainstream.\nWhile you are free doing so, I don\'t think it is a wise choice.\nVery few, if any, will be prepared to follow you.\n\n\n> This situation has never been observed in experiment.\n\nThe difference between kinematical and dynamical is one of convention,\nhence has nothing to do with observation. By choosing the description,\none chooses what is kinematical; everything else is dynamical.\nSomething which is up to the choice of the person describing an experiment\ncan never be distinguished experimentally.\n\n\n> 5. Could you please specify which are these "successful multiparticle\n> theories" which avoid contradiction with the CJS theorem?\n> Are you talking about "constraint dynamics" theories, or something\n> else?\n\nSomething else. See the Ph.D. thesis by Krassnigg at\nhttp://physik.uni-graz.at/~ank/dissertation-f.html\nand the entry\n\'Is there a multiparticle relativistic quantum mechanics?\'\nin my theoretical physics FAQ at\nhttp://www.mat.univie.ac.at/~neum/physics-faq.txt\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>Eugene Stefanovich wrote:

> 1. I don't think you can give an operational definition of such things
> as "timelike 4-vector" or "hyperboloid in the past". Experimentalists
> do not use these concepts.

I am not talking about operational concepts but about foundations - getting
the mathematical concepts right to be able to do correct physics.
Without correct concepts operational statements have no meaning.
The theory defines what a measurement is. Outside the immediate realm of
everyday experience, one needs already the conceptual basis to even
discuss what has operational meaning.

I am telling you the conventional way physicists view these things,
with some fine points added due to my own understanding.
(For example, I use a past hyperboloid instead of a future one,
which is mathematically equivalent but gives more intuition to the
formal construction.)
Physicists fared well with this view, hence this needs no further
justification. Experimentalists working on topics requiring a relativistic
description don't have any difficulties understanding my terminology,
since it is the standard one.

> 2. I think that simultaneous measurements of observables of separated
> particles are quite possible. At least, there should be no problem
> to measure positions and momenta of particles in a desktop experiment
> (the distances are of the order of 1m).
> with time resolution of 1 picosecond or so. So, notation
> r_1(t), p_1(t), r_2(t), p_2(t) has perfect meaning with time t being
> the same (of course, I assume the classical limit here,
> so there is no quantum "fuzziness").

This is not a _perfect_ meaning but only an approximate meaning
if it depends on simultaneity, since then you need to limit
the resolution. The view I presented has no resolution limit in the
classical setting and can be assumed to be exact (perfect, in your words),
hence serve as a foundation.

> 3. I do not understand your distinction between "instant observer" and
> "point observer".

I defined it. The instant observer is the fictitious and causally
inconsistent observer knowing all information on the 3-manifold t=const.
The point observer is the still idealized but caussally consistent observer
knowing all information on the 3-manifold (x-x^*)^2=L^2, x_0<x^*_0,
where for simplicity I took the position to be at x^*=0 (and L can be
taken as 1, by picking the right units).

> Suppose that we know a full description of the physical system by one
> observer. (In the quantum case such a description is given by the
> wave function. In the classical case, such a description is given by
> values of observables: positions of particles, their momenta, etc.)
> One of the most important tasks of physics is to find the descriptions
> of the same system by all other observers.

Agreed.

> Usually we are interested
> only in observers translated in time (dynamics), but other
> transformations (boosts, rotations, and space translations) are also
> important.

This is already the privileged point of view of the instant form,
which you take for inherently given although it isn't.

For the point form, one is primarily interested in all translation
in space or time, since these appear on equal footing, and one needs
to be able to translate the views of an observer at point x^* to an
observer at another point x^**. This is impossible without general
translations.

> 4. This problem is solved by the Dirac's formalism.
> [...] According to Dirac, consider two simplest choices
>
> P = P_0
> J = J_0
> K = K_0 + Z
> H = H_0 + V
>
> which is the instant form dynamics and
>
> P' = P_0 + Y
> J' = J_0
> K' = K_0
> H' = H_0 + V
>
> which is the point form dynamics.
> Now, there is a theorem (Sokolov) stating that if we have description
> of the system in the instant form dynamics (P,J,K,H), then one can
> find an unitary operator U which transforms this description to the
> point form dynamics, so that the S-matrix caluclated in both cases is
> the same. Your claim is that these two forms are physically completely
> equivalent.

Yes. Equivalence means that one can translate any physical statement in
one scheme into one in the other scheme and vice versa, and always remain
consistent. This is clearly the case, and more is not required.

> I disagree. Let us consider how observables of particle 1 transform
> with
> respect to space translations in different forms. We will use general
> equation (1). In the instant form [...]
> We obtain the familiar result that independent of the interaction in
> the system, space translations act kinematically.
>
> In the point form [...]
> the transformation results are interaction-dependent
> (dynamical).

Of course, by definition of the point form. In the point form, the
Lorentz transformations are kinematical. Your argument is circular.

In general, those transformations are kinematical which are also
symmetries of the surface one treats as kinematical reference surface.
By choosing a surface without symmetries (which Dirac did not consider
explicitly, but which is also a possible form of dynamics), _all_
transformations become dynamical. But these weird descriptions are
also equivalent to the nice ones.

Do you think Dirac did _not_ realize your simple observation??
He understood the problem well enough. In any case, this trivial fact
you take as the basis of your disagreement with tradition has been
well known for a long time. But no one felt compelled to draw your
radical conclusions. You may convince yourself of this by entering
the key words
kinematical point-form
or
kinematic point-form
into Google's new academic search engine
http://scholar.google.com/

You simply _postulate_ a particular 3-dimensional surface as
a priori reference surface, while any 3-dimensional surface in Minkowski
space does the job if it meets every world line with time like tangents
exactly once. (Dirac mentions this on p. 396 of his paper.)

By limiting yourself in this way and by demanding that others should
set themselves the same limits, you isolate yourself from the mainstream.
While you are free doing so, I don't think it is a wise choice.
Very few, if any, will be prepared to follow you.

> This situation has never been observed in experiment.

The difference between kinematical and dynamical is one of convention,
hence has nothing to do with observation. By choosing the description,
one chooses what is kinematical; everything else is dynamical.
Something which is up to the choice of the person describing an experiment
can never be distinguished experimentally.

> 5. Could you please specify which are these "successful multiparticle
> theories" which avoid contradiction with the CJS theorem?
> Are you talking about "constraint dynamics" theories, or something
> else?

Something else. See the Ph.D. thesis by Krassnigg at
http://physik.uni-graz.at/~ank/dissertation-f.html
and the entry
'Is there a multiparticle relativistic quantum mechanics?'
in my theoretical physics FAQ at
http://www.mat.univie.ac.at/~neum/physics-faq.txt

Arnold Neumaier

Eugene Stefanovich

Dec3-04, 04:52 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>Arnold Neumaier wrote:\n> Eugene Stefanovich wrote:\n>\n>\n>>1. I don\'t think you can give an operational definition of such things\n>> as "timelike 4-vector" or "hyperboloid in the past". Experimentalists\n>> do not use these concepts.\n>\n>\n> I am not talking about operational concepts but about foundations - getting\n> the mathematical concepts right to be able to do correct physics.\n> Without correct concepts operational statements have no meaning.\n> The theory defines what a measurement is. Outside the immediate realm of\n> everyday experience, one needs already the conceptual basis to even\n> discuss what has operational meaning.\n>\n> I am telling you the conventional way physicists view these things,\n> with some fine points added due to my own understanding.\n> (For example, I use a past hyperboloid instead of a future one,\n> which is mathematically equivalent but gives more intuition to the\n> formal construction.)\n> Physicists fared well with this view, hence this needs no further\n> justification. Experimentalists working on topics requiring a relativistic\n> description don\'t have any difficulties understanding my terminology,\n> since it is the standard one.\n\nThe notions of "timelike 4-vector" or "hyperboloid in the past" are\nrelated to the 4D Minkowski spacetime picture. I do not have this\npicture in my approach, so I am not using these notions.\n\n>\n>\n>\n>>2. I think that simultaneous measurements of observables of separated\n>> particles are quite possible. At least, there should be no problem\n>> to measure positions and momenta of particles in a desktop experiment\n>> (the distances are of the order of 1m).\n>> with time resolution of 1 picosecond or so. So, notation\n>> r_1(t), p_1(t), r_2(t), p_2(t) has perfect meaning with time t being\n>> the same (of course, I assume the classical limit here,\n>> so there is no quantum "fuzziness").\n>\n>\n> This is not a _perfect_ meaning but only an approximate meaning\n> if it depends on simultaneity, since then you need to limit\n> the resolution. The view I presented has no resolution limit in the\n> classical setting and can be assumed to be exact (perfect, in your words),\n> hence serve as a foundation.\n\nI assume that each observer can measure observables of different\nparticles simultaneously, independent of how far the particles are\napart. If particles are very far apart (like one particle is on Earth,\nand another particle is on Mars, and you rely on light signals to get\nthe info about the marsian particle), you can always adjust timing\nby R/c to figure out what were the simultaneous values in you reference\nframe. I do not see how this limits the resolution.\n\n>\n>\n>\n>>3. I do not understand your distinction between "instant observer" and\n>> "point observer".\n>\n>\n> I defined it. The instant observer is the fictitious and causally\n> inconsistent observer knowing all information on the 3-manifold t=const.\n\nSuppose that I want to know simultaneous positions of 2 particles.\nParticle E is in my laboratory, and particle M is on Mars. I know that\nlight travels from Mars to Earth in 30 min. I receive a signal from\nMars rover that the particle M is at point r_M. Then I look in my record\nof observations of the particle E, and find out that it was at\npoint r_E 30 min ago. Then I can state that instantaneous positions of\nthe two particles were r_M and r_E. In this way I\'ve realized "instant\nobserver", which you call inconsistent.\n\n\n> The point observer is the still idealized but caussally consistent observer\n> knowing all information on the 3-manifold (x-x^*)^2=L^2, x_0<x^*_0,\n> where for simplicity I took the position to be at x^*=0 (and L can be\n> taken as 1, by picking the right units).\n>\n>\n>\n>> Suppose that we know a full description of the physical system by one\n>> observer. (In the quantum case such a description is given by the\n>> wave function. In the classical case, such a description is given by\n>> values of observables: positions of particles, their momenta, etc.)\n>> One of the most important tasks of physics is to find the descriptions\n>> of the same system by all other observers.\n>\n>\n> Agreed.\n>\n>\n>\n>> Usually we are interested\n>> only in observers translated in time (dynamics), but other\n>> transformations (boosts, rotations, and space translations) are also\n>> important.\n>\n>\n> This is already the privileged point of view of the instant form,\n> which you take for inherently given although it isn\'t.\n>\n> For the point form, one is primarily interested in all translation\n> in space or time, since these appear on equal footing, and one needs\n> to be able to translate the views of an observer at point x^* to an\n> observer at another point x^**. This is impossible without general\n> translations.\n\nI think you missed my point. I said that we are always interested\nin results of ALL translations (temporal and spatial) as well as\nrotations and boosts. This is required for the full\ncharacterization of the system, and is independent on the form\nof dynamics.\n\nHowever, physicists pay more attention to time translations,\nbecause they\nare the most interesting (they involve reactions, decays, and other\nexciting stuff). Very little attention is paid to space translations\nand rotations, because they are found to be rather trivial\n(kinematical). For me this is not surprising, because I know that\ndynamics has instant form, and space translations and rotations MUST\nbe kinematical. 99 years ago Einstein initiated the study of boost\ntransformations and found some interesting (yet kinematical) effects,\nlike time dilation and length contraction. My claim is that these\neffects have also some dependence on interactions (they are actually\ndynamical),\nalthough this dependence is difficult to observe. First, the dynamical\neffects in boosts are small. Second, it is difficult to have a fast\nmoving observer.\n\nIf you say that nature is governed by the point form dynamics,\nthen you basically say that there should be dynamical effects\nassociated with a simple shift of observer in space. I find it hard to\nbelieve, because such effects would have been observed a long time\nago.\n\n>\n>\n>\n>>4. This problem is solved by the Dirac\'s formalism.\n>> [...] According to Dirac, consider two simplest choices\n>>\n>> P = P_0\n>> J = J_0\n>> K = K_0 + Z\n>> H = H_0 + V\n>>\n>> which is the instant form dynamics and\n>>\n>> P\' = P_0 + Y\n>> J\' = J_0\n>> K\' = K_0\n>> H\' = H_0 + V\n>>\n>> which is the point form dynamics.\n>> Now, there is a theorem (Sokolov) stating that if we have description\n>> of the system in the instant form dynamics (P,J,K,H), then one can\n>> find an unitary operator U which transforms this description to the\n>> point form dynamics, so that the S-matrix caluclated in both cases is\n>> the same. Your claim is that these two forms are physically completely\n>> equivalent.\n>\n>\n> Yes. Equivalence means that one can translate any physical statement in\n> one scheme into one in the other scheme and vice versa, and always remain\n> consistent. This is clearly the case, and more is not required.\n>\n>\n>\n>> I disagree. Let us consider how observables of particle 1 transform\n>> with\n>> respect to space translations in different forms. We will use general\n>> equation (1). In the instant form [...]\n>> We obtain the familiar result that independent of the interaction in\n>> the system, space translations act kinematically.\n>>\n>> In the point form [...]\n>> the transformation results are interaction-dependent\n>> (dynamical).\n>\n>\n> Of course, by definition of the point form. In the point form, the\n> Lorentz transformations are kinematical. Your argument is circular.\n>\n> In general, those transformations are kinematical which are also\n> symmetries of the surface one treats as kinematical reference surface.\n> By choosing a surface without symmetries (which Dirac did not consider\n> explicitly, but which is also a possible form of dynamics), _all_\n> transformations become dynamical. But these weird descriptions are\n> also equivalent to the nice ones.\n>\n> Do you think Dirac did _not_ realize your simple observation??\n> He understood the problem well enough. In any case, this trivial fact\n> you take as the basis of your disagreement with tradition has been\n> well known for a long time. But no one felt compelled to draw your\n> radical conclusions. You may convince yourself of this by entering\n> the key words\n> kinematical point-form\n> or\n> kinematic point-form\n> into Google\'s new academic search engine\n> http://scholar.google.com/\n>\n> You simply _postulate_ a particular 3-dimensional surface as\n> a priori reference surface, while any 3-dimensional surface in Minkowski\n> space does the job if it meets every world line with time like tangents\n> exactly once. (Dirac mentions this on p. 396 of his paper.)\n>\n> By limiting yourself in this way and by demanding that others should\n> set themselves the same limits, you isolate yourself from the mainstream.\n> While you are free doing so, I don\'t think it is a wise choice.\n> Very few, if any, will be prepared to follow you.\n>\n>\n>\n>>This situation has never been observed in experiment.\n>\n>\n> The difference between kinematical and dynamical is one of convention,\n> hence has nothing to do with observation. By choosing the description,\n> one chooses what is kinematical; everything else is dynamical.\n> Something which is up to the choice of the person describing an experiment\n> can never be distinguished experimentally.\n\nI strongly disagree. Take time evolution. You can always\ndistinguish the time evolution of a non-interacting system and\nthe time evolution of a system with interaction. This is not a matter\nof convention. This is a real observable difference.\n\nThe same with other inertial transformations. I believe that you can\nmeasure how particle observables transform to different frames of\nreference (shifted, rotated, boosted) and from these measurements\nyou can unambiguously decide\nwhich form of dynamics is working: instant or point or any other.\n\nOf course, you cannot do that if all your observations are restricted\nto asymptotic states of colliding particles and energies of bound\nstates. (This is the situation in modern high energy physics) Then\nyour knowledge is restricted to the S-matrix only, and different forms\nof dynamics are equivalent as far as the S-matrix is concerned.\n\n>\n>\n>\n>>5. Could you please specify which are these "successful multiparticle\n>> theories" which avoid contradiction with the CJS theorem?\n>> Are you talking about "constraint dynamics" theories, or something\n>> else?\n>\n>\n> Something else. See the Ph.D. thesis by Krassnigg at\n> http://physik.uni-graz.at/~ank/dissertation-f.html\n> and the entry\n> \'Is there a multiparticle relativistic quantum mechanics?\'\n> in my theoretical physics FAQ at\n> http://www.mat.univie.ac.at/~neum/physics-faq.txt\n\nI know Klink and Polyzou well, and I am familiar with their works.\nI once visited them in Iowa, and gave a seminar there. They do not\nendorse my ideas and stick to the same position as you: that different\nforms of dynamics are physically equivalent.\n\nYou are right that their "direct interaction" approach\n(this is also _my_ approach: in my book I cast QED in the form of\n"direct interaction" theory) solves the\nproblem raised in the CJS theorem. But this solution comes with\na price: one needs to reject the invariance of world lines. In the\ninstant form dynamics (the case considered by CJS) the world lines\nof interacting particles are not transforming in the manifestly\ncovariant way wrt boosts (because the boost operator has interaction\nterm). In the point form dynamics, the world lines have non-trivial\ntransformations wrt space translations (because the generator of\ntranslations is interaction-dependent).\n\nKlink and Polyzou do not want to accept these views. Their idea is\nthat positions are not observable (see section 4.4 in the review\nby Keister and Polyzou), so there is no point in talking about\nworld lines and their transformations (see also B.D. Keister\nnucl-th/9406032). I can agree that world lines don\'t have much\nmeaning in the context of modern high energy physics dominated by\nscattering events. However, I maintain that position is measurable\nas well as momentum, and in the classical limit particle trajectories\nare also measurable. The transformations of trajectories\n(or world lines) to different frames should be measurable as well,\nand the form of\ndynamics governing the interactions between particles can be\ndetermined from experiment.\n\nEugene Stefanovich\n\n\n>\n>\n> Arnold Neumaier\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>Arnold Neumaier wrote:
> Eugene Stefanovich wrote:
>
>
>>1. I don't think you can give an operational definition of such things
>> as "timelike 4-vector" or "hyperboloid in the past". Experimentalists
>> do not use these concepts.
>
>
> I am not talking about operational concepts but about foundations - getting
> the mathematical concepts right to be able to do correct physics.
> Without correct concepts operational statements have no meaning.
> The theory defines what a measurement is. Outside the immediate realm of
> everyday experience, one needs already the conceptual basis to even
> discuss what has operational meaning.
>
> I am telling you the conventional way physicists view these things,
> with some fine points added due to my own understanding.
> (For example, I use a past hyperboloid instead of a future one,
> which is mathematically equivalent but gives more intuition to the
> formal construction.)
> Physicists fared well with this view, hence this needs no further
> justification. Experimentalists working on topics requiring a relativistic
> description don't have any difficulties understanding my terminology,
> since it is the standard one.

The notions of "timelike 4-vector" or "hyperboloid in the past" are
related to the 4D Minkowski spacetime picture. I do not have this
picture in my approach, so I am not using these notions.

>
>
>
>>2. I think that simultaneous measurements of observables of separated
>> particles are quite possible. At least, there should be no problem
>> to measure positions and momenta of particles in a desktop experiment
>> (the distances are of the order of 1m).
>> with time resolution of 1 picosecond or so. So, notation
>> r_1(t), p_1(t), r_2(t), p_2(t) has perfect meaning with time t being
>> the same (of course, I assume the classical limit here,
>> so there is no quantum "fuzziness").
>
>
> This is not a _perfect_ meaning but only an approximate meaning
> if it depends on simultaneity, since then you need to limit
> the resolution. The view I presented has no resolution limit in the
> classical setting and can be assumed to be exact (perfect, in your words),
> hence serve as a foundation.

I assume that each observer can measure observables of different
particles simultaneously, independent of how far the particles are
apart. If particles are very far apart (like one particle is on Earth,
and another particle is on Mars, and you rely on light signals to get
the info about the marsian particle), you can always adjust timing
by R/c to figure out what were the simultaneous values in you reference
frame. I do not see how this limits the resolution.

>
>
>
>>3. I do not understand your distinction between "instant observer" and
>> "point observer".
>
>
> I defined it. The instant observer is the fictitious and causally
> inconsistent observer knowing all information on the 3-manifold t=const.

Suppose that I want to know simultaneous positions of 2 particles.
Particle E is in my laboratory, and particle M is on Mars. I know that
light travels from Mars to Earth in 30 min. I receive a signal from
Mars rover that the particle M is at point r_M. Then I look in my record
of observations of the particle E, and find out that it was at
point r_E 30 min ago. Then I can state that instantaneous positions of
the two particles were r_M and r_E. In this way I've realized "instant
observer", which you call inconsistent.

> The point observer is the still idealized but caussally consistent observer
> knowing all information on the 3-manifold (x-x^*)^2=L^2, x_0<x^*_0,
> where for simplicity I took the position to be at x^*=0 (and L can be
> taken as 1, by picking the right units).
>
>
>
>> Suppose that we know a full description of the physical system by one
>> observer. (In the quantum case such a description is given by the
>> wave function. In the classical case, such a description is given by
>> values of observables: positions of particles, their momenta, etc.)
>> One of the most important tasks of physics is to find the descriptions
>> of the same system by all other observers.
>
>
> Agreed.
>
>
>
>> Usually we are interested
>> only in observers translated in time (dynamics), but other
>> transformations (boosts, rotations, and space translations) are also
>> important.
>
>
> This is already the privileged point of view of the instant form,
> which you take for inherently given although it isn't.
>
> For the point form, one is primarily interested in all translation
> in space or time, since these appear on equal footing, and one needs
> to be able to translate the views of an observer at point x^* to an
> observer at another point x^**. This is impossible without general
> translations.

I think you missed my point. I said that we are always interested
in results of ALL translations (temporal and spatial) as well as
rotations and boosts. This is required for the full
characterization of the system, and is independent on the form
of dynamics.

However, physicists pay more attention to time translations,
because they
are the most interesting (they involve reactions, decays, and other
exciting stuff). Very little attention is paid to space translations
and rotations, because they are found to be rather trivial
(kinematical). For me this is not surprising, because I know that
dynamics has instant form, and space translations and rotations MUST
be kinematical. 99 years ago Einstein initiated the study of boost
transformations and found some interesting (yet kinematical) effects,
like time dilation and length contraction. My claim is that these
effects have also some dependence on interactions (they are actually
dynamical),
although this dependence is difficult to observe. First, the dynamical
effects in boosts are small. Second, it is difficult to have a fast
moving observer.

If you say that nature is governed by the point form dynamics,
then you basically say that there should be dynamical effects
associated with a simple shift of observer in space. I find it hard to
believe, because such effects would have been observed a long time
ago.

>
>
>
>>4. This problem is solved by the Dirac's formalism.
>> [...] According to Dirac, consider two simplest choices
>>
>> P = P_0>> J = J_0>> K = K_0 + Z>> H = H_0 + V
>>
>> which is the instant form dynamics and
>>
>> P' = P_0 + Y>> J' = J_0>> K' = K_0>> H' = H_0 + V
>>
>> which is the point form dynamics.
>> Now, there is a theorem (Sokolov) stating that if we have description
>> of the system in the instant form dynamics (P,J,K,H), then one can
>> find an unitary operator U which transforms this description to the
>> point form dynamics, so that the S-matrix caluclated in both cases is
>> the same. Your claim is that these two forms are physically completely
>> equivalent.
>
>
> Yes. Equivalence means that one can translate any physical statement in
> one scheme into one in the other scheme and vice versa, and always remain
> consistent. This is clearly the case, and more is not required.
>
>
>
>> I disagree. Let us consider how observables of particle 1 transform
>> with
>> respect to space translations in different forms. We will use general
>> equation (1). In the instant form [...]
>> We obtain the familiar result that independent of the interaction in
>> the system, space translations act kinematically.
>>
>> In the point form [...]
>> the transformation results are interaction-dependent
>> (dynamical).
>
>
> Of course, by definition of the point form. In the point form, the
> Lorentz transformations are kinematical. Your argument is circular.
>
> In general, those transformations are kinematical which are also
> symmetries of the surface one treats as kinematical reference surface.
> By choosing a surface without symmetries (which Dirac did not consider
> explicitly, but which is also a possible form of dynamics), _all_
> transformations become dynamical. But these weird descriptions are
> also equivalent to the nice ones.
>
> Do you think Dirac did _not_ realize your simple observation??
> He understood the problem well enough. In any case, this trivial fact
> you take as the basis of your disagreement with tradition has been
> well known for a long time. But no one felt compelled to draw your
> radical conclusions. You may convince yourself of this by entering
> the key words
> kinematical point-form
> or
> kinematic point-form
> into Google's new academic search engine
> http://scholar.google.com/
>
> You simply _postulate_ a particular 3-dimensional surface as
> a priori reference surface, while any 3-dimensional surface in Minkowski
> space does the job if it meets every world line with time like tangents
> exactly once. (Dirac mentions this on p. 396 of his paper.)
>
> By limiting yourself in this way and by demanding that others should
> set themselves the same limits, you isolate yourself from the mainstream.
> While you are free doing so, I don't think it is a wise choice.
> Very few, if any, will be prepared to follow you.
>
>
>
>>This situation has never been observed in experiment.
>
>
> The difference between kinematical and dynamical is one of convention,
> hence has nothing to do with observation. By choosing the description,
> one chooses what is kinematical; everything else is dynamical.
> Something which is up to the choice of the person describing an experiment
> can never be distinguished experimentally.

I strongly disagree. Take time evolution. You can always
distinguish the time evolution of a non-interacting system and
the time evolution of a system with interaction. This is not a matter
of convention. This is a real observable difference.

The same with other inertial transformations. I believe that you can
measure how particle observables transform to different frames of
reference (shifted, rotated, boosted) and from these measurements
you can unambiguously decide
which form of dynamics is working: instant or point or any other.

Of course, you cannot do that if all your observations are restricted
to asymptotic states of colliding particles and energies of bound
states. (This is the situation in modern high energy physics) Then
your knowledge is restricted to the S-matrix only, and different forms
of dynamics are equivalent as far as the S-matrix is concerned.

>
>
>
>>5. Could you please specify which are these "successful multiparticle
>> theories" which avoid contradiction with the CJS theorem?
>> Are you talking about "constraint dynamics" theories, or something
>> else?
>
>
> Something else. See the Ph.D. thesis by Krassnigg at
> http://physik.uni-graz.at/~ank/dissertation-f.html
> and the entry
> 'Is there a multiparticle relativistic quantum mechanics?'
> in my theoretical physics FAQ at
> http://www.mat.univie.ac.at/~neum/physics-faq.txt

I know Klink and Polyzou well, and I am familiar with their works.
I once visited them in Iowa, and gave a seminar there. They do not
endorse my ideas and stick to the same position as you: that different
forms of dynamics are physically equivalent.

You are right that their "direct interaction" approach
(this is also _my_ approach: in my book I cast QED in the form of
"direct interaction" theory) solves the
problem raised in the CJS theorem. But this solution comes with
a price: one needs to reject the invariance of world lines. In the
instant form dynamics (the case considered by CJS) the world lines
of interacting particles are not transforming in the manifestly
covariant way wrt boosts (because the boost operator has interaction
term). In the point form dynamics, the world lines have non-trivial
transformations wrt space translations (because the generator of
translations is interaction-dependent).

Klink and Polyzou do not want to accept these views. Their idea is
that positions are not observable (see section 4.4 in the review
by Keister and Polyzou), so there is no point in talking about
world lines and their transformations (see also B.D. Keister
http://www.arxiv.org/abs/nucl-th/9406032). I can agree that world lines don't have much
meaning in the context of modern high energy physics dominated by
scattering events. However, I maintain that position is measurable
as well as momentum, and in the classical limit particle trajectories
are also measurable. The transformations of trajectories
(or world lines) to different frames should be measurable as well,
and the form of
dynamics governing the interactions between particles can be
determined from experiment.

Eugene Stefanovich

>
>
> Arnold Neumaier
>

Eugene Stefanovich

Dec3-04, 04:57 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>Arnold Neumaier wrote:\n> Eugene Stefanovich wrote:\n\n>>2. I think that simultaneous measurements of observables of separated\n>> particles are quite possible. At least, there should be no problem\n>> to measure positions and momenta of particles in a desktop experiment\n>> (the distances are of the order of 1m).\n>> with time resolution of 1 picosecond or so. So, notation\n>> r_1(t), p_1(t), r_2(t), p_2(t) has perfect meaning with time t being\n>> the same (of course, I assume the classical limit here,\n>> so there is no quantum "fuzziness").\n>\n>\n> This is not a _perfect_ meaning but only an approximate meaning\n> if it depends on simultaneity, since then you need to limit\n> the resolution. The view I presented has no resolution limit in the\n> classical setting and can be assumed to be exact (perfect, in your words),\n> hence serve as a foundation.\n>\n>\n>\n>>3. I do not understand your distinction between "instant observer" and\n>> "point observer".\n>\n>\n> I defined it. The instant observer is the fictitious and causally\n> inconsistent observer knowing all information on the 3-manifold t=const.\n> The point observer is the still idealized but caussally consistent observer\n> knowing all information on the 3-manifold (x-x^*)^2=L^2, x_0<x^*_0,\n> where for simplicity I took the position to be at x^*=0 (and L can be\n> taken as 1, by picking the right units).\n>\n\nLet me give you an example (idealized, of course) of a measuring\napparatus which can collect information on a "3-manifold t=const".\nI prepare an array of particle detectors densely distributed in space\n(these could be small Geiger counters, or semiconductor detectors,\nor whatever). I connect all these detectors by wires of equal length R\nto the "central switch", where I am sitting. When I flip the switch,\nthe signals go through the wires to the detectors and activate them\nfor a short time (a picosecond, or a femtosecond...). So, all detectors\nbecome active at the same time t=R/c. After the measurement is done, I\ncan inspect my detectors and see where the particles in the system were\nsituated on the t=R/c "hyperplane".\n\nEugene Stefanovich.\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>Arnold Neumaier wrote:
> Eugene Stefanovich wrote:

>>2. I think that simultaneous measurements of observables of separated
>> particles are quite possible. At least, there should be no problem
>> to measure positions and momenta of particles in a desktop experiment
>> (the distances are of the order of 1m).
>> with time resolution of 1 picosecond or so. So, notation
>> r_1(t), p_1(t), r_2(t), p_2(t) has perfect meaning with time t being
>> the same (of course, I assume the classical limit here,
>> so there is no quantum "fuzziness").
>
>
> This is not a _perfect_ meaning but only an approximate meaning
> if it depends on simultaneity, since then you need to limit
> the resolution. The view I presented has no resolution limit in the
> classical setting and can be assumed to be exact (perfect, in your words),
> hence serve as a foundation.
>
>
>
>>3. I do not understand your distinction between "instant observer" and
>> "point observer".
>
>
> I defined it. The instant observer is the fictitious and causally
> inconsistent observer knowing all information on the 3-manifold t=const.
> The point observer is the still idealized but caussally consistent observer
> knowing all information on the 3-manifold (x-x^*)^2=L^2, x_0<x^*_0,
> where for simplicity I took the position to be at x^*=0 (and L can be
> taken as 1, by picking the right units).
>

Let me give you an example (idealized, of course) of a measuring
apparatus which can collect information on a "3-manifold t=const".
I prepare an array of particle detectors densely distributed in space
(these could be small Geiger counters, or semiconductor detectors,
or whatever). I connect all these detectors by wires of equal length R
to the "central switch", where I am sitting. When I flip the switch,
the signals go through the wires to the detectors and activate them
for a short time (a picosecond, or a femtosecond...). So, all detectors
become active at the same time t=R/c. After the measurement is done, I
can inspect my detectors and see where the particles in the system were
situated on the t=R/c "hyperplane".

Eugene Stefanovich.

Frank Hellmann

Dec4-04, 03:20 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>Eugene Stefanovich <eugenev@synopsys.com> wrote in message news:<41B0CFB0.907@synopsys.com>...\n> Arnold Neumaier wrote:\n> > Eugene Stefanovich wrote:\n>\n> >>2. I think that simultaneous measurements of observables of separated\n> >> particles are quite possible. At least, there should be no problem\n> >> to measure positions and momenta of particles in a desktop experiment\n> >> (the distances are of the order of 1m).\n> >> with time resolution of 1 picosecond or so. So, notation\n> >> r_1(t), p_1(t), r_2(t), p_2(t) has perfect meaning with time t being\n> >> the same (of course, I assume the classical limit here,\n> >> so there is no quantum "fuzziness").\n> >\n> >\n> > This is not a _perfect_ meaning but only an approximate meaning\n> > if it depends on simultaneity, since then you need to limit\n> > the resolution. The view I presented has no resolution limit in the\n> > classical setting and can be assumed to be exact (perfect, in your words),\n> > hence serve as a foundation.\n> >\n> >\n> >\n> >>3. I do not understand your distinction between "instant observer" and\n> >> "point observer".\n> >\n> >\n> > I defined it. The instant observer is the fictitious and causally\n> > inconsistent observer knowing all information on the 3-manifold t=const.\n> > The point observer is the still idealized but caussally consistent observer\n> > knowing all information on the 3-manifold (x-x^*)^2=L^2, x_0<x^*_0,\n> > where for simplicity I took the position to be at x^*=0 (and L can be\n> > taken as 1, by picking the right units).\n> >\n>\n> Let me give you an example (idealized, of course) of a measuring\n> apparatus which can collect information on a "3-manifold t=const".\n> I prepare an array of particle detectors densely distributed in space\n> (these could be small Geiger counters, or semiconductor detectors,\n> or whatever). I connect all these detectors by wires of equal length R\n> to the "central switch", where I am sitting. When I flip the switch,\n> the signals go through the wires to the detectors and activate them\n> for a short time (a picosecond, or a femtosecond...). So, all detectors\n> become active at the same time t=R/c. After the measurement is done, I\n> can inspect my detectors and see where the particles in the system were\n> situated on the t=R/c "hyperplane".\n>\n> Eugene Stefanovich.\n\nWhen you collect the information again it will take time R/c for the\ninformation to get to you. You are constructing the spacelike surface\nfrom slices of timelike surfaces in this Gedankenexperiment.\nYou will therefore find that the "they fire at the same time" is of\ncourse also not an invariant statement. An observer moving wrt you in\nthe center of your web will of course see them fire at different\ntimes. Still a spacelike 3 Manifold, but not at t=const.\n\nf\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>Eugene Stefanovich <eugenev@synopsys.com> wrote in message news:<41B0CFB0.907@synopsys.com>...
> Arnold Neumaier wrote:
> > Eugene Stefanovich wrote:
>
> >>2. I think that simultaneous measurements of observables of separated
> >> particles are quite possible. At least, there should be no problem
> >> to measure positions and momenta of particles in a desktop experiment
> >> (the distances are of the order of 1m).
> >> with time resolution of 1 picosecond or so. So, notation
> >> r_1(t), p_1(t), r_2(t), p_2(t) has perfect meaning with time t being
> >> the same (of course, I assume the classical limit here,
> >> so there is no quantum "fuzziness").
> >
> >
> > This is not a _perfect_ meaning but only an approximate meaning
> > if it depends on simultaneity, since then you need to limit
> > the resolution. The view I presented has no resolution limit in the
> > classical setting and can be assumed to be exact (perfect, in your words),
> > hence serve as a foundation.
> >
> >
> >
> >>3. I do not understand your distinction between "instant observer" and
> >> "point observer".
> >
> >
> > I defined it. The instant observer is the fictitious and causally
> > inconsistent observer knowing all information on the 3-manifold t=const.
> > The point observer is the still idealized but caussally consistent observer
> > knowing all information on the 3-manifold (x-x^*)^2=L^2, x_0<x^*_0,
> > where for simplicity I took the position to be at x^*=0 (and L can be
> > taken as 1, by picking the right units).
> >
>
> Let me give you an example (idealized, of course) of a measuring
> apparatus which can collect information on a "3-manifold t=const".
> I prepare an array of particle detectors densely distributed in space
> (these could be small Geiger counters, or semiconductor detectors,
> or whatever). I connect all these detectors by wires of equal length R
> to the "central switch", where I am sitting. When I flip the switch,
> the signals go through the wires to the detectors and activate them
> for a short time (a picosecond, or a femtosecond...). So, all detectors
> become active at the same time t=R/c. After the measurement is done, I
> can inspect my detectors and see where the particles in the system were
> situated on the t=R/c "hyperplane".
>
> Eugene Stefanovich.

When you collect the information again it will take time R/c for the
information to get to you. You are constructing the spacelike surface
from slices of timelike surfaces in this Gedankenexperiment.
You will therefore find that the "they fire at the same time" is of
course also not an invariant statement. An observer moving wrt you in
the center of your web will of course see them fire at different
times. Still a spacelike 3 Manifold, but not at t=const.

f

Eugene Stefanovich

Dec6-04, 07:16 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\nFrank Hellmann wrote:\n> Eugene Stefanovich <eugenev@synopsys.com> wrote in message news:<41B0CFB0.907@synopsys.com>...\n>\n>>Arnold Neumaier wrote:\n>>\n>>>Eugene Stefanovich wrote:\n>>\n>>\n>>\n>>>>2. I think that simultaneous measurements of observables of separated\n>>>> particles are quite possible. At least, there should be no problem\n>>>> to measure positions and momenta of particles in a desktop experiment\n>>>> (the distances are of the order of 1m).\n>>>> with time resolution of 1 picosecond or so. So, notation\n>>>> r_1(t), p_1(t), r_2(t), p_2(t) has perfect meaning with time t being\n>>>> the same (of course, I assume the classical limit here,\n>>>> so there is no quantum "fuzziness").\n>>>\n>>>\n>>>This is not a _perfect_ meaning but only an approximate meaning\n>>>if it depends on simultaneity, since then you need to limit\n>>>the resolution. The view I presented has no resolution limit in the\n>>>classical setting and can be assumed to be exact (perfect, in your words),\n>>>hence serve as a foundation.\n>>>\n>>>\n>>>\n>>>\n>>>>3. I do not understand your distinction between "instant observer" and\n>>>> "point observer".\n>>>\n>>>\n>>>I defined it. The instant observer is the fictitious and causally\n>>>inconsistent observer knowing all information on the 3-manifold t=const.\n>>>The point observer is the still idealized but caussally consistent observer\n>>>knowing all information on the 3-manifold (x-x^*)^2=L^2, x_0<x^*_0,\n>>>where for simplicity I took the position to be at x^*=0 (and L can be\n>>>taken as 1, by picking the right units).\n>>>\n>>\n>>Let me give you an example (idealized, of course) of a measuring\n>>apparatus which can collect information on a "3-manifold t=const".\n>>I prepare an array of particle detectors densely distributed in space\n>>(these could be small Geiger counters, or semiconductor detectors,\n>>or whatever). I connect all these detectors by wires of equal length R\n>>to the "central switch", where I am sitting. When I flip the switch,\n>>the signals go through the wires to the detectors and activate them\n>>for a short time (a picosecond, or a femtosecond...). So, all detectors\n>>become active at the same time t=R/c. After the measurement is done, I\n>>can inspect my detectors and see where the particles in the system were\n>>situated on the t=R/c "hyperplane".\n>>\n>>Eugene Stefanovich.\n>\n>\n> When you collect the information again it will take time R/c for the\n> information to get to you. You are constructing the spacelike surface\n> from slices of timelike surfaces in this Gedankenexperiment.\n> You will therefore find that the "they fire at the same time" is of\n> course also not an invariant statement. An observer moving wrt you in\n> the center of your web will of course see them fire at different\n> times. Still a spacelike 3 Manifold, but not at t=const.\n\nI agree with you completely. The moving observer will not recognize my\nmeasurements as instantaneous. But I don\'t care about other observers.\nThe question was whether one observer can arrange for measurements\nof observables on a fixed time slice. The answer is yes.\nOther observers can also do the same in their frames of references.\nBut two observers in relative motion will never agree whose\nobservation was instantaneous and whose not.\n\nThe Poincare transformations of observables allow me to connect\nresults of my instantaneous measurements with instantaneous\nmeasurements of other observers.\n\nEugene Stefanovich\n\n>\n> f\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>Frank Hellmann wrote:
> Eugene Stefanovich <eugenev@synopsys.com> wrote in message news:<41B0CFB0.907@synopsys.com>...
>
>>Arnold Neumaier wrote:
>>
>>>Eugene Stefanovich wrote:
>>
>>
>>
>>>>2. I think that simultaneous measurements of observables of separated
>>>> particles are quite possible. At least, there should be no problem
>>>> to measure positions and momenta of particles in a desktop experiment
>>>> (the distances are of the order of 1m).
>>>> with time resolution of 1 picosecond or so. So, notation
>>>> r_1(t), p_1(t), r_2(t), p_2(t) has perfect meaning with time t being
>>>> the same (of course, I assume the classical limit here,
>>>> so there is no quantum "fuzziness").
>>>
>>>
>>>This is not a _perfect_ meaning but only an approximate meaning
>>>if it depends on simultaneity, since then you need to limit
>>>the resolution. The view I presented has no resolution limit in the
>>>classical setting and can be assumed to be exact (perfect, in your words),
>>>hence serve as a foundation.
>>>
>>>
>>>
>>>
>>>>3. I do not understand your distinction between "instant observer" and
>>>> "point observer".
>>>
>>>
>>>I defined it. The instant observer is the fictitious and causally
>>>inconsistent observer knowing all information on the 3-manifold t=const.
>>>The point observer is the still idealized but caussally consistent observer
>>>knowing all information on the 3-manifold (x-x^*)^2=L^2, x_0<x^*_0,
>>>where for simplicity I took the position to be at x^*=0 (and L can be
>>>taken as 1, by picking the right units).
>>>
>>
>>Let me give you an example (idealized, of course) of a measuring
>>apparatus which can collect information on a "3-manifold t=const".
>>I prepare an array of particle detectors densely distributed in space
>>(these could be small Geiger counters, or semiconductor detectors,
>>or whatever). I connect all these detectors by wires of equal length R
>>to the "central switch", where I am sitting. When I flip the switch,
>>the signals go through the wires to the detectors and activate them
>>for a short time (a picosecond, or a femtosecond...). So, all detectors
>>become active at the same time t=R/c. After the measurement is done, I
>>can inspect my detectors and see where the particles in the system were
>>situated on the t=R/c "hyperplane".
>>
>>Eugene Stefanovich.
>
>
> When you collect the information again it will take time R/c for the
> information to get to you. You are constructing the spacelike surface
> from slices of timelike surfaces in this Gedankenexperiment.
> You will therefore find that the "they fire at the same time" is of
> course also not an invariant statement. An observer moving wrt you in
> the center of your web will of course see them fire at different
> times. Still a spacelike 3 Manifold, but not at t=const.

I agree with you completely. The moving observer will not recognize my
measurements as instantaneous. But I don't care about other observers.
The question was whether one observer can arrange for measurements
of observables on a fixed time slice. The answer is yes.
Other observers can also do the same in their frames of references.
But two observers in relative motion will never agree whose
observation was instantaneous and whose not.

The Poincare transformations of observables allow me to connect
results of my instantaneous measurements with instantaneous
measurements of other observers.

Eugene Stefanovich

>
> f
>

strong_field

Dec6-04, 07:17 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>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<41AE263E.90106@univie.ac.at>...\n> Eugene Stefanovich wrote:\n>\n> I am not talking about operational concepts but about foundations - getting\n> the mathematical concepts right to be able to do correct physics.\n> Without correct concepts operational statements have no meaning.\n> The theory defines what a measurement is. Outside the immediate realm of\n> everyday experience, one needs already the conceptual basis to even\n> discuss what has operational meaning.\n\nWhat you state above implies a chart like this:\n\n\n1) Foundation\n|\n|\nV\n2) Mathematics\n/\\\n/ \\\n/ \\\n3) Right Wrong\nConcepts Concepts\n| |\n| |\nV V\n4) Correct Incorrect\nPhysics Physics\n| |\n| |\nV V\n5) Good Bad\nTheory Theory\n| |\n| |\nV V\n6) Defines Defines\nMeasurement Measurement\n| |\n| |\nV V\n7) Meaningful Meaningless\nOperational Operational\nStatements Statements\n| |\n| |\nV V\n8) Measurement Measurement\n| |\n| |\nV V\n9) Measurement Measurement\nverifies verifies\nthe good the bad\ntheory theory\n\nYou seem to imply a hierarchical structure like the one above where\nsome elements belonging to a group called "foundations" is on top and\nelements called "operational statements" are way down.\n\nIn fact I am not clear what you, or physicists in general, mean by\n"operational." But the way you use "foundations" seems to mean a set\nof "definitions" that physicists agree upon.\n\nBut if you belive that physics is an experimental science, measurement\nand foundations should be on the same level\n\nfoundational definitions <---> meaningful measurements\n\nOtherwise, as you see in the hierarchical chart, measurements can\nverify both the "good" and the "bad" theory. But it all depends how\nyou define "operational."\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>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<41AE263E.90106@univie.ac.at>...
> Eugene Stefanovich wrote:
>
> I am not talking about operational concepts but about foundations - getting
> the mathematical concepts right to be able to do correct physics.
> Without correct concepts operational statements have no meaning.
> The theory defines what a measurement is. Outside the immediate realm of
> everyday experience, one needs already the conceptual basis to even
> discuss what has operational meaning.

What you state above implies a chart like this:

1) Foundation
|
|
V
2) Mathematics
/\
/ \/ \
3) Right Wrong
Concepts Concepts
| || |
V V
4) Correct Incorrect
Physics Physics
| || |
V V
5) Good Bad
Theory Theory
| || |
V V
6) Defines Defines
Measurement Measurement
| || |
V V
7) Meaningful Meaningless
Operational Operational
Statements Statements
| || |
V V
8) Measurement Measurement
| || |
V V
9) Measurement Measurement
verifies verifies
the good the bad
theory theory

You seem to imply a hierarchical structure like the one above where
some elements belonging to a group called "foundations" is on top and
elements called "operational statements" are way down.

In fact I am not clear what you, or physicists in general, mean by
"operational." But the way you use "foundations" seems to mean a set
of "definitions" that physicists agree upon.

But if you belive that physics is an experimental science, measurement
and foundations should be on the same level

foundational definitions <---> meaningful measurements

Otherwise, as you see in the hierarchical chart, measurements can
verify both the "good" and the "bad" theory. But it all depends how
you define "operational."