As a physicist, I love this thread youve created and the analogy I found enjoyable =D. One could also use the analogy of a coiled spring (which ive heard used in these forums), which has potential energy 1/2kx^2 (harmonic oscillator) which is very similar to the classical kinetic energy equation 1/2mv^2
if we say that the kinetic energy is entirely due to the expansion of a spring, then we can try and solve for k, the spring constant, which to extend your analogy 'would be a measure of how fast the share price moves in relation to the size of the move in price'
that does lead one to think how much easier investing would be if price action obeyed the relatively simpler laws of newtonian dynamics rather than those of stochastic calculus. Furthermore, the idea that price action could approximate a damped harmonic oscillator is not entirely stupid, with mean reversion being a strategy that assumes a damped oscillation about the mean as price approaches fair value and all information available is digested by the market (obviously theoretical case)
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