Juan R.:
Bilge ha escrito:

Obviously, that can't be true. Since my ``obvious problem with
action at a distance'' was posted right above your reply, it's
at least one place other than my head. In fact, it's in a place
where you could have posted a valid objection rather than blatantly
erroneous comment you did post.

:-) Nice reply, but has you perhaps detected that the important part on
above reply was on "obvious problem" not in the description?

Yes, i could post a vlaid objection but for what?

Preferably for what I posted, since I don't really see the point
in posting an objection to some issue on an unrelated topic.

If you are unable to understand some of most basic stuff that is
already available in literature, it is may be difficult explain to you
some advanced questions. Basically because you lack the basic
understanding of several ideas that are being currently debated in
specialized literature.

Oh, excuse me. I always assume that someone who is familiar with the
``specialized literature,'' is also capable of incorporating that
familiarity in what they post, rather than spending all of his efforts
digressing over semantic nit-picks to avoid it. Just think of how much
more efficient it would be if you just flat out said something instead of
trying to get me to guess in a game of 20 questions. I know, that would
be too obvious, so nevermind.

Clear! after you claim that i am using 'jargon'.

I still claim that, only you can add ``posturing'' as well.

Simply i want to state that your criticism on 'action at a distance
theory' in this thread is both completely wrong and outdated. Proof is
available on literature including several high-level journals on math
and physics.

Oh, really? By not outdatd, are you referring to the feynman-wheeler
absorber theory, you mentioned as an example? coughcough. Let me
give you a tip. Never try to be an asshole using vague generalizations
like, ``wrong and outdated'' or ``high-level journals on math and physics,
'' after you've cited a theory published in a 1945 issue of Rev. Mod. Phys.
Especially when the lead author decided not to continue pursuing the
theory in favor of something as widely held to be useful as feynman
diagrams. Some people notice the inconsistency.

You are also kidding yourself about where my objections are directed.
I'm not objecting to the _physical_ content of _any_ theory, old, new
or even otherwise, mostly wrong. My comments are directed specifically
at your (as well as eugene's) bizarre tendency to focus on anything
which is unphysical as an argument for new physics. It's as if you
would be embarassed to admit that there is any validity to a theory
which gets the right answer in any conventional way.

Read literature on the topic (NOT basic textbooks!) and when ready then
try again in this (or other thread).

Next time I go to the library, I'll see if the 1945 Rev. Mod. Phys.
is on the shelf. In the meantime, you might try posting your own
arguements rather than post a reference to someone else's argument
as the support for a dubious claim. I'm not going to play 20 questions
or argue over who has misinterpreted an article, unless you can arrange
for the author(s) to render a verdict and hang around in case I think
they're mistaken.

Bilge ha escrito:

Juan R.:
Bilge ha escrito:

Obviously, that can't be true. Since my ``obvious problem with
action at a distance'' was posted right above your reply, it's
at least one place other than my head. In fact, it's in a place
where you could have posted a valid objection rather than blatantly
erroneous comment you did post.

:-) Nice reply, but has you perhaps detected that the important part on
above reply was on "obvious problem" not in the description?

Yes, i could post a vlaid objection but for what?

Preferably for what I posted, since I don't really see the point
in posting an objection to some issue on an unrelated topic.

Ok! Begin writting what is the definition of action at a distance
interaction. Then we can discuss next if that violate experimental data
or not.

If you are unable to understand some of most basic stuff that is
already available in literature, it is may be difficult explain to you
some advanced questions. Basically because you lack the basic
understanding of several ideas that are being currently debated in
specialized literature.

Oh, excuse me. I always assume that someone who is familiar with the
``specialized literature,'' is also capable of incorporating that
familiarity in what they post, rather than spending all of his efforts
digressing over semantic nit-picks to avoid it. Just think of how much
more efficient it would be if you just flat out said something instead of
trying to get me to guess in a game of 20 questions. I know, that would
be too obvious, so nevermind.

If one can write a perturbation

Advanced knowledge = standard knowledge + small perturbation then, yes,
one can. The problem is when there is a great difference between ideas
will be cited and standard textbooks knowledge, then one is simply
unable (i recognize my limitations) to incorporating that 'familiarity'
in the posts.

Clear! after you claim that i am using 'jargon'.

I still claim that, only you can add ``posturing'' as well.

Simply i want to state that your criticism on 'action at a distance
theory' in this thread is both completely wrong and outdated. Proof is
available on literature including several high-level journals on math
and physics.

Oh, really? By not outdatd, are you referring to the feynman-wheeler
absorber theory, you mentioned as an example? coughcough. Let me
give you a tip. Never try to be an asshole using vague generalizations
like, ``wrong and outdated'' or ``high-level journals on math and physics,
'' after you've cited a theory published in a 1945 issue of Rev. Mod. Phys.

I thought that when one is new in a field one may begin from the most
simple and Wheeler/Feynmann is a classical paper. It is a good start
:-)

Do you know why Feynmann and Wheeler leave the field? Did they prove
that the way was incorrect, or just did they find technical
difficulties could not break? Wheeler promised a new lecture on the
topic but newer were able to obtain it? Perhaps other people has
already advanced in that way and obtained a generalization of
Wheeler/Feynmann theory that has passed already several experimental
tests that standard QED cannot.

Especially when the lead author decided not to continue pursuing the
theory in favor of something as widely held to be useful as feynman
diagrams. Some people notice the inconsistency.

Well, one can see that Feynmann work on QED is clearly inspired in his
early work. In fact, as explained in his manual on QED he used the
delta_{+} functions in computation of scattering amplitudes which he
clearly derived from his early thoughts on classical theory.

Moreover do not forget that Feynmann did not continue that research
line because technical diffculties. As clearly stated in his Feynmann
lecture on physics CED continue being an inconsistent theory and
quantization have not helped. QED continues being inconsistent in
several matters.

You are also kidding yourself about where my objections are directed.
I'm not objecting to the _physical_ content of _any_ theory, old, new
or even otherwise, mostly wrong. My comments are directed specifically
at your (as well as eugene's) bizarre tendency to focus on anything
which is unphysical as an argument for new physics. It's as if you
would be embarassed to admit that there is any validity to a theory
which gets the right answer in any conventional way.

Bizarre? Perhaps you would read bibliography. I cited some relevant
papers, including one (PRE published few years ago) where is
***proven*** that instantaneous action at a distance is a correct
component of general solutions of Maxwell equations and the traditional
retarded solution (LW potentials) just wrong.

Curiously that paper proves that Eugene's proposal of an instantaneous
interactions complementing usual retarded one (Eugene even wasted his
time doing a nice figure in his book) is not 'bizarre' as you,
incorrectly, claim.

Once you read and understand some basic literature then we could begin
to discuss some advanced topic :-)


Juan R.

Center for CANONICAL |SCIENCE)

Juan R.:

Bilge ha escrito:

Juan R.:
Bilge ha escrito:

Obviously, that can't be true. Since my ``obvious problem with
action at a distance'' was posted right above your reply, it's
at least one place other than my head. In fact, it's in a place
where you could have posted a valid objection rather than blatantly
erroneous comment you did post.

:-) Nice reply, but has you perhaps detected that the important part on
above reply was on "obvious problem" not in the description?

Yes, i could post a vlaid objection but for what?

Preferably for what I posted, since I don't really see the point
in posting an objection to some issue on an unrelated topic.

Ok! Begin writting what is the definition of action at a distance
interaction. Then we can discuss next if that violate experimental data
or not.

That's not an objection. It's a question.


If you are unable to understand some of most basic stuff that is
already available in literature, it is may be difficult explain to you
some advanced questions. Basically because you lack the basic
understanding of several ideas that are being currently debated in
specialized literature.

Oh, excuse me. I always assume that someone who is familiar with the
``specialized literature,'' is also capable of incorporating that
familiarity in what they post, rather than spending all of his efforts
digressing over semantic nit-picks to avoid it. Just think of how much
more efficient it would be if you just flat out said something instead of
trying to get me to guess in a game of 20 questions. I know, that would
be too obvious, so nevermind.

If one can write a perturbation

Advanced knowledge = standard knowledge + small perturbation then, yes,
one can. The problem is when there is a great difference between ideas
will be cited and standard textbooks knowledge, then one is simply
unable (i recognize my limitations) to incorporating that 'familiarity'
in the posts.

Clear! after you claim that i am using 'jargon'.

I still claim that, only you can add ``posturing'' as well.

Simply i want to state that your criticism on 'action at a distance
theory' in this thread is both completely wrong and outdated. Proof is
available on literature including several high-level journals on math
and physics.

Oh, really? By not outdatd, are you referring to the feynman-wheeler
absorber theory, you mentioned as an example? coughcough. Let me
give you a tip. Never try to be an asshole using vague generalizations
like, ``wrong and outdated'' or ``high-level journals on math and physics,
'' after you've cited a theory published in a 1945 issue of Rev. Mod. Phys.

I thought that when one is new in a field one may begin from the most
simple and Wheeler/Feynmann is a classical paper. It is a good start
:-)

Do you know why Feynmann and Wheeler leave the field? Did they prove
that the way was incorrect, or just did they find technical
difficulties could not break? Wheeler promised a new lecture on the
topic but newer were able to obtain it? Perhaps other people has
already advanced in that way and obtained a generalization of
Wheeler/Feynmann theory that has passed already several experimental
tests that standard QED cannot.

Especially when the lead author decided not to continue pursuing the
theory in favor of something as widely held to be useful as feynman
diagrams. Some people notice the inconsistency.

Well, one can see that Feynmann work on QED is clearly inspired in his
early work. In fact, as explained in his manual on QED he used the
delta_{+} functions in computation of scattering amplitudes which he
clearly derived from his early thoughts on classical theory.

Moreover do not forget that Feynmann did not continue that research
line because technical diffculties. As clearly stated in his Feynmann
lecture on physics CED continue being an inconsistent theory and
quantization have not helped. QED continues being inconsistent in
several matters.

You are also kidding yourself about where my objections are directed.
I'm not objecting to the _physical_ content of _any_ theory, old, new
or even otherwise, mostly wrong. My comments are directed specifically
at your (as well as eugene's) bizarre tendency to focus on anything
which is unphysical as an argument for new physics. It's as if you
would be embarassed to admit that there is any validity to a theory
which gets the right answer in any conventional way.

Bizarre? Perhaps you would read bibliography. I cited some relevant
papers, including one (PRE published few years ago) where is
***proven*** that instantaneous action at a distance is a correct
component of general solutions of Maxwell equations and the traditional
retarded solution (LW potentials) just wrong.

Curiously that paper proves that Eugene's proposal of an instantaneous
interactions complementing usual retarded one (Eugene even wasted his
time doing a nice figure in his book) is not 'bizarre' as you,
incorrectly, claim.

Once you read and understand some basic literature then we could begin
to discuss some advanced topic :-)


Juan R.

Center for CANONICAL |SCIENCE)

"Bilge" wrote in message
...
Eugene Stefanovich:
Bilge wrote:

Note the absence of primes on \Psi. Clearly, I can choose to apply
U to the state vectors to get \Psi' = U\Psi and write \Psi'|H|\Ps'.
Note there is no prime on that H. What you call ``case 3'' would
be something like, \Psi|U^{-1}U H U^{-1}U|\Psi = \Psi'|H'|\Psi'.

Agreed.
Then why did you say that unitary transformation of the Hamiltonian does
not change physics?

Because it hasn't changed. Obviously, H' isn't diagonaliazed by \Psi,
since you imposed the constraint that H and U don't commute. Since,

[H,U] = HU - UH,

U^{-1}HU = U^{-1} (UH + [H,U]) = H + U^{-1}[H,U]

= H + U^{-1} dU/dt

which implies that U^{-1}dU/dt = 0, if H and H' are equivalent.

I think it can be proven that H' = H if and only if dU/dt=0, i.e.,
[H,U] = 0. Formally, we can multiply both sides of

U^{-1}dU/dt = 0

by U in order to obtain this condition.



If the state vector is kept the same then expectation values of the
original Hamiltonian

\Psi|H|\Psi

and the transformed Hamiltonian (your eq. (1)) are clearly different.
The physics has changed.

They aren't different. You can easily see that what you've written
is equivalent to,

\Psi|H|\Psi = \Psi'|H|\Psi'

So, all you are doing is constructing a different set of states, since,

\Psi' = U\Psi = (1 - iS - S^2/2! +...)\Psi'

and, so

\Psi|U^{-1}H|\Psi = \Psi|(1 + iS +...) H (1 - iS + ...)|\Psi

= \Psi|H|\Psi + ...

So what?

I have a hard time following your reasonng. Let me formulate my statement in
the mathematical theorem/proof language, so that no ambiguities may arise.

Theorem: If H is a Hermitian operator in the Hilbert space (assume that H is
different
from simple multiplication by a real conatant) and U is a unitary operator
that
does not commute with H, then H' = U H U^{-1} is a Hermitian operator, and
there is at least one state vector |\Psi for which expectation values of H
and H' are different,
i.e.,

\Psi|H| \Psi \= \Psi|H'| \Psi

Proof: available by request.

Eugene.

Bilge ha escrito:

Juan R.:
Ok! Begin writting what is the definition of action at a distance
interaction. Then we can discuss next if that violate experimental data
or not.

That's not an objection. It's a question.

Begin... Next



Juan R.

Center for CANONICAL |SCIENCE)

Eugene Stefanovich:
"Bilge" wrote in message

which implies that U^{-1}dU/dt = 0, if H and H' are equivalent.

I think it can be proven that H' = H if and only if dU/dt=0, i.e.,
[H,U] = 0. Formally, we can multiply both sides of

U^{-1}dU/dt = 0

by U in order to obtain this condition.

OK...
[...]
They aren't different. You can easily see that what you've written
is equivalent to,

\Psi|H|\Psi = \Psi'|H|\Psi'

So, all you are doing is constructing a different set of states, since,

\Psi' = U\Psi = (1 - iS - S^2/2! +...)\Psi'

and, so

\Psi|U^{-1}H|\Psi = \Psi|(1 + iS +...) H (1 - iS + ...)|\Psi

= \Psi|H|\Psi + ...

So what?

I have a hard time following your reasonng.
Let me formulate my statement in
the mathematical theorem/proof language, so that no ambiguities may arise.

Theorem: If H is a Hermitian operator in the Hilbert space (assume that H
is different from simple multiplication by a real conatant) and U is a
unitary operator that does not commute with H, then H' = U H U^{-1} is a
Hermitian operator, and there is at least one state vector |\Psi for
which expectation values of H and H' are different, i.e.,

\Psi|H| \Psi \= \Psi|H'| \Psi

Proof: available by request.

I'm not disputing that. I'm merely pointing out the reason. If U and
H don't commute, then H and H' aren't simultaneously diagnolizable and
the \Psi cannot be eigenvectors of both H and H'.

Expectation values are not eigenvalues and \Psi can be an eigenvector of
(at most) one of H or H' (unless H and U commute). For example, suppose H
has an eigenvector |\Psi with angular momentum wavefunctions in the basis
|j,j_z. Then, one unitary transform is U = \exp(-iJ.\theta), with \theta
being a rotatation around any axis, say the y-axis. The matrix elements of
the new hamiltonian, U^{-1}HU in the basis |j,j_z is the same as the
matrix elements of the old hamiltonian operating on the rotated states.

i don bulive in such talk like this

Bilge wrote:

I have a hard time following your reasonng.
Let me formulate my statement in
the mathematical theorem/proof language, so that no ambiguities may arise.

Theorem: If H is a Hermitian operator in the Hilbert space (assume that H
is different from simple multiplication by a real conatant) and U is a
unitary operator that does not commute with H, then H' = U H U^{-1} is a
Hermitian operator, and there is at least one state vector |\Psi for
which expectation values of H and H' are different, i.e.,

\Psi|H| \Psi \= \Psi|H'| \Psi

Proof: available by request.

I'm not disputing that. I'm merely pointing out the reason. If U and
H don't commute, then H and H' aren't simultaneously diagnolizable and
the \Psi cannot be eigenvectors of both H and H'.

I agree.


Expectation values are not eigenvalues and \Psi can be an eigenvector of
(at most) one of H or H' (unless H and U commute).

I agree.

For example, suppose H
has an eigenvector |\Psi with angular momentum wavefunctions in the basis
|j,j_z. Then, one unitary transform is U = \exp(-iJ.\theta), with \theta
being a rotatation around any axis, say the y-axis. The matrix elements of
the new hamiltonian, U^{-1}HU in the basis |j,j_z is the same as the
matrix elements of the old hamiltonian operating on the rotated states.

I agree.
This was my case 3. of how unitary transformations are used in quantum
mechanics. If transformation U is applied to both the Hamiltonian
H' = U^{-1}HU and to states (you mentioned "rotated states") then matrix
elements do not change. This is a trivial change of representation that
does not have any effect on physics.

If you remember, we started this discussion from my assertion that
"dressing transformation" of the Hamiltonian (in spite of being unitary)
does change physics, because this transformation is applied only to
the Hamiltonian (and to the generator of boost transformations, which
is not that relevant for our present discussion). This transformation
IS NOT applied to state vectors. Therefore, the transformed Hamiltonian
H'
has matrix elements (in the old basis) different from those of the
original Hamiltonian H. The eigenvalues of the two Hamiltonians H and
H' are the same, but eigenvectors are different. The time evolutions
desribed by operators exp(iHt) and exp(iH't) are also different,
although the corresponding S-matrices are exactly the same.

That's all I wanted to say. If you like, I can put these statements
in the form Theorem/Proof to avoid any ambiguity.

Eugene.

Eugene Stefanovich wrote:
Bilge wrote:

I have a hard time following your reasonng.
Let me formulate my statement in
the mathematical theorem/proof language, so that no ambiguities may arise.

Theorem: If H is a Hermitian operator in the Hilbert space (assume that H
is different from simple multiplication by a real conatant) and U is a
unitary operator that does not commute with H, then H' = U H U^{-1} is a
Hermitian operator, and there is at least one state vector |\Psi for
which expectation values of H and H' are different, i.e.,

\Psi|H| \Psi \= \Psi|H'| \Psi

Proof: available by request.

I'm not disputing that. I'm merely pointing out the reason. If U and
H don't commute, then H and H' aren't simultaneously diagnolizable and
the \Psi cannot be eigenvectors of both H and H'.

I agree.


Expectation values are not eigenvalues and \Psi can be an eigenvector of
(at most) one of H or H' (unless H and U commute).

I agree.

For example, suppose H
has an eigenvector |\Psi with angular momentum wavefunctions in the basis
|j,j_z. Then, one unitary transform is U = \exp(-iJ.\theta), with \theta
being a rotatation around any axis, say the y-axis. The matrix elements of
the new hamiltonian, U^{-1}HU in the basis |j,j_z is the same as the
matrix elements of the old hamiltonian operating on the rotated states.

I agree.
This was my case 3. of how unitary transformations are used in quantum
mechanics. If transformation U is applied to both the Hamiltonian
H' = U^{-1}HU and to states (you mentioned "rotated states") then matrix
elements do not change. This is a trivial change of representation that
does not have any effect on physics.

If you remember, we started this discussion from my assertion that
"dressing transformation" of the Hamiltonian (in spite of being unitary)
does change physics, because this transformation is applied only to
the Hamiltonian (and to the generator of boost transformations, which
is not that relevant for our present discussion). This transformation
IS NOT applied to state vectors. Therefore, the transformed Hamiltonian
H'
has matrix elements (in the old basis) different from those of the
original Hamiltonian H. The eigenvalues of the two Hamiltonians H and
H' are the same, but eigenvectors are different. The time evolutions
desribed by operators exp(iHt) and exp(iH't) are also different,
although the corresponding S-matrices are exactly the same.

That's all I wanted to say. If you like, I can put these statements
in the form Theorem/Proof to avoid any ambiguity.

Eugene.

show your code implementation of your model, lets get some numerical
values from your model

Themistocles:
i don bulive in such talk like this

There exists an obvious solution: don't read this newsgroup.