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From: glen herrmannsfeldt on 4 May 2010 20:25
robert bristow-johnson <rbj(a)audioimagination.com> wrote:
(snip, I wrote)

>> You can change all +j to -j, but some is not enough.

> yup. if all textbooks and literature in math, physics, EE or whatever
> science or discipline, where changed so that +j and -j (and +i and -
> i) were switched, every fact and theorem would continue to be just as
> valid.

That is what they said about parity conservation before 1957.

-- glen
From: robert bristow-johnson on 5 May 2010 00:26
On May 4, 8:25 pm, glen herrmannsfeldt <g...(a)ugcs.caltech.edu> wrote:
> robert bristow-johnson <r...(a)audioimagination.com> wrote:
>
> (snip, I wrote)
>
> >> You can change all +j to -j, but some is not enough.
> > yup.  if all textbooks and literature in math, physics, EE or whatever
> > science or discipline, where changed so that +j and -j  (and +i and
> > -i) were switched, every fact and theorem would continue to be just
> > as valid.

that's a *mathematical* or conceptual equivalence (or non-preference)
of spin.

>
> That is what they said about parity conservation before 1957.
>

isn't that really a *physical* preference of spin?

for others'es information, a good reference i found is
http://physics.nist.gov/GenInt/Parity/parity.html . so, it seems that
our universe somehow made a "choice" about which direction of rotation
is preferred. but, suppose you woke up tomorrow in Mirror World where
everything was switched (you wrote with the other hand, the two sides
of your brain switched roles, your heart was more on what used to be
called your "right" side, etc.). would you know the difference?

the comparison to this +j/-j thing is if *everything* in reality were
switched, not just some things. isn't that right, Glen?

i dunno. this atomic physics stuff is too hard for my brain. but i
understand that if you spin some tiny atomic generator in some sense
around the z-axis and electrons fly out the bottom, you can't expect
(in the same world) to spin it in the opposite sense and see electrons
continue to fly out the same bottom. isn't it similar to assigning a
sign to the electron charge? once we decide (by convention) that the
electrons are negatively charged, it would be a wildly different world
if we came upon atoms that had these little particles flying about in
the atom's outside shells that were oppositely charged, no? maybe in
such a world, the opposite spin parity would be the case, no? (i
really don't know. just speculating.)

r b-j
From: glen herrmannsfeldt on 5 May 2010 02:34
robert bristow-johnson <rbj(a)audioimagination.com> wrote:

> that's a *mathematical* or conceptual equivalence
> (or non-preference) of spin.

(and I wrote)
>> That is what they said about parity conservation before 1957.

> isn't that really a *physical* preference of spin?

> for others'es information, a good reference i found is
> http://physics.nist.gov/GenInt/Parity/parity.html . so, it seems that
> our universe somehow made a "choice" about which direction of rotation
> is preferred. but, suppose you woke up tomorrow in Mirror World where
> everything was switched (you wrote with the other hand, the two sides
> of your brain switched roles, your heart was more on what used to be
> called your "right" side, etc.). would you know the difference?

The last chapter of "Feynman's Lectures on Physics" volumne 1 is
also a nice reference, and pretty readable even if you don't
understand all the physics.

> the comparison to this +j/-j thing is if *everything* in reality
> were switched, not just some things. isn't that right, Glen?

> i dunno. this atomic physics stuff is too hard for my brain. but i
> understand that if you spin some tiny atomic generator in some sense
> around the z-axis and electrons fly out the bottom, you can't expect
> (in the same world) to spin it in the opposite sense and see electrons
> continue to fly out the same bottom.

The Feynman explanation goes on with how to explain to a martian
which side is left. That explanation goes indirectly through the
"right hand rule." If you compare a physics experiment to a mirror
image of that experiment, the physics should be the same.
Another way to say it is that if you use a "left hand rule"
instead of a "right hand rule" the physics should be the same.

The distinction comes from the cross product, and axial vector
quantities such as angular momentum (spin) should not correlate
with normal (polar) vector quantities such as velocity.

As for your spin explanation, if you spin it in one sense, and
more electrons come out the bottom than the top, you already have
a parity violation. Conserved parity would require the same
probability for electrons to come out the top as the bottom.

> isn't it similar to assigning a
> sign to the electron charge? once we decide (by convention) that the
> electrons are negatively charged, it would be a wildly different world
> if we came upon atoms that had these little particles flying about in
> the atom's outside shells that were oppositely charged, no? maybe in
> such a world, the opposite spin parity would be the case, no? (i
> really don't know. just speculating.)

After parity violation was found in 1957, it was expected that CP
would be conserved. That is, that antimatter would have exactly
the opposite properties. It turns out that CP is also not conserved,
but only slightly. It seems that symmetry operations guarantee
that CPT is conserved. That is, if you take a mirror coordinate
system, change matter to antimatter, and invert the direction of
time, it is required that the physics be the same. I don't know
it well enough to explain that one, though.

-- glen
From: Clay on 5 May 2010 11:44
On May 4, 7:09 pm, robert bristow-johnson <r...(a)audioimagination.com>
wrote:
> On May 3, 5:09 pm, dbd <d...(a)ieee.org> wrote:
>
>
>
>
>
> > On May 3, 1:09 pm, robert bristow-johnson <r...(a)audioimagination.com>
> > wrote:
> > ...
>
> > > and the mapping is invertible.  really the DFT and iDFT are sorta the
> > > same thing because they can be redefined to be "unitary" by adjusting
> > > the constant in front of the summation:
> > ...
>
> > > and +j and -j are qualitatively the same thing.  both have equal claim
> > > to be the sqrt(-1). again n0 and k0 can be whatever integer you like.
>
> > ...
> > > r b-j
>
> > It isn't clear to me from what you have posted: Do you intend the
> > concepts of "sorta the same thing" and "qualitatively the same thing"
> > to apply to items that are functions of terms that are the square
> > roots of any real number or only the square roots of the same negative
> > real numbers? (I couldn't find either term in wikipedia or in the new
> > or old testaments of O&S.)
>
> this is what i mean in Wikipedia:
>
>  http://en.wikipedia.org/wiki/Imaginary_unit#i_and_.E2.88.92i
>
> +j and -j are qualitatively the same thing.  everything you say about
> +j is something you can say about -j.  but they are quantitatively
> *not* the same thing.  they are non-zero and are negatives of each
> other.  they are not the same number.  but their roles can be
> interchanged.  this qualitative equivalence is not true for the real
> unit +1 and its negative -1.  this is why imaginary numbers are more
> different than real numbers than just a matter of convention (the real
> axis is qualitatively different than the imaginary axis).  but the
> difference between +j and -j is merely one of convention.  and that
> means that (with scaling made so that the transforms are "unitary")
> the only difference between the forward and inverse Fourier Transform
> (and the DFT vs. iDFT) is merely a matter of convention.
>
> On May 3, 6:54 pm, glen herrmannsfeldt <g...(a)ugcs.caltech.edu> wrote:
>
> > robert bristow-johnson <r...(a)audioimagination.com> wrote:
>
> > (snip)
>
> > > and +j and -j are qualitatively the same thing.  both have equal claim
> > > to be the sqrt(-1).
>
> ...
>
> > You can change all +j to -j, but some is not enough.
>
> yup.  if all textbooks and literature in math, physics, EE or whatever
> science or discipline, where changed so that +j and -j  (and +i and -
> i) were switched, every fact and theorem would continue to be just as
> valid.
>
> r b-j- Hide quoted text -
>
> - Show quoted text -

It is wierd though that nature often prefers one way over another.
Even humans who in general have bilateral symmetry has some
asymmetries that happen mostly one way. For example the heart being
left of center and the left lung having only 2 lobes unlike the right
lung's 3. But every now and then nature will mess up and about 1 in
60000 individuals (wiki reports fewer than 1 in 10000) will have their
internal organs mirror reversed. You can read about it here:
http://en.wikipedia.org/wiki/Situs_inversus

The trick is how can nature code for one way over another. I've read
some interesting articles on how genetic coding picks one direction
over another. Even many basic life molecules have stereo isomers
(mirror image arrangments of their atoms) which behave chemically very
different. The amino acids making up the proteans in living organisms
are all the "left hand" variety. The handedness stems from which way
they rotate polarized light - CW or CCW. Often a bening left hand
molecule becomes "drug like" when it is converted over to a right hand
version and introduced into a world whose life forms use mostly left
hand molecules.

Glen has already mentioned the CP and CPT (Charge, Parity, Time)
symmetries and how CP is not always conserved. That discovery really
shook up things.

Another example of ambiguity is the difference between electron and
conventional current and its direction of flow. Common symbols on
schematic diagrams (diodes, transistors, etc) have arrows pointing in
the direction of conventional current. But a simple Hall Effect
measurement will reveal the polarity of the moving charges, and a
right Crookes tube will show their direction of motion.


But yes you can usually swap "j" and "-j" and as long as you
consistantly do it, your math tends to work out. We see this in the
argument of the exponential kernal in defintions of Fourier and
inverse Fourier transforms.

Clay





From: glen herrmannsfeldt on 5 May 2010 14:15
Clay <clay(a)claysturner.com> wrote:
(snip)

> It is wierd though that nature often prefers one way over another.
> Even humans who in general have bilateral symmetry has some
> asymmetries that happen mostly one way. For example the heart being
> left of center and the left lung having only 2 lobes unlike the right
> lung's 3. But every now and then nature will mess up and about 1 in
> 60000 individuals (wiki reports fewer than 1 in 10000) will have their
> internal organs mirror reversed. You can read about it here:
> http://en.wikipedia.org/wiki/Situs_inversus

As I remember it (first from some murder mystery show) it is most
common in twins. The handedness starts out with a chemical
concentration gradient. In the case of twins, the source from
the other twin is often enough to reverse the original handedness.

(snip)

> Another example of ambiguity is the difference between electron and
> conventional current and its direction of flow. Common symbols on
> schematic diagrams (diodes, transistors, etc) have arrows pointing in
> the direction of conventional current. But a simple Hall Effect
> measurement will reveal the polarity of the moving charges, and a
> right Crookes tube will show their direction of motion.

Hall effect will give you the average sign of the flowing
current carriers. Many metals, aluminum being a prime example,
have large hole and electron bands. At high magnetic fields,
aluminum has more holes than electrons as current carriers.
At lower fields, the electrons are in a slim majority.

As aluminum is used for most long distance power lines,
positive charge carriers (holes) account for a large fraction
of distributed power. As it is usually at higher voltage
and lower current, I am not so in the case of current.
Though with the overall length of long distance power lines,
integrating over volume should be enough to swamp the
current carrying copper.

> But yes you can usually swap "j" and "-j" and as long as you
> consistantly do it, your math tends to work out. We see this in the
> argument of the exponential kernal in defintions of Fourier and
> inverse Fourier transforms.

-- glen
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