Physical approach to elucidate stability and instability issues, and Elliott waves in financial systems: S & P-500 index as case study

The dynamics of financial systems depends not only on Brownian motion but also on wave-like behavior of fluctuations. Statistical mechanics and viscoelastic theory were used to elucidate it by using the daily data of S & P-500 from 1986 to 2019. The viscoelastic behavior of asset values or stock market index can be studied within the basis of "cause-and-effect" principle by using scattering diagram of the data. The angles between the consecutive vectors in scattering diagram reveal that some peculiar angles deviate from the main course of the percent occurrence. These angles correspond to relatively more stable states, and they can be expressed in terms of golden ratio. The Elliott waves and golden ratio observed in financial systems can be explained by the existence of these peculiar angles. Whenever stability is of major concern such as in sharp falls or sharp increases and also in Elliott waves these angles reveal more frequently. The formation principles of Elliott waves were established on physical and mathematical grounds.