Arnold Neumaier
Dec3-04, 04:48 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 wrote:\n> Arnold Neumaier wrote:\n>\n>>Transformations are just represent the same physics in different\n>>coordinate systems.\n>\n> For observer shifted by distance a, all positions of particles\n> appear shifted by -a. In the case of point form dynamics, this\n> simple rule does not work.\n\nOf course. Your rule is too simple. in the point form, the rules for\nLorentz transformations are simple, since they respect the kinematical\nobject (the past hyperboloid). Space translations move off the\nhyperboloid, hence have to be more complicated.\n\n\n\n>>>with that. The CJS theorem say that values of (p,r,t) and (p\',r\',t\')\n>>>are not connected by linear Lorentz transformations.\n>>\n>>Only under assumptions which must be rejected.\n>\n> Which are these assumptions?\n\nThat different observers see the same trajectories.\n\n\n\n>>Quantum chemists use QED to calculate the response of molecules to\n>>electromagnetic fields and laser impulses.\n>\n> I worked in quantum chemistry for many years, and I haven\'t seen\n> applications of full-fledged QED. Only some approximate models\n> "derived" from QED.\n\nOf course. All calculations in QED are based on approximate models\nonly. And they work.\n\nThe Hamiltonians you construct at each order are also only\napproximate models "derived" from QED.\nAnd you haven\'t even shown that they work...\n\n\n\n> I agree that my approach is not mature enough to be a viable\n> substitute for existing theories. There are lot of things to be done,\n> lot of questions to be answered.\n\nFinally a sign that I don\'t spend my time in vain.\nIt is better to make great claims when your work is mature than\nat a time when too much is undone to claim with credibility that\na big revolution in physics is needed, and you hold the key...\n\n\n\n>>I only dismiss your strange philosophy.\n>\n> I challenge you to prove that boost transformations of\n> physical observables are given by universal linear Lorentz formulas.\n\nI refer to all the work done by several generations of physicists.\nIt is up to _you_ to challence the established theory.\n\n\n> And I found that all predictions of the new theory are very close\n> to the old one\n\nIf you would work without approximations, you\'d find that all\npredictions of the new theory are identical to the old one.\nIf they aren\'t you are in trouble. QED is extremely well tested.\n\n\n\n>>>The simplicity is not in short expressions for the Hamiltonian and\n>>>other quantities. The simplicity is in adhering to well-tested\n>>>physical postulates, in clear physical meaning of all theoretical\n>>>ingredients, and in the absence of logical contradictions.\n>>\n>>Have you _anyone_ besides yourself convinced of that?\n>>\n>>There are exactly the same logical contradictions as in QED, namely the\n>>missing mathematical foundations that make sense nonperturbatively.\n>>Without that, there is no logical basis to decide about consistency.\n>\n> I agree that this problem is not solved neither in QED nor in my\n> approach. I don\'t think you expect me to solve all problems in\n> theoretical physics.\n\nNo. But I expect you to moderate your claims to match what you actually\ndid. If you claim \'the absence of logical contradictions\' in your approach\nwhile its presence in the traditional approach, you\'d make sure that\nyou work at a higher level of logical coherence than those you criticise.\n\n\n> The simplicity of my approach, as I see it, is in formulating\n> QFT in the language of ordinary quantum mechanics, where states are\n> described by wave functions, the time evolution is described by\n> a finite unitary operator, the bound states are calculated via\n> diagonalization of the Hamiltonian, etc.\n\nThis is also done in traditional quantum field theory, though you\napparently don\'t see it.\n\nDid you ever look at constructive field theory? It gives all you\ndesire in case of 2D quantum fields. There is a well-defined Hilbert\nspace, a well-defined Hamiltonian (in fact better defined than yours\nsince no perturbation theory is involved), a well-defined unitary dynamics,\nwell-defined bound states that are eigenstates of the Hamiltonian,\nand everything is invariant under the 2D Poincare group ISO(1,1).\n\nThe _only_ thing you might find wanting is an explicit formula for\nH in the form of H_0+V since H is constructed in a more abstract way\n(as analytic continuation of an operator in Euclidean field theory).\nBut you could pick your favorite H_0 and simply define the interaction\nas V=H-H_0.\n\nThat the 4D case is more difficult has to do with obstacles in getting\ntight enough bounds for the analytic estimates needed. These are\nmathematical difficulties, but not inconsistencies - no one proved that\nthere are contradictions, and the practice of QFT suggests that there\nare indeed none (at least for asymptotically free theories).\n\nOn the perturbative level, there is no difficulty at all - see, e.g.\nSalmhofer\'s book on renormalization.\n\nYour construction is on the perturbative level only, too - so you have\nno right to claim that all is bad with tradition, and all has become\ncorrected with your work.\n\n\nArnold Neumaier\n>>\n>\n>\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Eugene Stefanovich wrote:
> Arnold Neumaier wrote:
>
>>Transformations are just represent the same physics in different
>>coordinate systems.
>
> For observer shifted by distance a, all positions of particles
> appear shifted by -a. In the case of point form dynamics, this
> simple rule does not work.
Of course. Your rule is too simple. in the point form, the rules for
Lorentz transformations are simple, since they respect the kinematical
object (the past hyperboloid). Space translations move off the
hyperboloid, hence have to be more complicated.
>>>with that. The CJS theorem say that values of (p,r,t) and (p',r',t')
>>>are not connected by linear Lorentz transformations.
>>
>>Only under assumptions which must be rejected.
>
> Which are these assumptions?
That different observers see the same trajectories.
>>Quantum chemists use QED to calculate the response of molecules to
>>electromagnetic fields and laser impulses.
>
> I worked in quantum chemistry for many years, and I haven't seen
> applications of full-fledged QED. Only some approximate models
> "derived" from QED.
Of course. All calculations in QED are based on approximate models
only. And they work.
The Hamiltonians you construct at each order are also only
approximate models "derived" from QED.
And you haven't even shown that they work...
> I agree that my approach is not mature enough to be a viable
> substitute for existing theories. There are lot of things to be done,
> lot of questions to be answered.
Finally a sign that I don't spend my time in vain.
It is better to make great claims when your work is mature than
at a time when too much is undone to claim with credibility that
a big revolution in physics is needed, and you hold the key...
>>I only dismiss your strange philosophy.
>
> I challenge you to prove that boost transformations of
> physical observables are given by universal linear Lorentz formulas.
I refer to all the work done by several generations of physicists.
It is up to _you_ to challence the established theory.
> And I found that all predictions of the new theory are very close
> to the old one
If you would work without approximations, you'd find that all
predictions of the new theory are identical to the old one.
If they aren't you are in trouble. QED is extremely well tested.
>>>The simplicity is not in short expressions for the Hamiltonian and
>>>other quantities. The simplicity is in adhering to well-tested
>>>physical postulates, in clear physical meaning of all theoretical
>>>ingredients, and in the absence of logical contradictions.
>>
>>Have you _anyone_ besides yourself convinced of that?
>>
>>There are exactly the same logical contradictions as in QED, namely the
>>missing mathematical foundations that make sense nonperturbatively.
>>Without that, there is no logical basis to decide about consistency.
>
> I agree that this problem is not solved neither in QED nor in my
> approach. I don't think you expect me to solve all problems in
> theoretical physics.
No. But I expect you to moderate your claims to match what you actually
did. If you claim 'the absence of logical contradictions' in your approach
while its presence in the traditional approach, you'd make sure that
you work at a higher level of logical coherence than those you criticise.
> The simplicity of my approach, as I see it, is in formulating
> QFT in the language of ordinary quantum mechanics, where states are
> described by wave functions, the time evolution is described by
> a finite unitary operator, the bound states are calculated via
> diagonalization of the Hamiltonian, etc.
This is also done in traditional quantum field theory, though you
apparently don't see it.
Did you ever look at constructive field theory? It gives all you
desire in case of 2D quantum fields. There is a well-defined Hilbert
space, a well-defined Hamiltonian (in fact better defined than yours
since no perturbation theory is involved), a well-defined unitary dynamics,
well-defined bound states that are eigenstates of the Hamiltonian,
and everything is invariant under the 2D Poincare group ISO(1,1).
The _only_ thing you might find wanting is an explicit formula for
H in the form of H_0+V since H is constructed in a more abstract way
(as analytic continuation of an operator in Euclidean field theory).
But you could pick your favorite H_0 and simply define the interaction
as V=H-H_0.
That the 4D case is more difficult has to do with obstacles in getting
tight enough bounds for the analytic estimates needed. These are
mathematical difficulties, but not inconsistencies - no one proved that
there are contradictions, and the practice of QFT suggests that there
are indeed none (at least for asymptotically free theories).
On the perturbative level, there is no difficulty at all - see, e.g.
Salmhofer's book on renormalization.
Your construction is on the perturbative level only, too - so you have
no right to claim that all is bad with tradition, and all has become
corrected with your work.
Arnold Neumaier
>>
>
>
> Arnold Neumaier wrote:
>
>>Transformations are just represent the same physics in different
>>coordinate systems.
>
> For observer shifted by distance a, all positions of particles
> appear shifted by -a. In the case of point form dynamics, this
> simple rule does not work.
Of course. Your rule is too simple. in the point form, the rules for
Lorentz transformations are simple, since they respect the kinematical
object (the past hyperboloid). Space translations move off the
hyperboloid, hence have to be more complicated.
>>>with that. The CJS theorem say that values of (p,r,t) and (p',r',t')
>>>are not connected by linear Lorentz transformations.
>>
>>Only under assumptions which must be rejected.
>
> Which are these assumptions?
That different observers see the same trajectories.
>>Quantum chemists use QED to calculate the response of molecules to
>>electromagnetic fields and laser impulses.
>
> I worked in quantum chemistry for many years, and I haven't seen
> applications of full-fledged QED. Only some approximate models
> "derived" from QED.
Of course. All calculations in QED are based on approximate models
only. And they work.
The Hamiltonians you construct at each order are also only
approximate models "derived" from QED.
And you haven't even shown that they work...
> I agree that my approach is not mature enough to be a viable
> substitute for existing theories. There are lot of things to be done,
> lot of questions to be answered.
Finally a sign that I don't spend my time in vain.
It is better to make great claims when your work is mature than
at a time when too much is undone to claim with credibility that
a big revolution in physics is needed, and you hold the key...
>>I only dismiss your strange philosophy.
>
> I challenge you to prove that boost transformations of
> physical observables are given by universal linear Lorentz formulas.
I refer to all the work done by several generations of physicists.
It is up to _you_ to challence the established theory.
> And I found that all predictions of the new theory are very close
> to the old one
If you would work without approximations, you'd find that all
predictions of the new theory are identical to the old one.
If they aren't you are in trouble. QED is extremely well tested.
>>>The simplicity is not in short expressions for the Hamiltonian and
>>>other quantities. The simplicity is in adhering to well-tested
>>>physical postulates, in clear physical meaning of all theoretical
>>>ingredients, and in the absence of logical contradictions.
>>
>>Have you _anyone_ besides yourself convinced of that?
>>
>>There are exactly the same logical contradictions as in QED, namely the
>>missing mathematical foundations that make sense nonperturbatively.
>>Without that, there is no logical basis to decide about consistency.
>
> I agree that this problem is not solved neither in QED nor in my
> approach. I don't think you expect me to solve all problems in
> theoretical physics.
No. But I expect you to moderate your claims to match what you actually
did. If you claim 'the absence of logical contradictions' in your approach
while its presence in the traditional approach, you'd make sure that
you work at a higher level of logical coherence than those you criticise.
> The simplicity of my approach, as I see it, is in formulating
> QFT in the language of ordinary quantum mechanics, where states are
> described by wave functions, the time evolution is described by
> a finite unitary operator, the bound states are calculated via
> diagonalization of the Hamiltonian, etc.
This is also done in traditional quantum field theory, though you
apparently don't see it.
Did you ever look at constructive field theory? It gives all you
desire in case of 2D quantum fields. There is a well-defined Hilbert
space, a well-defined Hamiltonian (in fact better defined than yours
since no perturbation theory is involved), a well-defined unitary dynamics,
well-defined bound states that are eigenstates of the Hamiltonian,
and everything is invariant under the 2D Poincare group ISO(1,1).
The _only_ thing you might find wanting is an explicit formula for
H in the form of H_0+V since H is constructed in a more abstract way
(as analytic continuation of an operator in Euclidean field theory).
But you could pick your favorite H_0 and simply define the interaction
as V=H-H_0.
That the 4D case is more difficult has to do with obstacles in getting
tight enough bounds for the analytic estimates needed. These are
mathematical difficulties, but not inconsistencies - no one proved that
there are contradictions, and the practice of QFT suggests that there
are indeed none (at least for asymptotically free theories).
On the perturbative level, there is no difficulty at all - see, e.g.
Salmhofer's book on renormalization.
Your construction is on the perturbative level only, too - so you have
no right to claim that all is bad with tradition, and all has become
corrected with your work.
Arnold Neumaier
>>
>
>