What Causes the Gravitation?
| Scientific Paper | |
|---|---|
| Title | What Causes the Gravitation? |
| Read in full | Link to paper |
| Author(s) | Gyula I Szász |
| Published | 2006 |
| No. of pages | 11 |
Read the full paper here
Abstract
From the book Physics of Elementary Processes: Basic Approach in Physics and Astronomy
Overview
This eleven-page piece, dated Budapest, 21 April 2006, is a condensed presentation of material from Gyula I. Szász's book Physics of Elementary Processes: Basic Approach in Physics and Astronomy. It is laid out as slides rather than as a continuous paper: three figures, a set of video frames from a drop-tower experiment, and a numbered chain of equations.
Its thesis is that the two foundations of Newtonian gravitation both fail. The gravitational constant G is not constant, and gravitational and inertial mass are not equal — the ratio depends on the composition of the body. Szász argues this from three lines of evidence (a residual pattern in Kepler's third law across the planets, the historical scatter of G measurements, and the nuclear mass defect of the elements), then reports his own free-fall experiment in the Bremen drop tower as a direct test. From there he proposes a replacement: an elementary, invariant gravitational charge carried by four stable particles, obeying a field equation of Maxwellian form. The departure from the mainstream is total — the equivalence principle is abandoned, the neutron does not appear among the elementary constituents, and gravity becomes a vector field rather than spacetime curvature.
The argument
Three symptoms
Szász sets out Newton's law with the two masses kept distinct, m(body;i)a = −G M(g)m(body;g)/r2, and notes that only the assumed equality m(body) = m(body;g) = m(body;i) collapses this to the familiar form. He then asks how well the data actually support that assumption.
Kepler's third law. His Figure 1 plots the value of the "constant" R3j/T2j (1 + mj/Msun) for each planet, and reports that "the further a planet is from the sun, the larger the deviation of its 'constant' from 1." He proposes the ansatz that the true relation carries a factor mj(g)/mj(i), which is "verified if we assume a composition dependent relation" mj(g)/mj(i) = 1 + 0.15 %.
The scatter in G. Figure 2 collects measurements of G from Cavendish in 1798 to the present. Szász reports that the deviations "are unsystematic in a range of about 2.4 %", concludes that "G(Newton) is far away from being a constant", and notes that the CODATA 1998 value itself carries an uncertainty of 0.15 %.
The mass defect. Figure 3 shows the relative mass defect ΔA of the most abundant isotopes, referred to iron, as measured in mass spectrometers — that is, the defect in the inertial masses. The observation that ties the three together is that "the 0.15 % uncertainty of G(Newton) covers the whole range of the mass defects of elements".
The hypothesis and the drop experiment
Szász assumes that the gravitational mass of a nucleus is unchanged by its formation, so that all of the mass defect shows up in the inertial mass alone:
- m(isotope;i) = m(isotope;g) (1 − Δ(isotope))
whence the free-fall acceleration should depend on composition, a ~ const × (1 + Δ(isotope)).
To test this he dropped test bodies of Li, Be, B, C, Al, Fe and Pb 110 m in vacuum in the drop tower of the University of Bremen, the drop capsule itself being aluminium, and tracked their motion relative to the capsule on video at 1.2, 2.4, 3.6 and 4.6 s. Fitting s = v0t + (a/2)t2 he reports:
| Li | C | Pb | |
|---|---|---|---|
| v0 [cm/s] | 1.63(4) | 0.0 | 1.81(2) |
| a [cm/s2] | 0.434(5) | 0.150(3) | 0.102(8) |
| Δa/a [%] | 0.0442(5) | 0.0150(3) | 0.0104(8) |
His conclusion: "the acceleration depends on the composition of the test bodies", contradicting the equality of gravitational and inertial mass between lithium and aluminium at the level
- Δa/a = Δ(Al) − Δ(Li) = 0.044 % = Eötvös parameter.
Elementary gravitational charge
On the strength of this Szász posits a second fundamental property, alongside electric charge, for his four stable elementary particles — electron (e), positron (p), proton (P) and "elton" (E, the negatively charged proton, i.e. the antiproton):
- g(e) = −g m(e), g(p) = +g m(e), g(P) = +g m(P), g(E) = −g m(P)
with the universal gravitational constant then given by G(gravity) = g2/4π.
The consequences he draws are far-reaching:
- Gravitational mass never changes, being built from invariant elementary g-charges.
- G(gravity) is not G(Newton); it is 1.5 % smaller than the literature value, which "is only an average value".
- Between proton and electron — and between e and p, and P and E — the gravitational force is repulsive.
- Two kinds of neutrino exist, the (e,p) and the (P,E) neutrino, being bound states of those pairs, "7.03×10−14 cm and 3.83×10−17 cm large".
- For an isotope of mass number A and charge Z, the gravitational and inertial rest masses differ:
- m(A isotope;g) = A(m(P) − m(e))
- m(A,Z isotope;i) = A m(P) + (A + 2M(e,p))m(e) − E(bound)/c2
- E(bound) and the number M(e,p) of (e,p)-neutrinos in a nucleus follow from a variational principle with a Lagrange multiplier h(0) = h/387; Planck's constant is itself such a multiplier.
The field equation
The g-charges generate a field "very similar to the electromagnetic field", satisfying
- ∂α∂αAβ(g) = −jβ(g), with the Lorenz condition ∂βAβ(g) = 0.
"The minus sign causes that g-charges with the same sign attract each other." The g-field is described as covariant and non-conservative, of finite range within Minkowski space.
Assessment
The paper is admirably direct about what it is testing and how. Szász does not merely assert that the equivalence principle fails; he identifies a specific mechanism (the nuclear mass defect goes into the inertial mass only), derives a specific observable consequence (free-fall acceleration ordered by binding energy per nucleon), and goes to a real 110 m drop tower to look for it. The instinct to check whether the constancy of G is an assumption or a measurement is a good one, and his citation of the CODATA 1998 uncertainty is accurate — that adjustment did carry a relative uncertainty of 1.5×10−3, deliberately inflated because laboratory determinations disagreed. The internal arithmetic of the drop table is also correct: 0.434 cm/s2 divided by g = 981 cm/s2 is 4.4×10−4, and the other two entries check out likewise.
Beyond that the difficulties are severe, and they begin with the paper's own numbers.
The drop result does not reproduce the paper's own prediction. Szász's hypothesis makes Δa/a equal to the difference in relative mass defect. Taking binding energies per nucleon — 5.61 MeV for 7Li, 7.68 for 12C, 8.33 for 27Al, 7.87 for 208Pb, against 931.5 MeV per atomic mass unit — the predicted differences from aluminium are 0.29 % for Li, 0.070 % for C and 0.049 % for Pb. The measured values are 0.044 %, 0.015 % and 0.0104 %: smaller by factors of 6.6, 4.7 and 4.7. The ordering comes out right, but the magnitude is wrong by roughly a factor of five to seven, and not by a constant factor. A theory whose single quantitative prediction is out by that much in its own test experiment cannot be said to be confirmed by it.
The same ordering follows from residual gas drag. The densities of the three test bodies are 0.53, ~2.2 and 11.3 g/cm3, and a drag deceleration is inversely proportional to density — so any residual air in the tower produces exactly the observed ranking, lithium lagging most and lead least. The two explanations are confounded in this data set, and the paper does not report the residual pressure, the body geometry, or a null test with two bodies of the same composition and different density. The reported initial velocities compound the problem: v0 = 1.63 and 1.81 cm/s over a 4.6 s record contribute displacements of 7.5 and 8.3 cm, larger than the 4.6 cm the fitted acceleration produces. In a two-parameter fit s = v0t + (a/2)t2 over a single short arc, v0 and a are strongly correlated, and a release-velocity systematic of a centimetre per second is exactly what would masquerade as the effect sought.
The Kepler figure is very likely an artefact of the formula as written. Newton's version of the third law gives R3/T2 = G(M + m)/4π2, so the composition-independent constant is R3/[T2(1 + m/M)] — the planetary-mass factor belongs in the denominator. Written the other way, as R3/T2 × (1 + m/M), the factor is applied twice in the same direction and each planet acquires a spurious deviation of 2mj/Msun: 0.19 % for Jupiter, 0.06 % for Saturn, negligible for the inner planets. That is precisely the scale of the 0.15 % effect Szász reports, and it is far larger than any genuine deviation — modern planetary ephemerides fit R3/T2 to parts in 108 or better, so a real 0.15 % spread across the planets would have been the most conspicuous fact in celestial mechanics for three centuries. The typography of the source leaves the placement of the factor ambiguous, but on either reading the figure needs an explanation the paper does not supply.
The composition dependence is excluded by direct measurement, by many orders of magnitude. The Eötvös parameter Szász claims to have measured, η = 4.4×10−4, is the same quantity that torsion-balance and space experiments constrain. The Eöt-Wash rotating torsion balance bounds η for beryllium against aluminium — two of the very elements in his sample — below 10−12. Lunar laser ranging, comparing the fall of the Earth (with its large iron core) and the Moon (with almost none) toward the Sun, gives η < 1.4×10−13. The MICROSCOPE satellite reported η(Ti,Pt) = (−1.5 ± 2.3)×10−15 in 2022. Szász's claimed effect is between nine and eleven orders of magnitude above these limits; if it were real, none of those null results could have been obtained. The scatter in G measurements does not rescue it either, because that scatter is between apparatuses, not between materials: torsion balances using copper, tungsten, lead and zinc source masses return mutually consistent values, and the CODATA uncertainty on G has since shrunk from 1.5×10−3 to 2.2×10−5 while the central value moved by less than 0.02 %.
The particle model revives a picture already refuted. Equation (12) makes the gravitational mass of a nucleus A(m(P) − m(e)) — a nucleus of protons and electrons, with no neutron. That is the pre-1932 model, and it was abandoned for a reason that has nothing to do with gravity: a 14N nucleus built from 14 protons and 7 electrons contains 21 fermions and must have half-integer spin, whereas the measured spin of 14N is 1. The proposal that the neutrino is a bound (e,p) pair faces the same kind of obstacle — such a state is positronium, which annihilates to photons in nanoseconds, and cannot carry the lepton number that charged-current weak interactions demonstrably transfer, nor oscillate between three flavours as solar and atmospheric neutrino experiments require. It is also worth noting what the two quoted neutrino sizes are: 7.03×10−14 cm and 3.83×10−17 cm stand in the ratio 1835.5, essentially the proton-to-electron mass ratio, and the first is one quarter of the classical electron radius. They are a rescaling of a known length, not an independent prediction.
The field theory has known pathologies. A vector field with a Maxwell-type equation is a spin-1 theory, and for spin 1 like charges repel; flipping the sign to make them attract, as Szász does, gives the field negative energy, so its radiation carries energy away in the wrong direction and the vacuum is unstable. Such a theory also predicts no deflection of light by the Sun (the photon carries no g-charge in this scheme) and no gravitational redshift, both of which are measured — light bending to two parts in 105 by Cassini's radio tracking, redshift to parts in 104 by Gravity Probe A and by GPS clocks. It predicts dipole gravitational radiation from a binary system, whereas the orbital decay of PSR B1913+16 matches the quadrupole-only prediction to better than a percent. And the repulsion between proton and elton makes antimatter fall upward; the ALPHA-g experiment at CERN reported in 2023 that antihydrogen falls down, with an acceleration consistent with g.
What remains is the underlying question, which is legitimate: is the equality of gravitational and inertial mass a fact or a convention, and how would one know? Szász deserves credit for going to a drop tower to ask. But the answer the wider experimental record gives is unambiguous, and the paper's own data, examined against the paper's own prediction, do not support the conclusion drawn from them.