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The Building Blocks of Everything
The constituents of atoms electrons, protons and neutrons were supposed to be the building block of matter before scientists unveiled particles called quarks and leptons.
Studies is still going on about this basic question what is the smallest thing in the universe?This article is my personal view something which i have felt through my insight and studies in physics and mathematics.I have certain theories of various established scientists behind my hypothesis .
First i will be explaining the reason behind the building block of everything or rather the smallest particle.
In the year 1924,a young physicist De Borglie explained that frequency of matter waves is proportional to the total energy content.He proposed the wave particle duality and showed that wavelength is inversely proportional to the momentum of the particle and is called the De Borglie wavelength.
'FREQUENCY',The per second magic is in my view the building block of everything.its unit is hertz after the scientist Heinrich Rudolf Hertz who first proved the existence of electromagnetic wave.
Signals,the source of information,is made of frequency.Every signal can be grouped in either of the following categories discreet,continuous ,periodic and aperiodic in time and frequency.Sum of complex exponential signals can formulate any signal in this universe.Euler's basic formula gives further dimension to this theory that every signal in this universe is made of complex sinusoids.x(t)=Ce^at,the representation for complex sinusoids where C,a are complex numbers.
This theory was utilised by Sir Joseph Fourier in his work for fourier series and transform which is the very useful area of applied mathematics today.Infact it is the frequency content of signal or information which rules not only the communication industry but the whole world.Any periodic signal can be expressed as a sum of complex sinusoids. He approximated a periodic signal as a linear combination of harmonically related complex exponential and the error signal had the least energy.
But what about the aperiodic signals.So do we have another building block for these?No.Frequency tunes it too! An aperiodic signal is the periodic signal with period infinity and this was the idea behind the fourier transform.
Again many of you may question about the existence of fourier transform and series ,they have a boundary 'The Dirichlet's condition'.Yes,the conditions for fourier series for periodic signal and transform for aperiodic signal is that the signal should be absolutely integrable (in case of transform) and absolutely integrable over a period (for series),that they should have a finite number of discontinuity and a finite number of maxima and minima in any finite time interval.
Every signal in this physical world and for various application comes under this broad category yet there are some uncommon ones which do not .For their rescue came the laplace transform proposed by pierre simon laplace in his work of probability theory.the laplace transform exist for all signals for which fourier tansform does not. Introduction of a convergence factor (sigma) alongwith j(omega).These signals are represented by e^(st). and laplace transform is actually the fourier transform of x(t)e^(-(sigma)t).
Sir Edwin Schrodinger who provided the probabilistic description of wave is another great pioneer of mathematics and his work can be another theory provided for the' building block of everything'.his work can explain the probability that something frequency is there.
These works by eminent scientist in my opinion is very informative ,descriptive and can uncover many relevant issues.Frequency speaks,Frequency colours,Frequency composes as it is the best approximation for expanding any signal because the error signal contained the least energy .
© 2014 Pallavi Bharati