QuoteEvidence of the gravitational-like nature of the effect;
The gravitational-like nature of the effect is best demonstrated by its independence on the mass and composition of the targets (see Section 3). We are aware, of course, that gravitational interactions of this kind are absolutely unusual (see Sections 4.1, 4.3). For
this reason, several details of the experimental apparatus were designed with the explicit purpose of reducing spurious effects like mechanical and acoustic vibrations much below the magnitude order of the observed anomalous forces.
Indirect evidence for a gravitational effect comes from the fact that any kind of
electromagnetic shielding is ineffective. Note that if one can explain in some way the anomalous generation of a gravitational field in the superconductor, its undisturbed propagation follows as a well-known property of gravity (see Section 4.2). Indirect support for the gravitational hypothesis also comes from the partial similarity of this apparatus to that employed by Podkletnov for the stationary weak gravitational shielding experiment [1].
If the effect is truly gravitational, then the acceleration of any test body on which the impulse acts should be in principle independent on the mass of the body. Suppose that l is the length of a detection pendulum and g is the local gravitational acceleration. Let d be the half-amplitude of the oscillation. Let t be the duration of the impulse, and F its strength. F has the dimensions of an acceleration (m/s2) and can be compared with g.
One easily computes that the product of the strength of the impulse by its duration is
Ft = r2gl[1 - q1 - (d/l)2] (1)
If d « l, this formula can be simplified, and we have approximately Ft ~ q(g/l)d = 2d/T,
where T is the period of the pendulum. With the data of Table 1, taking t = 10-4 s, one
finds F ~ 103g.
Here, however, we encounter a conceptual difficulty. Suppose to place on the trajectory of the beam a very massive pendulum (say, 103 Kg). If the effect is gravitational, then the acceleration of a test mass should not depend on its mass. However, it is clear that in order to give this mass the same oscillation amplitude of the small masses employed in the experiment, a huge energy amount is necessary, which cannot be provided by the device.
Therefore the effect would seem to violate the equivalence principle. Considering the backreaction is probably necessary, namely the fact that the test mass exerts a reaction on the source of the impulse. This reaction is negligible as long as we use small test masses.
Anomalous features of the observed "radiation";
Independently from any interpretation, the abnormal character of this radiation appears immediately clear. It appears to propagate through walls and metal plates without noticeable absorption, but this is not due to a weak coupling with matter, because the radiation acts with significant strength on the test masses free to move. Furthermore, this radiation conveys an impulse which is certainly not related to the carried energy by the usual dispersion relation E = p/c. A corresponding energy transfer to the test masses is not in fact observed (unless one admits perfect reflection, which seems however very
unlikely).
The denomination "radiation" is actually unsuitable, and one could possibly envisage an unknown quasi-static force field. In this way one could explain why an impulse is transmitted to the test masses. However, it is hard to understand how such a field could be so well focused.
A possible theoretical explanation. Basic concepts;
The following Sections contain an informal introduction to a theoretical model originally developed by one of the authors [18, 19, 20, 21, 22] in order to explain the weak gravitational shielding effect by HTC superconductors [1, 2]. We suggest that this theory may be a starting point for the explanation of the impulsive gravitational-like forces described in the present paper.
The quantum properties of the gravitational field play an essential role in this model.
These properties are not adequately known yet, therefore the proposed model is still in a preliminary development phase and its predictive capabilities are quite limited. Its primary merit is to envisage a new dynamic mechanism which could account for the effect. However, a full theory which justifies the model does not exist so far. This should be, in fact, a theory of the interaction between gravity (including its quantum aspects), and a particular state
of matter - that of a HTC superconductor - which in turn is not completely known.
(a) Weakness of the standard coupling with gravity. Anomalous coupling;
The standard coupling of matter to gravity is obtained from the Einstein equations by including the material part of the system into the energy-impulse tensor. Since the coupling constant is G/c4, very large amounts of matter/energy, or at least large densities, are always
necessary in order to obtain gravitational effects of some importance. This holds also at the quantum level, in weak field approximation. It is possible to quantize the gravitational field by introducing quantum fluctuations with respect to a classical background, and then calculate the graviton emission probabilities associated to transitions in atomic systems.
These always turn out to be extremely small, still because of the weakness of the coupling. What we proved in our cited works is that a peculiar "anomalous" coupling mechanism exists, between gravity and matter in a macroscopic quantum state. In this state matter is described by a collective wave function. Also in this state the energy-impulse of matter couples to the gravitational field in the standard way prescribed by the equivalence
principle. However, the new idea is that besides this standard coupling there is another effect, due to the interference of the Lagrangian L of coherent matter with the "natural" vacuum energy term /8G which is present in the Einstein equations. The two quantities have in fact the same tensorial form but possibly different sign, and it turns out that their
interference can lead to a dramatic enhancement of vacuum fluctuations.
(b) Contribution of a quantum condensate to the vacuum energy density;
It is well known that the "natural" vacuum energy, or cosmological term, is very small. Until recently, it was thought to be exactly null. The most recent observations give a value different from zero, but in any case very tiny [23, 47], of the order of 0.1 J/m3.
This is usually supposed to be relevant at cosmological level, in determining the curvature and expansion rate of the universe on very large scales.
The observed value can be regarded as the residual of a complex interplay, in a still unknown high energy sector of particle physics, between positive and negative vacuum energy densities. According to [24], the observed residual should also be scale-dependent and this dependence could appear most clearly at length scales corresponding to the mass of the lightest particles like neutrinos or unidentified scalars.
Glossary:
Cosmological term = vacuum energy density: see (b).
Lagrangian L = action density. Minimization of the action of a system gives its dynamical equations.
Quantum condensate in a superconductor: ensemble of the Cooper pairs, with collective wave function
GL (also called an "order parameter") supposed to obey the Ginzburg-Landau (GL) equation. In the
non-relativistic limit, the Lagrangian density of the condensate is just the opposite of the GL free energy density.
Zero-modes of the Einstein action = gravitational dipolar fluctuations: see (c).
Critical region: region of the condensate with positive Lagrangian density. According to the GL theory,
it can only exist for constant solutions of the GL equation or in the neighbourhood of a local relative
maximum of the Cooper pair density | GL|2. See (f).
Noise source = density matrix: a formal way to express the fact that inside a critical region the gravitational
field undergoes strong dipolar fluctuations and therefore takes on at random values h2/i with probability i. See (h), (i).
QuoteIn certain conditions, the action density of a Bose condensate in condensed matter can be greater than the cosmological term, but it is nonetheless very small. Its effect on the local space curvature is absolutely negligible.
(c) The gravitational zero modes and the polarization of the gravitational vacuum.
Why so do we think that the interference of these two terms, which are in any
case very small, can lead to some observable gravitational effect? Because we proved the existence of gravitational field configurations in vacuum, for which the value of the pure Einstein action (without the cosmological term) is exactly null, like for flat space. We called these configurations "zero modes of the Einstein action". At the quantum level, where fluctuations are admitted with respect to flat space, they are free to grow unrestrained.
In a certain sense, the quantum space-time is unstable and has a natural tendency not to stay in the flat state, but to fall into these configurations, with a definite probability. They are virtual configurations, in the sense that they are permitted in the Feynman integral describing the quantum theory. In the Feynman integral all the possible configurations are admitted - not only those satisfying the field equations - each weighed with probability equal to the exponential of its action divided by ¯h. All these configurations (fluctuations)
take part in defining the state of the system.
The zero-modes of the Einstein action are in all the same as fields produced by
mass dipoles. In nature, mass dipoles do not exist as real sources. Nevertheless, the dipolar fluctuations mathematically have such a form. Being vacuum fluctuations, they are invariant under translations and Lorentz transformations, they are homogeneously allocated in space and at all length scales. That is, the dipolar fluctuations correspond to the fields produced by dipoles of various sizes, distributed in a uniform way. They can
only show their presence if, in some way, their homogeneity and uniformity are broken. We are in presence of an analogue of the vacuum polarization in quantum electrodynamics. In that case, virtual couples of electrons/positrons pop up in the vacuum, and then quickly annihilate, generating uniform fluctuations. It is well known that these virtual processes must be taken into account, because they affect, for instance, the bare charge of the particles
and their couplings. However, quantum corrections are, as a rule, very small in quantum electrodynamics.
It is important to be aware that the gravitational dipolar fluctuations we are talking about are neither the ordinary fluctuations of perturbation theory nor the well known "spacetime foam" fluctuations, which appear in quantum gravity at very short distances.
Their nature is completely different. Although their intensity can be very large, they have null action, thanks to the compensation of positive and negative curvature between adjacent zones of space-time. The dipolar fluctuations are not zero-modes of the Lagrangian, but of the action. Their existence is possible thanks to the fact that the gravitational Lagrangian is not defined positive, unlike the Lagrangian of electromagnetic and gauge fields.
(d) The vacuum energy cuts the gravitational zero-modes to a certain level;
Let us go back to the cosmological term. One finds that it is related to the dipolar fluctuations, because it sets an upper limit on their amplitude. The contribution of a dipolar fluctuation to the cosmological term is typically of the form [21]
S = Mr2Q (2)
where natural units are used (¯h = c = 1); is the duration of the fluctuation, M is the order of magnitude of the virtual +/- masses, r their distance and Q is an adimensional function which depends on the detailed form of the dipole. If S » 1, then the fluctuation is suppressed.
With an electromagnetic analogy (not to be pushed too far) we could then say that the cosmological term sets the gravitational polarizability of free space. One expects that in a full non-perturbative theory of quantum gravity the bare value of the gravitational constant G should be renormalized by this effect. However, as long as the cosmological term is uniform in space and time, there are no observable consequences. On the other hand, if the vacuum energy density changes locally, this can have observable effects. In particular, if there are positive local contributions which subtract from the natural density,
the result can be a local increase in the gravitational polarizability.
(e) The anomalous coupling is only active when the condensate is in certainparticular states;
Our model can also explain why only certain superconductors in certain conditions show evidence of anomalous coupling with the gravitational field. The key point is not simply the presence of a quantum condensate, nor the density of this condensate. In fact, if this was the case, anomalous gravitational effects would be observed also with low temperature superconductors, or with superfluids. But even in the static Podkletnov
experiment, only in certain conditions observable effects are obtained, and their intensity is variable.
Therefore the presence of the condensate is not sufficient to cause the effect. What are the necessary conditions? The anomalous contribution to the cosmological term is given by the Lagrangian density of the condensate, according to the following equations.
Consider a scalar field interacting with gravity (we use units ¯h = c = 1; SI units will be restored in eq. (12)). The interaction action is obtained from the energy-momentum tensor:
At this point it goes into some complex equations that i can't even print here :) but it's all in the PDF linked in the 'man' page, which i will copy here;
http://www.mediafire.com/view/?t6wqhd8j9qxaurf (http://www.mediafire.com/view/?t6wqhd8j9qxaurf)
Enjoy!