Re: h bar and Lorentz transformation

From: Ken S. Tucker (dynamics_at_vianet.on.ca)
Date: 03/26/05 

Date: 26 Mar 2005 11:11:41 -0800

Non Ame wrote:
> "Ken S. Tucker" <dynamics@vianet.on.ca> writes:
>
> >Non Ame wrote:
> >> "Ken S. Tucker" <dynamics@vianet.on.ca> writes:
> >>
> >> >To Bilge & Non Ame...
> >>
> >> >Bilge wrote:
> >> >> Ken S. Tucker:
> >> >> >Non Ame wrote:
> >> >>
> >> E(r,t) is the electric field at position r and time t. B(r',t) is
> >the
> >> magnetic field at position r' and time t. B(r',t') is the
magnetic
> >field
> >> at position r' and time t'.
>
> >That notation is clear now.
>
> >> E_x(r,t) B_y(r',t') - B_y(r',t') E_x(r,t)
>
> >>is the commutator of E_x(r,t) and B_y(r',t').
>
> >That makes no sense to me, does he have a
> >tensor? I don't have the book you recommended,
> >likely I'm missing something.
>
> Perhaps you need an introductory book on quantum mechanics. There
was no
> reason for us to expect you to know the correct formula for
>
> E_x(r,t) B_y(r',t') - B_y(r',t') E_x(r,t),
>
> which was why I gave the explicit formula. But it is surprising that
you
> are surprised that E_x(r,t) B_y(r't') and B_y(r',t') E_x(r,t) may not
be
> equal in the case of the quantum EM field. If you had any
understanding
> of quantum mechanics, you would have known that that was a
possibility.

Notation convolution.

> E_x(r,t) and B_y(r',t') are real q-numbers, to use the parlance of
Dirac,
> so, from that information alone, it is possible to conclude that
>
> E_x(r,t) B_y(r',t') - B_y(r',t') E_x(r,t)
>
> is an imaginary q-number, but no more can be determined.
Specifically,
> the imaginary q-number need not be equal to zero.
>
> >>E_x(r,t) B_y(r',t) - B_y(r',t) E_x(r,t)
>
> >>is a special case when E_x and B_y are
> >>evaluated at exactly the same time.
>
> >> Schiff gives the formulae
> >>
> >> E_s(r,t) E_{s'}(r',t') - E_{s'}(r',t') E_s(r,t)
> >>
> >> = B_s(r,t) B_{s'}(r',t') - B_{s'}(r',t') B_s(r,t)
> >>
> >> = 4 pi i hbar ((delta_{ss'}/c^2) d/dt d/dt' - d/dr_s d/dr'_{s'})
> >>
> >> D(r - r', t - t'),
> >>
> >> E_s(r,t) B_{s'}(r',t') - B_{s'}(r',t') E_s(r,t)
> >>
> >> = - 4 pi i hbar epsilon_{ss's"} d/dr_{s"} d/dt' D(r - r', t -
t'),
> >>
> >> for s, s' = x, y, z, where delta_{ss'} is the Kronecker delta,
> >> epsilon_{ss's"} is the Levi-Civita symbol determined by
epsilon_{xyz}
> >= 1,
> >> summation is taken over all values of s" in the last line above,
and
> >>
> >> D(rho, tau) = (4 pi |rho|)^{-1} [delta(|rho|+c tau) -
delta(|rho|-c
> >tau),
> >>
> >> where delta(r) is the Dirac delta function on R^3.
> >>
> >> When t' = t, these equations reduce to
> >>
> >> E_s(r,t) E_{s'}(r',t) - E_{s'}(r',t) E_s(r,t)
> >>
> >> = B_s(r,t) B_{s'}(r',t) - B_{s'}(r',t) B_s(r,t)
> >>
> >> = 0,
>
> >That's what I thought in the first place.
>
> But you thought it for the wrong reason.

Your solution is imaginary, very much so.

> >> E_s(r,t) B_{s'}(r',t) - B_{s'}(r',t) E_s(r,t)
> >>
> >> = - 4 pi i hbar c epsilon_{ss's"} d/dr_{s"} delta(r - r')
> >>
> >> = 4 pi i hbar c epsilon_{ss's"} d/dr'_{s"} delta(r - r'),
> >>
> >> for s, s' = x, y, z.
> >>
> >> Note that E_x(r,t) and B_x(r',t') commute for all values of r, r',
t,
> >t'.
>
> >I'd be careful there.
>
> Not at all. It is a fact that, for the quantum radiation EM field in

> Minkowski space, these two fields must commute for all pairs of
events.

Why not just write down the appropriate asymmetrical
tensor.

> >Suppose Non Ame (K) and I (K') are sitting in a
> >tree K.I.S.S.I.N.G. we can agree r = -r' in our
> >relative spatial relation, between kisses.
> > But the time t = t' holds during the passion.
>
> Cut that out, you sleazeoid. You really revolt me.

You missed the point.
My daughter is a P.Geo/P.Eng. In HS she was
having problems with chemistry, specifically
electrolysis. So I studied up on the subject
and took her for a boat ride out to the middle
of our lake, shut-off the motor and sat in the
sun and talked awhile. It's was very quiet and
peaceful, the occasional lap of a wave on the
side of the boat.
  She is by nature a high achiever, and I was
quite concerned with how to explain electrolysis,
to alleviate her frustration.
  I chose an analogy of dating, something akin
to her thinking, and I spoke about how positive
ions attract negative ions on the side.
  After a couple of hours she was peaceful and
felt she really understood the problem.
  We did that sort of thing quite often and her
marks took an upswing. She went on to obtain a
BSc honors, cum something or another, then I
think a Master of Geo and now a P Geo, she has
lots of alphabet behind her name, it's like a
hobby for her.

>We are supposed to be
> discussing the quantum electromagnetic field in special relativity
here,
> not inter-personal relationships and groping. You are obviously
obsessed
> with sex,

Probably, because I'm one of them.

>and seem to think that all women are your inferiors. We are not
> inferior to men at all. I would love to see you suffer the same
degree of
> extreme pain that a woman does during childbirth,

You've never given birth.

>because then you might
> give women the respect we deserve. Get your mind out of the gutter
and
> turn your thoughts to what is really important here.

You seem to be setting a narrow agenda,
SR bores me to tears, and QM is a sleeper.

> >> All components of the field strengths must commute if (r,t) and
> >(r',t')
> >> are separated by a space-like interval, otherwise causality would
be
> >> violated.
>
> >Ah, set up the experiment using *radar ranging*
> >between the bodies and determine (r,t) and (r't').
>
> And what is the relevance of this comment to the discussion?

Photonic relation ((Platonic too)).

> >> Schiff comments that because all components of the field strengths
> >commute
> >> if the interval between (r,t) and (r',t') is not light-like,
>
> >What is "not light-like" where measuring intervals
> >(like ds) are concerned?
>
> In Minkowski space, the interval between (r,t) and (r',t'), where
(r,t)
> and (r't') are not equal, is called:
>
> light-like if |r-r'|^2 = c^2 (t-t')^2,
>
> space-like if |r-r'|^2 > c^2 (t-t')^2,
>
> time-like if |r-r'|^2 < c^2 (t-t')^2.

You could have merely explained what you meant,
in the context of your arguement,( no need to type
out a dictionary).

> This classification of intervals is Lorentz invariant (moreover, the
> classification is Poincare invariant). Two events are separated by a

> space-like interval iff there exists a reference frame in which the
two
> events are simultaneous (but at different places). Two events are
> separated by a time-like interval iff there is a reference frame in
which
> the two events are in the same place (but at different times). Two
events
> are separated by a light-like interval iff it is possible for light
in a
> vaccuum to travel from the earlier event to the later event.

I hear Australia is going to legalize nudity.

> Light-like motion means that ds = 0, and in the case of General
> Relativity, light-like motion is described by the formula ds = 0.

Is it true Australia is using sharks to
control over-population?

> >>the quantized
> >> electromagnetic field is propagated at the classical speed of
light,
> >c.
>
> >There are too many double negatives to sort
> >threw in this post.
>
> That's "through", not "threw". You really should get a dictonary.
Your
> mistake is also quite unforgivable, as I have already gone to
considerable
> trouble to correct you about this error on your part. As I have
already
> informed you, the word 'threw' is the past tense of 'throw'.

Are you threw? or are you through?

> Schiff's statement was to the effect that all components of the
quantized
> EM field at one event commute with all components of the quantized EM

> field at another event,

Of course they commute, how else would they
get there.

>if the interval separating the events is either
> space-like or time-like. He also stated that as a consequence of
this,
> the quantized EM field propagates at speed c.

So you have spent the better portion of an hour
to explain the speed of light is "c", and
"through" a few spit-balls.
Would you like to tell us why you think "h"
is invariant?

Regards
Ken S. Tucker

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