Re: Gravity at the Molecular Level

[Rock Brentwood]

Subject: Re: Gravity at the Molecular Level
sci.physics.research
2008 February 18
http://groups.google.com/group/sci.physics.research/msg/baf3e2fa2ddad990?dmode=source

Uncle Al wrote:
> Chemical composition appears in no theory of gravitation.

Tom Roberts wrote:
> OK. So why do you think that left-handed and right-handed crystal
> isomers will have different outcomes in Eotvos-like experiments? After
> all, they clearly differ only by chemical composition (i.e. structure at
> the atomic-electron level).

Uncle Al wrote:
>Yours is a statement of profound ignorance in all of its parts.
>Chirality arises from nonsuperposability of coordinate-inverted mass
>distribution. Geometric chirality has no units.

Chemical chirality has nothing to do with physical chirality. That's
why, for instance, you will see two separate entries in the Wikipedia
(or any other dictionary or encyclopedic reference) on-line or off.

The former sense isn't even well-defined as a physical concept. One,
it's only defined in reference to a particular coordinate system; two,
it's not coordinate invariant (i.e. invariant under general coordinate
transformations) and therefore doesn't accord with what most people
would consider an observable, in the first place, in a generally
covariant setting.

It's a fine line distinction that can easily be broken physically.
Take the example of the bromochlorofluoromethane (left and right
variant). Simply move the F atom under the C between the H and Br and
it's opposite (chemical) parity.

Physical parity cannot be defined for any finite set of points. The
only diffeomorphism invariant (even when restricting to orientation-
preserving diffeomorphisms and restricting even further to those with
unit Jacobian) is number. For any two sets of n points (p1,p2,...,pn),
and (q1,q2,..,qn) there is a continuous 1-parameter family of unit
Jacobian diffeomorphisms that will transform the first into the
second.

This has ramifications along the lines of "the Law of Unintended
Ramifications"

Suppose one found equivalence principle divergence between a vat of
left molecules (of that God-forsaken long name above what I won't
retype) and right chiral molecules. Put them each in black boxes, just
for the sake of argument.

Presto, we find a divergence in, say, a Cavendish balance experiment.
Now, we will put the rubber to the pavement on the lack of
diffeomorphism invariance.

Scenario #1: Engineer a force (this requires nanotechnology that we
don't have yet) that slowly and progressively moves the F atom of each
molecule in box #1 under the C between the H and Br until be becomes
the molecule of the opposite parity.

Does the purported divergence suddenly snap the moment F passes under?
What's "under" and what's the snapping point? If there is one, then
the experiment has just found an absolute orientation -- a severe
violation of the principle of relativity. Maybe there is one ... but
good luck proving it.

If, on the other hand, it doesn't snap but the divergent behavior
gradually dampens as the transformation is ensued, this shows an EP
divergent behavior of the molecules in their initial state with the
molecules in the SAME CHIRAL configuration, but with the F displaced.

Either way, check mate. Unintended interpertation: either (a) chemical
chirality is irrelevant to the find of EP divergence or (b) there is
an absolute orientation.

Now we're going to go full speed with the diffeomorphism issue.

Scenario #2: start as before. Raise the temperature of each vat
gradually, keeping both at the same temperature as one another all
throughout. At some point the melting point is reach and exceeded,
both sets of crystals become liquid (or gaseious) pools within theire
respective boxes.

Is the EP divergence still present? If so, how? The two pools are
undistinguishable. There's no such thing as chirality in liquids or
gases.

If not, then the divergent behavior literally melted away. Hence, EP
divergence is found to be temperature-dependent.

Thus, once again the Law of Unintended Ramifications comes to bear. If
we find -- presto -- there is EP divergence between the two sets, then
either (a) it remains even when the two substances become identical --
in which case we have EP divergence of an entirely mysterious origin
that has nothing to do with anything known, or (b) the EP divergence
melts away as the temperature is raised.

To tie the loop into a knot, refreeze the two pools so that the two
substances each have the opposite chiralities they had in the
beginning. NOW ... if there is EP divergence based on chemical
chirality, it's leading to a history-dependent EP behavior for the
SAME material, as its temperature is raised and lowered (and 1/2 of a
hysteresis loop is enacted).

The same argument about continuity applies here as well. If the cross-
over between the divergence from (in solid state) left-right to (in
liquid state) nil to (back in solid-state opposite) right-left was
gradual then it was taking place even while the respective substances
still retained their original chirality (or retained their new
chirality). Hence the divergence is found for the SAME chirality and
has nothing to do with chemical chirality.

Otherwise, the transition takes place in a snap, the very instant
everything becomes liquid. Good luck defining "an instant something
becomes liquid". (Otherwise, we're back to the other scenario, that
the liquid, itself, has a vestigal divergent behavior ... hence back
to the EP-divergence-of-mysterious-origin scenario).

To put it simply the conception behind the experiment is ill-founded
and based on the misunderstanding and confusion of chemical and
physical parity. Physical chiral anomaly is, indeed, a valid issue in
gravity theory. But this has absolutely nothing to do with chirality
in chemistry.

Now, suppose one finds an actual behavior

http://en.wikipedia.org/wiki/Chirality_(chemistry)

Petitjean's ab initio CHI for normalized geometric parity divergence
(or Avnir's semi-empirical quantative geometric parity divergence),
quantitative chirality in all directions, can be calculated. All
single crystals in enantiomorphic space groups P3(1)21 (right-handed
screw axes) and P3(2)21 (left-handed screw axes) explicitly calculate
as extreme parity divergent cases,

http://www.mazepath.com/uncleal/qzdense.png
quartz (light elements)
http://www.mazepath.com/uncleal/hgsdense.png
cinnabar (heavy elements)
http://www.mazepath.com/uncleal/bzdense.png
benzil (for parity calorimetery)
http://www.mazepath.com/uncleal/tedense.png
tellurium

Slope is exactly -2 in theory. Smaller intercept is more rapid growth
of geometric parity divergence with radius. Benzil including
hydrogens, 78 atoms in its crystallographic unit cell, will be out by
Friday 22 February after 1250 CPU-hrs in an AMD FX-55 booted Linux.

CHI is pretty good stuff. Twistane is a mostly spherical blob of
polycyclic alkane with no chromophores, no dipole moment, no
non-bonded electrons, and no optical absorbance below 250 nm. It has
[alpha]D = 440 degrees at 100% ee. CHI = 0.72.

> Even if spacetime has a chiral structure at ~ the Planck level,

As a pseudoscalar vacuum background. Don't parade straw men.

> why
> would one think this could influence experiments performed at scales
> ~10^25 larger? Indeed, your website has the statement "Chirality
> vanishes at lengths smaller than a screw's pitch." -- the "screws" you
> are using have a pitch of order 10^-10 m, so why do you think they might
> detect chirality ~10^25 times smaller than their pitch?

First, there is no physical basis for your objection, none at all.
Second, [alpha]D is measured at 589 nm. Single molecules are wholly
adequate rotators with typical diameters around 5 nm. Third, look at
the change of CHI with /_\R/R. The smallest radial increment that
results in a change of CHI for the crystal lattice incredibly
contracts with increasing overall radius. When you (OK, maybe not
you) work the maths, for r = 0.5 cm the minimum radial increment that
changes CHI is 4x10^(-25) meters. That is about 10^(-10) of a
proton's radius. Is that a small enough basis scale for CHI for you?

> While I agree that the experiment should be performed, I think you have
> not given any compelling reason....

I have deluged this newsgroup and others with deep and inescapable
reasons. This is a reason derived within affine gravitation,

http://www.mazepath.com/uncleal/lajos.htm#a9

"Term 5 obtains a parity-violating term that drops out for pure
gravitation. Free field equations with the preceding Lagrangian will
be identical to those for ordinary General Relativity. One of the
Lagrangian-derived equations will be (torsion = 0). Einstein-Cartan
and General Relativity are identical in the absence of matter - even
with addition of a parity-violating term to the Lagrangian."

Now, the boojum....

"Term 5 acts when gravitation is combined with matter - a mass sector
parity divergence empirically falsifying General Relativity. The
parity calorimetry experiment and the parity Etovs experiment test for
coupling with Term 5."

End of argument. This is the only place where General Relativity can
macroscopiclaly fail and not contradict prior observation. There
exist no naturally occuring resolved chiral astronomical bodies.
Nobody has ever reported a parity Eotvos experiment despite its easy
access in commercial single crystal quartz.

Somebody should look.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2

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[Tom Roberts]

Rock Brentwood wrote:
> [...]

Your article reminded me of an earlier thought I had on this:

If two chemical isomers have different potential energy in a
gravitational field, but the two isomers can be disassembled and
reassembled into each other without requiring any net energy, then one
could in principle construct a perpetual motion machine. This implies
that current limits on the equality of the masses of those isomers can
be used to put a limit on the difference in their behavior under gravity.

How good are the limits on the mass difference between the isomers of
Uncle Al's crystals?


Tom Roberts

[Uncle Al]

Tom Roberts wrote:
>
> Rock Brentwood wrote:
> > [...]
>
> Your article reminded me of an earlier thought I had on this:
>
> If two chemical isomers have different potential energy in a
> gravitational field, but the two isomers can be disassembled and
> reassembled into each other without requiring any net energy, then one
> could in principle construct a perpetual motion machine. This implies
> that current limits on the equality of the masses of those isomers can
> be used to put a limit on the difference in their behavior under gravity.

You said that if things are different but the same then they cannot be
different. Aside from ignoring differential energy of disassembly,
loopholes for growth are opened by non-linear behavior, below.

> > How good are the limits on the mass difference between the isomers of
> Uncle Al's crystals?

Do not confuse gravitational and inertial masses. Given a chiral
vacuum background (left foot) plus imposed local non-parallel inertial
and gravitational accelerations, can local vacuum free fall paths be
non-parallel? Can gravitational and inertial masses decouple? For
contrasted socks, no. For a left shoe against a sock, not by much.
For contrasted left and right shoes, a lot! Put on two left shoes,
try to walk a straight line with your eyes closed.

http://www.ift.unesp.br/gcg/tele.pdf
Chapter 9, Eq. 9.52, p. 75,

"a self dual (anti-self dual) torsion couples only to the left-hand
(right-hand) component of the spinor field. In other words,
gravitation becomes a chiral interaction, a property that may
eventually have important consequences at the microscopic level."

Now to your argument. A 10^(-13) relative mass-mass EP parity
violation for enantiomorphic space groups P3(1)21 and P3(2)21 benzil
is 8.99 cal/gram /_\/_\H(fusion) divergence, (mass-mass)c^2 in 112
cal/g average background. A larger divergence than that is unlikely.
0.9 cal/gram is detectable to high confidence in a 0.1% precision DSC
(i.e., (+/-)0.112 cal/g for benzil background with repeated
measurements). 10^(-14) mass-mass at about six sigma as detailed is
much better than 5x10^(-14) 2(mass-mass)/(mass+mass) at one sigma -
the best Eotvos balance operation as of January 2008.

http://www.mazepath.com/uncleal/shoes.jpg

Crystallize benzil from solution (with no stirring to disperse initial
seed crystals). Trivially calculate a statistical imbalance in
spontaneous occurance of left- and right-handed crystals from the
difference in /_\H. Run 1000 96-well plates and see if |L-R|>310
instances occur. Aside from obvious nuisance (96,000 chirality
determinations) and the small /_\H vs. RT at room temp... it won't
work.

Initial seed configuration determines the whole crystal. The initial
seed is only a few molecules. As soon as order locks in the seed the
whole crystal is locked. /_\H affects initial seed crystal chirality
only. Angstrom dimensions and large difference in crystal moments of
inertia (benzil grows as long thin needles) do not develop CHI (with
DSI=0 and COR = 1),

http://www.mazepath.com/uncleal/bzhdense.png
for solid spheres

Seed configuration is not measurably affected by the difference in
energy of its opposite parities in a chiral background because there
is asymptotically no difference. Once the seed forms there will be an
energy difference rapidly growing with radius to 8.99 cal/gram - but
it evolves way too late to affect and effect enantiomer ratio skew.

Equivalence Principle parity anomalies are bulletproof. It only
remains to observe whether they exist,

http://www.mazepath.com/uncleal/qz4.pdf
technical readout
http://www.mazepath.com/uncleal/lajos.htm#a2
parity calorimetry experiment

I have a couple of theorists on board looking at the Pereira pdf,
above, to decide whether macroscopic effects are defensible. The math
is brutal. More input is welcome. Patience.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2

[Rock Brentwood]

This part of the my reply was accidentally left in from the original
article (sorry) and is from Uncle Al, not me. Bad cutting and pasting.

Rock Brentwood wrote:
> Now, suppose one finds an actual behavior
> http://en.wikipedia.org/wiki/Chirality_(chemistry)
...
> Uncle Al [rest of signature]

Additional notes on my earlier reply:
> Chemical chirality has nothing to do with physical chirality. That's
> why, for instance, you will see two separate entries in the Wikipedia
> (or any other dictionary or encyclopedic reference) on-line or off.

Petitjean [1], himself, said so:

"any further occurrence [in the body of this paper] of the word
"chirality" is to be taken in some geometric meaning, but not in any
physical or chemical sense."


> Scenario #2: start as before. Raise the temperature of each vat
> gradually, keeping both at the same temperature as one another all
> throughout. At some point the melting point is reach and exceeded,
> both sets of crystals become liquid (or gaseious) pools within theire
> respective boxes.

If the molecules, themselves, are chiral even in a gas, then raise the
temperature further to the point where they become atomized. The point
is not changed, either way: at some temperature the systemic feature
is "melted" (or vaporized) away.

Immediately after the earlier remark, Petitjean [1] went on to further
qualify:
"Provided some point in EUCLIDEAN space ..."
emphasis mine.

i.e., the treatment first assumes spacetime is space+time with space
Euclidean and time "static" (the measure only applies to static
configurations) and selects out a particular type of coordinate.

i.e., not useful as a measure for any physical experiement.

Much of what was developed is already standard fare and stands more in
the class of "reinventing the wheel". In fact, there's already a
standard treatment of distributions -- the cumulant expansion. If all
you wanted were parity asymmetry measures, then any sufficiently large
number of the odd-order cumulants would be good enough. The author
Petitjean, himself, even pointed this out: making brief mention of the
3rd cumulant. But, then, for some reason he neglected to mention that
it undercuts the entire necessity of the exercise of the paper. The
cumulant expansion is already complete, anything that can be said
about any distribution is contained in the cumulants. For any
distribution of N points, any N independent cumulants suffice to
completely reconstruct the distribution.

The fact that the distribution may be "colored" (i.e. comprising a
vector of attributes, rather tham just a single one) is inessential.
One then does the cumulant expansion over the linear space comprising
the attribute vectors.

But no matter. Even by Petitjean's own account, the measure has an
essential coordinate-dependence.

It is only defined in reference to a particular type of space
(foliated spacetime with Euclidean layers) and coordinate system
(Cartesian x E(1) for time). Picking up an "equivalence principle"
violation based on it would essentially amount to physically observing
an absolute coordinate system and a particular type of spacetime: one
foliated by 3-dimensional Euclidean spaces.

It's not physically invariant, due to its coordinate-dependence. Even
the ability to generalize 0th and 1st order moments to invariant form
has to be counted as somewhat of a miracle. The only reason you can
convert the 1st order moment x^m P^n (for position 4-vector x,
momentum/energy 4-vector P) is that you have the law of momentum
conservation to allow you to "borrow a d" from the P and put it onto
the x. Thus, when P is written as a 3-form current
P_a = (sum epsilon_{mnrs} P^m_a dx^n ^ dx^r ^ dx^s)
the conservation law says dP_a = 0. From it, one can define the
"dynamic potential" 2-form p_a by dp_a = P_a (at least locally) and
proceed to write
x^a P_b = x^a dp_b = d(x^a p_b) - dx^a ^ p_b = d(...) - e^a ^ p_b
where e^a = dx^a is the frame co-vector and the d(...) is of little
consequence in the integral of the density.

For 2nd and higher order moments? Not likely! You already borrowed on
d from P, there's no more left to borrow. dp_a = 0 is not true, so p_a
= d(p2_a) can't be constructed and used.

There is major roadblock in the way to define (i) any local density
for 2nd or higher order moments; and therefore (ii) any that's
coordinate-invariant.

It requires one to even assign remote simultaneity. There is no such
thing as a "static" configuration, in the first place. All
configurations are dynamic. So, then: what set of "points" comprising
a configuration count as being at the "same time" so that we can plug
them into the Petitjean (or other static-configuration) measure?

There is no physical process known, of any kind, for fundamental
interactions that has dependence on essentially-macroscopic variables,
let alone on inherently coordinate-dependent measures (let alone, any
that displays an absolute simultaneity reference). That would break
coordinate invariance and put us back in a situation long ago believed
to hold (an absolute frame).

Even as a chemical measure, it's not well-defined. What's the
chirality of a set of ammonia molecules, for instance? They're each in
quantum superpositions of opposite-chirality states and are not in an
eigenstate of any of Petitjean's measures.

Even the premise behind the measure ("colored distributions") is
ambiguous. What are the "colors" of the measure? Does one weight
subatomic particles, atoms, or molecules? What you get depends on
which of these you count as the building blocks. And why would Nature
care which one you count as building blocks? How would fundamental
interactions know to count distributions by atoms rather than by
subatomic particles when all it sees, knows or cares about are
otherwise undifferentiated assemblages of subatomic particles (if even
that)?

Now ... you may very well find some coordinate-dependent effect on
gravity in any experiment; one that selects out a particular
simultaneity reference or selects out a particular way to count
objects. But that's for the experimentalist to justify before-hand,
not for someone else to "explain afterwards". Experiments are
generally conceived to test between two or more theories, not as
random shots in the dark against a single theory with no account for
why the shot in the dark may yield something. If an experimentalist is
going to use other peoples' equipment (particularly, equipment that is
not cheap to make and/or not cheap to maintain), it is the
experimentalists' burden to justify on what ground and by what theory
it may yield results other than what 500 years of development and
consensus in Physics since Galileo say it won't.

The analogous situation would be to insist on someone do a test with
their million-dollar equipment on astrology in order to "plug the
remaining holes in physical law", with the refrain "it's for the
theorist to explain, [sic] if we find something, so we ought to do the
experiment because we might find something". And the analogy is quite
appropriate: you're talking about non-local systemic measures having
an impact on fundamental physical law; i.e., teleological influences
of the very same type as what characterize astrology.

It will not play well with those who actually have Eotvos balances,
and dialogue with them is likely to proceed in a "one way" only
direction (you sending queries and getting little or no reply).

If you want to test for teleological effects (i.e., the influence of
essentially-macroscopic variables on fundamental processes), you're
going to have to make your own equipment and prepare and conduct your
own experiments.

Otherwise -- the more likely scenario: just chalk it up to a simple
misunderstanding (that a reading of Petitjean's sentence above would
have avoided) that came from confusing physical chirality with
chemical or other notions of chirality. You're not the only one to
have had that misunderstanding.

A final note: the "chiral" in physical chirality (e.g. spin, helicity)
is independent of: frame or coordinates (unlike chemical chirality),
position (unlike angular momentum), scale, dynamic vs. static (unlike
chemical chirality), temperature (particuarly: it does not require
everything to be in static equilibrium to measure it), etc. It is
invariant under orientation-preserving diffeomorphisms. In contrast
(as described in the previous article), NO systemic feature of a
finite configuration is diffeomorphism-invariant (not even with
respect to orientation-preserving diffeomorpisms nor even unit-
Jacobian diffeomorphisms), except number.

Reference:
[1] "Chirality and Symmetry Measures: A Transdisciplinary Review"
Michel Petitjean
Entropy 2003, 5, 271-312

[Uncle Al]

Rock Brentwood wrote:
[snip]

> Even as a chemical measure, it's not well-defined. What's the
> chirality of a set of ammonia molecules, for instance? They're each in
> quantum superpositions of opposite-chirality states and are not in an
> eigenstate of any of Petitjean's measures.
[snip]

> Reference:
> [1] "Chirality and Symmetry Measures: A Transdisciplinary Review"
> Michel Petitjean
> Entropy 2003, 5, 271-312

$(US)Billion Sepracor earned its money by resolving chiral
pharmaceuticals and marketing one optical isomer as the therapeutic
moiety. This broke dozens of hugely profitable racemate patents for a
few $hundred each and required no product safety testing at all (the
racemate already passed). If Mr. Brentwood can mathematically prove
that Sepracor did nothing - and make it stick in court - Mr. Brentwood
will be very quickly fabulously wealthy.

0) Hund's Paradox is elegant quantum physics and a bunch of hooey
in the macroscopic real world. In principle one could put a single
rigid chiral molecule (e.g., [R]-camphor) into a Rabi vacuum
oscillation cavity with the impedence of free space and, upon exit,
have no pre-determined sense of chirality, [R] or [S], to observe.
Two molecules at a time won't do it, nor will larger cavities.
Despite the tenure-grabbing elegance of the result, nobody has
demonstrated racemization from quantum indeterminacy.

1) The ammonia molecule has point group C_3v. If somebody can
explain how a molecule with three independent mirror planes of
symmetry can be chiral, Uncle Al would like to hear it. No molecule
or array of points overall can be chiral if it contains one or more
improper axes of symmetry - no mirror planes of symmetry, no inversion
point of symmetry, no higher improper axes of symmetry (e.g., S_4
symmetry of a baseball seam).

2) As an ammonia molecule inverts it remains C_3v until at the hump
it is point group D_3h. If somebody can explain how a molecule with
four independent mirror planes of symmetry can be chiral, Uncle Al
would like to hear it.

3) An array of ammonia molecules is a gas. It has no persistent
configuration. An array of ammonia molecules is a liquid. It has no
persistent configuration. An array of ammonia molecules is a crystal
with a primitive cubic crystal structure. It is not a chiral crystal
structure or an enantiomorphic space group. Ammonia glass is not
chiral either.

4) Ammonia is not a chiral molecule. No gas or condensed phase of
ammonia is chiral.

The proffered argument makes assumptions that support its desired
conclusion. Testing the empirical validity of a founding postulate
cannot embrace that postulate as part of a failed disproof.

DO LEFT AND RIGHT SHOES VIOLATE THE EQUIVALENCE PRINCIPLE? Do
chemically identical, opposite geometric parity mass distributions
have their local centers of mass vacuum free fall along non-identical
(non-parallel) trajectories? Nobody knows because nobody has looked.

In November 1956 it was OBVIOUS that nuclear physics was symmetric to
parity. On 01 January 1957 it was OBVIOUS that the Weak interaction
was strictly left-handed. Yang and Lee got the 1957 Nobel
Prize/Physics.

We know by observation that strong interactions are strongly
symmetry-preserving. We know by observation that increasing weaker
interactions are heir to increasingly common symmetry breakings.
Gravitation as the weakest interaction would then be the prime
candidate for a parity anomaly - no matter who doesn't like it or for
what reason. One must look to know. Theory will thereafter predict
what it is told to predict - with the same elegant sincerity as before
the switch.

One can claim that the whole of chemistry is included in physics. We
have seen an apt demonstration of why making an aspirin first requires
making a chemist.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2