Time, Parameter, Operator

Ali

<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">  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

Igor Khavkine

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On 2005-06-13, Ali <ph_question@yahoo.com> wrote:\n> Dear Members,\n>\n> on p.68 of Sakurai\'s "Modern Quantum Mechanics" we read "... Time\n> is just a parameter in quantum mechanics, not an operator. In\n> particular, Time is not an observable in the language of the previous\n> chapte." What is the deference between a "parameter" and " operator"\n> from a physical point of view?\n\nVery briefly, there is no fuzziness in a parameter, it is specified\nexternally. OTOH, there is fuzziness in a dynamical variable represented\nby an operator, because its expectation value is specified by the state.\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">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On [itex]2005-06-13,[/itex] Ali <ph_question@yahoo.com> 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

Eugene Stefanovich

<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\nAli wrote:\n> Dear Members,\n>\n> on p.68 of Sakurai\'s "Modern Quantum Mechanics" we read "... Time\n> is just a parameter in quantum mechanics, not an operator. In\n> particular, Time is not an observable in the language of the previous\n> chapte." What is the deference between a "parameter" and " operator"\n> from a physical point of view?\n\nYou put your finger on the central problem of modern theoretical\nphysics.\n\nConsider the difference between "time" and "position"\nin quantum mechanics. You can talk about "position of a particle",\nso position is an observable that can be measured on\n(is a characteristic\nof) a physical system (e.g., particle). The measured position of a\nparticle depends on the state in which you find the particle.\nIn QM such observables as position are described by Hermitian\noperators, and the\nmeasured values are described by matrix elements of these operators.\n\nOn the other hand, you cannot measure "time of a particle".\nTime is not a property of the particle, time does not depend on\nthe state of the particle. In other words, time is not an\nobservable. Then what is time?\n\nIn each laboratory we have a classical device called "clock"\nthat gives us a numerical parameter called "time". The time label\nis attached to all measurements performed in the laboratory.\nSo, time is just a classical numerical parameter in quantum mechanics.\n\nThis is very different from the way time and position are treated\nin special (and general) relativity. Einstein\'s relativity declares\nthat time and position are just coordinates in the 4D space-time\nmanifold. From the point of view of different observers these\ncoordinates are interchangeable. This is reflected in the way\ntime and position form components of a 4-vector in the Einstein\'s\ntheory.\n\nAs we saw above, this "equivalence" of time and position has no analog\nin quantum mechanics. I believe, this contradiction is the main\nobstacle for all current attempts to "quantize gravity". There are\nmany reviews regarding the "problem of time" on arxiv.org.\nMy personal opinion is that the only way to reconcile the principle\nof relativity with quantum mechanics is to reject the 4D space-time\n"unification" of space and time. This idea is, actually, not so scary.\nI explored its consequences in physics/0504062 and the resulting theory\nlooks good, though non-conventional.\n\nEugene.\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>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.

Igor Khavkine

<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> In each laboratory we have a classical device called "clock" that\n> gives us a numerical parameter called "time". The time label is\n> attached to all measurements performed in the laboratory. So, time\n> is just a classical numerical parameter in quantum mechanics.\n>\n> This is very different from the way time and position are treated in\n> special (and general) relativity. [...]\n>\n> As we saw above, this "equivalence" of time and position has no\n> analog in quantum mechanics. I believe, this contradiction is the\n> 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> My personal opinion is that the only way to reconcile the principle\n> of relativity with quantum mechanics is to reject the 4D space-time\n> "unification" of space and time. This idea is, actually, not so\n> scary. I explored its consequences in physics/0504062 and the\n> 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">  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
> 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.

> 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

Eugene Stefanovich

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

apn82

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

Souvik

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

> 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

Ralph E. Frost

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On a common sense and experimental level, things clearly proceed as a\nfunction of the influences of everything else, and NOT as a function of\ntime. The "time" imagery is a feature of the map that people,\nincluding physicists, have projected onto the party. Thus, the\ncorrect concept is "experience exists; time does not".\n\n"Time" is a mis-labeling, or a simplified approximation of "the\ninfluences of everything else".\n\nIts use facilitates books full of helpful abstract math modeling, but\nwhen it comes all the way down to considering fundamentals, time is\nnot.\n\n\n-- Ralph Frost\n"To get the concept, first work the equation out in analog math."\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On 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."

Marcel LeBel

<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>Ralph E. Frost wrote:\n\n"experience exists; time does not".\n>\n\nRalph,\n\nIt is well known that the passage of time affect the rate of evolution\nof spontaneous events. When the said event is a clock, we call it\n"time". Clocks are all based on a spontaneous event e.g. sand in\nhourglass, relaxation time of a quartz crystal, spontaneous electronic\ntransition etc. etc. because we trust that time can\'t be rushed.\n\nThe passage of time varies in a gravitational field, and the same\nclock can be brought up or down and it will accordingly beat faster or\nslower.\nThe clock is only an indicator of the local rate of passage of time\nwhere it is located. The passage of time is a true (ontological)\ndynamical substance out there (GR already gives clues about its\nproperties). The passage of time exists and varies in gravitational\nfield and in relativistic context.---The integration of the passage of\ntime as Duration is\\is just an experience which does not have any\nreality beyond our perception.\n\nThe EXPERIENCE is important BUT it is only a relation between you and\nthe subject matter; it has no existence outside that relationship of\nwhich you are an inseparable part. What interests me is the Real\nuniverse, the one about which clues are found FROM our experience of it.\nThat\'s the real stuff! The real universe.\n\nMarcel,\n\nlebel@muontailpig.com remove particle\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>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 [itex]is\is[/itex] 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

Arnold Neumaier

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

Uncle Al

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

Eugene Stefanovich

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

Eugene Stefanovich

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

Igor Khavkine

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On 2005-06-14, Eugene Stefanovich <eugenev@synopsys.com> wrote:\n> Igor Khavkine wrote:\n\n> The manifest covariance (= equivalence of space and time coordinates)\n> is the hallmark of one particular (not self-consistent, but,\n> nevertheless, very popular) interpretation of the principle of\n> relativity, i.e., that belonging to Einstein. I recommend you to read\n> the book which explains that the manifest covariance is an additional\n> assumption of Einstein\'s theory. This assumption does not agree with\n> the presence of interactions. It is, at best, an approximation.\n\nThe problem with the above statement has already been pointed out, but\nit seems it must be pointed out again. There is no such thing as a\nprinciple of *manifest* covariance. There does exists the principle of\ncovariance, which says that two sides of the same equation must\ntransform alike under active and passive coordinate transformations.\nThe manifest part is only a matter of taste.\n\nLets leave the alleged logical consistency issue aside for now. Can you\nlocate references that make reference to manifest covariance other than\nas a preferred form for writing down equations?\n\n>> It is also rash to offer the opinion of "looks good" of your own theory\n>> before it had a change to go through peer review.\n>\n> If you require a formal review process, then you have it: I have 3\n> papers in peer-reviewed journals. These papers fully cover the theory\n> presented in the book.\n\nIf these publications indeed "look good", are there any published papers\nthat have made this judgement? Note that papers on the arXiv are not\nnecessarily published (no peer review). Nor is a paper that accepts\nnone of your strange philosophy a glowing review.\n\n>> Especially in the\n>> absence of theoretical and experimental tests.\n\n[...]\n> If you happen to notice any logical\n> inconsistency in the book, I would like to know that, and I\'d\n> gladly correct it.\n\nYou contradict special relativity and classical Maxwell theory. Please,\ndo correct this.\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">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On [itex]2005-06-14,[/itex] Eugene Stefanovich <eugenev@synopsys.com> 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

Seratend

<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> Consider the difference between "time" and "position"\n> in quantum mechanics. You can talk about "position of a particle",\n> so position is an observable that can be measured on\n> (is a characteristic\n> of) a physical system (e.g., particle). The measured position of a\n> particle depends on the state in which you find the particle.\n> In QM such observables as position are described by Hermitian\n> operators, and the\n> measured values are described by matrix elements of these operators.\n>\n> On the other hand, you cannot measure "time of a particle".\n> Time is not a property of the particle, time does not depend on\n> the state of the particle. In other words, time is not an\n> observable. Then what is time?\n>\nIn classical QM, time is an observable but not of the configuration\nhilbert space. In other words, the operator associated to the time\nparameter commutes with all the operators on the configuration space.\nThere is nothing contradictory with such an affirmation, all the\ncurrent classical QM experiments are based on this property.\nThis is why we may consider the time as a parameter in non relativistic\nQM: we obtain a measurement "a" result @time t of the observable A =3D>\n(a,t) is the measurement result of the commuting set of observables\n(time observable,A).\n\nFor a formal example explaining this topic, see:\nhttp://www.physicsforums.com/s=ADhowthread.php?t=3D72181\n\nSeratend.\n\nP.S. I have never understood why one always tries to define a time\noperator acting on the configuration space of the particle.\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:
>
> 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 [itex]A =3D>(a,t)[/itex] 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.

Eugene Stefanovich

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

Eugene Stefanovich

<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\nIgor Khavkine wrote:\n> On 2005-06-14, Eugene Stefanovich <eugenev@synopsys.com> wrote:\n>\n>>Igor Khavkine wrote:\n>\n>\n>>The manifest covariance (= equivalence of space and time coordinates)\n>>is the hallmark of one particular (not self-consistent, but,\n>>nevertheless, very popular) interpretation of the principle of\n>>relativity, i.e., that belonging to Einstein. I recommend you to read\n>>the book which explains that the manifest covariance is an additional\n>>assumption of Einstein\'s theory. This assumption does not agree with\n>>the presence of interactions. It is, at best, an approximation.\n>\n>\n> The problem with the above statement has already been pointed out, but\n> it seems it must be pointed out again. There is no such thing as a\n> principle of *manifest* covariance. There does exists the principle of\n> covariance, which says that two sides of the same equation must\n> transform alike under active and passive coordinate transformations.\n> The manifest part is only a matter of taste.\n>\n> Lets leave the alleged logical consistency issue aside for now. Can you\n> locate references that make reference to manifest covariance other than\n> as a preferred form for writing down equations?\n\nI call "manifest covariance" the following statement (Assertion F in my\nbook):\n\n"Every general law of nature must be so constituted that it\ntransformed into a law of exactly the same form when, instead of the\nspace-time variables x, y, z, t of the original coordinate system K,\nwe introduce new space-time variables x\', y\', z\', t\' of a coordinate\nsystem K\'. In this connection the relation between the ordinary and\nthe accented magnitudes is given by the Lorentz transformation.\nOr in brief: General laws of nature are co-variant with respect to\nLorentz transformations." (A. Einstein, "Relativity: The Special and\nGeneral Theory", (Methuen and Co., 1920)\n\nThis also means that observables normally form 4-scalars, 4-vectors,\n4-tensors, etc. that transform from K to K\' via simple universal linear\ntransformation laws (Lorentz transformations). An important point\nof special relativity is that these laws do not depend on the\ncomposition of the observed physical system and interactions acting\nthere. In special relativity, these laws are universal, they are\nmanifestations of the 4D unified nature of the space-time.\n\nAt closer inspection, this statement of special relativity is a\nnon-proven postulate. I agree that so far this postulate worked well\nand did not contradict any experiment.\n\nCan we do better than just simply postulate such an important statement?\nYes we can. In quantum mechanics, the transformations of observables\nbetween different reference frames (K and K\') are given by unitary\noperators. For example if p and p\' are momentum operators (of a particle\nin an interacting system of particles) in the frames K and K\',\nrespectively, then the connection between them is\n\np\' = exp(iB.theta) p exp(-iB.theta) (1)\n\nwhere B is the generator of boost, and theta is the boost parameter.\nIf the mentioned system of particles is non-interacting, then B = B_0\nand eq. (1) results in the familiar Lorentz transformation.\nIf there is interaction, then B is not equal to B_0, and the relationship\nbetween components of p and p\' is non-linear. It depends on positions\nand momenta of other particles in the system, and on interactions\nbetween them.\n\n>\n>\n>>>It is also rash to offer the opinion of "looks good" of your own theory\n>>>before it had a change to go through peer review.\n>>\n>>If you require a formal review process, then you have it: I have 3\n>>papers in peer-reviewed journals. These papers fully cover the theory\n>>presented in the book.\n>\n>\n> If these publications indeed "look good", are there any published papers\n> that have made this judgement? Note that papers on the arXiv are not\n> necessarily published (no peer review). Nor is a paper that accepts\n> none of your strange philosophy a glowing review.\n\nThere is a paper\n\nM.I. Shirokov, Decay law of moving unstable\nparticle, Int. J. Theor. Phys., 43 (2004), 1541.\n\nthat reaches basically the same conclusions as in chapter 13\nof my book. See also\n\nL. A. Khalfin, Quantum theory of unstable particles and\nrelativity, Preprint of Steklov Mathematical Institute, St. Petersburg\nDepartment, PDMI-6/1997 (1997).\nhttp://www.pdmi.ras.ru/preprint/1997/97-06.html\n\nThe "dressed particle" approach is also referenced in\n\nV.Yu. Korda, A.V. Shebeko CLOTHED PARTICLE REPRESENTATION IN QUANTUM\nFIELD THEORY: MASS RENORMALIZATION.\nPhys.Rev.D 70 (2004) 085011.\n\nI am not suggesting that these authors subscribe to my "strange\nphilosophy". But so far, nobody have shown that my logic and conclusions\nare wrong. You are welcome to make your own contribution to these\ndiscussions.\n\n\n> You contradict special relativity and classical Maxwell theory. Please,\n> do correct this.\n\nAs I demonstrated above, special relativity (= manifest covariance)\ncontradicts the Poincare group properties, when applied to interacting\nsystems. Classical Maxwell theory is not a shining beacon either.\nIt fails to explain the stability of atoms, photo-electric effect,\nand radiation reaction.\n\nEugene.\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>Igor Khavkine wrote:
> On [itex]2005-06-14,[/itex] Eugene Stefanovich <eugenev@synopsys.com> 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

[itex]p' = \exp(iB.\theta) p \exp(-iB.\theta)[/itex] (1)

where B is the generator of boost, and [itex]\theta[/itex] is the boost parameter.
If the mentioned system of particles is non-interacting, then [itex]B = B_0[/itex]
and eq. (1) results in the familiar Lorentz transformation.
If there is interaction, then B is not equal to [itex]B_0,[/itex] 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, [itex]\Int[/itex]. 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.

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