## Time, Parameter, Operator

<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>Dear Members,\n\non p.68 of Sakurai\'s "Modern Quantum Mechanics" we read "... Time\nis just a parameter in quantum mechanics, not an operator. In\nparticular, Time is not an observable in the language of the previous\nchapte." What is the deference between a "parameter" and " operator"\nfrom a physical point of view?\n\ncheers,\n\nAli\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Dear Members,

on p.68 of Sakurai's "Modern Quantum Mechanics" we read "... Time
is just a parameter in quantum mechanics, not an operator. In
particular, Time is not an observable in the language of the previous
chapte." What is the deference between a "parameter" and " operator"
from a physical point of view?

cheers,

Ali

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On $2005-06-13,$ Ali wrote: > Dear Members, > > on p.68 of Sakurai's "Modern Quantum Mechanics" we read "... Time > is just a parameter in quantum mechanics, not an operator. In > particular, Time is not an observable in the language of the previous > chapte." What is the deference between a "parameter" and " operator" > from a physical point of view? Very briefly, there is no fuzziness in a parameter, it is specified externally. OTOH, there is fuzziness in a dynamical variable represented by an operator, because its expectation value is specified by the state. Igor



Ali wrote: > Dear Members, > > on p.68 of Sakurai's "Modern Quantum Mechanics" we read "... Time > is just a parameter in quantum mechanics, not an operator. In > particular, Time is not an observable in the language of the previous > chapte." What is the deference between a "parameter" and " operator" > from a physical point of view? You put your finger on the central problem of modern theoretical physics. Consider the difference between "time" and "position" in quantum mechanics. You can talk about "position of a particle", so position is an observable that can be measured on (is a characteristic of) a physical system (e.g., particle). The measured position of a particle depends on the state in which you find the particle. In QM such observables as position are described by Hermitian operators, and the measured values are described by matrix elements of these operators. On the other hand, you cannot measure "time of a particle". Time is not a property of the particle, time does not depend on the state of the particle. In other words, time is not an observable. Then what is time? In each laboratory we have a classical device called "clock" that gives us a numerical parameter called "time". The time label is attached to all measurements performed in the laboratory. So, time is just a classical numerical parameter in quantum mechanics. This is very different from the way time and position are treated in special (and general) relativity. Einstein's relativity declares that time and position are just coordinates in the 4D space-time manifold. From the point of view of different observers these coordinates are interchangeable. This is reflected in the way time and position form components of a 4-vector in the Einstein's theory. As we saw above, this "equivalence" of time and position has no analog in quantum mechanics. I believe, this contradiction is the main obstacle for all current attempts to "quantize gravity". There are many reviews regarding the "problem of time" on arxiv.org. My personal opinion is that the only way to reconcile the principle of relativity with quantum mechanics is to reject the 4D space-time "unification" of space and time. This idea is, actually, not so scary. I explored its consequences in http://www.arxiv.org/abs/physics/0504062 and the resulting theory looks good, though non-conventional. Eugene.

## Time, Parameter, Operator

<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&gt; In each laboratory we have a classical device called "clock" that\n&gt; gives us a numerical parameter called "time". The time label is\n&gt; attached to all measurements performed in the laboratory. So, time\n&gt; is just a classical numerical parameter in quantum mechanics.\n&gt;\n&gt; This is very different from the way time and position are treated in\n&gt; special (and general) relativity. [...]\n&gt;\n&gt; As we saw above, this "equivalence" of time and position has no\n&gt; analog in quantum mechanics. I believe, this contradiction is the\n&gt; main obstacle for all current attempts to "quantize gravity".\n\nIt is, at best, rash to attempt to extract a solution of the "problem\nof time" from non-relativistic quantum mechanics. Relativistic QM has\nnever claimed to be in a position to offer such insight.\n\n&gt; My personal opinion is that the only way to reconcile the principle\n&gt; of relativity with quantum mechanics is to reject the 4D space-time\n&gt; "unification" of space and time. This idea is, actually, not so\n&gt; scary. I explored its consequences in physics/0504062 and the\n&gt; resulting theory looks good, though non-conventional.\n\nIt is also rash to offer the opinion of "looks good" of your own theory\nbefore it had a change to go through peer review. Especially in the\nabsence of theoretical and experimental tests. Humility is the burden\nthat all theorists must bear, until proven otherwise.\n\nIgor\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Eugene Stefanovich wrote:

> In each laboratory we have a classical device called "clock" that
> gives us a numerical parameter called "time". The time label is
> attached to all measurements performed in the laboratory. So, time
> is just a classical numerical parameter in quantum mechanics.
>
> This is very different from the way time and position are treated in
> special (and general) relativity. [...]
>
> As we saw above, this "equivalence" of time and position has no
> main obstacle for all current attempts to "quantize gravity".

It is, at best, rash to attempt to extract a solution of the "problem
of time" from non-relativistic quantum mechanics. Relativistic QM has
never claimed to be in a position to offer such insight.

> My personal opinion is that the only way to reconcile the principle
> of relativity with quantum mechanics is to reject the 4D space-time
> "unification" of space and time. This idea is, actually, not so
> scary. I explored its consequences in http://www.arxiv.org/abs/physics/0504062 and the
> resulting theory looks good, though non-conventional.

It is also rash to offer the opinion of "looks good" of your own theory
before it had a change to go through peer review. Especially in the
absence of theoretical and experimental tests. Humility is the burden
that all theorists must bear, until proven otherwise.

Igor



Igor Khavkine wrote: > Eugene Stefanovich wrote: > > >>In each laboratory we have a classical device called "clock" that >>gives us a numerical parameter called "time". The time label is >>attached to all measurements performed in the laboratory. So, time >>is just a classical numerical parameter in quantum mechanics. >> >>This is very different from the way time and position are treated in >>special (and general) relativity. [...] >> >>As we saw above, this "equivalence" of time and position has no >>analog in quantum mechanics. I believe, this contradiction is the >>main obstacle for all current attempts to "quantize gravity". > > > It is, at best, rash to attempt to extract a solution of the "problem > of time" from non-relativistic quantum mechanics. Relativistic QM has > never claimed to be in a position to offer such insight. The theory I developed in http://www.arxiv.org/abs/physics/0504062 is fully relativistic. The evidence for that is that there is a representation of the Poincare group in the Hilbert (Fock) space of the considered system. Nevertheless, in this theory there is no symmetry between time and space coordinates. Position is a quantum observable (Hermitian operator), and time is a numerical parameter. The manifest covariance (= equivalence of space and time coordinates) is the hallmark of one particular (not self-consistent, but, nevertheless, very popular) interpretation of the principle of relativity, i.e., that belonging to Einstein. I recommend you to read the book which explains that the manifest covariance is an additional assumption of Einstein's theory. This assumption does not agree with the presence of interactions. It is, at best, an approximation. >>My personal opinion is that the only way to reconcile the principle >>of relativity with quantum mechanics is to reject the 4D space-time >>"unification" of space and time. This idea is, actually, not so >>scary. I explored its consequences in http://www.arxiv.org/abs/physics/0504062 and the >>resulting theory looks good, though non-conventional. > > > It is also rash to offer the opinion of "looks good" of your own theory > before it had a change to go through peer review. If you require a formal review process, then you have it: I have 3 papers in peer-reviewed journals. These papers fully cover the theory presented in the book. > Especially in the > absence of theoretical and experimental tests. I can agree with your point regarding the experimental tests. RQD makes specific predictions which could be tested in routine experiments (though rather high precision is required). However, such decisive experiments have not been done yet. I do not agree on the "theoretical" point, though. If you happen to notice any logical inconsistency in the book, I would like to know that, and I'd gladly correct it. Eugene.



Eugene Stefanovich wrote: > > In each laboratory we have a classical device called "clock" > that gives us a numerical parameter called "time". The time label > is attached to all measurements performed in the laboratory. > So, time is just a classical numerical parameter in quantum mechanics. Why would Position be an intrinsic attribute of a quantum particle (other than by convention) when their decay times suggest to me that Time is just as much an intrinsic attribute for them. If anything I would think they were more like Clocks than like Rulers. > This is very different from the way time and position are treated > in special (and general) relativity. Einstein's relativity declares > that time and position are just coordinates in the 4D space-time > manifold. From the point of view of different observers these > coordinates are interchangeable. This is reflected in the way > time and position form components of a 4-vector in the Einstein's > theory. OK, Time and Position are more easily integrated in Relativity. Does that remain true in spaces with very high curvatures ?



Eugene Stefanovich wrote: > On the other hand, you cannot measure "time of a particle". > Time is not a property of the particle, time does not depend on > the state of the particle. In other words, time is not an > observable. Then what is time? > Eugene. Hey Eugene and Ali, Time of a particle does not make sense. What makes sense is to talk about the time of an 'event'. You might want to construct a picture of the universe out of events (like measurement events) instead of particles or fields. So, is there a fuzziness in the time component of an event? In my opinion, it is hopeless trying to relativise quantum mechanics by constructing a time operator and assuming it doesn't commute with the Hamiltonian. You end up with negative energies and a fundamental ambiguity in what measurement means in such a theory. Ali, you should take a look at the Feynman path integral way (I like to just call it the space-time way) of doing quantum mechanics. You can do quantum mechanics without operators entirely. -Souvik



On a common sense and experimental level, things clearly proceed as a function of the influences of everything else, and NOT as a function of time. The "time" imagery is a feature of the map that people, including physicists, have projected onto the party. Thus, the correct concept is "experience exists; time does not". "Time" is a mis-labeling, or a simplified approximation of "the influences of everything else". Its use facilitates books full of helpful abstract math modeling, but when it comes all the way down to considering fundamentals, time is not. -- Ralph Frost "To get the concept, first work the equation out in analog math."



Ralph E. Frost wrote: "experience exists; time does not". > Ralph, It is well known that the passage of time affect the rate of evolution of spontaneous events. When the said event is a clock, we call it "time". Clocks are all based on a spontaneous event e.g. sand in hourglass, relaxation time of a quartz crystal, spontaneous electronic transition etc. etc. because we trust that time can't be rushed. The passage of time varies in a gravitational field, and the same clock can be brought up or down and it will accordingly beat faster or slower. The clock is only an indicator of the local rate of passage of time where it is located. The passage of time is a true (ontological) dynamical substance out there (GR already gives clues about its properties). The passage of time exists and varies in gravitational field and in relativistic context.---The integration of the passage of time as Duration $is\is$ just an experience which does not have any reality beyond our perception. The EXPERIENCE is important BUT it is only a relation between you and the subject matter; it has no existence outside that relationship of which you are an inseparable part. What interests me is the Real universe, the one about which clues are found FROM our experience of it. That's the real stuff! The real universe. Marcel, lebel@muontailpig.com remove particle



Ralph E. Frost wrote: > On a common sense and experimental level, things clearly proceed as a > function of the influences of everything else, and NOT as a function of > time. The "time" imagery is a feature of the map that people, > including physicists, have projected onto the party. Thus, the > correct concept is "experience exists; time does not". > > "Time" is a mis-labeling, or a simplified approximation of "the > influences of everything else". > > Its use facilitates books full of helpful abstract math modeling, but > when it comes all the way down to considering fundamentals, time is > not. By exactly the same, argument, ''experience exists; space does not'' ''experience exists; mass does not'' ''experience exists; charge does not'' ''experience exists; gravitation does not'' etc. Physics is exactly about these things that are substituted for experience to make experience quantitatively predictable. In this deeper sense, time, space, mass, charge, gravitation etc. exist. Arnold Neumaier



Marcel LeBel wrote: > > Ralph E. Frost wrote: > > "experience exists; time does not". > > > > Ralph, > > It is well known that the passage of time affect the rate of evolution > of spontaneous events. When the said event is a clock, we call it > "time". Clocks are all based on a spontaneous event e.g. sand in > hourglass, relaxation time of a quartz crystal, spontaneous electronic > transition etc. etc. because we trust that time can't be rushed. > > The passage of time varies in a gravitational field, and the same > clock can be brought up or down and it will accordingly beat faster or > slower. I'd be careful about that. The clock that travels through the most space accumulates the least time. There is no in-frame way of detecting an absolute rate of passage of time. Clocks are only interesting upon comparison. > The clock is only an indicator of the local rate of passage of time > where it is located. That is a sloppy statement. Clocks are only interesting upon comparison. Within a frame no anomalies are evident, nor should they be. The anomaly resides in external comparison. > The passage of time is a true (ontological) > dynamical substance out there (GR already gives clues about its > properties). No. Time is arbitrary, depending upon the observer. > The passage of time exists and varies in gravitational > field and in relativistic context.---The integration of the passage of > time as Duration $is\is$ just an experience which does not have any > reality beyond our perception. Tell that to an unstable particle in a particle accelerator, or to atmospheric muon showers from cosmic ray-atom collisions. > The EXPERIENCE is important BUT it is only a relation between you and > the subject matter; it has no existence outside that relationship of > which you are an inseparable part. What interests me is the Real > universe, the one about which clues are found FROM our experience of it. > That's the real stuff! The real universe. TILT. Annalen der Physik 4 XVII pp$. 891-921$ (1905) Annalen der Physik 4 XLIX $pp. 769-822$ (1916) Heisenberg Uncertainty and quantum mechanics Only observation exists. Be glad that the universe does not tolerate internal inconsistency. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf



apn82 wrote: > Eugene Stefanovich wrote: > >>In each laboratory we have a classical device called "clock" >>that gives us a numerical parameter called "time". The time label >>is attached to all measurements performed in the laboratory. >>So, time is just a classical numerical parameter in quantum mechanics. > > > Why would Position be an intrinsic attribute of a quantum particle > (other than by convention) when their decay times suggest to me > that Time is just as much an intrinsic attribute for them. If anything > I would think they were more like Clocks than like Rulers. When experimentalists measure the decay law of unstable particles, they measure the probability of finding the system in a certain quantum state. For example, the probability of finding the system in the form of $\mu-meson$ as opposed to the (decayed) state of electron + two neutrinos. In this case, the quantum observable is the projection operator on the subspace of $\mu-meson$ states. The decay law is the time dependence of the expectation value of this operator. Time still plays a role of a classical parameter. The question "what is time of decaying particle?" makes no sense. You should ask "what is the probability of finding $\mu-meson at$ time t?" > > >>This is very different from the way time and position are treated >>in special (and general) relativity. Einstein's relativity declares >>that time and position are just coordinates in the 4D space-time >>manifold. From the point of view of different observers these >>coordinates are interchangeable. This is reflected in the way >>time and position form components of a 4-vector in the Einstein's >>theory. > > > OK, Time and Position are more easily integrated in Relativity. > Does that remain true in spaces with very high curvatures ? You probably wanted to ask "...in space-times with high curvatures?" My point is that since space and time do not form a unified 4D manifold in the absence of gravity, then describing gravitational fields by curved space-time manifolds does not make sense either. There should be other ways to describe gravity without using space-times and their curvature. At this point I have no idea how to do that. Eugene.



Souvik wrote: > Eugene Stefanovich wrote: > > >>On the other hand, you cannot measure "time of a particle". >>Time is not a property of the particle, time does not depend on >>the state of the particle. In other words, time is not an >>observable. Then what is time? > > >>Eugene. > > > Hey Eugene and Ali, > > Time of a particle does not make sense. What makes sense is to talk > about the time of an 'event'. Exactly right! The simplest example of such events is the intersection of trajectories of two particles. In subsection 7.3.7 of the book I demonstrate that time and position of such events transform according to Lorentz formulas if two particles are non-interacting. This remains true even in the absence of position-time symmetry: Position is expectation value of a quantum operator, time is a parameter. The Lorentz transformation formulas are no longer valid if the two particles interact with each other (see subsection 12.3.2). Eugene.



On $2005-06-14,$ Eugene Stefanovich wrote: > Igor Khavkine wrote: > The manifest covariance (= equivalence of space and time coordinates) > is the hallmark of one particular (not self-consistent, but, > nevertheless, very popular) interpretation of the principle of > relativity, i.e., that belonging to Einstein. I recommend you to read > the book which explains that the manifest covariance is an additional > assumption of Einstein's theory. This assumption does not agree with > the presence of interactions. It is, at best, an approximation. The problem with the above statement has already been pointed out, but it seems it must be pointed out again. There is no such thing as a principle of *manifest* covariance. There does exists the principle of covariance, which says that two sides of the same equation must transform alike under active and passive coordinate transformations. The manifest part is only a matter of taste. Lets leave the alleged logical consistency issue aside for now. Can you locate references that make reference to manifest covariance other than as a preferred form for writing down equations? >> It is also rash to offer the opinion of "looks good" of your own theory >> before it had a change to go through peer review. > > If you require a formal review process, then you have it: I have 3 > papers in peer-reviewed journals. These papers fully cover the theory > presented in the book. If these publications indeed "look good", are there any published papers that have made this judgement? Note that papers on the arXiv are not necessarily published (no peer review). Nor is a paper that accepts none of your strange philosophy a glowing review. >> Especially in the >> absence of theoretical and experimental tests. [...] > If you happen to notice any logical > inconsistency in the book, I would like to know that, and I'd > gladly correct it. You contradict special relativity and classical Maxwell theory. Please, do correct this. Igor



Eugene Stefanovich wrote: > > Consider the difference between "time" and "position" > in quantum mechanics. You can talk about "position of a particle", > so position is an observable that can be measured on > (is a characteristic > of) a physical system (e.g., particle). The measured position of a > particle depends on the state in which you find the particle. > In QM such observables as position are described by Hermitian > operators, and the > measured values are described by matrix elements of these operators. > > On the other hand, you cannot measure "time of a particle". > Time is not a property of the particle, time does not depend on > the state of the particle. In other words, time is not an > observable. Then what is time? > In classical QM, time is an observable but not of the configuration hilbert space. In other words, the operator associated to the time parameter commutes with all the operators on the configuration space. There is nothing contradictory with such an affirmation, all the current classical QM experiments are based on this property. This is why we may consider the time as a parameter in non relativistic QM: we obtain a measurement "a" result @time t of the observable $A =3D>(a,t)$ is the measurement result of the commuting set of observables (time observable,A). For a formal example explaining this topic, see: http://www.physicsforums.com/s=ADhow....php?t=3D72181 Seratend. P.S. I have never understood why one always tries to define a time operator acting on the configuration space of the particle.



Seratend wrote: > In classical QM, time is an observable but not of the configuration > hilbert space. In other words, the operator associated to the time > parameter commutes with all the operators on the configuration space. There is just one Hilbert space where state vectors and operators of observables are defined. You can choose different bases in this Hilbert space, e.g., position (or configuration) representation or momentum representation. The choice of the basis set does not affect state vectors or operators. If time is an operator, then it ought to act in this Hilbert space. > There is nothing contradictory with such an affirmation, all the > current classical QM experiments are based on this property. > This is why we may consider the time as a parameter in non relativistic > QM: we obtain a measurement "a" result @time t of the observable $A =3D>$ > (a,t) is the measurement result of the commuting set of observables > (time observable,A). Suppose that we constructed such a "time operator" that has continuous spectrum from -infinity to +infinity and commutes with all other observables. Then, according to postulates of quantum mechanics, for each state $|\Psi>$ of a physical system we should be able to calculate/measure the expectation value of time $<\Psi|T|\Psi>$. We also should be able to prepare linear combinations of systems with different values of time. All this does not make any sense to me. Moreover, if T commutes with all operators, including the generator of boosts K, then the time of events should not depend on the velocity of observer. How would you explain the Lorentz transformations for time and position in such a theory? In my view, it is better not to use words "time" and "operator" in one sentence. Time is just a numerical label assigned to each measurement by looking at the wall-clock. Eugene.



Igor Khavkine wrote: > On $2005-06-14,$ Eugene Stefanovich wrote: > >>Igor Khavkine wrote: > > >>The manifest covariance (= equivalence of space and time coordinates) >>is the hallmark of one particular (not self-consistent, but, >>nevertheless, very popular) interpretation of the principle of >>relativity, i.e., that belonging to Einstein. I recommend you to read >>the book which explains that the manifest covariance is an additional >>assumption of Einstein's theory. This assumption does not agree with >>the presence of interactions. It is, at best, an approximation. > > > The problem with the above statement has already been pointed out, but > it seems it must be pointed out again. There is no such thing as a > principle of *manifest* covariance. There does exists the principle of > covariance, which says that two sides of the same equation must > transform alike under active and passive coordinate transformations. > The manifest part is only a matter of taste. > > Lets leave the alleged logical consistency issue aside for now. Can you > locate references that make reference to manifest covariance other than > as a preferred form for writing down equations? I call "manifest covariance" the following statement (Assertion F in my book): "Every general law of nature must be so constituted that it transformed into a law of exactly the same form when, instead of the space-time variables x, y, z, t of the original coordinate system K, we introduce new space-time variables x', y', z', t' of a coordinate system K'. In this connection the relation between the ordinary and the accented magnitudes is given by the Lorentz transformation. Or in brief: General laws of nature are co-variant with respect to Lorentz transformations." (A. Einstein, "Relativity: The Special and General Theory", (Methuen and Co., 1920) This also means that observables normally form 4-scalars, 4-vectors, 4-tensors, etc. that transform from K to K' via simple universal linear transformation laws (Lorentz transformations). An important point of special relativity is that these laws do not depend on the composition of the observed physical system and interactions acting there. In special relativity, these laws are universal, they are manifestations of the 4D unified nature of the space-time. At closer inspection, this statement of special relativity is a non-proven postulate. I agree that so far this postulate worked well and did not contradict any experiment. Can we do better than just simply postulate such an important statement? Yes we can. In quantum mechanics, the transformations of observables between different reference frames (K and K') are given by unitary operators. For example if p and p' are momentum operators (of a particle in an interacting system of particles) in the frames K and K', respectively, then the connection between them is $p' = \exp(iB.\theta) p \exp(-iB.\theta)$ (1) where B is the generator of boost, and $\theta$ is the boost parameter. If the mentioned system of particles is non-interacting, then $B = B_0$ and eq. (1) results in the familiar Lorentz transformation. If there is interaction, then B is not equal to $B_0,$ and the relationship between components of p and p' is non-linear. It depends on positions and momenta of other particles in the system, and on interactions between them. > > >>>It is also rash to offer the opinion of "looks good" of your own theory >>>before it had a change to go through peer review. >> >>If you require a formal review process, then you have it: I have 3 >>papers in peer-reviewed journals. These papers fully cover the theory >>presented in the book. > > > If these publications indeed "look good", are there any published papers > that have made this judgement? Note that papers on the arXiv are not > necessarily published (no peer review). Nor is a paper that accepts > none of your strange philosophy a glowing review. There is a paper M.I. Shirokov, Decay law of moving unstable particle, $\Int$. J. Theor. Phys., 43 (2004), 1541. that reaches basically the same conclusions as in chapter 13 of my book. See also L. A. Khalfin, Quantum theory of unstable particles and relativity, Preprint of Steklov Mathematical Institute, St. Petersburg Department, PDMI-6/1997 (1997). http://www.pdmi.ras.ru/preprint/1997/97-06.html The "dressed particle" approach is also referenced in V.Yu. Korda, A.V. Shebeko CLOTHED PARTICLE REPRESENTATION IN QUANTUM FIELD THEORY: MASS RENORMALIZATION. Phys.Rev.D 70 (2004) 085011. I am not suggesting that these authors subscribe to my "strange philosophy". But so far, nobody have shown that my logic and conclusions are wrong. You are welcome to make your own contribution to these discussions. > You contradict special relativity and classical Maxwell theory. Please, > do correct this. As I demonstrated above, special relativity (= manifest covariance) contradicts the Poincare group properties, when applied to interacting systems. Classical Maxwell theory is not a shining beacon either. It fails to explain the stability of atoms, photo-electric effect, and radiation reaction. Eugene.