[SOLVED] Einstien's principle of equivalence [Archive]

Oh No

Dec7-06, 05:00 AM

Thus spake Cyberkatru <perapera77@yahoo.com>
>Einsteins principle of equivalence, as usually explained, seems strange (to
>me) from the point of view of (pseudo) Riemannian geometry.
>As explained in some relativity texts, the principle states roughly that
>there is no (local) physical difference between effects due to an
>accelerating frame and effects due to a gravitational field. However,
>choosing an accelerating frame seems like just a certain choice of
>curvilinear spacetime coordinates. But isn't gravity supposed to be
>curvature due to a metric tensor? But whether a Lorentz manifold has zero
>curvature or not certainly doesn't depend on a choice of coordinates. How
>can I produce curvature on a flat spacetime just by a choice of chart? I
>can't! The whole thing seems especially weird since metric and curvature are
>defined as geometric objects with an existence that doesn't even need a
>chart at all to make sense.
>So I don't see what the equivalence principle could really amount to.
>What am I missing?

The force of gravity as a linear force in a local reference frame is
indeed simply a choice of coordinates. But gravity itself is not so
straightforward. For example, the gravity around the Earth cannot be
modelled as equivalent to a linear acceleration. The effect of curvature
is that, when you bolt together a lot of small local reference frames in
each of which gravity is linear, the net result is no longer linear.
>
>The principle of general covariance is also a problem for me. Does it amount
>to anything more than the statement that the laws of gravitational physics
>can be expressed in terms of tensor fields?

No. That is it.

>It seems to me that, all sorts
>of ad hoc laws could be expressed in this way. In fact, if spacetime had
>trivial topology then one chart would do and any law written in that chart
>could just be expressed in any other chart by brute force anplication of
>tensor trnasformation laws. In this case the idea of general covariance
>starts to seem empty.
>What am I missing?
>
To get an idea of the meaning of this law it is quite good to think of
electromagnetism. By calling on the principle of general covariance you
can simply write down a tensorial law for the force acting on a current

Force^i = F^ij(x) J_j(x)

Where J is the 4-current. Don't quote me on where the minus signs go,
because I'm doing this from memory and there is little chance I will get
them right, but in essence it is not hard to see that with the tensor

F^ij = (0 Ex Ey Ez)
(-Ex 0 -Bz -By)
(-Ey Bz 0 -Bx)
(-Ez By Bx 0)

this give you electric and magnetic forces. You can do stuff like, start
with a pure electric field

F^ij = (0 Ex Ey Ez)
(-Ex 0 0 0)
(-Ey 0 0 0)
(-Ez 0 0 0)

Do a lorentz transformation, and bingo, you have shown that a magnetic
field is just an electric field from the point of view of a moving
observer.

Likewise, it is fairly straightforward to show that Maxwell's equations
take a very simple form when expressed in terms of the Faraday tensor,
F^ij.

Regards

--
Charles Francis
substitute charles for NotI to email

Igor

Dec7-06, 05:00 AM

Igor Khavkine

Dec7-06, 06:57 PM

Cyberkatru wrote:
> Einsteins principle of equivalence, as usually explained, seems strange (to
> me) from the point of view of (pseudo) Riemannian geometry.
> As explained in some relativity texts, the principle states roughly that
> there is no (local) physical difference between effects due to an
> accelerating frame and effects due to a gravitational field. However,
> choosing an accelerating frame seems like just a certain choice of
> curvilinear spacetime coordinates. But isn't gravity supposed to be
> curvature due to a metric tensor? But whether a Lorentz manifold has zero
> curvature or not certainly doesn't depend on a choice of coordinates. How
> can I produce curvature on a flat spacetime just by a choice of chart? I
> can't! The whole thing seems especially weird since metric and curvature are
> defined as geometric objects with an existence that doesn't even need a
> chart at all to make sense.
> So I don't see what the equivalence principle could really amount to.
> What am I missing?

As usually sated, the Equivalence Principle (EP) states that a
*constant* gravitational field is equivalent to uniform acceleration.
So, effects of gravity can be removed by a coordinate transformation
only as far as the gravitational field can be approximated to be
constant. This is entirely consistent with the well known mathematical
fact that at any point x on a (pseudo-)Riemannian manifold, there
exists a coordinate system in which the Christoffel symbols are zero at
x, since it is the Christoffel symbol components that correspond to the
gravitational force field. Curvature makes an appearance only when
derivatives of the Christoffel symbols are evaluated, which is
completely consistent with the EP.

> The principle of general covariance is also a problem for me. Does it amount
> to anything more than the statement that the laws of gravitational physics
> can be expressed in terms of tensor fields?

Rather more strongly, must be expressible in terms of tensor fields.

> It seems to me that, all sorts
> of ad hoc laws could be expressed in this way. In fact, if spacetime had
> trivial topology then one chart would do and any law written in that chart
> could just be expressed in any other chart by brute force anplication of
> tensor trnasformation laws. In this case the idea of general covariance
> starts to seem empty.
> What am I missing?

To see importance of general covariance, you have to look at how it is
used. And the fact is that in practice it is used not as a guiding
principle, but as an algorithm. It is an algorithm for deducing the
form of physical laws in any coordinate system. Suppose that there is a
preferred reference frame or coordinate system where a physical law is
easy to express, say the rest frame of a given system. Knowing that the
same law is expressible in terms of tensors, one makes a guess at the
tensor form and verifies that it reproduces the correct expression in
the preferred coordinate system (if not, one keeps guessing). Once in
tensor form, this law easily lends itself to expression in an arbitrary
coordinate system. With practice, even the guessing stage can be
automated. Thus, for example, knowing Maxwell's equations in an
inertial frame is easily translated to tensor notation and from there
to any other coordinate system.

Hope this helps.

Igor

carlip-nospam@physics.ucdavis.edu

Dec7-06, 06:57 PM

Cyberkatru <perapera77@yahoo.com> wrote:

> The principle of general covariance is also a problem for me.
> Does it amount to anything more than the statement that the
> laws of gravitational physics can be expressed in terms of
> tensor fields? It seems to me that, all sorts of ad hoc laws
> could be expressed in this way. In fact, if spacetime had
> trivial topology then one chart would do and any law written
> in that chart could just be expressed in any other chart by
> brute force anplication of tensor trnasformation laws. In
> this case the idea of general covariance starts to seem empty.

The argument over whether general covariance has any physical
content goes back at least to 1917, when Erich Kretschmann wrote
a paper making essentially the same argument you are presenting.
One standard answer, which I find convincing, is that general
covariance should be supplemented with the requirement that
there should be no preferred "background" structure.

For example, suppose you have a trivial topology. Then, as you
say, you can take any law in a chosen coordinate system and
declare it to be tensorial. But in doing so, you've chosen a
background structure, namely the coordinate system you started
with; the "invariant" form of the law will have to refer back
to some extra functions, the original coordinates, that have
no independent physical significance.

(For example, suppose you have a "law" that the time component
V_0 of some vector is zero in a chosen coordinate system. You
can make this covariant by defining a new vector u^a such that
u^a=(1,0,0,0) in your chosen coordinates; then V_a u^a=0 is a
nice tensorial law. But it depends on the new "background" field
u^a, which is now a fixed, nondynamical object.)

There's a nice discussion of this kind of issue in an old book
by Anderson, _Principles of Relativity Physics_, which is worth
reading. There are also some nice links in the Wikipedia page
on Kretschmann, http://en.wikipedia.org/wiki/Erich_Kretschmann.

Steve Carlip

Tom Roberts

Dec8-06, 05:00 AM

carlip-nospam@physics.ucdavis.edu wrote:
> The argument over whether general covariance has any physical
> content goes back at least to 1917, [...]

IMHO the requirement on physical theories is not really "general
covariance with no background structure", but rather that models of
physical quantities must be independent of coordinates. After all,
natural phenomena quite clearly proceed without benefit of coordinates,
which are, after all, purely a product of human imaginations. Since the
actual phenomena are independent of coordinates, valid models of them
must be also.

It is rather difficult to formulate the notion that there be no
"background structures" -- after all, in GR we do impose the "background
structure" that the manifold be Lorentzian [#][@]. And in GR there is
the puzzle that while the equations of the theory determine the metric
on the manifold, they do not determine its topology....

[#] Yes, this is at a lower level than an a priori metric,
which is usually how the "no background structures" is
applied. But that prohibition seems far more general than
applying just to metrics. IMHO string/brane/M-theory is
an improvement in this respect, because in some sense it is
working in an arbitrary-dimension manifold, and then using
cancellation of anomalies to restrict the dimensionality....

[@] Of course an appeal to our observations of the world
is valid for a physical theory, and yields a Lorentzian
manifold. At least approximately -- while I think that
Helmholtz's original argument about the Riemannian nature
of space is valid, I'm not wholly convinced about the
necessity of it holding for spacetime (though theories
based on that assumption work exceedingly well)....

The above requirement can clearly be met by expressing all physical
quantities as tensors, and all physical theories as equations among
them. Indeed the modern version of GR is a prime example of this. But it
leaves open the tantalizing question: are there other formulations of
physical theories that meet this requirement?

Tom Roberts

Uncle Al

Dec9-06, 05:00 AM

Cyberkatru wrote:
>
> Einsteins principle of equivalence, as usually explained, seems strange (to
> me) from the point of view of (pseudo) Riemannian geometry.
> As explained in some relativity texts, the principle states roughly that
> there is no (local) physical difference between effects due to an
> accelerating frame and effects due to a gravitational field. However,
> choosing an accelerating frame seems like just a certain choice of
> curvilinear spacetime coordinates. But isn't gravity supposed to be
> curvature due to a metric tensor? But whether a Lorentz manifold has zero
> curvature or not certainly doesn't depend on a choice of coordinates. How
> can I produce curvature on a flat spacetime just by a choice of chart? I
> can't! The whole thing seems especially weird since metric and curvature are
> defined as geometric objects with an existence that doesn't even need a
> chart at all to make sense.
> So I don't see what the equivalence principle could really amount to.
> What am I missing?
[snip]

Einstein-Cartan theory operates in Riemann-Cartan spacetime U^4 - a
paracompact, Hausdorff, connected, C^(infinity), and oriented
four-dimensional manifold on which are defined a local Lorentz metric
"g" and a linear affine connection "Gamma." Curvature and torsion
tensors can be obtained from "Gamma" on U^4:

1. If the torsion tensor vanishes, Riemann-Cartan spacetime becomes
pseudo-Riemannian spacetime, V^4 (General Relativity's description of
gravitation) with spacetime curvature;
2. If the curvature tensor vanishes, it becomes Weitzenböck
spacetime, A^4 (in which the teleparallel gravitational
energy-momentum pseudotensor is anti-symmetric to parity
transformation) with spacetime torsion;
3. If both tensors vanish, it becomes Minkowski spacetime, M^4.

If you do not like spacetime curvature, use spacetime torsion. Affine
and teleparallel gravitation provide all of General Relativity
(Equivalence Principle postulated) plus examples of Equivalence
Principle violation by angular momenta: Physically spinning, quantum
spin, and opposite geometric parity bodies. The first two are
demonstrated in theory and by observation (binary pulsars and Gravity
Probe-B; zero external field paramagnet and Adelberger's ferromagnet
torsion balance experiments) to be well below detection limits if they
exist at all. The third would be a 9% differential signal in a parity
calorimetry experiment if there were a corresponding 10^(-13)
difference/average net signal in a parity Eotvos experiment. We
expect to get some numbers for geometric parity destruction by melting
in contrasted opposite parity P3(1)21 vs. P3(2)21 benzil single
crystal /_\H(fusion) in January 2007.

Then, we will know.

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

Ilja Schmelzer

Dec9-06, 05:00 AM

"Cyberkatru" <perapera77@yahoo.com> schrieb
> Einsteins principle of equivalence, as usually explained, seems strange
(to
> me) from the point of view of (pseudo) Riemannian geometry.
> As explained in some relativity texts, the principle states roughly that
> there is no (local) physical difference between effects due to an
> accelerating frame and effects due to a gravitational field. However,
> choosing an accelerating frame seems like just a certain choice of
> curvilinear spacetime coordinates. But isn't gravity supposed to be
> curvature due to a metric tensor? But whether a Lorentz manifold has zero
> curvature or not certainly doesn't depend on a choice of coordinates.

Correct. It holds only in a weak, local sense, where effects of
curvature may be ignored.

> So I don't see what the equivalence principle could really amount to.

It is the condition that the theory of gravity should be a metric theory.
IOW, that the matter Lagrangian should be covariant.

> The principle of general covariance is also a problem for me. Does it
amount
> to anything more than the statement that the laws of gravitational physics
> can be expressed in terms of tensor fields? It seems to me that, all sorts
> of ad hoc laws could be expressed in this way.

Indeed. This has been critizised by Kretschmann and acknowledged by
Einstein a few years after publication of GR (1917?). A way to describe,
for example, Newtonian mechanics in a covariant way can be found in
MTW.

> In this case the idea of general covariance starts to seem empty.
> What am I missing?

Nothing. Covariance is only a form of presentation of a theory.
What remains is that in this particular form GR looks easier in
comparison with other theories like NM.

Ilja

cyberkatru@gmail.com

Dec9-06, 05:00 AM

You said
>To get an idea of the meaning of this law it is quite good to think of
> electromagnetism. By calling on the principle of general covariance you
> can simply write down a tensorial law for the force acting on a current
>
> Force^i = F^ij(x) J_j(x)
>
> Where J is the 4-current. Don't quote me on where the minus signs go,
> because I'm doing this from memory and there is little chance I will get
> them right, but in essence it is not hard to see that with the tensor
>
> F^ij = (0 Ex Ey Ez)
> (-Ex 0 -Bz -By)
> (-Ey Bz 0 -Bx)
> (-Ez By Bx 0)
>

But that is not really general covariance because you are restricted to
Lortents frames and Lorents transformations.

HallsofIvy

Dec9-06, 05:00 AM

There is no deep PHYSICAL significance to covariance- it doesn't "give"
physical laws- but is has enormous significance for how you can write
equations representing those physical laws. The basic idea is that
"physical laws" are *given* by nature (or phyics if you will) while
coordinate systems are made up by us and are not "natural". Therefore
all physical quantities have to be independent of the particular
coordinate system we happen to use- the same equation should work in
any coordinate system. In simpler physics we can do that by using
vectors- the "components" of a vector may be different in different
coordinate systems but the vector itself is not: The equations
Fx= max[sub] , F[sub]y= may may work
in one coordinate system but not another (polar coordinates for
example) but if the vector equation F= ma is true in coordinate system,
it is true any any.
In more complicated physics, general relativity or even just
classical theory of strains and stresses in deformable bodies, vectors
aren't sufficient and we need tensors.

--
HallsofIvy

"Euclid alone has looked on beauty bare"
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dextercioby

Dec9-06, 05:00 AM

Cyberkatru;1181152 Wrote:
> Einsteins principle of equivalence, as usually explained, seems strange
> (to
> me) from the point of view of (pseudo) Riemannian geometry.
> As explained in some relativity texts, the principle states roughly
> that
> there is no (local) physical difference between effects due to an
> accelerating frame and effects due to a gravitational field. However,
> choosing an accelerating frame seems like just a certain choice of
> curvilinear spacetime coordinates. But isn't gravity supposed to be
> curvature due to a metric tensor? But whether a Lorentz manifold has
> zero
> curvature or not certainly doesn't depend on a choice of coordinates.
> How
> can I produce curvature on a flat spacetime just by a choice of chart?
> I
> can't! The whole thing seems especially weird since metric and
> curvature are
> defined as geometric objects with an existence that doesn't even need
> a
> chart at all to make sense.
> So I don't see what the equivalence principle could really amount to.
> What am I missing?

How did you get those ideas ?

Cyberkatru;1181152 Wrote:
> The principle of general covariance is also a problem for me. Does it
> amount
> to anything more than the statement that the laws of gravitational
> physics
> can be expressed in terms of tensor fields?

Spinorial tensors to be more exact. See chapter 13 from R. Wald's GR
text.

Cyberkatru;1181152 Wrote:
> In fact, if spacetime had
> trivial topology then one chart would do and any law written in that
> chart
> could just be expressed in any other chart by brute force anplication
> of
> tensor trnasformation laws. In this case the idea of general
> covariance
> starts to seem empty.
>

What exact do you mean by that ?

Daniel.

--
dextercioby

\"Nothing is more practical than a good theory\"

* Kurt Lewin *.

\"Theoretical physics is a science locally isomorphic to mathematics\"

* Unknown *
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Hans Aberg

Dec9-06, 05:00 AM

In article <ZguRc9Y19fdFFwWb@charlesfrancis.wanadoo.co.uk>, Oh No
<NotI@charlesfrancis.wanadoo.co.uk> wrote:

> >The principle of general covariance is also a problem for me. Does it amount
> >to anything more than the statement that the laws of gravitational physics
> >can be expressed in terms of tensor fields?
>
> No. That is it.

No, this is wrong. Covariance is an action principle, in math, an
invariance. In the spin, covariance forces equal amounts of spin and
anti-spin. By contrast, coordinate dependence, "expressing spin as
tensors", admits any spin. Covariance and invariance*transforms with
inverses relative to each other in the Dirac equation.

I view covariance as a change-observer principle. This form may then be
fit into GR. Otherwise, covariance forces (at least in the case of a
positive definite metric) conditions on the curvature, which would not
work well with GR, as the curvature*communicates*gravitation.

--
Hans Aberg

Hans Aberg

Dec9-06, 05:00 AM

In article <1165470519.941369.314830@80g2000cwy.googlegroups.c om>, Igor
Khavkine <igor.kh@gmail.com> wrote:

> As usually sated, the Equivalence Principle (EP) states that a
> *constant* gravitational field is equivalent to uniform acceleration.

I thought it just was the equivalence between inertial and gravitational
mass. That is, if one measures these of an object, they turn out to be the
same. Then one can construct physical*theories having this property built
in. There is an article:
* http://en.wikipedia.org/wiki/Equivalence_principle

--
Hans Aberg

Igor Khavkine

Dec10-06, 05:00 AM

Hans Aberg wrote:
> In article <1165470519.941369.314830@80g2000cwy.googlegroups.c om>, Igor
> Khavkine <igor.kh@gmail.com> wrote:
>
> > As usually sated, the Equivalence Principle (EP) states that a
> > *constant* gravitational field is equivalent to uniform acceleration.
>
> I thought it just was the equivalence between inertial and gravitational
> mass. That is, if one measures these of an object, they turn out to be the
> same. Then one can construct physical theories having this property built
> in. There is an article:
> http://en.wikipedia.org/wiki/Equivalence_principle

The two statements are basically equivalent. A particle's equation of
motion in a constant gravitational field is m a = q g, where m -
inertial mass, a - acceleration, g - gravitational force, q -
gravitational "charge". A priori, q need not have any relation to m,
after all electric charge doesn't. To remove such a constant force, we
can introduce an acceleration A = - (m/q) g. Then the equation of
motion becomes just m (a + A) = 0. However, if there is more than one
particle in the picture and these particles have different masses and
charges, m_i and q_i for particle i, then the *same* A can be used to
remove the gravitational force for *all* the particles only if
(m_i/q_i) is the same for all i. That is, if we have the
proportionality m_i ~ q_i, or, choosing the right units and making the
proportionality constant 1, the equality m_i = q_i.

Thus the equivalence principle in the above form is equivalent to the
statement that q_i = m_i, or that inertial mass is the same as
gravitational mass/charge.

Igor

Oh No

Dec11-06, 05:00 AM

Thus spake cyberkatru@gmail.com
>You said
>>To get an idea of the meaning of this law it is quite good to think of
>> electromagnetism. By calling on the principle of general covariance you
>> can simply write down a tensorial law for the force acting on a current
>>
>> Force^i = F^ij(x) J_j(x)
>>
>> Where J is the 4-current. Don't quote me on where the minus signs go,
>> because I'm doing this from memory and there is little chance I will get
>> them right, but in essence it is not hard to see that with the tensor
>>
>> F^ij = (0 Ex Ey Ez)
>> (-Ex 0 -Bz -By)
>> (-Ey Bz 0 -Bx)
>> (-Ez By Bx 0)
>>
>
>But that is not really general covariance because you are restricted to
>Lortents frames and Lorents transformations.
>

That's right. In general relativity the manifold is Lorentzian.
Essentially that means it is locally Minkowski at any point, and Lorentz
transformation can be used at any point. Tensors are defined at a point,
so as to obey Lorentz transformation, so the principle of general
covariance that laws of physics can be expressed in tensorial form
basically makes a statement that local laws locally obey Lorentz
transformation.

In addition a connection has to be defined which, together with the
metric, gives the manifold its geometrical properties. The connection in
general relativity is affine, meaning that it is defined between points
in the limit as the distance between points goes to zero. This is what
we mean by saying that general relativity is a local theory.

Regards

--
Charles Francis
substitute charles for NotI to email

Hans Aberg

Dec11-06, 05:00 AM

In article <1165693896.661239.188910@l12g2000cwl.googlegroups. com>, Igor
Khavkine <igor.kh@gmail.com> wrote:

> > > As usually sated, the Equivalence Principle (EP) states that a
> > > *constant* gravitational field is equivalent to uniform acceleration.
> >
> > I thought it just was the equivalence between inertial and gravitational
> > mass. That is, if one measures these of an object, they turn out to be the
> > same. Then one can construct physical theories having this property built
> > in. There is an article:
> > http://en.wikipedia.org/wiki/Equivalence_principle
>
> The two statements are basically equivalent. A particle's equation of
> motion in a constant gravitational field is m a = q g, where m -
> inertial mass, a - acceleration, g - gravitational force, q -
> gravitational "charge". A priori, q need not have any relation to m,
> after all electric charge doesn't. To remove such a constant force, we
> can introduce an acceleration A = - (m/q) g. Then the equation of
> motion becomes just m (a + A) = 0.

No, because you put in an assumptions about constant graviatational
fields, whereas the formulation a I gave does not have any such
assumptions: it is valid without any theory. For example, intertial frames
do not exist in GR in a fmoral mathemactial manner.

The form I gave is not "Einstein's principle of equivalence", but the
princile of the equivalence between inertial and gravitational mass. It
was well known long before Einstein. In fact, Einstein wanted to cmobine
this principle with SR, and was led to do this via the curvature of a
Lorentz manidold, which some intutively led to his constrction of GR.
(Hilbert did this via metric varition principle.)

--
Hans Aberg

Daryl McCullough

Dec11-06, 05:00 AM

Tom Roberts says...

>It is rather difficult to formulate the notion that there be no
>"background structures" -- after all, in GR we do impose the "background
>structure" that the manifold be Lorentzian [#][@]. And in GR there is
>the puzzle that while the equations of the theory determine the metric
>on the manifold, they do not determine its topology....

A limited version of "no background structure" is this: There are no
non-dynamic vector or tensor fields, and there are no non-dynamic,
nonconstant scalar fields. Special Relativity has a tensor field,
g_uv, which is non-dynamic. Newtonian physics has a nonconstant
scalar field, universal time, which is non-dynamic. In contrast,
General Relativity has no nondynamic scalar, vector or tensor fields.

--
Daryl McCullough
Ithaca, NY

Hendrik van Hees

Dec11-06, 05:00 AM

Igor Khavkine wrote:

> The two statements are basically equivalent. A particle's equation of
> motion in a constant gravitational field is m a = q g, where m -
> inertial mass, a - acceleration, g - gravitational force, q -
> gravitational "charge". A priori, q need not have any relation to m,
> after all electric charge doesn't. To remove such a constant force, we
> can introduce an acceleration A = - (m/q) g. Then the equation of
> motion becomes just m (a + A) = 0. However, if there is more than one
> particle in the picture and these particles have different masses and
> charges, m_i and q_i for particle i, then the *same* A can be used to
> remove the gravitational force for *all* the particles only if
> (m_i/q_i) is the same for all i. That is, if we have the
> proportionality m_i ~ q_i, or, choosing the right units and making the
> proportionality constant 1, the equality m_i = q_i.
>
> Thus the equivalence principle in the above form is equivalent to the
> statement that q_i = m_i, or that inertial mass is the same as
> gravitational mass/charge.

That's a nice argument, but I think it is a little bit misleading. The
General Theory of Relativity (GRT) can be described as any
relativistical field theory: Assuming the weak equivalence principle as
explained in the cited Wikipedia article one can show that the most
simple field describing such an interaction is a massless spin-2 field,
the gravitational field, g_{mu nu}, which must (at least minimaly)
couple to the energy-momentum tensor describing freely falling test
particles. Thus, it is not the mass to which the gravitational field
couples but the energy-momentum density of the test particles.

The assumption of the strong equivalence principle implies that this
holds also for the energy of the gravitational field, and the resulting
self-interaction of the gravitational fields gives the whole construct
the structure of a non-abelian gauge theory implying the universality
of the coupling constant. The gauge group is the local GL(4) of the
space-time coordinates (what Einstein called "general covariance" which
gave the whole theory the name "General Theory of Relativity").

This structure of a gauge theory allows the gravitational field to be
reinterpreted as the fundamental form of a pseudo-Riemannian spacetime
which was the historical starting point in Einstein's derivation of the
GTR.

It is important to realise that mass is not the "charge of gravity" but
Casimir operators of the (local) Poincare symmetry, i.e., the statement
that in each point of spacetime it is always possible to introduce a
local inertial reference frame where the laws of special relativity are
valid.

Only in the non-relativistic limit where the mass terms in the
energy-momentum tensor are dominant compared to the kinetic energy of
the particles (or fields) an interpretation of mass as "charge of
gravitation" makes sense.

--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/faq mailto:hees@comp.tamu.edu

Gerry Quinn

Dec13-06, 05:00 AM

In article <LvNeh.425$oS1.353@newsfe20.lga>, hees@comp.tamu.edu says...

> It is important to realise that mass is not the "charge of gravity" but
> Casimir operators of the (local) Poincare symmetry, i.e., the statement
> that in each point of spacetime it is always possible to introduce a
> local inertial reference frame where the laws of special relativity are
> valid.
>
> Only in the non-relativistic limit where the mass terms in the
> energy-momentum tensor are dominant compared to the kinetic energy of
> the particles (or fields) an interpretation of mass as "charge of
> gravitation" makes sense.

What seems more interesting is to forget about mass and think in terms
only of energy. By the principle of equivalence (simple version) any
mass could be replaced by a massless box with mirrors on the inside,
filled with a suitable quantity of electromagnetic radiation, and it
would act gravitationally just like the original mass.

You could even replace any mass with a pair of mirrors in which the
radiation passes back and forth in one particular direction (the
mirrors must of course be physically linked so they do not fly apart.

This means a typical gravitational interaction can be reduced to a very
simple system whose interaction should be identical with the original.
For example:

M <---------> M

M <---------> M

(two sets of photons bouncing between pairs of linked mirrors)

...should behave like two point masses as the distance between each pair
of mirrors is reduced to zero. And the same if one or both systems is
rotated by ninety degrees.

It seems like a good starting point for thinking about field
interpretations of gravity. But I think it may also form the basis of
a half-way sensible beginners' answer to the question of why matter
falls towards a star around which spacetime is curved.

The assumption in popular explanations tends to be that curved
spacetime is too complicated a concept, but curved space can be
comprehended by readers. Curved space explains light-bending quite
naturally, but when the awkward question of why a mass falls towards a
star is introduced, it is either ignored or answered in a completely
nonsensical fashion involving a pseudo-gravitational force applying to
objects moving on a rubber sheet.

If matter is thought of as a sealed box of energy, we can easily see
how the bending and/or red-shift of photons bouncing within it leads to
a force in the direction of the star.

I don't say it's a great explanation, and relativity purists won't like
it, but surely it's better than what tends to be given?

- Gerry Quinn

Chalky

Dec14-06, 05:00 AM

Hans Aberg wrote:

> In article <1165470519.941369.314830@80g2000cwy.googlegroups.c om>, Igor
> Khavkine <igor.kh@gmail.com> wrote:
>
> > As usually sated, the Equivalence Principle (EP) states that a
> > *constant* gravitational field is equivalent to uniform acceleration.
>
> I thought it just was the equivalence between inertial and gravitational
> mass. That is, if one measures these of an object, they turn out to be the
> same. Then one can construct physical theories having this property built
> in.

Quite so. What most people have referred to as the Equivalence
Principle here is, in fact, Einstein's General Postulate of Relativity
(as distinguished from his General Principle of Relativity) and is
defined as such by Einstein in his popular exposition. The title of the
relevant chapter (XX) is: The Equality of Inertial and Gravitational
Mass as an _Argument for_ the General Postulate of Relativity.

Unfortunately, confusion of these two terms seems to have become
ubiquitous in the writings of subsequent authors on relativity theory.
If I recall correctly, Stephen Wienberg even says (in Gravitation and
Cosmology) that he is not sure whether Einstein could make a clear
distinction in his mind between the General Principle and the
Equivalence Principle (by which Wienberg meant the General Postulate).
I find that statement remarkable since both distinctions are clear to
me from the reading of Einstein's own popular exposition.

Chalky

Hans Aberg

Dec14-06, 05:00 AM

In article <1166037763.240052.267340@73g2000cwn.googlegroups.c om>, Chalky
<chalkyspam@bleachboys.co.uk> wrote:

> > > As usually sated, the Equivalence Principle (EP) states that a
> > > *constant* gravitational field is equivalent to uniform acceleration.
> >
> > I thought it just was the equivalence between inertial and gravitational
> > mass. That is, if one measures these of an object, they turn out to be the
> > same. Then one can construct physical theories having this property built
> > in.
>
> Quite so. What most people have referred to as the Equivalence
> Principle here is, in fact, Einstein's General Postulate of Relativity
> (as distinguished from his General Principle of Relativity) and is
> defined as such by Einstein in his popular exposition. The title of the
> relevant chapter (XX) is: The Equality of Inertial and Gravitational
> Mass as an _Argument for_ the General Postulate of Relativity.

I find your quote interesting, because the wording makes it clear that he
is aware of that he does not present a formal deduction, but uses it as an
argument to intuitively construct a theory with the desired properties. In
general, with curvature present, inertial frames, which I take it is the
same as a "constant* gravitational field" do not in general exits locally,
but only infinitesimally (at the stalk). So it is not possible from this
form you say is named the General Postulate of Relativity to deduct GR.

> Unfortunately, confusion of these two terms seems to have become
> ubiquitous in the writings of subsequent authors on relativity theory.
> If I recall correctly, Stephen Wienberg even says (in Gravitation and
> Cosmology) that he is not sure whether Einstein could make a clear
> distinction in his mind between the General Principle and the
> Equivalence Principle (by which Wienberg meant the General Postulate).
> I find that statement remarkable since both distinctions are clear to
> me from the reading of Einstein's own popular exposition.

Yes, there seem to be claims that Einstein did not know what he did; I
have heard some different variations on the theme: but that seems to not
be true. :-)

--
Hans Aberg

cosmopot

Dec14-06, 09:49 AM

Cyberkatru wrote:
> Einsteins principle of equivalence, as usually explained, seems strange (to
> me) from the point of view of (pseudo) Riemannian geometry.
> As explained in some relativity texts, the principle states roughly that
> there is no (local) physical difference between effects due to an
> accelerating frame and effects due to a gravitational field. However,
> choosing an accelerating frame seems like just a certain choice of
> curvilinear spacetime coordinates. But isn't gravity supposed to be
> curvature due to a metric tensor? But whether a Lorentz manifold has zero
> curvature or not certainly doesn't depend on a choice of coordinates. How
> can I produce curvature on a flat spacetime just by a choice of chart? I
> can't! The whole thing seems especially weird since metric and curvature are
> defined as geometric objects with an existence that doesn't even need a
> chart at all to make sense.
> So I don't see what the equivalence principle could really amount to.
> What am I missing?

As usually sated, the Equivalence Principle (EP) states that a
*constant* gravitational field is equivalent to uniform acceleration.
So, effects of gravity can be removed by a coordinate transformation
only as far as the gravitational field can be approximated to be
constant. This is entirely consistent with the well known mathematical
fact that at any point x on a (pseudo-)Riemannian manifold, there
exists a coordinate system in which the Christoffel symbols are zero at
x, since it is the Christoffel symbol components that correspond to the
gravitational force field. Curvature makes an appearance only when
derivatives of the Christoffel symbols are evaluated, which is
completely consistent with the EP.

Igor

The comments are smart ones but commit to the simple mistake: consider curvilinear coordinates as flat-spacetime rectangular coordinates which have the direct meaning of distance and time.
However, only when spacetime is flat does there exist one coordinate system which has direct meaning of time, distance, angle, and vice verse. This is the famous Riemann theorem.

You have *constant* gravitational field and, therefore, you have non-linear coordinate transformation between the two coordinate system you know what they mean. The serious problem is that, which coordinate system has direct meaning of distance. People always choose the non-freely-falling earth coordinate system and all experiments did confirm the same coordinate system to have the direct meaning of distance, time. According to curved spacetime, however, the coordinate system used by the freely falling people have the direct meaning of distance, time!

It is amazing that, over 90 yrs, people when confronting GR to observational data, calculate time, distance, or angle by directly using the coordinates in Schwarzschild solution or in post Newtonian formulation, or in gravitational radiation. They never realized that the practice contradicts the assumption of curved spacetime.

Honestly say, people in fact never know how to calculate distance and time and angle in curved spacetime!

Tom Roberts

Dec15-06, 05:00 AM

Daryl McCullough wrote:
> Tom Roberts says...
>> It is rather difficult to formulate the notion that there be no
>> "background structures" -- after all, in GR we do impose the "background
>> structure" that the manifold be Lorentzian [#][@]. And in GR there is
>> the puzzle that while the equations of the theory determine the metric
>> on the manifold, they do not determine its topology....
>
> A limited version of "no background structure" is this: There are no
> non-dynamic vector or tensor fields, and there are no non-dynamic,
> nonconstant scalar fields.

Sure. But the usual statement of "no background structure" seems to me
to be far more general than that, and all of our current theories
violate the more general statement, as we do impose a non-dynamic
"background" structure by restricting ourselves to Lorentzian manifolds.

Yes, using tensors addresses the primary issue. But to me the
tantalizing question is: are there other formulations of physical
theories that meet this requirement?

In particular: current notions about quantum gravity imply that beyond
the Planck scale the whole notion of a continuous manifold may well be
invalid -- how can we model that, in a way consistent with current
observations?

Tom Roberts

Igor Khavkine

Dec15-06, 05:00 AM

> > > Igor Khavkine wrote:
> > > > As usually sated, the Equivalence Principle (EP) states that a
> > > > *constant* gravitational field is equivalent to uniform acceleration.

> > Hans Aberg wrote:
> > > I thought it just was the equivalence between inertial and gravitational
> > > mass.

> In article <1165693896.661239.188910@l12g2000cwl.googlegroups. com>, Igor
> Khavkine <igor.kh@gmail.com> wrote:
> > The two statements are basically equivalent. [...snip demonstration...]

Hans Aberg wrote:
> No, because you put in an assumptions about constant graviatational
> fields, whereas the formulation a I gave does not have any such
> assumptions: it is valid without any theory. For example, intertial frames
> do not exist in GR in a fmoral mathemactial manner.

I'm not sure what you are objecting to. Both statements, equivalence of
inertial and gravitational masses and equivalence of uniform
acceleration and uniform gravity, are local in character. That is, we
can apply them in a neighborhood of a point where the gravitational
field can be approximated as constant. In such a situation it is easy
to show how one statement follows from the other, as I did in my
previous post, and vice versa. There is no need to talk of inertial
frames, adding an acceleration is a well defined local coordinate
transformation.

> The form I gave is not "Einstein's principle of equivalence", but the
> princile of the equivalence between inertial and gravitational mass.

Oddly enough, a few paragraphs up you offered the equivalence of
inertial and gravitational masses as a statement of the Equivalence
Principle. Perhaps I misunderstood what you were trying to say.

Note that I did not qualify the term Equivalence Principle with an
adjective, such as weak, strong or Einstein's. I simply gave the
version that's most often seen in textbooks. If you're trying to be
more precise, you may want to suitable qualify what you mean by the EP.

Igor

Ilja Schmelzer

Dec15-06, 05:00 AM

<carlip-nospam@physics.ucdavis.edu> schrieb
> For example, suppose you have a trivial topology. Then, as you
> say, you can take any law in a chosen coordinate system and
> declare it to be tensorial. But in doing so, you've chosen a
> background structure, namely the coordinate system you started
> with; the "invariant" form of the law will have to refer back
> to some extra functions, the original coordinates, that have
> no independent physical significance.
>
> (For example, suppose you have a "law" that the time component
> V_0 of some vector is zero in a chosen coordinate system. You
> can make this covariant by defining a new vector u^a such that
> u^a=(1,0,0,0) in your chosen coordinates; then V_a u^a=0 is a
> nice tensorial law. But it depends on the new "background" field
> u^a, which is now a fixed, nondynamical object.)

The question appears how to distinguish the "nondynamical" objects
from "dynamical" objects.

For example, in the non-covariant theory
L = eta_ab g^mn X^a_,m X^b_,n sqrt(-g) + L_cov
the X^a are the chosen preferred coordinates. But we obtain
(as the Euler-Lagrange equation) a nice dynamical equation
for them - the harmonic equation.

AFAIU, the only difference between preferred coordinates
and dynamical fields in this situation are global restrictions
on the allowed solutions (the X^a have to define a valid
system of global coordinates). But it is not a property
of having a dynamical equation.

Ilja

Thomas Johnson

Dec16-06, 05:00 AM

Uncle Al wrote:

> If you do not like spacetime curvature, use spacetime torsion. Affine
> and teleparallel gravitation provide all of General Relativity
> (Equivalence Principle postulated) plus examples of Equivalence
> Principle violation by angular momenta: Physically spinning, quantum
> spin, and opposite geometric parity bodies. The first two are
> demonstrated in theory and by observation (binary pulsars and Gravity
> Probe-B; zero external field paramagnet and Adelberger's ferromagnet
> torsion balance experiments) to be well below detection limits if they
> exist at all. The third would be a 9% differential signal in a parity
> calorimetry experiment if there were a corresponding 10^(-13)
> difference/average net signal in a parity Eotvos experiment. We
> expect to get some numbers for geometric parity destruction by melting
> in contrasted opposite parity P3(1)21 vs. P3(2)21 benzil single
> crystal /_\H(fusion) in January 2007.

Your grand language would have more weight if you understood basic
physics.

Your experiment makes no sense. The fact that no one has pointed this
out yet means that no one is taking it seriously enough to look
closely.

First---the basic premise. When a chiral crystal forms, it will have a
slightly different mass depending on whether it is right-handed (RH) or
left-handed (LH). Since E=mc^2, this should manifest in a different
total energy and hence a different heat of fusion. The mass might be
10^-13 different--too small for an Eotvos balance, but Uncle Al saves
the day with a calorimeter.

OK, except for this--you now have two masses: Inertial (mi) and
Gravitational (mg). So, which mass is in E=mc^2? Is it E=(mg)c^2 or
e=(mi)c^2? Or, is it a combination, e.g. an average? You don't seem
to even have realized that there is a question here, as shown below.

Which mass is changed? Is it mg or mi? Let's say, for argument's
sake, that there is an EP violation. Let's say that mg changes. So,
if E=(mi)c^2, you won't see anything.

Even if the EP violation exists, you have a significant chance that
your experiment will not see it. Given Ocham's razor, it would seem
likely that if there is a difference in the masses, it wouldn't be the
mass that results in a change in energy.

Now, let's say this is wrong. You predict a very large difference in
the delta-H values. Think for a second, what does this mean to the
prevalence of RH and LH crystals? Why, your crystalization dish should
be primarily the low-energy crystals. Ooops. You can test your
experiment without a calorimeter. That is where thinking like a
physicist will save you airfare going to some lattitude to do your
experiment.

Which brings up another point--Eotvos balances aren't placed at the
lattitude because the mass is different there. They are placed at the
given lattitude because the signal is maximized. The combination of
earth's rotation, earth's gravity, moon's gravity and sun's gravity all
exert a force on the masses. That is what you are measuring.

Going to a specific lattitude and doing the eperiment at a specific
time demonstrates clearly that you have no understanding of the
measurement being done.

What do you say in http://www.mazepath.com/uncleal/lajos.htm#a2 ?

"HOW: The angle between Earth's inertial angular acceleration and
gravitational orbital acceleration cycles 360° each 24 hours. An added
pair of opposite party test masses aligned north-south or east-west
forms a continuously inverting coordinate frame. If the vacuum
background is chiral, the relative energies of insertion of opposite
shoes will cycle as the two accelerations vary from orthogonal to
parallel. Critical points and nodes are local 0600 hrs, noon, 1800 hrs,
and midnight.

WHERE: The maximum horizontal component of Earth's angular acceleration
is at 44.950° latitude (WGS84; Earth is a distorted oblate ellipsoid).
The experiment should be located between 40° and 50° latitude (98.5%
outputs). Portland, Minneapolis-St. Paul; Ottawa and Montreal, Canada;
Bordeaux, France; Turin and Milan, Italy; Belgrade, Serbia, Bucharest
Bulgaria.

WHEN: Maximum terrestrial orbital gravitational acceleration occurs at
perihelion. The experiment is best conducted between 01 October and 01
April (98.4% outputs. 100% on 03 January; minimum is 93.5% on 04 July).
Background 981 cm/sec2 gravity is inert."

Besides not being very clearly written, the above would imply that the
mass (either inertial or gravitaional) will vary depending on time and
lattitude. More importantly, you seem to indicate that mass depends on
acceleration for non-relativistic speeds.

Why not just put a thermocouple on the crystal and measure the
temperature as a function of time, since "the relative energies of
insertion of opposite shoes will cycle...".

If you can't tell that the above was not a serious suggestion, you are
in deep trouble.

You do have one correct statement on your webpage:
"There are no observables coupled to geometric parity divergence. "

Thomas.

Uncle Al

Dec16-06, 05:00 AM

Igor Khavkine wrote:
[snip]

> Hans Aberg wrote:
> > No, because you put in an assumptions about constant graviatational
> > fields, whereas the formulation a I gave does not have any such
> > assumptions: it is valid without any theory. For example, intertial frames
> > do not exist in GR in a fmoral mathemactial manner.
>
> I'm not sure what you are objecting to. Both statements, equivalence of
> inertial and gravitational masses and equivalence of uniform
> acceleration and uniform gravity, are local in character. That is, we
> can apply them in a neighborhood of a point where the gravitational
> field can be approximated as constant. In such a situation it is easy
> to show how one statement follows from the other, as I did in my
> previous post, and vice versa. There is no need to talk of inertial
> frames, adding an acceleration is a well defined local coordinate
> transformation.
>
> > The form I gave is not "Einstein's principle of equivalence", but the
> > princile of the equivalence between inertial and gravitational mass.
[snip]

Igor Khavkine wrote:

|A particle's equation of
|motion in a constant gravitational field is m a = q g, where m -
|inertial mass, a - acceleration, g - gravitational force, q -
|gravitational "charge". A priori, q need not have any relation to m,
|after all electric charge doesn't. To remove such a constant force, we
|can introduce an acceleration A = - (m/q) g. Then the equation of
|motion becomes just m (a + A) = 0. However, if there is more than one
|particle in the picture and these particles have different masses and
|charges, m_i and q_i for particle i, then the *same* A can be used to
|remove the gravitational force for *all* the particles only if
|(m_i/q_i) is the same for all i. That is, if we have the
|proportionality m_i ~ q_i, or, choosing the right units and making the
|proportionality constant 1, the equality m_i = q_i.
|
|Thus the equivalence principle in the above form is equivalent to the
|statement that q_i = m_i, or that inertial mass is the same as
|gravitational mass/charge."

The equivalence between the effects of a massive body and an
accelerating geometry in perturbative string theory follows from the
state-operator correspondence and the BRST invariance of the graviton
vertex operators.

http://www.lepp.cornell.edu/spr/2000-03/msg0023259.html
BRST formalism

That is rigorous! Can it have exceptions? Of course it can - at the
postulate level. Rigorous axiomatic theory is no better than its
unprovable founding postulates. Plane geometry fell to being a
special case given curved space geometries.

The EP postulates isotropic vacuum. One can trivially construct local
EP violation of detectable amplitude consistent with all prior
observations. If the vacuum has a chiral pseudoscalar background
(affine and teleparallel gravitation theories; Einstein-Cartan theory,
Weitzenböck spacetime) then (*only*) extreme enantiomorphic mass
distributions will fall along *non-parallel* minimum action vacuum
free fall trajectories. They will diastereomerically interact with
the chiral background as opposite shoes fit differently upon a given
foot.

First, other observations limit such a chiral divergence EP violation
to less than 10 parts-per-trillion. It would be lost in the noise of
common observation but readily observable in specialist experiments.

Second, detectable amplitudes would be limited to the most extreme
parity divergent (opposite chirality in all directions) *mass
distributions.* Massless particles (photons and EM fields) are
excluded as are massed single particles. Non-rigid lattices are
excluded.

Third, chemical composition and bonding are gravitationally
invisible. All physical variables are demonstrated invisible to
gravitation. Hydrogen falls identically to uranium. A significantly
different kind of calculated opposite test mass pair is required.
Only the relative positions of anonymous atoms locked in space would
be operative - a geometric not composition test mass contrast:
opposite geometric parity single crystals of identical chemical
composition. Opposite parity crystallographic space groups P3(1)21
and P3(2)21 (the quartz groups) are especially good.

Geometric parity divergence of a mass distribution can be
quantitatively calculated atom by atom. A parity calorimetry
experiment - one that destroys the parity divergence of opposite party
test masses to a common achiral (not racemic!) state - run under
Eotvos experiment rules would be sensitive past the
part-per-quadrillion level. It would be inexpensive to configure and
rapid to run and repeat in common commercial hardware.

http://www.mazepath.com/uncleal/lajos.htm#a2

We have large solution-grown opposite parity benzil single crystals in
hand. We are on track to know the answer in January 2007. The smart
money is on no differential output whatsover. "Smart" has an
uncomfortable habit of changing over time when empirical reality is
given a chance to vote. We will see.

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

Richard Saam

Dec20-06, 05:00 AM

Thomas Johnson wrote:
> Uncle Al wrote:
>
>
>>If you do not like spacetime curvature, use spacetime torsion. Affine
>>and teleparallel gravitation provide all of General Relativity
>>(Equivalence Principle postulated) plus examples of Equivalence
>>Principle violation by angular momenta: Physically spinning, quantum
>>spin, and opposite geometric parity bodies. The first two are
>>demonstrated in theory and by observation (binary pulsars and Gravity
>>Probe-B; zero external field paramagnet and Adelberger's ferromagnet
>>torsion balance experiments) to be well below detection limits if they
>>exist at all. The third would be a 9% differential signal in a parity
>>calorimetry experiment if there were a corresponding 10^(-13)
>>difference/average net signal in a parity Eotvos experiment. We
>>expect to get some numbers for geometric parity destruction by melting
>>in contrasted opposite parity P3(1)21 vs. P3(2)21 benzil single
>>crystal /_\H(fusion) in January 2007.
>
>
> Your grand language would have more weight if you understood basic
> physics.
>
> Your experiment makes no sense. The fact that no one has pointed this
> out yet means that no one is taking it seriously enough to look
> closely.
>
> First---the basic premise. When a chiral crystal forms, it will have a
> slightly different mass depending on whether it is right-handed (RH) or
> left-handed (LH). Since E=mc^2, this should manifest in a different
> total energy and hence a different heat of fusion. The mass might be
> 10^-13 different--too small for an Eotvos balance, but Uncle Al saves
> the day with a calorimeter.

Calculation indicates mass sensitivity
2.8 x 10^-13
for benzil (as proposed by Uncle Al)

with logic as follows:

A racemate crystal is almost always lower in energy than that of a resolved
enantiomer perhaps because of entropy of mixing.

entropy = - R summation(i) X(i) ln(X(i))

Component 1 Component 2 X(1)ln(X(1)) + X(2)ln(X(2))
1.00 0 0
0.90 0.1 0.325082973
0.80 0.2 0.500402424
0.70 0.3 0.610864302
0.60 0.4 0.673011667
0.50 0.5 0.693147181 < maximum entropy
0.40 0.6 0.673011667
0.30 0.7 0.610864302
0.20 0.8 0.500402424
0.10 0.9 0.325082973
0.00 1 0

entropy = .69 x R = .69 *8.32 x 10^7 erg / mole K
then change in free energy due to entropy would be on the order of:
..69 * 8.32 x 107 erg / mole K x 298 K
or
1.7108 erg/mole
on an energy mass equivalent basis this would be
1.7108/c^2 or 1.7108/(3 x 10^10 )^2
or
5.84 x 10^-11 gram / mole
for benzil at molecular weight 210.23 g/mol
the required sensitivity would be
5.84 x 10^-11 / 210.23 = 2.8 x 10^-13
and that is 2.8 parts per 10^13

> OK, except for this--you now have two masses: Inertial (mi) and
> Gravitational (mg). So, which mass is in E=mc^2? Is it E=(mg)c^2 or
> e=(mi)c^2? Or, is it a combination, e.g. an average? You don't seem
> to even have realized that there is a question here, as shown below.
>
> Which mass is changed? Is it mg or mi? Let's say, for argument's
> sake, that there is an EP violation. Let's say that mg changes. So,
> if E=(mi)c^2, you won't see anything.
>
> Even if the EP violation exists, you have a significant chance that
> your experiment will not see it. Given Ocham's razor, it would seem
> likely that if there is a difference in the masses, it wouldn't be the
> mass that results in a change in energy.
>
> Now, let's say this is wrong. You predict a very large difference in
> the delta-H values. Think for a second, what does this mean to the
> prevalence of RH and LH crystals? Why, your crystalization dish should
> be primarily the low-energy crystals. Ooops. You can test your
> experiment without a calorimeter. That is where thinking like a
> physicist will save you airfare going to some lattitude to do your
> experiment.
>
> Which brings up another point--Eotvos balances aren't placed at the
> lattitude because the mass is different there. They are placed at the
> given lattitude because the signal is maximized. The combination of
> earth's rotation, earth's gravity, moon's gravity and sun's gravity all
> exert a force on the masses. That is what you are measuring.
>
> Going to a specific lattitude and doing the eperiment at a specific
> time demonstrates clearly that you have no understanding of the
> measurement being done.
>
> What do you say in http://www.mazepath.com/uncleal/lajos.htm#a2 ?
>
> "HOW: The angle between Earth's inertial angular acceleration and
> gravitational orbital acceleration cycles 360° each 24 hours. An added
> pair of opposite party test masses aligned north-south or east-west
> forms a continuously inverting coordinate frame. If the vacuum
> background is chiral, the relative energies of insertion of opposite
> shoes will cycle as the two accelerations vary from orthogonal to
> parallel. Critical points and nodes are local 0600 hrs, noon, 1800 hrs,
> and midnight.
>
> WHERE: The maximum horizontal component of Earth's angular acceleration
> is at 44.950° latitude (WGS84; Earth is a distorted oblate ellipsoid).
> The experiment should be located between 40° and 50° latitude (98.5%
> outputs). Portland, Minneapolis-St. Paul; Ottawa and Montreal, Canada;
> Bordeaux, France; Turin and Milan, Italy; Belgrade, Serbia, Bucharest
> Bulgaria.
>
> WHEN: Maximum terrestrial orbital gravitational acceleration occurs at
> perihelion. The experiment is best conducted between 01 October and 01
> April (98.4% outputs. 100% on 03 January; minimum is 93.5% on 04 July).
> Background 981 cm/sec2 gravity is inert."
>
> Besides not being very clearly written, the above would imply that the
> mass (either inertial or gravitaional) will vary depending on time and
> lattitude. More importantly, you seem to indicate that mass depends on
> acceleration for non-relativistic speeds.
>
> Why not just put a thermocouple on the crystal and measure the
> temperature as a function of time, since "the relative energies of
> insertion of opposite shoes will cycle...".

Temperature sensitivity would have to greater than

2.8 parts per 10^13
for benzil

Is that possible?

>
> If you can't tell that the above was not a serious suggestion, you are
> in deep trouble.
>
> You do have one correct statement on your webpage:
> "There are no observables coupled to geometric parity divergence. "
>
> Thomas.
>

E.Tartempion

Dec20-06, 05:00 AM

"Thomas Johnson" ha scritto:

> Your grand language would have more weight if you understood basic
> physics.

"Basic physics" isn't "basic widely accepted *theories* about physics".

> Your experiment makes no sense.

An experiment always makes sense, physics is an experimental science.

> The fact that no one has pointed this out yet means that no one is taking
> it seriously enough to look closely.

Yet they should.

> First---the basic premise. When a chiral crystal forms, it will have a
> slightly different mass depending on whether it is right-handed (RH) or
> left-handed (LH). Since E=mc^2, this should manifest in a different
> total energy and hence a different heat of fusion. The mass might be
> 10^-13 different--too small for an Eotvos balance, but Uncle Al saves
> the day with a calorimeter.
>
> OK, except for this--you now have two masses: Inertial (mi) and
> Gravitational (mg). So, which mass is in E=mc^2? Is it E=(mg)c^2 or
> e=(mi)c^2? Or, is it a combination, e.g. an average? You don't seem
> to even have realized that there is a question here, as shown below.
>
> Which mass is changed? Is it mg or mi? Let's say, for argument's
> sake, that there is an EP violation. Let's say that mg changes. So,
> if E=(mi)c^2, you won't see anything.

No, you make a hidden assumption: the one that General Relativity is valid,
and that only one mass changes. The Eotvös experiment aims ad showing that
GR is wrong, through a deviation from the Equivalence Principle. It isn't
about some mass depending on chirality, it is about the law of gravity
(again, not GR, and not necessarily the use of some mass concett) depending
on chirality, and thus not reconcilable with GR.

> Even if the EP violation exists, you have a significant chance that
> your experiment will not see it. Given Ocham's razor, it would seem
> likely that if there is a difference in the masses, it wouldn't be the
> mass that results in a change in energy.

No, Occam's razzor is about teories, not about physics. Physics is what it
is, and we have a choice for theories. In other words, if the mass that
results in a change in energy changes, let it be. We have no way to impede
it.

E.Tartempione

Dec20-06, 05:00 AM

"Thomas Johnson" ha scritto:

> Your grand language would have more weight if you understood basic
> physics.

"Basic physics" isn't "basic widely accepted theories about physics".

> Your experiment makes no sense.

An experiment always makes sense, physics is an experimental science.

> The fact that no one has pointed this out yet means that no one is taking
> it seriously enough to look closely.

Yet they should.

> First---the basic premise. When a chiral crystal forms, it will have a
> slightly different mass depending on whether it is right-handed (RH) or
> left-handed (LH). Since E=mc^2, this should manifest in a different
> total energy and hence a different heat of fusion. The mass might be
> 10^-13 different--too small for an Eotvos balance, but Uncle Al saves
> the day with a calorimeter.
>
> OK, except for this--you now have two masses: Inertial (mi) and
> Gravitational (mg). So, which mass is in E=mc^2? Is it E=(mg)c^2 or
> e=(mi)c^2? Or, is it a combination, e.g. an average? You don't seem
> to even have realized that there is a question here, as shown below.
>
> Which mass is changed? Is it mg or mi? Let's say, for argument's
> sake, that there is an EP violation. Let's say that mg changes. So,
> if E=(mi)c^2, you won't see anything.

No, you make a hidden assumption: the one that General Relativity is valid,
and that only one mass changes. The Eotvös experiment aims ad showing that
GR is wrong, through a deviation from the Equivalence Principle. It isn't
about some mass depending on chirality, it is about the law of gravity
(again, not GR, and not necessarily the use of some mass concett) depending
on chirality, and thus not reconcilable with GR.

> Even if the EP violation exists, you have a significant chance that
> your experiment will not see it. Given Ocham's razor, it would seem
> likely that if there is a difference in the masses, it wouldn't be the
> mass that results in a change in energy.

No, Occam's razzor is about teories, not about physics. Physics is what it
is, and we have a choice for theories. In other words, if the mass that
results in a change in energy changes, let it be. We have no way to impede
it.

Thomas Johnson

Dec26-06, 05:00 AM

E.Tartempion wrote:
> No, you make a hidden assumption: the one that General Relativity is valid,
> and that only one mass changes.

I was allowing for gravitational and inertial masses to be different.
This is not assuming that GR is valid.

You make an excellent point in the second part of the sentence. You
are quite correct to suggest yet another flaw in Mr. Schwartz' proposed
experiment. If both masses change he will see a signal in a
calorimeter. Consider the special case where the masses change by the
same amount. The equivalence principle will still be valid since the
two masses are, well, equivalent.

To repeat--even if he sees a signal (and, more importantly, even if
someone else does), he will not have clearly demonstrated EP violation.

Thomas.

Thomas Johnson

Dec26-06, 05:00 AM

Uncle Al wrote:
> http://www.mazepath.com/uncleal/lajos.htm#a2
>
> We have large solution-grown opposite parity benzil single crystals in
> hand. We are on track to know the answer in January 2007. The smart
> money is on no differential output whatsover. "Smart" has an
> uncomfortable habit of changing over time when empirical reality is
> given a chance to vote. We will see.

On your website you state:

"Two local differential scanning calorimeters located between 40°-50°
latitude (optimal 44.95° latitude) preferably between 06 October and
01 April (optimal 03 January) are separated and positioned so that
their sample pans are located along a north-south line. Each holds a ~3
mm diameter ~17 mg solid single crystal sphere of benzil, one in space
group P3121 (right-handed) and one in P3221 (left-handed). H(fusion)
for both are simultaneously run. The procedure is run with new crystals
at 0600 hrs, noon, 1800 hrs, and midnight local time. If all Hfusion at
all times are not equal within experimental error (differential output
would be maximum signal, null, maximum, null), the experiment is
repeated the next day with the calorimeters aligned east-west to
confirm. The Hfusion will have a six hour phase shift on the second day
if the signal is real. "

You have clearly misunderstood the Eotvos balance experiment. The
signal involved varies with time because the *forces* vary with time.
For example, the centripital forces on the masses vary depending on the
whether the force due to force due to the earth's rotation adds or
subtracts with that due to the earth's orbit.

Your experiment is supposed to measure direct differences in *mass*.
Mass doesn't change with time, low-speed accelerations, lattitude or
compass directions.

Even if there is EP violation, there is no reason why a calorimeter
would show different signals depending on the time of day or the
orientation of the crystals with respect to the earth's frame of
reference.

If you see a "six hour phase shift" this will be an example that you
have at best made a serious mistake. At worst, it will put you in line
to follow Jan Hendrick Shon into the history books.

If you have a clear reason why a mass would depend on a
non-relativistic acceleration, please submit it to Science, Nature or
Phys. Rev. Letters. Believe me, it will make an even bigger splash than
an EP violation.

Again, quoting your website:
"The angle between Earth's inertial acceleration spin and gravitational
acceleration orbit rotates 360°/24 hours. This originates a
composition Eotvos experiment signal. Add parity benzil test masses
aligned N-S or E-W and the coordinate frame cycles chiral, achiral,
opposite chiral, achiral every 24 hours. A sinusoidal Hfusion will
appear. "

Take a moment to think--if there is an 8% difference in the heat of
fusion of a crystal, varying with time, a well-isolated crystal will
vary in temperature during the day.

Even given years studying this problem, you have failed to understand
the very basics of the experiment.

Thomas.

Uncle Al

Dec27-06, 05:01 AM

Thomas Johnson wrote:
>
> E.Tartempion wrote:
> > No, you make a hidden assumption: the one that General Relativity is valid,
> > and that only one mass changes.
>
> I was allowing for gravitational and inertial masses to be different.
> This is not assuming that GR is valid.

GR postulates the Equivalence Principle to create spacetime curvature
- the elevator Gedankenexperiment. Read it,

Jahrbuch der Radioaktivität u. Electronik 4 411 (1907)

"The Collected Papers of Albert Einstein," Vol. 2 English translation,
A. Beck, trans. (Princeton University Press: Princeton, NJ, 1989) p.
252.

If there is empirical EP violation there is no basis for General
Relativity. Tell us how allowing EP violation does not assume GR
validity. Empirical EP violation falsifies General Relativity at its
founding postulate. This leaves only validated affine and
teleparallel classical theories of gravitation. That is why folks do
EP violation experiments.

> You make an excellent point in the second part of the sentence. You
> are quite correct to suggest yet another flaw in Mr. Schwartz' proposed
> experiment. If both masses change he will see a signal in a
> calorimeter. Consider the special case where the masses change by the
> same amount. The equivalence principle will still be valid since the
> two masses are, well, equivalent.

If identical composition opposite parity masses change mass
proportionally under Eotvos experiment rules then their /_\H(fusion)
to a common achiral melt must still change and a net signal is
detected. Look at the image,

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

If opposite parity cases in a chiral pseudoscalar vacuum background
are symmetric about the isotropic vacuum value, there is a net
/_\/_\H(fusion) output. If they are both on the same side of the
isotropic vacuum value, there is a net /_\/_\H(fusion) output and
/_\H(fusion) changes. IF THEY ARE COINCIDENT on the same side of the
isotropic vacuum value, there is a zero /_\/_\H(fusion) net output...
but /_\H(fusion) changes. The parity calorimetry experiment is
utterly air-tight. You study that graph and get back to us. The
diastereotopic interaction divergence cannot be identical and zero in
energy vs. isotropic vacuum if it occurs in an anisotropic vacuum
background.

CHI calculation is one-parameter modeled to be dependent only upon the
crystal structure helix angle defined here by the carbony-carbonyl
dihedral angle. This is validated, modeled vs. calculation, for
selenium, tellurium, quartz, and benzil. Benzil's hydrogen atoms
decorate each benzene ring's periphery, 10/molecule. Is the hydrogen
sublattice parity divergent? It is unrelated, certainly in principle,
to the operative dihedral angle. File number is the lattice ball
radius in angstroms. Values are from Petitjean's fully rigorous QCM
software:

ATOMS CHI DSI COR
bz04.hin 9 0.371922 0.382795 2
bz05.hin 17 0.832066 0.000000 1
bz06.hin 31 0.793326 0.000000 1
bz07.hin 53 0.858571 0.000000 1
bz08.hin 79 0.880145 0.000000 1
bz09.hin 109 0.917254 0.000000 1
bz10.hin 149 0.948448 0.000000 1
bz11.hin 193 0.983175 0.000000 1
bz12.hin 262 0.947514 0.000000 1
bz13.hin 329 0.964482 0.000000 1
bz14.hin 414 0.974646 0.000000 1
bz15.hin 506 0.971405 0.000000 1
bz16.hin 610 0.981262 0.000000 1
bz17.hin 743 0.983111 0.000000 1
bz18.hin 862 0.965345 0.000000 1
bz19.hin 1029 0.990810 0.000000 1

That is consistently parity divergent to small scale,
DSI=0/COR=1/CH->1. The P3(1)21 lattice is centered at x/a=0.33000,
y/b=0.09900, z/c=0.21330 that is one of the five unique hydrogen
positions within the unit cell. Any other chosen point could give
different CHI values at each radius and will give identical log(1-CHI)
vs. radius slope and intercept. The lattice is self-similar and
therefore homogeneous at larger than unit cell volumes. 4, 5, and 6 A
radii are 268.08, 523.60, and 904.78 A^3. Benzil unit cell volume is
834.81 A^3 containing three formula units or 30 hydrogens. Very nice
results.

ANY experiment that demonstrates a net reproducible macroscopic
physical property divergence in enantiomeric bodies is a sea change
for all of science. Any Eotvos experiment with a non-null output,
even 10^(-13) difference/average mass/mass at 1-sigma, would be front
page above the fold news. At that inertial/gravitational mass
divergence the parity calorimetry experiment output would be 8%
energy/mass difference or more than 15 sigma. It is reproducible
every two days. 16 paired runs over four days would contain 8 nulls,
4 maxima, and 4 reversed maxima rigidly predicted vs. time of day and
geographic orientation of the opposite parity masses by Eotvos
experiment rules. The results are utterly unambiguous and trivially
reproducible rapidly and at low cost by anybody. The divergence
amplitude would be trivially modulated by latitude and time of year,
providing two more sets of validations.

Unlike custom-built Eotvos balances, differential scanning
calorimeters are an industrial commodity. Thousands if not tens of
thousands of them are in the field worldwide, complete with NIST or
European Standard calibration at will. Powdered benzil is an NIST
calorimetry calibration standard.

> To repeat--even if he sees a signal (and, more importantly, even if
> someone else does), he will not have clearly demonstrated EP violation.

Uncle Al does not perform the experiment. Uncle Al has never met the
experimenter nor visited his facilities. Extraordinary claims require
extraordinary proof and reproduciblty. A non-zero net output is EP
parity violation perfectly demonstrated to the highest standards of
experimentation, run by Eotvos experiment rules for contrasted
composition test masses. Read the literature.

You have no understanding of any Equivalence Principle test since
Galileo. I will not requote Adelberger's and Newman's abundant
publications explaining the theoretical basis and empirical reductions
to practice of the Eotvos experiment since Dicke's brilliant
innovation. Look up Dicke's paper for the bonehead descripton. I
posted the citation, too.

There is no basis in physics or chemistry for enantiomeric mass
distributions or enantiomeric charge or other fields to have any
macroscopic divergent physical properties other than in a
diasteromeric interaction. Absolute enantiomeric symmetry requires
(CPT and quantum field theory) matter-antimatter substitution. The
divergence using matter/matter is immeasurably small.

Weak interaction z-zero exchange between an atomic nucleus and
electron orbitals with an anti-node at the nucleus renders every atom
identically chiral in sign. The calculated most extreme parity
violating energy divergences are on the close order of 8x10^(-12) eV.
The most extreme calculated asymmetric heavy atom cases amenable to IR
detection are a very small fraction of a reciprocal centimeter. Read
the literature. No detection. Optical chirality in monoatomic heavy
atom gases has been detected to spec in thallium, mercury, and
bismuth. I've posted those links, too.

Optical diasteroeptic interaction (gyrotropy) is trivially observed
via unequal distereotopic refractive indices, linearly polarized
(equal mix of circularly polarized) light vs. a chiral medium
(homogeneous liquid, liquid crystal, ordered solid state, strained
glass...). The diasteromeric refractive index divergence must
integrate to ZERO over the entire electromagnetic spectrum: f-sum
rule, Thomas-Reiche-Kuhn sum rule, Kramers-Kronig relationship. The
difference between two (n-1) for orthogonal polarizations sums to zero
overall.

Only parity calorimetry or parity Eotvos experiments can empirically
falsify the EP and vacuum Lorentz Invariance consistent with orthodox
classical theory while not contradicting any of 400+ years of prior
observations in any venue at any scale. You whine, libel, and slander
demanding that the look never be made. Know a man by his fears. We
are going to look. Folks are lining up to help.

http://www.mazepath.com/uncleal/bzdense.png

As stated in the title, this is benzil parity divergence calculated
without its hydrogens, 48 atoms/unit cell vs. 78 including hydrogens.
We could not calculate the full atom set in available hardware. QCM
(to small radii) and the model said the results would be identical. A
newly built 4 teraFLOPS multicore-CPU cluster wants diagnostics to run
it flat out for a week or more with determined outputs. We are
discussing gratis 5000+ core-days to run full benzil to 5x10^17 atoms
total at high sampling density. That is ~1.1 million angstroms radius
and a 0.22 mm diameter solid ball calculated long_double_precision.
We expect to be granted the time and expect no surprises when the
output is graphed and fitted to the one-parameter model.

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

Schmidt

Jan2-07, 05:00 AM

"Thomas Johnson" <thomas_johnson00@hotmail.com> schrieb im Post
news:1167012363.502279.138230@a3g2000cwd.googlegro ups.com

> Even if there is EP violation, there is no reason why a calorimeter
> would show different signals depending on the time of day or the
> orientation of the crystals with respect to the earth's frame of
> reference.

I cant understand that sentence. Which EP violation do you speak about?

> If you see a "six hour phase shift" this will be an example that you
> have at best made a serious mistake. At worst, it will put you in line
> to follow Jan Hendrick Shon into the history books.
>
> If you have a clear reason why a mass would depend on a
> non-relativistic acceleration, please submit it to Science, Nature or
> Phys. Rev. Letters. Believe me, it will make an even bigger splash than
> an EP violation.

It seems you have difficulties to think outside of a mathematical model.
The only reason I could see, is I measure a dependency of mass on a
non-relativistic acceleration. Kepler didn't see "a reason why the orbit is
an ellipse." He observed elliptical orbits, and that three simple laws
describe it. They allowed Newton to have a clear reason why the moon would
obey the same equation of motion than an apple near earth surface, but... he
failed to account for the orbit of Mercury. Only theories need reasons.

Schmidt

Jan2-07, 05:00 AM

E.Tartempion wrote:

>> No, you make a hidden assumption: the one that General Relativity is
>> valid, and that only one mass changes.

"Thomas Johnson" <thomas_johnson00@hotmail.com> schrieb im Post
news:1166805583.871031.204590@f1g2000cwa.googlegro ups.com

> I was allowing for gravitational and inertial masses to be different.
> This is not assuming that GR is valid.

That's right, since it is at the basis of GR. Though, it isn't the only way
to depart from GR. Another one is Newtons theory, that have a different
prediction for the orbit of Mercury, although having equal inertial and
gravitational masses.

> You make an excellent point in the second part of the sentence. You
> are quite correct to suggest yet another flaw in Mr. Schwartz' proposed
> experiment. If both masses change he will see a signal in a
> calorimeter. Consider the special case where the masses change by the
> same amount. The equivalence principle will still be valid since the
> two masses are, well, equivalent.

No necessarily, like in Newtons theory.

> To repeat--even if he sees a signal (and, more importantly, even if
> someone else does), he will not have clearly demonstrated EP violation.

GR predicts there is no signal, right? Then he would have clearly
demonstrated that GR is wrong. Isn't it enough?

Uncle Al

Jan3-07, 05:00 AM

Schmidt wrote:
>
> E.Tartempion wrote:
>
> >> No, you make a hidden assumption: the one that General Relativity is
> >> valid, and that only one mass changes.
>
> "Thomas Johnson" <thomas_johnson00@hotmail.com> schrieb im Post
> news:1166805583.871031.204590@f1g2000cwa.googlegro ups.com
>
> > I was allowing for gravitational and inertial masses to be different.
> > This is not assuming that GR is valid.
>
> That's right, since it is at the basis of GR. Though, it isn't the only way
> to depart from GR. Another one is Newtons theory, that have a different
> prediction for the orbit of Mercury, although having equal inertial and
> gravitational masses.
>
> > You make an excellent point in the second part of the sentence. You
> > are quite correct to suggest yet another flaw in Mr. Schwartz' proposed
> > experiment. If both masses change he will see a signal in a
> > calorimeter. Consider the special case where the masses change by the
> > same amount. The equivalence principle will still be valid since the
> > two masses are, well, equivalent.
>
> No necessarily, like in Newtons theory.
>
> > To repeat--even if he sees a signal (and, more importantly, even if
> > someone else does), he will not have clearly demonstrated EP violation.
>
> GR predicts there is no signal, right? Then he would have clearly
> demonstrated that GR is wrong. Isn't it enough?

Theory must bow to observation, as stated. Stern measured the "wrong"
proton gyromagnetic moment. Pauli ate his words and theory that could
not be wrong was rewritten. Yang and Lee observed strictly
left-handed beta-decay. Theory that could not be wrong was
rewritten. The first GPS satellite was not corrected for General
Relativity, though its three atomic clocks did contain an offset
oscillator just in case. "Just in case" happened.

A mas sector parity experiment seeking a diastereotopic observation
has never been performed. There is an observable effect or there is
not. Both outcomes are strongly supported by orthodox physics more
than 70 years old. GR cannot contain spin-orbit coupling given
Einstein tensor symmetry; isotropic vacuum is postulated.
Einstein-Cartan theory does contain spin-orbit coupling and trivially
allows an anisotropic vacuum background. Parity divergence
experiments' net result is not a 50:50 chance. Snisotropic vacuum is
favored. It is the only place nobody has ever looked.

If space has a detectable chiral pseudoscalar background as allowed by
affine and teleparallel gravitation theories then metric gravitation
loses at least one of two founding postulates - isotropic vacuum and
the Equivalence Principle. No prior observation at any scale in any
venue would be contradicted given the chiral dependence and small size
of a parity divergence. Calculated parity calorimetry experiments
require about $(US)100 in consummables and two days in commercial
equipment. What is not to look?

Solution growing benzil crystals of suitable size and quality is
outside an analytical chemist's metier. I'll bring him up to speed.
We do this as a hobby out of our own wallets, as gentlemen natural
philosophers.

http://www.mazepath.com/uncleal/benzil8.jpg
Good size, inadequate quality. They should be clear as pale yellow
glass.

There are two independent empirical observations of vacuum anisotropy
in the mass sector:

1) EP violation, e.g. the parity Eotvos experiment. If identical
chemical composition opposite parity test masses - enantiomorphic
crystallographic space group P3(1)21 and P2(2)21 alpha-quartz - give a
reproducible net signal, it must be sourced. All physical observables
except mass configuration exactly cancel. There are 420+ years of
composition experiments for systematic and experimental error
controls. NOTHING gave a net signal. Bleeding edge is 10^(-13)
difference/average mass/mass over 90 days in Adelberger's or Newman's
apparatus. A parity Eotvos experiment is parity-retaining. The test
masses are not altered during the experiment.

2) Vacuum insertion violation, e.g., the parity calorimetry
experiment. If space is a left foot then otherwise identical left and
right shoes fit with different energies and all socks fit
identically. P3(1)21 and P2(2)21 benzil will not grow with different
thermodynamics. Growth is a surface monolayer that calculates to
asymptotic zero parity divergence. Each incoming solution, molten, or
gas-phase benzil molecule is achiral. As it enters the lattice it
twists consistent with prior solid state structure. The carbon
skeleton becomes a helix. Even the hydrogens form a helix,

http://www.mazepath.com/uncleal/bz4a.png
Lattice 3-fold helix, 4 molecules displayed in 3-D
http://www.mazepath.com/uncleal/bz4b.png
Net hydrogens
http://www.mazepath.com/uncleal/bz4c.png
Hydrogens grouped

Parity calorimetry is *parity-destroying* (NOT racemizing). Opposite
chirality benzil crystals melt into a common achiral (NOT racemic)
liquid. If single crystal starting states had different energies
given diasterotopic chiral vacuum insertion and the ending states are
molten identical, there must obtain different transition energies,

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

It makes no difference how the crystal melts. The thermodynamic
transition arises from starting and ending states only. Path is
irrelevant to outcome.

10^(-13) mass/mass divergnce is 8% energy/mass divergence. Commercial
differential scanning calorimeters are 0.1% precise. A run requires
less than 15 minutes. Parity divergence plus EP violation under
Eotvos experiment rules are 8 paired enthalpy of fusion determinations
over two days. What is not to look?

If all benzil enthalpies of fusion are identical within experimental
error then nothing in physics changes. If all benzil enthalpies of
fusion are reproducibly NOT identical within experimental error and
net outputs are consistent with chiral configuration and relative
geographic orientation, then all of physics must be rewritten. It has
happened before.

How often is any reader here privileged to do something original and
important with no hint as to the final result?

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

jacques.fric@neuf.fr

Jan4-07, 05:00 AM

Cyberkatru a écrit :

> Einsteins principle of equivalence, as usually explained, seems strange (to
> me) from the point of view of (pseudo) Riemannian geometry.
> As explained in some relativity texts, the principle states roughly that
> there is no (local) physical difference between effects due to an
> accelerating frame and effects due to a gravitational field.

+++
That's only true at first order
+++

However,
> choosing an accelerating frame seems like just a certain choice of
> curvilinear spacetime coordinates. But isn't gravity supposed to be
> curvature due to a metric tensor?

+++
Yes, spacetime curvature is traced by a non vanishing 4D Riemann
Tensor.
+++

But whether a Lorentz manifold has zero
> curvature or not certainly doesn't depend on a choice of coordinates. How
> can I produce curvature on a flat spacetime just by a choice of chart?

++++
You can't.
A Flat spacetime implies a vanishing 4D Riemann tensor in any frame.
So to know whether spacetime is flat or not, compute the Riemann
tensor. If it is nul, space time is flat, otherwise it is curved.
But whether you foliate the 4D manifold into submanifolds (ie 3D space
sections) these sections may be curved even in a flat Minkowski space,
that's some confusing topic..
So stick to the 4D Riemann tensor criterion, you can't be mistaken in
this way.
+++
> can't! The whole thing seems especially weird since metric and curvature are
> defined as geometric objects with an existence that doesn't even need a
> chart at all to make sense.
> So I don't see what the equivalence principle could really amount to.
> What am I missing?
>
> The principle of general covariance is also a problem for me.
++++
This principle is not specific to GR ( many modern theories include
it).
In fact, as acknoledged by Einstein in "Die Naturwissenschaft vol VIII
1920 p 1010-1011", answering to some remarks (the covariance relies on
the "form" of the equation of the theory , not to its content) from
Ernst Reichenbacher (in the same review) the relativity principle
(covariance requirement) is not even necessary for founding the Theory
of GR, but it is just useful for convenience.
+++
Does it amount
> to anything more than the statement that the laws of gravitational physics
> can be expressed in terms of tensor fields? It seems to me that, all sorts
> of ad hoc laws could be expressed in this way. In fact, if spacetime had
> trivial topology then one chart would do and any law written in that chart
> could just be expressed in any other chart by brute force anplication of
> tensor trnasformation laws. In this case the idea of general covariance
> starts to seem empty.
> What am I missing?

jambaugh

Jan4-07, 05:00 AM

Cyberkatru wrote:
> Einsteins principle of equivalence, as usually explained, seems strange (to
> me) from the point of view of (pseudo) Riemannian geometry.
> As explained in some relativity texts, the principle states roughly that
> there is no (local) physical difference between effects due to an
> accelerating frame and effects due to a gravitational field. However,
> choosing an accelerating frame seems like just a certain choice of
> curvilinear spacetime coordinates. But isn't gravity supposed to be
> curvature due to a metric tensor? But whether a Lorentz manifold has zero
> curvature or not certainly doesn't depend on a choice of coordinates. How
> can I produce curvature on a flat spacetime just by a choice of chart? I
> can't! The whole thing seems especially weird since metric and curvature are
> defined as geometric objects with an existence that doesn't even need a
> chart at all to make sense.
> So I don't see what the equivalence principle could really amount to.
> What am I missing?
>
> The principle of general covariance is also a problem for me. Does it amount
> to anything more than the statement that the laws of gravitational physics
> can be expressed in terms of tensor fields? It seems to me that, all sorts
> of ad hoc laws could be expressed in this way. In fact, if spacetime had
> trivial topology then one chart would do and any law written in that chart
> could just be expressed in any other chart by brute force [application] of
> tensor [transformation] laws. In this case the idea of general covariance
> starts to seem empty.
> What am I missing?

Imagine first a curved space-time. Then pick a coordinate system and
define all the metric and connection tensors.

Now draw a set of curves representing the dynamic evolution of test
particles in this space-time manifold. Especially allow non-geodesic
curves which you may assume are the empirically determined paths of
physical test particles. This will give you a case of curved
space-time PLUS a gravitational field. {This assumes the choice of
paths for a test particle depend only on its velocity and not on
other charges.}

Now the Equivalence principle then implies that you can change the
geometry and doing so changes what you mean by an additional
gravitational field. There is no empirical way to distinguish
between two choices of geometry + dynamic gravitational field of
force.

Thus provided we stay away from any singularities which introduce
topological artifacts you can pick a flat space-time and introduce a
dynamic gravitational field or (as is the usual case) choose your
space-time so that the dynamical gravitational field is nil and all
the dynamics is "explained" by the geometry.

The two cases are only distinguished by how you interpret the Riemann
tensor and covariant derivatives. Of course you can also split the
curvature into "intrinsic" (i.e. geometric) and "extrinsic" (i.e.
dynamical)
parts in an infinite variety of ways. The equivalence principle says
that the choice doesn't matter physically.

Thus we never actually observe empirically the geometry of space-time.
We rather observe the dynamic behavior of test particles and infer a
geometry which would yield a zero extrinsic gravitational field.

Regards,
James Baugh

enrique

Jan8-07, 06:49 AM

Hi guys
I think that the equivalence principle is simply a good approximation of what happens really because Einstein says that it is valid only "locally" and in complete absence of any tipe of radiation, moreover the gravitational field has to be "uniform".
Therefore I think that since real bodies have finite mass and finite extension, they cannot be unaffected by "mareal" forces, even if they are very small in a "local" reference frame (i.e. when the body is very small).
Gravity is a "central" force and in principle, one can distinguish it from inertial force because the lines of force, in the first case are "convergent" while in the second case they are parallel. In fact in the second case there are no mareal effects to be considered!!!! So in principle, the two forces can be ALWAYS distinguished. Moreover we have to consider that also it is impossible to nullify all tipes of radiation on bodies: we cannot create a perfect shieldind, it is only an ''ideal'' situation.
In conclusion I think that the principle of equivalence is valid as a good approximation, but rigorously speaking it will never be valid!!!!
Maybe this fact can take into accound for "dark matter", Stefan's quintet radiation anomalies, Pioneer 10 anomalies and Allais effect on pendula during Solar eclipses.
Gravity and inertial masses should be linked by a radiation dependance which should be taken into account when measuring the masses of galaxies. I think that gravitational mass is reduced by radiation effects as the brazilian Prof. De Aquino has generalized starting from Donhogue & Holstein discovery of temperature dependance between gravitational and inertial masses: they are perfectly equal only at 0°K temperature.
De Aquino extends the dependance to all types of radiations, not only thermal. On CERN document server and he has published preprints of his papers, also @ Los Alamos National Laboratory.
What do you think about that?
Bye