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We discuss recent laboratory experiments with rotating superconductors and show that three so far unexplained experimentally observed effects (anomalous acceleration signals, anomalous gyroscope signals, Cooper pair mass excess) can be physically explained in terms of a possible interaction of dark energy with Cooper pairs. Our approach is based on a Ginzburg-Landau-like model of electromagnetic dark energy, where gravitationally active photons obtain mass in the superconductor. We show that this model can account simultaneously for the anomalous acceleration and anomalous gravitomagnetic fields around rotating superconductors measured by Tajmar et al. and for the anomalous Cooper pair mass in superconductive Niobium, measured by Cabrera and Tate. It is argued that these three different physical effects are ultimately different experimental manifestations of the simultaneous spontaneous breaking of gauge invariance and of the principle of general covariance in superconductive materials.

The existence of dark energy in the universe, as indicated by numerous astrophysical observations, represents one of the most challenging problems in theoretical physics at present [

While it is clear that dark energy has measurable effects on cosmological scales (such as the accelerated expansion of the universe as seen from supernovae observations), it is much less clear what the effects of dark energy could be on smaller scales. These effects, if any, depend very much on the model considered. For example, if dark energy is due to the existence of compactified dimensions with a diameter of the order of the micron scale, then this would lead to modifications of the gravitational interaction potential on these scales. This can be tested in laboratory precision experiments. Tests by Kapner et al. [

Other more recent models of dark energy, such as the electromagnetic dark energy model of Beck and Mackey [

In models of dark energy like the above one it is the

In this paper we look at recent experiments that were performed with rotating superconductors. There are three observed anomalies that cannot be explained with conventional theories. One dates back already 20 years. Tate et al. [

We will show that all three effects can be quantitatively understood by assuming a possible interaction between Cooper pairs and dark energy as described in the model of Beck and Mackey [

This paper is organized as follows. In Sections

Tajmar et al. have established a research programme at Austrian Research Centers GmbH-ARC with the objective of peering into new possible gravitational properties of superconductive materials. Two different types of experiments have been carried out.

(

(

Based on the known laws of physics, and taking into account all known physical effects in the experimental setup described above in (1) and (2), neither the accelerometers nor the laser gyros should indicate any significant signal above the noise level. This is not what Tajmar's experiments demonstrated. Rather, an azimuthal acceleration signal, which could be associated with an anomalous gravitational field, directly proportional to the superconductive ring angular acceleration, and an angular velocity signal orthogonal to the ring's equatorial plane, which could be associated with an anomalous gravitomagnetic field, have been measured in type-1 and type-2 experiments, respectively [

In Tajmar's experiment, the superconducting ring has a radius of

Like the gravitational field produced by the mass of a physical body, the measured acceleration,

The above value of the coupling is based on single-sensor measurements and the evaluation of maximum acceleration peaks [

Acceleration peaks were also observed when the superconductor passed through its critical temperature while it was rotating at constant angular velocity. These signals had opposite signs for the transition from the normal to the superconductive state and vice versa.

What could be the origin of the measured anomalous acceleration inside the central region of an angularly accelerated Niobium superconductive ring? What could account for the measured coupling (

In the limit of small field strengths and for nonrelativistic movements, the Einstein equations yield a set of Maxwell-like equations which describe so-called gravitomagnetic fields [

The most recent experiments of Tajmar et al. use laser gyroscopes to detect gravitomagnetic fields. A laser gyroscope is an interferometer, measuring the phase difference between two beams of coherent electromagnetic waves with equal frequency,

The same effect, a phase difference, can be caused by a gravitomagnetic flux crossing a laser gyroscope at rest, since a gravitomagnetic field

Superconductors at rest expell any magnetic field. But when they exhibit rotational motion, a magnetic field

By measuring the

Motivated by the absence of any apparent solution of this disagreement in the existing literature, one of us (C. de Matos) formulated the conjecture that an additional gravitomagnetic term must be added to the Cooper pairs' canonical momentum:

The properties of superconductors (zero resistivity, Meissner effect, London moment, flux quantization, Josephson effect, etc.) can be understood from the spontaneous breaking of electromagnetic gauge invariance when the material is in the superconductive phase [

Taking the curl of (

In analogy with the electromagnetic fields produced by a Cooper pair condensate, which are described by the set of Maxwell-Proca equations (

In the 1-dimensional case we obtain the solution of (

So far the Einstein-Maxwell-Proca equations considered in the previous section were not coupled to the electrodynamics of Cooper pairs. We now consider possible interactions, based on the model of dark energy as proposed by Beck and Mackey in [

A nonvanishing cosmological constant (CC)

Whereas details of this dark energy model are described in [

Here we introduce the following additional hypotheses with respect to the original model in [

(

(

(

(

Beck and Mackey's Ginzburg-Landau-like theory leads to a finite dark energy density dependent on the frequency cutoff

In the interior of superconductors, according to Assumption 2, the effective cutoff frequency can be different from that in (

An experimental effort is currently taking place at University College London and the University of Cambridge to measure the cosmological cutoff frequency through the measurement of the spectral density of the noise current in resistively shunted Josephson junctions, extending earlier measurements of Koch et al. [

In [

Let us now come to our physical explanation of the observed experimental effects, using the dark energy model of the previous section. In Tajmar's type-1 experiments, a strong angular acceleration applied to the superconductive ring can break the bound between a Cooper pair and its associated graviphoton. In that process the Cooper pair looses the mass

If the superconductive ring rotates with constant angular velocity and the temperature

We suggest to call this coherent emission of graviphotons by accelerated superconductors the “

Let us first provide a short derivation of the ordinary electromagnetic London moment–-after that we will proceed to the gravitomagnetic London moment. The Cooper pairs in a superconductor can be regarded as a condensate described by the wave function

In close analogy to the above derivation, let us now proceed to a gravitomagnetic London moment as produced by dark energy. As seen before, our central hypothesis is that the gravitational quantum condensate is related to dark energy. We may assume that cosmological quanta of energy

From the Einstein-Maxwell-Proca equations of our electromagnetic model of dark energy with massive bosons we can derive the inertial properties of a superconductive cavity. Taking the gradient of (

We may define a Planck-Einstein temperature

Let us evaluate the theoretically predicted coupling for various types of superconductors, starting with Aluminium and ending with High-

We note that for YBCO, with

Predicted coupling

Superconductive material | ||
---|---|---|

High- | ||

At this point one remark is at order. Our theoretical derivation presented in this paper strictly speaking holds only for conventional low-

Our approach raises interesting perspectives for future experiments.

(

(

(

Let us end this paper with some general remarks. General Relativity is founded on the

the equation holds in the absence of gravitation; that is, it agrees with the laws of special relativity when the metric tensor

the equation is generally covariant; that is, it preserves its form under a general coordinate transformation

Any physical principle such as the PGC, which takes the form of an invariance principle but whose content is actually limited to a restriction on the interaction of one particular field, is called a dynamic symmetry. Local gauge invariance, which governs the electromagnetic interaction, is an important example of a dynamic symmetry. We can actually say that the Principle of General Covariance in general relativity is the analogue of the Principle of Gauge Invariance in electrodynamics. The breaking of gauge invariance leads to superconducting states. The breaking of general covariance leads to nonconservation of energy momentum (in the covariant sense) [

There are several possibilities to make the above ideas on the breaking of PGC more concrete. One is based on geometric algebra and gauge theories of gravity [

In this paper we have investigated in detail the possibility that the dark energy of the universe may interact with Cooper pairs in superconductors, thus leading to effects that can be observed in the laboratory. Whether or not such an interaction is a realistic assumption depends very much on the dark energy model considered. The electromagnetic dark energy model of Beck and Mackey [

There are first experimental hints that one might be on the right track with these types of theoretical models. The graviphotonic effect, the gravitomagnetic London moment, and nonclassical inertia in rotating superconductive cavities are three different experimentally observed effects which can all be explained by the proposed model of dark energy—not only qualitatively but also quantitatively. The model ultimately relies on the spontaneous breaking of gauge invariance and the spontaneous breaking of the principle of general covariance in the interior of superconductors.

The considerations presented in this paper, if confirmed by further independent experiments, would imply that the dark energy of the universe produces measurable effects not only on cosmological scales but also in the interior and the vicinity of superconductors. This opens up the way for a variety of new possible laboratory experiments testing the nature of dark energy and constraining the interaction strength with Cooper pairs. In our model gravitationally active vacuum fluctuations underlying dark energy lead to a strong enhancement of gravitomagnetic fields, in quantitative agreement with the anomalies seen in the experiments of Tate et al. [

The authors would like to thank Dr. Martin Tajmar for useful comments on an early version of this paper.