Some characterisitic language used in the description of symmetries
existing or lacking in physical law seems to be rather misleading. For
example:

"The essence of Charge Parity (CP) is the concept of
symmetry. Both C and P are symmetries that are
conserved in most particle interactions."

"C represents swapping the electric charges of all the
sub-atomic particles in an interaction; in other words,
swapping particles and antiparticles. P is called parity
and it corresponds to looking in a mirror that reverses
all three spatial co-ordinates."

http://news.bbc.co.uk/1/hi/sci/tech/1330190.stm

The symmetries are said to be "conserved", but the conservation of a
physical quantity is not implied; there is no conserved physical
quantity called "parity". It so happens electric charge _is_ a
conserved quantity, but this merely adds to the confusion. What is
meant is that physical law is either invariant in form, or not, under
the reversal of charge or coordinates.

Edward Green wrote:

Some characterisitic language used in the description of symmetries
existing or lacking in physical law seems to be rather misleading. For
example:

"The essence of Charge Parity (CP) is the concept of
symmetry. Both C and P are symmetries that are
conserved in most particle interactions."

"C represents swapping the electric charges of all the
sub-atomic particles in an interaction; in other words,
swapping particles and antiparticles. P is called parity
and it corresponds to looking in a mirror that reverses
all three spatial co-ordinates."

http://news.bbc.co.uk/1/hi/sci/tech/1330190.stm

The symmetries are said to be "conserved", but the conservation of a
physical quantity is not implied; there is no conserved physical
quantity called "parity".

Oh yes there is! Your ignorance does not influence reality's
content.

http://physics.nist.gov/GenInt/Parity/cover.html

http://pdg.lbl.gov/2005/tables/contents_tables.html
"TESTS OF CONSERVATION LAWS"

Metric theories of gravitation wth tensors are parity-symmetric.
[(+/-)x,(+/-)y,(+/-)z) and [(-/+)x,(-/+)y,(-/+)z] give identical
answers (also, Newtonian gravitation and Green's function).
Affine-teleparallel theories of gravitation with pseudotensors can be
parity-antisymmetric. [(+/-)x,(+/-)y,(+/-)z) and
[(-/+)x,(-/+)y,(-/+)z] can give different answers.

The disjoint overlap of metric and affine gravitation is the only
apparent way remaining to empirically falsify General Relativity. It
allows all prior physical observations to remain unmolested while
falsifying the mathematical structure of General Relativity and
validating the mathematical structure of affine-teleparallel
gravitation.

http://www.physics.indiana.edu/~kostelec/faq.html

It so happens electric charge _is_ a
conserved quantity, but this merely adds to the confusion. What is
meant is that physical law is either invariant in form, or not, under
the reversal of charge or coordinates.

Local symmetries create conservation laws through Noether's theorem. A
conserved quantity derives from each symmetry commuting with time, and
the reverse. A divergence-free current (conserved property) arises if
the Lagrangian or the action is invariant under continuous
transformation.

1) To each continuous symmetry of an action there corresponds a
conserved quantity because of the Euler-Lagrange equations of the
Lagrangian, and the reverse.
2) To each gauge symmetry of an action there corresponds an
identity among Euler-Lagrange equations of the Lagrangian, and the
reverse.

A physical system with a Lagrangian invariant with respect to the
symmetry transformations of a Lie group has, in the case of a group
with a finite (or countably infinite) number of independent
infinitesimal generators, a conservation law for each such generator,
and certain "dependencies" in the case of a larger infinite number of
generators (General Relativity and the Bianchi identities). The
reverse is true.

A symmetry can be broken explicitly - a term in the action or
equations of motion may not be invariant. A symmetry can be broken
anomalously - not all classical theory symmetries exist in the
corresponding quantum theory. Quantum field theory anomaly spoils
renormalizability. Anomaly absence in the Standard Model is crucial. A
symmetry can be broken spontaneously if it is an exact symmetry of the
equations of motion but not of a particular solution therein.
Noether's theorem holds if the symmetry is not broken explicitly.
Conservations can be relaxed in subsystems displaying reduced symmetry
(Born scattering approximation, Fermi's golden rule, Snell's law).

PARITY is unique for not being a Noetherian symmetry. Inversion of
all coordinates is a discrete process that cannot be approximated by a
Taylor series. Parity the symmetry is linked to parity the property
by other strong correspondences. Parity is conserved by strong
interactions but commonly violated by weak interactions (including the
Weak Interaction). As gravitation is the weakest known force, one
might optimistically expect a metric (parity-conserving) vs. affine
(parity-violating) gravitation anomaly.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

Uncle Al wrote:

Edward Green wrote:

Some characterisitic language used in the description of symmetries
existing or lacking in physical law seems to be rather misleading.

The symmetries are said to be "conserved", but the conservation of a
physical quantity is not implied; there is no conserved physical
quantity called "parity".

Oh yes there is! Your ignorance does not influence reality's
content.

http://physics.nist.gov/GenInt/Parity/cover.html

"Between Christmas of 1956 and New Year's Day, the first exciting
results emerged from a difficult but fundamental scientific experiment
at the National Bureau of Standards (NBS) in Washington, DC [currently
the National Institute of Standards and Technology (NIST)]. The
experiment showed, strikingly and convincingly, that in at least one
fundamental physical process, our world is distinguishable from its
mirror image."

Thus far I have no quarrel.

"Physicists had long assumed the opposite. They constructed their
theories so as to ensure that the corresponding mathematical property,
called parity, remains unaltered - is conserved - in all subatomic
processes. Thus this experiment brought about the fall of parity from
its exalted position alongside such well conserved physical quantities
as energy, momentum, and electric charge."

Well then, Al, either this is simply another example of poor language,
or I am indeed mistaken. I have no doubt many professionals _say_
"parity is conserved" or "parity is not conserved", but I think they
speak this way out of habit rather than reflection.

...

It so happens electric charge _is_ a
conserved quantity, but this merely adds to the confusion. What is
meant is that physical law is either invariant in form, or not, under
the reversal of charge or coordinates.

Local symmetries create conservation laws through Noether's theorem. A
conserved quantity derives from each symmetry commuting with time, and
the reverse. A divergence-free current (conserved property) arises if
the Lagrangian or the action is invariant under continuous
transformation.

N.B. _continuous_ transformation

Charge reversal, time reversal and parity reversal are not continuous
transformations, and as far as I know no conserved quantities attach to
discrete symmetries through Noether's theorem.

I know just enough to be dangerous. ;-)

1) To each continuous symmetry of an action there corresponds a
conserved quantity because of the Euler-Lagrange equations of the
Lagrangian, and the reverse.
2) To each gauge symmetry of an action there corresponds an
identity among Euler-Lagrange equations of the Lagrangian, and the
reverse.

A physical system with a Lagrangian invariant with respect to the
symmetry transformations of a Lie group has, in the case of a group
with a finite (or countably infinite) number of independent
infinitesimal generators, a conservation law for each such generator,
and certain "dependencies" in the case of a larger infinite number of
generators (General Relativity and the Bianchi identities). The
reverse is true.

A symmetry can be broken explicitly - a term in the action or
equations of motion may not be invariant. A symmetry can be broken
anomalously - not all classical theory symmetries exist in the
corresponding quantum theory. Quantum field theory anomaly spoils
renormalizability. Anomaly absence in the Standard Model is crucial. A
symmetry can be broken spontaneously if it is an exact symmetry of the
equations of motion but not of a particular solution therein.
Noether's theorem holds if the symmetry is not broken explicitly.
Conservations can be relaxed in subsystems displaying reduced symmetry
(Born scattering approximation, Fermi's golden rule, Snell's law).

PARITY is unique for not being a Noetherian symmetry.

You should have read your own crib more carefully. :-)

And no, I do not think it is "unique". Charge reversal, time reversal
.... and for that matter any of the finite groups are not "Noetherian"
symmetries.

Inversion of
all coordinates is a discrete process that cannot be approximated by a
Taylor series. Parity the symmetry is linked to parity the property
by other strong correspondences. Parity is conserved by strong
interactions but commonly violated by weak interactions (including the
Weak Interaction). As gravitation is the weakest known force, one
might optimistically expect a metric (parity-conserving) vs. affine
(parity-violating) gravitation anomaly.

As usual, you have loaded your canon with every bit of scrap you found
lying on the field, and some of it I do not recognize nor can I answer.
It is an old technique. Nonetheless, I have the conviction of a
simple conceptual clarity: A physical law is invariant with respect to
a certain symmetry if the corresponding change of variables leaves the
form of the law unchanged. Now, it might be that every physicist in
the world speaks of a physical law or interaction having this property
with respect to coordinate reflection as "conserving parity", but I
would respectfully point out, sir or ma'am, that I honor the weight of
culture, but your habitual language is inexact.

By the way, the Lorentz symmetry group is a continuous symmetry group,
so we might expect that it _is_ a "Noether symmetry". So what is the
corresponding conserved quanity?

Edward Green wrote:

Uncle Al wrote:

Edward Green wrote:

Some characterisitic language used in the description of symmetries
existing or lacking in physical law seems to be rather misleading.

The symmetries are said to be "conserved", but the conservation of a
physical quantity is not implied; there is no conserved physical
quantity called "parity".

Oh yes there is! Your ignorance does not influence reality's
content.

http://physics.nist.gov/GenInt/Parity/cover.html

"Between Christmas of 1956 and New Year's Day, the first exciting
results emerged from a difficult but fundamental scientific experiment
at the National Bureau of Standards (NBS) in Washington, DC [currently
the National Institute of Standards and Technology (NIST)]. The
experiment showed, strikingly and convincingly, that in at least one
fundamental physical process, our world is distinguishable from its
mirror image."

Thus far I have no quarrel.

"Physicists had long assumed the opposite. They constructed their
theories so as to ensure that the corresponding mathematical property,
called parity, remains unaltered - is conserved - in all subatomic
processes. Thus this experiment brought about the fall of parity from
its exalted position alongside such well conserved physical quantities
as energy, momentum, and electric charge."

Well then, Al, either this is simply another example of poor language,
or I am indeed mistaken. I have no doubt many professionals _say_
"parity is conserved" or "parity is not conserved", but I think they
speak this way out of habit rather than reflection.

Ignorant idiot.

[snip]

Charge reversal, time reversal and parity reversal are not continuous
transformations, and as far as I know no conserved quantities attach to
discrete symmetries through Noether's theorem.

You are light on math and empty of known content.

I know just enough to be dangerous. ;-)

You harbor unbounded delusions of competence.

[snip]

Inversion of
all coordinates is a discrete process that cannot be approximated by a
Taylor series. Parity the symmetry is linked to parity the property
by other strong correspondences. Parity is conserved by strong
interactions but commonly violated by weak interactions (including the
Weak Interaction). As gravitation is the weakest known force, one
might optimistically expect a metric (parity-conserving) vs. affine
(parity-violating) gravitation anomaly.

As usual, you have loaded your canon with every bit of scrap you found
lying on the field, and some of it I do not recognize nor can I answer.
It is an old technique. Nonetheless, I have the conviction of a
simple conceptual clarity: A physical law is invariant with respect to
a certain symmetry if the corresponding change of variables leaves the
form of the law unchanged. Now, it might be that every physicist in
the world speaks of a physical law or interaction having this property
with respect to coordinate reflection as "conserving parity", but I
would respectfully point out, sir or ma'am, that I honor the weight of
culture, but your habitual language is inexact.

Empirical demonstration of parity nonconservation in January 1957

http://physics.nist.gov/GenInt/Parity/cover.html

made Tsung Dao Lee and Chen Ning Yang Noble Laureates/Physics in
December 1957. The speed record still stands. The first test of
gravitational parity violation will be complete in mid-September. The
whole of physics is looking for Lorentz violation,

http://www.physics.indiana.edu/~kostelec/faq.html

Uncle Al simply got there first - unburdened by PERT charts, budget,
staff, management, equipment, progress reports... or expectations of
productivity. He called out to the Severely Gifted and they
volunteered an Army of Light. If it succeeds at the end, so much the
better.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

Uncle Al wrote:

Edward Green wrote:

...

Ignorant idiot.

Every time I dare politely dispute one of your oracles, you resort to
insult and bluster?

[snip]

Charge reversal, time reversal and parity reversal are not continuous
transformations, and as far as I know no conserved quantities attach to
discrete symmetries through Noether's theorem.

You are light on math and empty of known content.

Unresponsive.

Does Noether's theorem apply to discontinuous symmetries, or not?

Don't you know, or don't you want to admit that you shot from the hip
yet again and hit yourself in the foot still bleeding from the last
time? The long section which you copied into your post, without
attribution, shows you both wrong and too careless to read the material
you were plagiarizing.

Tsk.

I know just enough to be dangerous. ;-)

You harbor unbounded delusions of competence.

In this instance I happened to be right. Tant pis for you.

[snip]

Empirical demonstration of parity nonconservation in January 1957

http://physics.nist.gov/GenInt/Parity/cover.html

My suggestion was merely that the conventional phrase "parity
conservation" is poorly chosen, and that there is no physical quantity
called "parity", analogous to charge or momentum, which is conserved.
The fact that an experiment completed in 1957 tended to demonstrate
that known physics is not invariant with respect to parity inversion is
not in dispute. The fact that this lack of invariance in not
infrequently labeled "parity nonconservation" is neither in dispute.
But I do suggest that the conventional phrase is carelessly chosen and
misleading.

Since you are so wrought up about my simple semantic point, could you
perhaps explain to me how "parity", which you feel is indeed a
conserved quantity in the conventional sense and one predicted from
Noether's theorem, is to be measured experimentally?

made Tsung Dao Lee and Chen Ning Yang Noble Laureates/Physics in
December 1957. The speed record still stands. The first test of
gravitational parity violation will be complete in mid-September. The
whole of physics is looking for Lorentz violation,

http://www.physics.indiana.edu/~kostelec/faq.html

Uncle Al simply got there first - unburdened by PERT charts, budget,
staff, management, equipment, progress reports... or expectations of
productivity. He called out to the Severely Gifted and they
volunteered an Army of Light. If it succeeds at the end, so much the
better.

Well, if you do succeed, it will be illustrative of something -- that a
persistant but flawed person can make a difference even if burdened by
entire swarms of conceptual errors -- no doubt happens in business all
the time. Chutzpa and energy helps. Watch that tendency to cover
yourself with insult and BS when you feel cornered. People will notice.

On 19 Aug 2005 13:19:19 -0700, Edward Green wrote:

I know just enough to be dangerous. ;-)

I believe that. You are a person that just knows enough
to have ego issues with roaches.


--

"ruze bi'Abi az shAshe mush AsiyAb migardeh."

On Fri, 19 Aug 2005 14:36:33 -0700, Uncle Al wrote:

Uncle Al simply got there first - unburdened by PERT charts, budget,
staff, management, equipment, progress reports... or expectations of
productivity. He called out to the Severely Gifted and they
volunteered an Army of Light. If it succeeds at the end, so much the
better.

How gifted. If it "suceeds" some people will come and
look into this sham and kick your asses around the way
it meant to be. Why do you think a **** like Mensa is
still there? Remember the first rule of any cult: Do
not open yourselves up for inspections. Cults don't
survive them.

--

"zane bado agar tu shisheh ham bokonan kAre
khodesho mikoneh."

Edward Green wrote:

Some characterisitic language used in the description of symmetries
existing or lacking in physical law seems to be rather misleading. For
example:

"The essence of Charge Parity (CP) is the concept of
symmetry. Both C and P are symmetries that are
conserved in most particle interactions."

"C represents swapping the electric charges of all the
sub-atomic particles in an interaction; in other words,
swapping particles and antiparticles. P is called parity
and it corresponds to looking in a mirror that reverses
all three spatial co-ordinates."

http://news.bbc.co.uk/1/hi/sci/tech/1330190.stm

The symmetries are said to be "conserved", but the conservation of a
physical quantity is not implied; there is no conserved physical
quantity called "parity". It so happens electric charge _is_ a
conserved quantity, but this merely adds to the confusion. What is
meant is that physical law is either invariant in form, or not, under
the reversal of charge or coordinates.

In QM a parity transformation is given by an operator P acting on the
Hilbert space H of the theory. The fact that P^2 = 1 implies that the
Hilbert space splits up as a direct sum of eigenspaces of P with
eigenvalues +-1. A state in one of these eigenspaces is said to have
parity charge +-1 depending on its eigenvalue.

A system has parity symmetry iff the Hamiltonian is invariant under
parity, i.e.:

PHP^(-1) = H

This is equivalent to [P,H] = 0. If this holds then the Heisenberg
equation for P is:

dP/dt = [P,H] = 0

i.e. P is a conserved quantity.

Or if you prefer the Schrodinger picture, note that [P,H] = 0 is
equivalent to the statement that e^(-iHt) P e^(iHt) = P and so given a
state |psi(t_0):

e^(-iHt) P e^(iHt) |psi(t_0) = P |psi(t_0)

i.e.

P |psi(t_0+t) = e^(iHt) P |psi(t_0)

In particular if |psi(t_0) has parity charge n = +-1 then:

P |psi(t_0+t) = e^(iHt) n |psi(t_0)
= n |psi(t_0+t)

so the final state |psi(t_0+t) also has charge n. Therefore if a given
reaction starts with say a state with parity charge 1 and ends with
parity charge -1 then you can rule out this reaction (as long as your
system is parity invariant).

michaeld wrote:

In QM a parity transformation is given by an operator P acting on the
Hilbert space H of the theory. The fact that P^2 = 1 implies that the
Hilbert space splits up as a direct sum of eigenspaces of P with
eigenvalues +-1. A state in one of these eigenspaces is said to have
parity charge +-1 depending on its eigenvalue.

A system has parity symmetry iff the Hamiltonian is invariant under
parity, i.e.:

PHP^(-1) = H

This is equivalent to [P,H] = 0. If this holds then the Heisenberg
equation for P is:

dP/dt = [P,H] = 0

i.e. P is a conserved quantity.

Or if you prefer the Schrodinger picture, note that [P,H] = 0 is
equivalent to the statement that e^(-iHt) P e^(iHt) = P and so given a
state |psi(t_0):

e^(-iHt) P e^(iHt) |psi(t_0) = P |psi(t_0)

i.e.

P |psi(t_0+t) = e^(iHt) P |psi(t_0)

In particular if |psi(t_0) has parity charge n = +-1 then:

P |psi(t_0+t) = e^(iHt) n |psi(t_0)
= n |psi(t_0+t)

so the final state |psi(t_0+t) also has charge n. Therefore if a given
reaction starts with say a state with parity charge 1 and ends with
parity charge -1 then you can rule out this reaction (as long as your
system is parity invariant).

Thank you for the breath of fresh air.

Math Freak wrote:

...

I did a quick search on Google, and I see the closest thing to a recent
substantive post under your name was a stupid puzzle about taking roots
carelessly to demonstrate that "x = -x": other than that, it's pure
politics and character attacks.

You are all noise and no signal.