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Ken Stahl
science forum beginner
Joined: 20 May 2006
Posts: 2
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 Posted: Sat May 20, 2006 10:30 pm Post subject:
Unifield Field
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Can anyone tell me if Einstein hoped to extract from a Unifield Field
Theory, the Electric Field, the Magnetic Field, the Weak Field, and the
Strong Field? Or did he hope to so generalize the Field, that the
Gravitational Field would also 'fall out' under suitable constraints? |
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Oh No
science forum addict
Joined: 06 Apr 2006
Posts: 82
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| Posted: Sun May 21, 2006 12:52 pm Post subject:
Re: Unifield Field
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Thus spake Ken Stahl <kenstahl@verizon.net>
| Quote: | Can anyone tell me if Einstein hoped to extract from a Unifield Field
Theory, the Electric Field, the Magnetic Field, the Weak Field, and the
Strong Field? Or did he hope to so generalize the Field, that the
Gravitational Field would also 'fall out' under suitable constraints?
Essentially he was trying to find a theory in which the gravitational |
field and the electromagnetic field would take the same form, and appear
in the same way.
Regards
--
Charles Francis
substitute charles for NotI to email |
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Igor
science forum Guru
Joined: 15 May 2005
Posts: 315
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| Posted: Tue May 23, 2006 5:46 pm Post subject:
Re: Unifield Field
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Ken Stahl wrote:
| Quote: | Can anyone tell me if Einstein hoped to extract from a Unifield Field
Theory, the Electric Field, the Magnetic Field, the Weak Field, and the
Strong Field? Or did he hope to so generalize the Field, that the
Gravitational Field would also 'fall out' under suitable constraints?
|
When he first started working on unification around 1920, although the
nucleus had been discovered and beta decay was observed, the weak and
strong fields were completely unknown. His goal was to unify EM and
gravitation into one basic metric geometry. He made various attempts
over the years, but his pet theory seemed to always be his theory of
non-symmetric field. The inertial fields were still part of a
symmetric submetric while the EM fields were an antisymmetric part.
Unfortunately, he was never able to duplicate even Maxwell's equations,
so any real hopes of true unification were dashed.
As far as the gravitational field 'falling out', that seems to be more
of the modern string theory approach -- construct a mathematically
elegant theory and hope that everything we understand about the world
falls out of it. I don't believe that was ever Einstein's approach at
all. He appeared to prefer to start with things that were known and to
see how they might actually fit together. While he never succeeded, I
tend to believe that that is probably still a better way to go. |
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Ken Stahl
science forum beginner
Joined: 20 May 2006
Posts: 2
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| Posted: Thu May 25, 2006 6:48 pm Post subject:
Re: Unifield Field
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"Igor" <thoovler@excite.com> wrote in message
news:1148322222.045637.238150@38g2000cwa.googlegroups.com...
| Quote: | Ken Stahl wrote:
Can anyone tell me if Einstein hoped to extract from a Unifield Field
Theory, the Electric Field, the Magnetic Field, the Weak Field, and the
Strong Field? Or did he hope to so generalize the Field, that the
Gravitational Field would also 'fall out' under suitable constraints?
When he first started working on unification around 1920, although the
nucleus had been discovered and beta decay was observed, the weak and
strong fields were completely unknown. His goal was to unify EM and
gravitation into one basic metric geometry. He made various attempts
over the years, but his pet theory seemed to always be his theory of
non-symmetric field. The inertial fields were still part of a
symmetric submetric while the EM fields were an antisymmetric part.
Unfortunately, he was never able to duplicate even Maxwell's equations,
so any real hopes of true unification were dashed.
As far as the gravitational field 'falling out', that seems to be more
of the modern string theory approach -- construct a mathematically
elegant theory and hope that everything we understand about the world
falls out of it. I don't believe that was ever Einstein's approach at
all. He appeared to prefer to start with things that were known and to
see how they might actually fit together. While he never succeeded, I
tend to believe that that is probably still a better way to go.
I like the "... start with things that were (are) known." Now then, a |
question; is it proper to ask; Do the Electric Field, Magnetic Field, Weak
Field, and Strong Field, qualify as 'known' in this, Einstein, sense? And if
so, would an 'Einstein' of today, be trying to find a single, integrated
field, which under suitable constraints, would yield these four fields? |
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Igor
science forum Guru
Joined: 15 May 2005
Posts: 315
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| Posted: Tue May 30, 2006 10:02 pm Post subject:
Re: Unifield Field
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Ken Stahl wrote:
| Quote: | "Igor" <thoovler@excite.com> wrote in message
news:1148322222.045637.238150@38g2000cwa.googlegroups.com...
Ken Stahl wrote:
Can anyone tell me if Einstein hoped to extract from a Unifield Field
Theory, the Electric Field, the Magnetic Field, the Weak Field, and the
Strong Field? Or did he hope to so generalize the Field, that the
Gravitational Field would also 'fall out' under suitable constraints?
When he first started working on unification around 1920, although the
nucleus had been discovered and beta decay was observed, the weak and
strong fields were completely unknown. His goal was to unify EM and
gravitation into one basic metric geometry. He made various attempts
over the years, but his pet theory seemed to always be his theory of
non-symmetric field. The inertial fields were still part of a
symmetric submetric while the EM fields were an antisymmetric part.
Unfortunately, he was never able to duplicate even Maxwell's equations,
so any real hopes of true unification were dashed.
As far as the gravitational field 'falling out', that seems to be more
of the modern string theory approach -- construct a mathematically
elegant theory and hope that everything we understand about the world
falls out of it. I don't believe that was ever Einstein's approach at
all. He appeared to prefer to start with things that were known and to
see how they might actually fit together. While he never succeeded, I
tend to believe that that is probably still a better way to go.
I like the "... start with things that were (are) known." Now then, a
question; is it proper to ask; Do the Electric Field, Magnetic Field, Weak
Field, and Strong Field, qualify as 'known' in this, Einstein, sense? And if
so, would an 'Einstein' of today, be trying to find a single, integrated
field, which under suitable constraints, would yield these four fields?
|
Well, the EM, weak, and strong fields have already hypothetically been
unified There are various gauge models that accomplish this None of
them have ever made a prediction that I'm aware of that's been
experimentally verified. Probably the biggest prediction ever made
from some of these models was proton decay. As far as I know, ir has
never been observed.
All we can really say at this point is that we have the Standard Model,
which consists of separate EM, weak, and strong gauge fields. And then
there's gravity, which is described by GR and is, in a sense, a gauge
theory itself. To answer your first question, yes, these are the four
'knowns' here. I think that in order to unify them all, rather than
starting from some purely mathematical approach and working back down
to physical reality, as string theory seems to, you would want to find
a way to unify any two of the fields directly and then generalize it.
Then try to fit the next field into this puzzle, and so on. This is
more of a bottom-up approach. |
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markwh04@yahoo.com
science forum Guru Wannabe
Joined: 12 Sep 2005
Posts: 137
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| Posted: Thu Jun 08, 2006 8:03 am Post subject:
Re: Unifield Field
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|
Ken Stahl wrote:
| Quote: | Can anyone tell me if Einstein hoped to extract from a Unifield Field
Theory, the Electric Field, the Magnetic Field, the Weak Field, and the
Strong Field? Or did he hope to so generalize the Field, that the
Gravitational Field would also 'fall out' under suitable constraints?
|
There was no solid notion of anything beyond the electromagnetic field
and gravity for most of Einstein's life. Yang-Mills theory didn't even
come into being until around the time of Einstein's death, nor the
fitting of the other forces within this or any framework.
The goal was to provide a consistent geometric interpretation of all
dynamics. The primary obstacle is that a geometric space-time
interpretation, itself, requires the foundation of the Equivalence
Principle. It's what justifies making gravity epiphenomenal to
space-time curvature. It's even what justifies retrofitting Newtonian
theory into a curved spacetime theory of Newton-Cartan general
relativity. One could conceivably even do the same for Aristotle's
spacetime physics. In all cases, the geometrization process requires
the Equivalence Principle.
Yet, it's obviously false, when taken at face value, for just about
every instance one can conceive of in the real world. Two objects
proceed to diverge in their subsequent motions, even when set about
identically. Two lovers in an embrace eventually go their separate
ways.
So, either the Equivalence Principle is wrong or the apparent motions
seen in the everyday world are just a shadow of the actual motions the
objects undergo, with the divergence of subsequent motion being a
consequence of the initial (unseen) parts of the motions having been
initially different.
Einstein never directly made the (geometry requires EP -> EP fails at
face value -> imposing EP requires unseen motion components that lie
beyond face value) line of argument. But it's implicit in everything he
did, and had someone been around to present to him the very words I
wrote, as I just wrote them (ahem), it probably would have set him back
into focus on his "message".
Even in classical theory there is already a strong hint at something
beyond the manifest at work. The equations of motion for a test charge
dp/dt = e (E + v x B)
and energy law for the energy H
dH/dt = e v.E
under the electromagnetic field, defined in terms of the potentials A,
phi by
E = -grad phi - dA/dt; B = curl A
yields equations in the following form
d(p + eA)/dt = grad(e(v.A - phi))
d(H + e phi)/dt = grad(e(phi - v.A)).
Maxwell coined the integral of A.dr around a circuit the
"electromagnetic momentum", implicitly recognizing the true nature of
A.
In effect, the momentum of the object now comprises a kinetic part
p = m v/(1-(v/c)^2)^{1/2} = m dr/ds
plus an extra component arising from the field, with the contribution
being the product of the charge and potential: eA. The energy comes
from a kinetic part
H = mc^2/(1-(v/c)^2)^{1/2} = mc^2 dt/ds
and the field: e phi.
Combining this using differential forms, one obtains
d( ((H + e phi)Dt - (p + eA).Dr )/dt = D(e(phi -
v.A))
or
d((H + e phi)Dt - (p + eA).Dr) = D(e(phi dt - A.dr)).
The energy-momentum differential on the left now acquires an extra
component proportional to the charge
H Dt - p.Dr -> H Dt - p.Dr + e(phi Dt - A.Dr).
In effect, the charge is an extra component of the momentum associated
with an apparent motion given by the differential phi.Dt - A.Dr, which
implicitly expresses a "reference" in the unseen dimension(s) that the
motion is taken relative to.
Moving this to the right, one finds the Lorentz law
d (H Dt - p.Dr) = e (D(phi dt - A.dr) - d(phi Dt
- A.Dr)).
If the references were able to consistently combined to define an
overall "level" surface for the extra dimension(s), the right hand side
would be 0. Thus, it represents an "arbitrage" defect (to use an
economists' term) in the "even exchange rate" given by the differential
(phi dt - A.dr). This is fhe field strength.
One can then consider the more general notion of a charge with a
"complexion", the complexion described by 2 or more components to the
charge, the idea being that the components collectively give you the
magnitude of the charge, the unit vector the "complexion".
Maxwell even briefly dabbled into a foray on this idea in his treatise,
considering a then-old theory that electro-magnetism and gravity could
be combined by a 2-component charge (the postive and negative charges
laying along slightly different directions in 2-dimensional
charge-space). When this combined force is transformed to a normal
mode, the result is an electromagnetic force plus a residue that is
either universally attractive or universally repulsive, depending on
how the relative strengths of interaction of positive-positive,
positive-negative and negative-negative (the determine of the 2x2
matrix gives you the sign of the residue force). The "mixing angle" in
the 2-dimensional charge space is slightly off from 45 degrees. So, one
of the components is (p + n), where p and n are the magnitudes of the
positive and negative charges, the other component is (p - n). The
former gives you an effective measure of mass, the latter, an effective
measure of charge.
That was the earliest instance of unification contemplated by a
non-trivial mixture involving a "mixing angle". Folklore in Physics
attributes the idea to the developers of electroweak theory in the
1960's over 100 years after Maxwell raised the idea.
More generally, you can consider the field above to be generalized then
to a vector-valued charge:
e (phi dt - A.dr) --> e_a (phi^a dt - A^a.dr)
each component (phi^a,A^a) representing a copy of the potentials, the
expression on the right understood to be summed over all values of the
index a=1,2,...,N, with the charge vector being (e_1,e_2,...,e_N).
Since the charge represents a constraint in the overall system (its
conjugate coordinate is unseen and therefore does not appear in the
dynamics), then it's natural to assume that it's a first class
constraint. Then the requirement of consistency with the underlying
dynamics comes down to imposing the two conditions:
{e_a,e_b} = sum f^c_{ab} e_c
{e_a,H} = sum d^c_a e_c
for suitable coefficients f^c_{ab} and d^c_a, where H is now the
overall Hamiltonian of the system.
The coefficients f^c_{ab} define a gauge group. The generalized field
is thus a gauge field, which is what generalizes the Maxwell field.
The coefficients of the second equation, under somewhat general
assumptions, can be proven to take the form
d^c_a = sum f^c_{ab} u^b,
for some vector (u_1,u_2,...,u_N). This gets us almost all the way to
Wong's equations, which describe the precession of the charge's
complexion in time.
The requirement that the magnitude of the charge be preserved, with
respect to a suitably defined quadratic form
|e|^2 = sum mu^{ab} e_a e_b
will get you most of the way to Wong's equations, as well as
determining what mu is.
The gauge field has more or less standard interpretation in the higher
dimensional geometry known as a Principal Bundle. It's possible to
generalize this interpretation further to what are known as Homogeneous
Spaces to bring in the Higgs; and to generalize it further still
(allowing the gauge metric mu^{ab} to be variable) to bring in another
set of scalar fields that represent dilatons and endow the vacuum with
the very kind of effective structure as a polarizing dielectric medium
that Maxwell had originally hypothesized it to have. |
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markwh04@yahoo.com
science forum Guru Wannabe
Joined: 12 Sep 2005
Posts: 137
|
| Posted: Thu Jun 08, 2006 8:04 am Post subject:
The Spectre Of Electroweak-Gravity Unification Within The Standard Model (was: Unifield Field)
|
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|
Igor wrote:
| Quote: | All we can really say at this point is that we have the Standard Model,
which consists of separate EM, weak, and strong gauge fields.
|
We have the clear spectre of more than that, superposed on the model.
A test charge moving in a Yang-Mills field will have a charge vector
that precesses over time, yet the square magnitude will remain
constant.
If this fails to occur at the microscopic level, one will see
fluctuations at the macroscopic level and a deviation from this law.
Therefore, one should expect that there be a quadratic invariant of
some sort in the fermion spectrum.
The most notable features of the Standard Model is that (1) it has
none, (2) it very nearly has 2.
Ironically, the missing element that comes to the rescue is a close
historical analogue of the very kind of "displacement current" that
charge conservation had originally motivated Maxwell to consider.
In the minimal Standard Model (before the discovery of neutrino
oscillation) -- where quadratic invariants fail to be found -- a clear
argument could be posed to basically clamp down on the charge spectrum.
Because of the assymmetric way that the charge spectrum is arrayed for
the electroweak part of the force, an anomaly emerges. An anomaly
occurs when one attempts to promote classical symmetries to the quantum
domain and defects emerge to spoil the day.
Initially only presented in the perturbative realm (the triangle
anomaly), it soon became understood as the chiral anomaly (a
non-perturbative expression for the effective Lagrangian later came).
Its removal requires clamping down on the fermion spectrum.
In effect, the only charge that respects the neutrino being only
one-handed, and respects the 3-fold degeneracy of the fermion spectrum,
while cohabiting with electroweak and the strong force -- up to a
choice of unit -- the hypercharge.
With that set, the quadratic invariant is doomed.
Hence, by redictio ad absurdum, the argument that led to this is
doomed. Something more must exist in the spectrum. A "displacement
current".
The obvious choice -- the other handed neutrinos -- not only fills in
the fermion spectrum nicely and suddenly makes everything nice and
symmetric, it opens up the issue completely.
The fermion spectrum with the extra neutrino has the (SU(2),SU(3),U(1))
decomposition:
(1,1,6) + (2,1,3) + (1,1,0) +
(1,3,4) + (2,3,1) + (1,3,-2) +
(1,3*,2) + (2,3*,-1) + (1,3*-4) +
(1,1,0) + (2,1,-3) + (1,1,-6).
A surprising pattern clearly emerges.
Now... repeating the same argument about anomaly removal -- but this
time allowing the the extra neutrino sectors (1,1,0) to participate --
one finds that in addition to the hypercharge, an extra charge is
potentially allowed: the baryon number, which I'll call G.
The pattern above becomes more obvious when G is subtracted from Y
(using the scaling +/- 1 for leptons and +/- 3 for baryons). The result
-- written in (SU(2),Y-G,SU(3),G) form is
(1,3,1,3) + (2,0,1,3) + (1,-3,1,3) +
(1,3,3,1) + (2,0,3,1) + (1,-3,3,1) +
(1,3,3*,-1) + (2,0,3*,-1) + (1,-3,3*,-1) +
(1,3,1,-3) + (2,0,1,-3) + (1,-3,1,-3)
effectively factoring into
(1,3)+(2,0)+(1,-3) x (1,3) + (3,1) + (3*,-1) +
(1,-3)
for U(2)_{I,Y-G} = SU(2)_I x U(1)_{Y-G}, and U(3)_{L,G} = SU(3)_L x
U(1)_G.
And the clincher: lo and behold there are now 2 quadratic invariants.
For weakly interacting modes I^2 = 3/4, otherwise I^2 = 0. At the same
time Y-G is 0 for the former case, +/- 3 for the latter. Thus,
I^2 + 3 ((Y-G)/6)^2 = 3/4
is the first invariant.
For quarks, L^2 = 4/3 and for leptons, L^2 = 0. The baryon numbers,
respectively are +/-1 and +/- 3. Thus,
L^2 + G^2/6 = 3/2
Associated with each are a set of casimir operators that take only the
values +/- 1/2. For U(2), one has
I3 +/- (Y-G)/6 = +/- 1/2
For U(3), one has the (L3,L weights set at, for the triplet 3:
red = (1/2,k), green = (0, -2k), blue = (-1/2, k).
where k = (1/12)^{1/2}. For the triplet 3* they are all of opposite
signs
cyan = (-1/2, -k), magenta = (0, 2k), amber = (1/2, -k).
Thus
G/6 + 2 L8 /3^{1/2} = +/- 1/2
G/6 - L8 +/- L3 = +/- 1/2
The 2 U(2) operators yield the 4 combinations of U(2) states in the
quadruplet
4 = (1,3) + (2,0) + (1,-3).
The 3 U(3) operators yield the 8 combinations of U(3) states in the
"color cube"
8 = (1,3) + (3,1) + (3*,-1) + (1,-3)
with (1,3) joining the spectrum as "white" and (1,-3) as "black".
All of these are the characteristic pattern of a Dirac spinor in the
Dirac algebra associated with SO(10,1). The algebra, itself, is
isomorphic to the algebra of 32x32 complex matrices.
That's the first punchline.
The second punchline comes about when revisiting the issue of parity.
Though the charge spectrum is not parity symmetric, the occurrence of
Y-R = I3R is clearly a right-handed analogue to SU(2)_I, suggesting
that there is an underlying SU(2)_I x SU(2)_X at work here.
But the funny thing is how parity enters the picture. The fermion
vacuum is associated with a local frame field that, itself, already has
an SO(3,1) = SU(2)_L x SU(2)_R symmetry.
When doing a parity reversal, the doublet (1,3),(1-3) exchanges with
(2,0), and one loses the form of the original field.
However, when the parity switch is combined with a SECOND partity
operator over SU(2)_I x SU(2)_X, then one regains the original charge
spectrum. However, the bosons have swapped.
This not only suggests that it's not the interaction that's
parity-violating, but the vacuum, itself; but that there is a
non-trivial intermixing of the local SO(3,1) group with the extended
"electroweak" SU(2)_I x SU(2)_X group.
If Coleman-Mandula is respected, this indicates that there is a
non-trivial factoring into the TRUE SO(3,1) and a second SO(3,1) (or
maybe SU(2)xSU(2)), but at a mixing angle from the one associated with
the SU(2)_I x SU(2)_X electroweak part and local frame SO(3,1) part.
In other words, the second punchline is that the unification that may
bring about the regularities described above involves the local
spacetime symmetry group in the mix.
The gauge part of gravity is mixed with the Yang-Mills field associated
with the electroweak force. |
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Uncle Al
science forum Guru
Joined: 24 Mar 2005
Posts: 1226
|
| Posted: Fri Jun 09, 2006 7:18 am Post subject:
Re: The Spectre Of Electroweak-Gravity Unification Within The Standard
|
|
|
markwh04@yahoo.com wrote:
| Quote: |
Igor wrote:
All we can really say at this point is that we have the Standard Model,
which consists of separate EM, weak, and strong gauge fields.
We have the clear spectre of more than that, superposed on the model.
A test charge moving in a Yang-Mills field will have a charge vector
that precesses over time, yet the square magnitude will remain
constant.
If this fails to occur at the microscopic level, one will see
fluctuations at the macroscopic level and a deviation from this law.
Therefore, one should expect that there be a quadratic invariant of
some sort in the fermion spectrum.
The most notable features of the Standard Model is that (1) it has
none, (2) it very nearly has 2.
Ironically, the missing element that comes to the rescue is a close
historical analogue of the very kind of "displacement current" that
charge conservation had originally motivated Maxwell to consider.
[big snip] |
| Quote: | The second punchline comes about when revisiting the issue of parity.
Though the charge spectrum is not parity symmetric, the occurrence of
Y-R = I3R is clearly a right-handed analogue to SU(2)_I, suggesting
that there is an underlying SU(2)_I x SU(2)_X at work here.
But the funny thing is how parity enters the picture. The fermion
vacuum is associated with a local frame field that, itself, already has
an SO(3,1) = SU(2)_L x SU(2)_R symmetry.
When doing a parity reversal, the doublet (1,3),(1-3) exchanges with
(2,0), and one loses the form of the original field.
However, when the parity switch is combined with a SECOND partity
operator over SU(2)_I x SU(2)_X, then one regains the original charge
spectrum. However, the bosons have swapped.
This not only suggests that it's not the interaction that's
parity-violating, but the vacuum, itself; but that there is a
non-trivial intermixing of the local SO(3,1) group with the extended
"electroweak" SU(2)_I x SU(2)_X group.
If Coleman-Mandula is respected, this indicates that there is a
non-trivial factoring into the TRUE SO(3,1) and a second SO(3,1) (or
maybe SU(2)xSU(2)), but at a mixing angle from the one associated with
the SU(2)_I x SU(2)_X electroweak part and local frame SO(3,1) part.
In other words, the second punchline is that the unification that may
bring about the regularities described above involves the local
spacetime symmetry group in the mix.
The gauge part of gravity is mixed with the Yang-Mills field associated
with the electroweak force.
|
Might one posit that parity asymmetry in the Weak Interaction then
would be coupled to parity asymmetry in gravitational interaction, a
chiral pseudoscalar vacuum background? If so, then testable
diastereotopic interactions with opposite parity (chiral along all
axes) masses obtain. One parity of test mass, a left shoe on a left
foot, should vacuum free fall along an unremarkable minimum action
trajectory. The opposite parity test mass, a right shoe on a left
foot, should also vacuum free fall along a minimum action trajectory -
but NOT parallel to the prior one.
It's a simple test in existing apparatus opposing enantiomorphic space
group P3(1)21 and P3(2)21 quartz single crystal solid sphere (no
directional bias) test masses. Somebody should peform the parity
Eotvos experiment.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz3.pdf |
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