Fourier's Transform of the Quantum - Revision history

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	\| published = 2009		\| published = 2009
	\| journal = [[Galilean Electrodynamics]]		\| journal = [[Galilean Electrodynamics]]
	\| volume = [[20]]		\| volume = 20
	\| number = [[4]]		\| number = 4
	\| pages = 74-80		\| pages = 74-80
	}}		}}

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	[[Category:Scientific Paper\|fourier 's transform quantum]]		[[Category:Scientific Paper\|fourier 's transform quantum]]

			[[Category:Quantum Theory]]

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	{{Infobox paper		{{Infobox paper
	\| title = Fourier\'s Transform of the Quantum		\| title = Fourier's Transform of the Quantum

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	==Abstract==		==Abstract==

	I show that the quantum relations, <em>E = hv</em> and <em>p = h / L</em> are sufficient for deriving the two corresponding uncertainties, and need no help from the Fourier analysis, as is the typical method.  If <em>v</em> involves a period <em>t > 0</em> that is the minimum time interval needed to define <em>E</em>, then defining <em>E</em> any sooner will introduce an uncertainty in its value proportional to how much sooner.  And if <em>L</em> stands for a minimum distance needed to define <em>p</em>, then defining <em>p</em> in any shorter distance will introduce an uncertainty in its value, proportional to the amount shorter.  Since, however, <em>E</em> is to be defined over <em>t</em>, and not sooner, <em>Et = h</em>. And since <em>p</em> is to be defined over <em>L</em>, and not shorter, <em>pL = h</em>. Hence, altogether,  <em>dEdt, dpdq >= h</em>.  In the Fourier treatment, however, <em>E = hv</em> does not suffice to deduce <em>dEdt >= h</em>; another premise, <em>dvdt >= 1</em>, is equally necessary to the deduction. Inclusion of this extraneous premise literally transforms this uncertainty from a lim-ited, and therefore manageable, energy-time opposition, into an unlimited, and therefore unmanageable, opposition, demanding all kinds of absurdities for its satisfaction, as several reliable commentators have noted since the early 60?s. These problems are inherent in the Fourier approach, but my derivation escapes them.[[Category:Scientific Paper]]		I show that the quantum relations, <em>E = hv</em> and <em>p = h / L</em> are sufficient for deriving the two corresponding uncertainties, and need no help from the Fourier analysis, as is the typical method.  If <em>v</em> involves a period <em>t > 0</em> that is the minimum time interval needed to define <em>E</em>, then defining <em>E</em> any sooner will introduce an uncertainty in its value proportional to how much sooner.  And if <em>L</em> stands for a minimum distance needed to define <em>p</em>, then defining <em>p</em> in any shorter distance will introduce an uncertainty in its value, proportional to the amount shorter.  Since, however, <em>E</em> is to be defined over <em>t</em>, and not sooner, <em>Et = h</em>. And since <em>p</em> is to be defined over <em>L</em>, and not shorter, <em>pL = h</em>. Hence, altogether,  <em>dEdt, dpdq >= h</em>.  In the Fourier treatment, however, <em>E = hv</em> does not suffice to deduce <em>dEdt >= h</em>; another premise, <em>dvdt >= 1</em>, is equally necessary to the deduction. Inclusion of this extraneous premise literally transforms this uncertainty from a lim-ited, and therefore manageable, energy-time opposition, into an unlimited, and therefore unmanageable, opposition, demanding all kinds of absurdities for its satisfaction, as several reliable commentators have noted since the early 60?s. These problems are inherent in the Fourier approach, but my derivation escapes them.

			[[Category:Scientific Paper\|fourier 's transform quantum]]

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{{Infobox paper
| title = Fourier\'s Transform of the Quantum

| author = [[Constantin Antonopoulos]]
| keywords = [[Fourier Transform]], [[Quantum Mechanics]]
| published = 2009
| journal = [[Galilean Electrodynamics]]
| volume = [[20]]
| number = [[4]]
| pages = 74-80
}}

==Abstract==

I show that the quantum relations, E = hv and p = h / L are sufficient for deriving the two corresponding uncertainties, and need no help from the Fourier analysis, as is the typical method.  If v involves a period t > 0 that is the minimum time interval needed to define E, then defining E any sooner will introduce an uncertainty in its value proportional to how much sooner.  And if L stands for a minimum distance needed to define p, then defining p in any shorter distance will introduce an uncertainty in its value, proportional to the amount shorter.  Since, however, E is to be defined over t, and not sooner, Et = h. And since p is to be defined over L, and not shorter, pL = h. Hence, altogether,  dEdt, dpdq >= h.  In the Fourier treatment, however, E = hv does not suffice to deduce dEdt >= h; another premise, dvdt >= 1, is equally necessary to the deduction. Inclusion of this extraneous premise literally transforms this uncertainty from a lim-ited, and therefore manageable, energy-time opposition, into an unlimited, and therefore unmanageable, opposition, demanding all kinds of absurdities for its satisfaction, as several reliable commentators have noted since the early 60?s. These problems are inherent in the Fourier approach, but my derivation escapes them.[[Category:Scientific Paper]]