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<B> A RECONCILIATION OF QUANTUM PHYSICS AND SPECIAL REALITIVITY </B>
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According to existing theory the matter wave emerges from the Fourier addition of component waves. This method requires
an infinite number of component waves. Natural infinities do not exist within a finite universe. The potential and kinetic components
of a wave retain their phase during a Fourier localization. The aligned phase condition is a property of a traveling wave.
The Fourier process cannot pin a field or stop a traveling wave.
<br><br>
Texts in quantum physics commonly employ the Euler formula in their analysis. The Euler formula is given below:
<br><br>
e <sup>j<FONT FACE="Symbol">q</FONT></sup> = cos<FONT FACE="Symbol">q</FONT> + j sin<FONT FACE="Symbol">q</FONT>
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The Euler formula describes the simple harmonic motion of a standing wave. The sin component represents the potential energy
of a standing wave. The cos component represents the kinetic energy of a standing wave. The kinetic component is displaced by
90 degrees and has a j associated with it. The localization of a traveling wave through a Fourier addition of component waves is in error.
To employ this method of localization and then to describe the standing wave with the Euler formula is inconsistent. This author corrected this error through the introduction of restraining forces. The discontinuity produced at the elastic limit of space restrains the matter wave. The potential and kinetic components of the restrained wave are displaced by 90 degrees.
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Mass energy ( E<sub>M</sub> ) is a standing wave.
A standing wave is represented on the Y axis of a complex plane.
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<pre><b>
^
|
| E<sub>M</sub> = Mc<sup>2</sup>
|
|
|_90<sup>o</sup>
</b>
</pre>
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The phase of a standing wave is 90 degrees. All standing waves are localized by restraining forces.
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A traveling wave has its kinetic and potential components aligned in phase. The traveling wave expresses itself through the relativistic
momentum "P" of matter.
<br><br>
P = Mv / (1- v<sup>2</sup> / c <sup>2</sup> )<sup>1/2</sup>
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A relationship between the momentum "P" and the energy "E" of a traveling wave is given below.
<BR><BR>
P = E/c
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Substituting yields the relativistic flow of energy "E<sub>q</sub>". Energy flows are represented on the X axis of a complex plane.
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<pre><b>
E<sub>q</sub> = Mvc / (1- v<sup>2</sup> / c <sup>2</sup> )<sup>1/2</sup>
|---------------------->
0<sup>o</sup>
</B>
</pre>
The vector sum of the standing ( E<sub>M</sub> ) and traveling ( E<sub>q</sub> ) components equals the relativistic
energy ( E<sub>r</sub> ) of moving matter.
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( E<sub>r</sub> )<sup>2</sup> = ( E<sub>M</sub> )<sup>2</sup> + ( E<sub>q</sub> )<sup>2</sup>
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The relativistic energy is represented by the length of the hypotensue on a complex plain.
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E<sub>r</sub> = Mc<sup>2</sup> / (1- v<sup>2</sup> / c <sup>2</sup> )<sup>1/2</sup>
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The ratio of [ E<sub>M</sub> / E<sub>r</sub> ] reduces to (1- v<sup>2</sup> / c <sup>2</sup> )<sup>1/2</sup>. This
function express the properties of special relativity. The arc sin of this ratio is the phase;
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<FONT FACE="Symbol">q</FONT> = arc sin (1- v<sup>2</sup> / c <sup>2</sup> )<sup>1/2</sup>
<br><br>
The phase expresses the angular separation of the potential and kinetic energy of matter.
The physical length of a standing wave is determined to the spatial displacement of its potential and kinetic
energy. This displacement varies directly with the phase <FONT FACE="Symbol">q</FONT> of the wave.
This effect produces the length contraction associated with special relativity.
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Time is represented on the Z (out of the plain) axis on a complex diagram. The rotation of a vector around the
X axis into the Z axis represents the change in potential energy with respect to time. The rotation of a vector around the
Y axis into the Z axis represents a change in potential energy with respect to position. Relativistic energy
is reflected on both axes. The loss in time by the relativistic component E<sub>r</sub> is compensated for by gain in position.
<br><br>
This phase <FONT FACE="Symbol">q</FONT> of of a wave expresses the displacement
of its potential and the kinetic energy.
When placed on a complex diagram the phase directly determines the relativistic
momentum, mass, time, and length.
These effects reconcile special relativity and quantum physics.
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