ÿþ<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <html> <head> <title>ByAndByGones.com</title> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <META http-equiv=Content-Type content="text/html; charset=windows-1252"> <meta name="keywords" content="special relativity, boost, rapidity, calculus, photons, matrices, Gram-Schimdt process, Riemann zeta function, infinity, Cantor transfinites, natural log function, infinite series, dot product, inner product, cross product, basis vectors, orthonormal basis set, Einstein's addition of velocity formula, mappings, linear independence, inertial reference frames, imaginary number, complex number, rectangular hyperbola, cosh, sinh, mathematics, lightcone, science, tensor, space dimensions, subspace, cos, sin, Euclidean space metric, wave-particle duality, relativity, Dirac hamiltonian, lagrangian, time, space, spacetime, velocity, Lorentz transformation, Lorentz factor, spin, spinor, de Broglie wave, momentum, Heisenberg representation, operator, statefunction, statevector, antiparticle, commutator, anticommutator, Poisson bracket, Schroedinger wave mechanics, hermitian conjugate, lagrangian conjugate, phase velocity, group velocity, frequency, kinetic energy, matrices, Pauli spinors, Dirac spinors, Bohr, zitterbewegung, unobservables, acceleration, classical, canonical, covariant, invariant, parellelicity operator, quantum numbers, postulate, coulomb potential, Hilbert space, atoms, energy levels, coupling, function, integral, negative energy, charge current, current density, four-vector, four-force, four-velocity, four-accelaration, conservation, relativistic particle, speed of light, postulate, particle, Klein vector transformation, eigenstate, eigenvector, eigenvalue, field of force, Euler rotation, Euler angles, Argand diagram, component, mass, Planck constant, h-bar, inverse, annihilation, creation operator, pythogorean, analysis, hyberbolic function, Lorentz frame, time-well, fictitious force, mass-energy creator, renormalization, phenomenological, degeneracy, probability density, constants of the motion, geometric series, physics"> <meta name="description" content="proof that special theory of relativity and general theory of relativity are flawed. proof that dirac's relativistic quantum mechanics is flawed. proof that minkowski M<sub>4</sub> spacetime does not exist. proof that the lorentz transformation and the lorentz factor do not exist. proof that imaginary number, complex number, imaginary space or vector space, and complex space or vector space do not exist. proof that imaginary and complex orthogonal axes or reference frames do not exist. proof that the natural log definition and exponential definition are flawed. proof that the integral calculus is paradoxical."> <meta name="Author" content="x.x.xxxxxxxx redesign of interspire.com's free gs019 -zzzzzz"> <meta name="Publisher" content="x.x.xxxxxxxx redesign of interspire.com's free gs019 -zzzzzz"> <meta name="robots" content="index, follow"> <!-- (Robot commands: All, None, Index, No Index, Follow, No Follow) --> <meta name="revisit-after" content="1000 days"> <meta name="distribution" content="global"> <meta name="rating" content="general"> <meta name="Content-Language" CONTENT="english"> <script language="JavaScript" type="text/JavaScript" src="http://www.byandbygones.com///script.js"></script> <link href="style.css" rel="stylesheet" type="text/css"> <style type="text/css"> <!-- .style1 {color: #FFFFFF} --> </style> </head> <BODY style="MARGIN: 0px" background="http://www.byandbygones.com///image80.gif" background="http://www.byandbygones.com///pixi_darkgrey.gif" bgcolor= "#CCFFFF"; "#DBF0F7"> <TABLE height=971 cellSpacing=0 cellPadding=0 width=1060 border=0> <TBODY> <TR> <TD vAlign=top width=1055 colSpan=3 height=150> <TABLE height=206 cellSpacing=0 cellPadding=0 width=1054 border=0> <TBODY> <TR> <TD width=1054 background=http://www.byandbygones.com///topnavbg.gif height=55><IMG style="WIDTH: 401px; HEIGHT: 39px" height=35 src="http://www.byandbygones.com///toppic1.gif" width=304><A href="http://www.byandbygones.com/index.htm"></A><IMG style="WIDTH: 3px; HEIGHT: 35px" height=35 src="http://www.byandbygones.com///navspacer.gif" width=2><FONT size=7>ByAndByGones<IMG style="WIDTH: 3px; HEIGHT: 35px" height=35 src="http://www.byandbygones.com///navspacer.gif" width=2><IMG style="WIDTH: 336px; HEIGHT: 39px" height=35 src="http://www.byandbygones.com///toppic1f.GIF" width=319></FONT></TD></TR> <TR> <TD width=1054 background=http://www.byandbygones.com///navbasebg.gif height=2><IMG height=2 src="http://www.byandbygones.com///navbasebg.gif" width=1></TD></TR> <TR> <TD width=1054 background=http://www.byandbygones.com///pic1cellbg.gif height=120> <P align=center><IMG style="WIDTH: 461px; HEIGHT: 65px" height=65 src="http://www.byandbygones.com///toppic2f.GIF" width=443><IMG style="WIDTH: 351px; HEIGHT: 65px" height=65 src="http://www.byandbygones.com///toppic2.gif" width=419></P>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<FONT color=#fffbf0 size=5>Challenging Theories and Fields</FONT></TD></TR> <TR> <TD width=1054 height=29><IMG height=29 src="http://www.byandbygones.com///toppic03.gif" width=748></TD></TR></TBODY></TABLE></TD> <TD width=5 background=http://www.byandbygones.com///rightsidebg.gif height=150>&nbsp;</TD></TR> <TR> <TD vAlign=top width=534 height=781><IMG height=30 src="http://www.byandbygones.com///pixi_clear.gif" width=230> <TABLE cellSpacing=0 cellPadding=0 width="100%" border=0> <TBODY> <TR> <TD width=37>&nbsp;</TD> <TD> <H1 align=center>&nbsp;ByAndByGones</H1> <P><FONT face=Arial,Helvetica size=-1><FONT face=Arial,Helvetica size=5><B>00000000000000000000000000000000000000</B></FONT><BR><FONT face="Comic Sans MS,Helvetica" size=5><I><B><PRE><FONT color=green size=6> 0o, 0o oo 0000 ooo<BR>0000 ooo oooo 0000,<BR> oo 000000 oooo 000<BR>oo ooo 00000000</FONT></PRE>0000000ooooooo0000000ooooooo0000000<PRE><FONT color=blue size=6> O0 oo oo 0000 ooo<BR> ooo 00000 oo ooo<BR><CENTER>000000000 oo 0o0o0oo0</CENTER></FONT></PRE>0000000ooooooo0000000ooooooo0000000<PRE><FONT color=orange size=6> O0 oo ooo 0o0 <BR> oo ooo 0000000 <CENTER> 0 ooo </FONT><FONT size=6>0o0o0o0o0</FONT><FONT color=orange size=6>?</FONT></CENTER></PRE>000000000000000000000000000000000</B></I></FONT><BR> <P></P></FONT></TD> <TD width=33>&nbsp;</TD></TR></TBODY></TABLE></TD> <TD vAlign=top width=2 background=http://www.byandbygones.com///pixi_orange.gif height=781><IMG height=1 src="http://www.byandbygones.com///pixi_orange.gif" width=1></TD> <TD vAlign=top width=521 height=781><IMG height=30 src="http://www.byandbygones.com///pixi_clear.gif" width=517> <TABLE cellSpacing=0 cellPadding=0 width="100%" border=0> <TBODY> <TR> <TD width=28>&nbsp;</TD> <TD vAlign=top> <H1 align=center>ByAndByGones</H1> <P align=center><FONT size=4><B>Quantum Theory </B> <BR><STRONG><I>Relativity Theory </I><BR>Natural Log </STRONG></FONT></P><BR><BR> <P align=center><B>special relativity and the theory of four-vectors ... </B><A href="http://www.byandbygones.com/paper1.htm"><FONT color=blue>paper1</FONT></A></P> <P align=center><B>orthognonal transformations and heisenberg<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;analysis of dirac hamiltonian ... </B><A href="http://www.byandbygones.com/paper2.htm"><FONT color=blue>paper2</FONT></A></P> <P align=center><B>abnormal success of relativity ... </B><A href="http://www.byandbygones.com/paper3.htm"><FONT color=blue>paper3</FONT></A></P> <P align=center><B>natural log integral ... </B><A href="http://www.byandbygones.com/paper4.htm"><FONT color=blue>paper4</FONT></A></P> <P align=center><B>chaotic manifolds ... </B><A href="http://www.byandbygones.com/paper0.htm"><FONT color=blue>paper0</FONT></A></P> <P align=center><STRONG>On whether the LT implies the GT</STRONG> ... </B><A href="http://www.byandbygones.com/ePR.htm"><FONT color=blue>ePR</FONT></A></P> <P align=center><B>Forbidden coordinates in the LT ... </B><A href="http://www.byandbygones.com/PIE.htm"><FONT color=blue>PIE</FONT></A></P></TD> <TD width=65>&nbsp;</TD></TR></TBODY></TABLE> <P>&nbsp;</P> <P>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <FONT color=blue size=5>Err Or:</FONT></P> <P><FONT face=Arial><STRONG>Four-Vector Relativity&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; General Dirac Hamiltonian </STRONG><FONT face=Times>ooo ooooooooooo ooo &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; oooo ooo ooo oooooooooo &nbsp;oooo&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ooo oooooooo oo ooooooo &nbsp;oooooo <BR>ooo oooooooooo oooo oo ooo&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; oooo ooo &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ooooooooo oooo oo ooooooo&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; oooooooo ooooooooo oo ooo oooooooooo &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;ooo ooooooooooo oo ooo oooooooooo oooooooooooooo ooooooooooo ooooooooo.</FONT><BR></FONT>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<A href="http://www.byandbygones.com/paper1.htm"><FONT color=blue>paper1</FONT></A>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <A href="http://www.byandbygones.com/paper2.htm"><FONT color=blue>paper2</FONT></A></P> <P>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<FONT color=#fffbf0 size=5>Challenging Theories and Fields </FONT><A href="http://www.byandbygones.com/PIE.htm"><FONT color=blue size=3>PIE</FONT></A>&nbsp;<FONT color=black size=4></FONT>.</FONT></P></TD> <TD width=5 background=http://www.byandbygones.com///rightsidebg.gif height=781>&nbsp;</TD></TR> <TR> <TD vAlign=bottom align=right width=1055 colSpan=3 height=19></TD> <TD width=5 background=http://www.byandbygones.com///rightsidebg.gif height=19>&nbsp;</TD></TR> <TR> <TD vAlign=bottom width=1117 colSpan=3 height=21><IMG height=17 src="http://www.byandbygones.com///picanglebase01.gif" width=230><IMG height=17 src="http://www.byandbygones.com///picanglebase02.gif" width=260>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 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