The selection of sustainable indicators is crucial in measuring and understanding the required targets within the theme of sustainability for an energy system. This is because sustainability, as a term, is used in several fields and covers a variety of indicators based on the problem’s context and identity. Each researcher looks at sustainability from their own perspective and selects the indicators which align best with their objectives and their understanding of the topic. This paper aims to implement a systematic approach to choosing the sustainable indicators for Bahrain’s electrical production with renewables. The proposed framework analyses the frequency of indicators in a sample of 73 studies and screens them in accordance with the selection principles and experts’ views. The results reveal 15 indicators with strong relevance to sustainable growth for the power sector with renewables. These indicators are classified as either qualitative or quantitative, depending on our case study’s context and the appropriate practice according to the literature. Finally, each of the selected indicators was defined to reflect its intended purpose in our study, since the common practice within the present literature is to provide such indicators without explaining their actual purpose.

The Three Wave Hypothesis (TWH) has been proposed by Horodecki in 1981. Sanduk attributed TWH to a classical kinematical model of two rolling circles in 2007. In a previous project in 2012, it is shown that the position vector of a point in a system of two rolling circles can be transformed to a complex vector under the effect of partial observation. The present work tries to develop this concept of transformation. Under this transformation, it is found that the kinematical equations of the motion of point can be transformed to equations analogise the relativistic quantum mechanics equations. Many analogies have been found and are listed in a comparison table. These analogies may sagest that both of the quantum mechanics and the special relativity are emergent, and are of the same origin.

The complex formulation plays a serious roll in the quantum mechanics. Physicists do not agree on physical or philosophical explanations for this complex mathem

Euler’s formula is a pure mathematical formula. In spite of its nonphysical nature, the form of this formula has a genuine fundamental role in quantum mechanics, but with no physical reason for this role. Philosophically, Heisenberg has proposed Kantian ideas in physics like “nature in itself”, unobservable nature, and “nature as appears”. He proposed a possibility of mathematical formulation for a system in nature in itself. In the present work, a mathematical model of rolling circles in real space has been proposed as a model for a system in nature in itself. Observation process acts as a transformation of the system to a model in observable nature. Partial observation transforms the real position vector of a point in that system to a form similar to the Euler’s formula. That causes the appearance of the imaginary unit. Interestingly, the transformed real kinematical forms exhibit similarity with the forms of relativistic quantum mechanics.

Three Wave Hypothesis (TWH) is of a relativistic quantum foundation. The formulation of TWH has perfect similarities with bevel gear model. The rest mass is considered within TWH and as a consequence of similarity, between TWH and the gear model, it is found that rest mass frequency is related the frequency of touch point of the gear in relative to the large wheel. In regarding this frequency instead of the small wheel frequency, the gear model leads to four-vector representation of a particle.