Uncertainty Principle of Mathematics

Transcription

1 Septeber 27 Ucertaity Priciple of Matheatics Shachter Mourici Israel, Holo Preface This short paper prove that atheatically, Reality is ot real. This short paper is ot about Heiseberg's ucertaity priciple of quatu physics. There is aother ucertaity priciple that depeds solely o atheatical arguets ad explais why our world ca't be easily equated. Or ore accurately ca be describe i ifiitely differet ways all of those represetatios are atheatically correct. Which ea that the represetatio of ay physical pheoea is ot uique.. Derivig the Matheatical Ucertaity Priciple It is well kow that ay periodical shape has a Fourier series ad o periodical shapes has a Fourier trasfor. Suppose oe wat to fid fourier series for a ifiit flat trai. A sectio of that ugly atheatical trai is described i the picture below. Two copoets of the Fourier series are also show; of course the uber of copoets is ifiite x

2 Fourier series for the trai are as follow ] A f x A cos kx B kx ( ) = + [ ( ) + si( )] 2 = f ( x) = k = = C e jkx The Fourier series i Eq. describe a trai at rest. I order to ove the trai with a costat velocity ν, the Fourier series will be chaged as follow 3] A f x vt A cos kx t B kx t ( ) = + [ ( ( ω )) + si( ( ω ))] 2 = f ( x vt) = C e = k = ω = = f T j( kx ωt) The speed of the trai is give by ω 4] v = = = f k T Phase represetatio cos( kx ωt) Now let ivestigate cos( kx ωt) cos( kx ωt) appears Eq 3 N ties. I will show that each cos( kx ωt) ca be represeted i M differet ways. The followig idetities ca be easily verified ad is used i 3 phase electrical power lie syste (ELECTRIC POWER GRID) 2

3 5] 2 kx t = t + kx + + t + kx + + t + kx + 3 cos( ω ) [cos( ω ) cos( ) cos( ω 2 ) cos( 2 ) cos( ω 24 ) cos( 24 )] 2 π π cos( kx ωt) = [cos( ωt)cos( kx) + cos( ωt + )cos( kx + ) + cos( ωt + )cos( kx + )] I a 3 phase electrical syste the phasor diagra is as i the picture below Eq 5. is ot liited to a 3 phase syste. Now, if the circle is divided ito M phasors where M is a iteger, ad the agle betwee two phasors is /M. Tha Iagiary Iagiary Real Real 2 6] M 2 cos( kx ωt) = [cos( ωt + ) cos( kx + )] M M M = The idetity ca be easily verified usig coplex variable (Euler) 7] j( kx ωt ) e = kx ωt + j kx ωt cos( ) si( ) Fro Eq 7. 8] e = e [ e ] M M j( kx ) j( ωt ) j( kx ωt ) M M * = * eas cojugate ( a jb)* = a + jb 3

4 Coclusio Every ter i the Fourier series i Eq 3. Is of the for 9] M 2 cos( ( kx ωt))] = cos( k ' x ω ' t)] = [cos( k ' x + ) cos( ω ' t + )] M = M M ω ' = ω k ' = k ad M ca be ay iteger { < M } Sice the uber of ters i Fourier series is N, the uber of cobiatio with M is M N ad sice ] M N The liit is of the order of ℵ ] M N ℵ Now, suppose we are sittig i the ciea ad starig at a trai ovig o the scree. Of course the audiece kows the trai is ot real because they bought a ticket to see a illusio i the ciea, ad what they see is light waves coig fro the scree. At the ed of the fil, the audieces go out to the real world ad looks aroud ad see light waves coig fro objects aroud the. There is o differece betwee the light coig fro the scree ad fro the real word. Matheatically i both cases we use Fourier to describe both cases ad I proved that the atheatical uber of represetatios is ifiite. Now ay be that the audiece theselves are produced fro aother ciea projector so that they are also ot real. Ad the uber of ways to ake reality ot real is at least ℵ What is preseted i this paper sees to be useless but it is ot. Oe of the coplicate theories i electrical egieerig is: "The uified theory of electrical achies". The ost popular solutios to this theory was give i a thick book "The uified theory of electrical achies". Writte by [Charles Vicet Joes] 4 Coets

5 Joes used Matrix ad Tesors ad ore tha 3 pages to prove this theory. I order to solve the sae theory "The uified theory of electrical achies" I use oly Eq 6 ad the theory was derived i about pages (ot 3 pages) My proof to "The uified theory of electrical achies" is foud o the iteret at ad aother paper at If Eq 6 was useful i solvig "The uified theory of electrical achies" it will be useful i solvig ay other probles. fi 5