Dynamic Weighing Experiments - the Way to New Physics of Gravitation
| Scientific Paper | |
|---|---|
| Title | Dynamic Weighing Experiments - the Way to New Physics of Gravitation |
| Read in full | Link to paper |
| Author(s) | Alexander L Dmitriev |
| Keywords | Gravity Force, Weighing, Acceleration, Free Falling, Gyro, Equivalence Principle |
| Published | 2010 |
| No. of pages | 11 |
Read the full paper here
Abstract
Dynamic weighing is a measuring of size of the average gravity force acting on a test body which is in the state of accelerated movement. The acceleration of a body, or its microparticles, can be caused both by forces of gravitation, and by a direct, electromagnetic in nature, influence on the part of other bodies. It is just dynamic weighing of bodies which is informative in studying the features of electromagnetic and gravitational forces interaction. The report gives a brief review of results of experiments with weighing of accelerated moving bodies – in case of shock phenomena, in state of rotation, and in heating. Special attention is given to measurements of free fall accelerations of a mechanical rotor. In majority of the laboratory experiments executed with the purpose of checking the equivalence principle, the axis of a rotor was oriented verticallly. In our experiment we measured the free fall accelerations of the closed container inside which a mechanical rotor (gyroscope) with a horizontal axis of rotation was installed. There was observed an appreciable, essentially exceeding errors of measurements increase of acceleration of free falling of the container at angular speed of rotation of a rotor up to 20 000 rev/min. The physical conditions of free vertical falling of a body essentially differ from conditions of rotary (orbital) movement of a body in the field of gravity and the result obtained by us does not contradict the results of measurements of a gyroscope precession on satellites. Experiments with dynamic weighing of bodies give useful information on complex properties of the gravity force which are beyond the scope of well-known theories. Their careful analysis will allow to expand and supplement the concepts based on the general theory of relativity, and probably to open a way to new physics of gravitation and to new principles of movement.
Keywords: Gravity Force, Weighing, Acceleration, Free Falling, Gyro, Equivalence Principle.
Overview
Alexander L. Dmitriev, with E. M. Nikushchenko and S. A. Bulgakova of St Petersburg State University of Information Technologies, Mechanics and Optics, presented this paper to the Space, Propulsion and Energy Sciences International Forum. It is part programme statement, part review of the group's own decade of weighing experiments, and part report of one new measurement: the free fall of a sealed container holding two mechanical gyroscopes spinning about a horizontal axis.
The programme rests on a distinction the authors think has been quietly ignored. Weighing can be static — the body at rest, its weight balanced by an elastic or electromagnetic force — or dynamic, the body oscillating, spinning, impacting or being heated. Metrology treats the two as equivalent; Dmitriev argues they are physically different states, and that gravity may respond to a body's acceleration. His organising analogy is electromagnetic: gravity should have "a gravitational analogue of Faraday's law of induction and Lenz's rule", so that a body accelerated by external non-gravitational forces sees its own gravitational acceleration altered in a way that opposes the change. He quotes Mendeleev in support of the method: "If it is possible to achieve something in understanding of gravitation and weight, then in no other way and most likely by the most precise weighings."
The departure from the mainstream is a departure from geometry. Dmitriev explicitly prefers a "field" concept of gravitation to a "geometrical" one, precisely because a field concept permits the electromagnetic analogies and their direct experimental test, and he holds that the ratio of inertial to gravitational mass "generally speaking, is not a constant."
The argument
The Lenz-rule postulate and the origin of inertia
The core assumption is his equation (1): when a body is accelerated by external, non-gravitational forces with acceleration a, the acceleration of gravity acting on it changes by Δgp,c = −αp,ca, where the subscripts distinguish acceleration parallel ("passing", p) from antiparallel ("contrary", c) to the normal gravity vector g0. From earlier weighing of coupled rotors and from shock experiments, the authors quote for non-magnetic metals αc ≈ 10−2 and a much smaller difference (αp − αc) ≈ 10−7. That the two coefficients are unequal is then said to explain their reported negative temperature dependence of weight, and the weight anisotropy of a crystal with strongly direction-dependent sound speeds.
The postulate is next used to derive inertia, following Mach. Balancing the elastic and gravitational forces exerted on a test mass by all remote matter gives mi ∝ mg(αp + αc), i.e. inertial and gravitational mass are proportional but not necessarily in a fixed ratio. Refined, equation (3) makes the increment depend on the total gravitational field gΣ produced by the remote masses in a hemisphere: Δgp,c = −Ap,c(gΣ ± g0). Because the contributions of the two opposing hemispheres cancel for a body at rest, gΣ exerts no net force but does, in this picture, determine the body's inertia.
Anisotropy of inertial mass, and the watch experiment
The consequence Dmitriev singles out is that inertial mass should differ between vertical and horizontal acceleration. For a harmonic oscillator, the vertical average inertial mass carries the extra term 2g0 while the horizontal one does not, so the fractional difference is of order 2g0/gΣ. Since the period of a mechanical oscillator is T = 2π√(I/C), a balance wheel oscillating in a vertical plane should have a longer period than one oscillating in a horizontal plane: "the ideal mechanical watch in position 'on an edge' goes more slowly, than in position 'flatwise'."
The authors tested this on twenty-one specimens of the Soviet Raketa 2609 movement from the Petrodvortsovy watch factory, comparing average daily rate flat against edge-on, each averaged over two orientations. The mean delay on edge was about 15 seconds per day, i.e. ε ≈ 1.7 × 10−4. To their credit, they immediately flag the confound: "The question of what part of the given value ε is caused by action of physical factors ... and what – by technical imperfection of the mechanism of watch still remains open", and note that adjustment can null a real effect just as easily as a spurious one. Taken at face value, the number would imply that the "interstellar" field gΣ is roughly a thousand times the Earth's surface gravity.
The free-falling horizontal gyroscope
The new measurement is deliberately different from the standard gyroscope tests, which the authors note were mostly done with a vertical spin axis and returned null results. Two coaxial gyroscope rotors, spun to 20 000 rpm with a maximum total angular momentum of 0.2 kg·m2/s, were sealed in a container carrying a stable pulse generator driving two differently coloured LEDs. The container was dropped and photographed with a digital camera at 0.6–0.8 s exposure, so the trajectory appears as a train of light marks; the pulse frequency was 56.25 Hz, the LED separation 76.25 mm gave the image scale, and pulse duration was 0.13 ms. Acceleration was extracted from successive segment lengths by
g = F2(Δℓ2 − Δℓ1)/N2,
with the scale averaged over three readings up the frame to reduce lens distortion. More than 200 photographs were processed in cycles of the form: rotors at rest, rotors spinning, rotors at rest again after spin-down.
The reported result is a systematic increase in free-fall acceleration when the rotors spin, averaging about 2 cm/s2, falling smoothly to zero as the rotors slow. Two controls are reported: the geographical orientation of the spin vector (N–S or W–E) made no difference, and no diurnal variation was seen. The authors state candidly that the absolute value they measure with rotors at rest, about 990 cm/s2, differs from the standard value at the latitude of St Petersburg, about 982 cm/s2, and attribute the discrepancy to scale and generator-frequency errors.
The paper closes by defending the result against the satellite gyroscope-precession measurements — "free falling of masse oscillated along a vertical physically essentially differs from circular (orbital) movement" — and by proposing that nuclei with aligned spins might serve as microscopic rotors, with implications for propulsion.
Assessment
There is something genuinely worth taking seriously in the framing. The static/dynamic distinction is a real one, most gravitational tests really are performed on quasi-static bodies, and the call for a systematic programme of dynamic weighing is a reasonable experimental proposal rather than a theoretical assertion. The authors are also unusually honest: they describe their own results as "certainly of a preliminary character", they name the horological confound in the watch experiment themselves, and they report the absolute-g discrepancy instead of hiding it. The kinematics of equation (9) is correct — for marks at equal time intervals 1/F, successive equal-count segments differ in length by a(N/F)2 — and the arithmetic of the watch result checks: 15 s in 86 400 s is 1.74 × 10−4, matching the quoted 1.7 × 10−4.
But the reported absolute-g discrepancy is fatal to the free-fall claim as it stands, and by the paper's own numbers. Measuring 990 cm/s2 where the true value is 982 is an error of 8 cm/s2, or 0.8 per cent. The claimed effect is 2 cm/s2, or 0.2 per cent. The uncontrolled systematic is thus four times larger than the signal. Since the error is attributed to the image scale ℓ and the generator frequency F, and since g in equation (9) is proportional to F2 and to the scale, a drift of a few tenths of a per cent in either between the "rotors at rest" and "rotors spinning" photographs would reproduce the entire effect. The measurement sequence makes this worse rather than better: the cycles run rest → spinning → rest in fixed time order, over runs of 14–15 minutes, so any slow drift in camera position, focal length, temperature or generator frequency aliases directly onto the signal. Randomising the order, or interleaving, would be the obvious remedy. A second unaddressed systematic is that a container holding 0.2 kg·m2/s of angular momentum will not fall like a passive body: any tumbling, nutation or slight rotation of the container changes the apparent LED separation and hence the scale, and the rotors' own heating during a 15-minute run would, in the authors' own framework, change the weight through the temperature dependence they claim elsewhere.
The claimed magnitude is also far outside the limits set by the very experiments the paper cites. Nitschke and Wilmarth (1990), Faller and colleagues (1990), Quinn and Picard (Nature, 1990) and Luo and colleagues (2002) all searched for exactly this kind of rotation-dependent weight change and all reported nulls, at sensitivities several orders of magnitude finer than 2 × 10−3. Dmitriev's answer — that those experiments used vertical spin axes — is legitimate in principle but does not cover the free-fall geometry, and it does not address the routine performance of ballistic absolute gravimeters, which drop a corner cube in vacuum and agree with static superconducting gravimeters at the microgal level, about 2 parts in 109. That agreement between a dynamic and a static method is precisely the comparison the paper says has never been made, and it is made every day.
The inertial-mass anisotropy fares worse. Dmitriev cites Hughes, Robinson and Beltran-Lopez (1960) for the proposition that "GR excludes the practical observability of anisotropy of inertia", but that paper is a measurement: it looked for a direction-dependent splitting of the lithium-7 nuclear magnetic resonance and set an upper limit on the fractional mass anisotropy of about 10−20. Modern Hughes–Drever experiments push this many orders further still. A claimed anisotropy of 1.7 × 10−4 sits some sixteen orders of magnitude above the 1960 bound in the paper's own reference list. Independently, the watch result has an entirely ordinary explanation: position sensitivity is a standard property of every mechanical watch, arising because in vertical positions the balance staff pivots bear sideways against their jewels, increasing friction, reducing amplitude and slowing the rate. This is why watches are regulated in multiple positions, and 15 s/day between flat and edge on a mass-market movement is unremarkable. Dmitriev says as much; but having said it, he then uses the same number to infer gΣ ≈ 103g0, which is not a conclusion the data can bear.
Two theoretical points deserve notice. First, the fitted coefficients are doing the work the mechanism claims to do. Equations (4) and (5) reproduce the proportionality of inertial and gravitational mass only because the product (Ap + Ac)gΣ is effectively set to unity; the equivalence principle is not derived from the Lenz-rule postulate but imposed on it, and the residual anisotropy is then whatever gΣ is chosen to make it. With gΣ itself inferred from the watch data, the scheme has no independent predictive content in this paper. Second, αc ≈ 10−2 is a very large number to assert. A body acted on by elastic forces at ordinary accelerations would then show per-cent-level weight changes, and the modern torsion-balance tests of the equivalence principle constrain differential accelerations at the 10−13 level. The paper does not reconcile the two.
What survives is the experimental programme rather than the results. The list of proposed measurements at the end — temperature dependence of weight, dynamic weighing of bodies oscillating in a vertical plane, free fall of rotors at various axis orientations, direction dependence of the coefficient of restitution — is concrete and, with modern interferometric or atom-interferometric readout rather than photographed LED trains, cheaply testable. The authors themselves ask for exactly that. On the evidence presented here, though, the effects reported are of the size one expects from uncontrolled systematics, and the paper's own absolute-g discrepancy says so.