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Comment on УSketch of a New 5-dimensional Projective Unified Field TheoryФ.

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Annalen der Physik. 7. Folge, Band 47, Heft 6, 1990, S. 605-506
J. A. Barth, Leipzig
Comment on "Sketch of a New 5-dimensional Projective
Unified Field Theory"
By Josh A. FERRARI
Institut fur Theoretische Physik, Technische Universitlit Berlin (West)
Kommentar zu ,,Skizze einer neuen 5-dimensionalen Projektiven Einheitlichen
Feldthe~rie'~
E. Schmutzer has recently published a new version of a 5-dimensional Projective
Unified Field Theory unifying gravitation, electromagnetism and a new interaction called scalarism [ l].
I n this theory a qualitatively new physical quantity (scalaric substrate density)
occurs as a source term for scalarism. Since this quantity stems from the nongeometrized
matter (substrate),i t must be handled as an ansatz (i.e., the source term for scalarism
cannot be deduced from the geometrized theory).
I n [ l ] the author make the tentative hypothesis that leptons (c.g. electrons and positrons) could possess the scalarism inducing property.
I n the quasi-Newtonian approximation, the equation of motion of a test-body with
"scalaric body parameter" Tois given by (eq. (go), [l])
+
i = -(I
I'0j70/3) grad @ ,
(1)
where @ is the Newtonian potential and yo is the scalaric substrate parameter of the
sources of the external fields. To is defined by (eq. (94), [l])
here mOeand mOlzare taken as the electron rest inass and the nucleon rest mass, respectively; N a is the number of atoms of sort 52 in the sources of the external fields; Za
is the atomic number (i.e., electrons per atom) and An is the number of nucleon per
atom of sort 52.
Tois given by an equation similar to eq. 2 (see eqs. (85)-(89), [l]).
Eq. (1) predicts a composition-dependent gravitational-to-inertial mass ratio for
the test-body given by
mclmr = 1 i-Fobyo/3
(i.e., it depends on the composition of the test-body itself and on the composition of
the source).
We will here point out that this composition-dependent ratio contradicts the experimental results of Dicke et al. [2], and Braginskii et al. [3]; these are the main experiments on the validity of the principle of eqiiivalence.
506
Ann. Physik Leipzig 47 (1990) 6
Dicke et al. investigated the difference of gravitational-to-inertial mass ratios for
Aluminium (Al) and Gold (Au) in the field of the Sun. They found
j (mG/ml)al - ( ~ G / m l ) A uI < 3 x
(3)
Braginskii and Panov compared Aluminium and Platinum (Pt) also in the field of the
Sun, and found
I (mO/ml)*l - (mc/mr)rt j < 0.9 x
(4)
To compare the above mentioned composition-dependent ratio with Dicke’s and Braginskii’s results, we have to calculate I‘, for Al, Au arid Pt, and a lower limit for To.
Since (ZR/An)2 1/3 holds for all elements, from eq. (2) we get
For the scalaric body parameter
r,
I‘,,we have (eq. (89), [1])
5.45 x 10-4 Z/A,
hence, we obtain
2.62 x
( Z / A M 0.48),
( Z / A = 0.40),
I‘(;pt)
M 2.18 x
(see footnote l)).
Then, the difference of gravitational-to-inertial mass ratio for A1 and Au is
M
M
2.18~
(7)
(8)
(9)
and for A1 and Pt, we also have
I (mG/mI)Al
- (mG/mI)Pt
I
I~o(AI)
1
- r o ( p t ) 7 0 / 3 > 2.6 X
lop9.
(11)
Thus, we have a contradiction with the experimental results shown in (3) and (4).
References
[l] SCHMUTZER,
E.: Ann. Physik (Leipzig) 45 (1988) 678.
R. ; DIUKE,
R. H. : Ann. of Physics 26 (1964) 442.
[2] ROLL,P. G.; KROTKOV,
[3] BRAGINSKII,
V. B.; PANOV,
V. I.: Zh. Eksp. Teor. Fiz. 61 (1971) 873 /Sov. Phys. JETP 34 (1972)
4631.
Bei der ltedaktion eingegangen am 24. Juli 1989.
Anschr. d. Verf.: Dr. J. A. FERRARI
Institut fur Theoretische Physik
Technische Universitat Berlin
Hardenbergstr. 36
D-1000 Berlin (West) 12
I) In the computation of To for Pt we must use the more general formula given in eq. (85),
[l], which is similar to eq. (2); that is, we must “average” over the natural isotopes of Pt, and weight
its contributions according to its relative frequency in the nature. In this case
R
2 NnAn
R
M 0.40.
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