Demand curve and the de Broglie wave function
It follows, that if this is all so, then the demand curve is also (directly) related to quantum mechanics –
|Fig. 1 The de Broglie diagram|
It was not until I saw the above diagram (Fig. 1) in an elementary physics textbook, that I realised that there maybe a direct relationship between demand and quantum - and something more significant to say about this most ‘unlikely’ of coincidences. The classical demand curve (fig. 2 below) is also a downward sloping log. log. function.
|Fig.2 The demand curve|
If there is any relationship between fig. 1 and fig. 2 then it maybe as simple as finding a connect between the variables price and quantity demanded (from classic economics) and the variables wavelength and momentum (from quantum mechanics).
I am laying down a theory here. What I see. I expect there to be problems, and discussion. With this in mind, fractal theory would suggest from the outset that the two should be connected, universal, unbounded - irrespective of scale.
One at a time, I have been analysing these variables and other related patterns, but have found no direct relationship as yet.
1. Price and Wavelength
|Fig. 3 Please excuse the misleading label 'Fig. 1' - near the title of this diagram.|
1.2 Fractal wave and superposition
More recent discoveries from the fractal (in this blog) have suggested that there is a wave like nature to fractal development and that the MA curve above shows all the (infinite) positions (super position) of the triangles. Amplitudes (A), wavelengths (λ) frequency (f) are derived from, and can be demonstrated in, every fractal development, and they all increase in their magnitudes in an exponential manner that corresponds to the quantum nature of electromagnetic spectrum.
1. 3 Is price (derived from the marginal area in the fractal) really the same as the wavelength in the de Broglie diagram?
Directly, no. The price (as far as understood) is the amplitude of the wave, and not the wavelength. This should end the discussion, but for the fact that - and not withstanding the understanding that both Wavelength (λ) and the Amplitude (A) are independent of each other in classical wave theory - that the two (in the case of the fractal) are both inextricably linked as having an exponential nature, and both share infinity in their scale. It is as if λ is equal to or related to f . In discussions with mathematician's and from readings, it is suggested that this it quite possible.
In Ian Stewart's, Taming The Infinite, Quercus Publishing 2008, page 124: on Bassel functions ' The amplitudes of these waves still vary sinusoidally with time, but their spatial structure is more complicated.' 'The wave equation is exceedingly important. Waves arise not only in musical instruments, in the physics of light and sound. Euler found a three dimensional version of the wave equation... Clark Maxwell extracted the same mathematical expression from his (Euler's) equations for the electromagnetism, and predicted the existence of radio waves.'
And, from wikipedia: '... and based on the theory of Fourier decomposition, a real wave must consist of the superposition of an infinite set of sinusoidal frequencies.' on the subject of electromagnetic wave equations.
2. Quantity Demanded (Qd) and Momentum (mv)
- Qd: is the quantity demanded for a good in a specific time period - so is a rate, or frequency.
- Qd is said to be exponential in nature, and is shown and demonstrated to be exponential (by use of the fractal) in this blog.
As I have pointed out, the fractal shows no concept of distance: so what to do, leave it?