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1088 lines
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<title>Solutions to quantum puzzles</title>
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<meta name="author" content="Amr Gharbeia">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font color="#993366"><font face="Verdana, sans-serif"><b>S<img src="data:image/png;base64,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" name="TtsOtkCLQm_17" align="right" hspace="5" width="200" height="59" border="0">olutions
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to quantum puzzles.</b></font></font> The nature of the three forms
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of quantum matter has explained several quantum puzzles, and Bohm’s
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interpretation of the Schrödinger wavefunction points the way to a
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solution of those that remain. We have seen how both photons and
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particles with rest mass have both a wave-like and particle-like
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nature, though they are fundamentally different forms of matter on
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this explanation and have fundamentally different explanations.
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Photons are waves that have a particle-like nature because each such
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bit of matter is a complete cycle of quantum events, whereas
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particles with rest mass have a wave-like nature because their motion
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is constituted by another form of matter attached to the rest mass
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that endures through time as a series of cycles of quantum events.
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This points the way to a certain kind of ontological explanation of
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quantum mechanics, and in order to test its adequacy, let us consider
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how it would handle the three quantum puzzles: the structure of the
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atom, Heisenberg’s uncertainty principle, and the Bell
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correlations.</font></font></font></p>
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<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font face="Verdana, sans-serif">S<img src="data:image/png;base64,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" name="TtsOtkCLQm_18" align="right" hspace="5" width="200" height="31" border="0">tructure
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of the atom.</font> Bohm’s interpretation of the Schrödinger
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equation is the key an ontological explanation of the structure of
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that atom. Schrödinger’s equation determines a wavefunction for
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the conditions that hold in atoms, with a positively charged nucleus
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surrounded by electrons (but since it is too complex to solve when
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many electrons are involved, each electron is usually treated
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separately, taking the mean position of the other electrons as
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boundary conditions). The time-independent Schrödinger wavefunction
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for the atom has an amplitude for the electron that varies with
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locations in space, and as Max Born suggested, the square of that
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amplitude (when normalized) in any region of space can be interpreted
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as the probability of finding an electron located there. The
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wavefunction describes various orbitals, or regions of space relative
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to the nucleus where two electrons (with opposite orientations of
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spin) are most likely to be found. This is the structure that
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explains the periodic table of elements and is used to explain
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chemical bonds among atoms. </font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
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orbitals of the atom are identified by quantum numbers, such as the
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principle quantum number (indicating the energy levels: <i>n = 1, 2,
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3 . .</i>), the orbital angular momentum quantum number (<i>l = 0, 1,
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2, . . </i>), and the magnetic quantum number (<i>m, </i>which
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determines the orientation of the orbital angular momentum as a
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magnetic moment it has in a magnetic field imposed in some
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direction). Electrons also have an intrinsic spin quantum number, <i>s
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= ½</i>, and two electrons, with opposite orientations of spin can
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occupy each orbital. Here is a rough description of the possible
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orbitals. </font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif">Electrons
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occupy shells, corresponding to different energy levels, and in the
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lowest energy shell (<i>n = 1</i>), there is only one
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orbital (the <i>s </i>orbital), which can contain two electrons (with
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opposite intrinsic spin). It has no orbital angular momentum (<i>l = 0</i>).
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The probability of finding the electron in the s orbital is highest
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at the center of the nucleus, and the probability of finding it
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farther away falls off exponentially. </font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif">In the
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second shell (<i>n = 2</i>), with the next higher permitted
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energy, there is not only an <i>s </i>orbital, but also three
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different <i>p </i>orbitals. The <i>p </i>orbitals correspond to
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electrons having an orbital angular momentum (<i>l = 1</i>,
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as if they were in orbit around the nucleus), and each such orbital
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has a node running through the nucleus, indicating that a <i>p</i>
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electron will never be found to be located where the nucleus is.
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Moreover, in the plane in which it has its orbital angular momentum,
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the real (that is, non-complex) component of the wavefunction’s
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amplitude has the <i>p </i>electron located in one or another region
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on opposite sides of the nucleus, that is, 180<sup>o</sup> apart.
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Thus, since there are three <i>p </i>orbitals at the second energy
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level, atoms in which the second shell of electrons is full have
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(real valued) orbitals arranged in 3-D space that look like three,
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mutually perpendicular barbells. </font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif">In the
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third shell, at the next energy level, there is another s orbital,
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three p orbitals, and five d orbitals with a more complex geometrical
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structure, and so on through the energy levels of the atom. Since
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each orbital can contain two electrons (with opposite intrinsic spin
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orientations), the number of protons in the nucleus determines the
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structure of the lowest energy atom of each elemental kind. </font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">In
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order to explain the structure of the atom ontologically, we need to
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recognize that it is constituted by three forms of matter and an
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interaction between them that can be seen as involving something in
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the nature of a photon (that is, virtual photons). </font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><i>Rest
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mass matter.</i> The particles with rest mass include the neutrons
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and protons that make up the nucleus as well as the electrons. But
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each proton and electron carries an electric charge, which is a form
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of force-field matter that helps constitute each particle, though as
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we have seen, the quantity of such matter is already counted in the
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rest masses of the particles. </font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><i>Kinetic
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energy matter.</i> Both the nucleus and the electrons are in motion
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as a result of their interaction, but the nucleus is so much more
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massive than the electrons that its quantum kinetic energy cycles are
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very small compared to those of electrons (and can be ignored in
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estimating quantities). Bohr assumed that electrons are in motion
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relative to the nucleus in order to explain the structure of the
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hydrogen atom, and despite doubts about electrons following
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determinate trajectories like classical material objects, it is clear
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that electrons have some kind of motion. (Electrons must move in
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order to have orbital angular momentum, and unless electrons in the s
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orbital had some kind of motion, there would be no explanation of how
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there could be s orbitals at higher energy levels.) Thus, according
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to this ontological explanation of the forms of matter, the electrons
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bound to the nucleus in an atom must have kinetic matter in addition
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to their rest mass matter, that is, the electrons are moved around by
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quantum kinetic cycles. </font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><i>Force-field
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matter.</i> Since protons and electrons carry opposite electric
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charges, they jointly impose a force field on the part of space
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occupied by the atom. The forces that these particles exert on one
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another change how they move, and the attraction of positive and
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negative charges is great enough to bind the electrons to the nucleus
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(with the negative potential energy representing the loss of some
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force-field matter that was counted in their rest masses as
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independent objects). But part of the force-field matter that the
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particles have given up still exists in the atom as the kinetic
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energy matter by which the electrons (and the nucleus) move across
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space as time passes, and the motion of electrons relative to the
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nucleus entails a change in the force field that is jointly imposed
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by them. </font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><i>Virtual
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photons.</i> The interaction between these particles is a process
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that is continually converting potential energy into kinetic energy
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and kinetic energy into potential energy, that is, converting matter
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between force-field matter and quantum kinetic cycles. Electrons (and
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the nucleus) are continually either giving up force-field matter and
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acquiring kinetic energy matter or giving up kinetic energy matter
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and acquiring force-field matter, and such transfers of matter are
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represented in the gauge field theory for electrodynamics as bosons,
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called "virtual photons." </font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
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structure of the atom can be explained by the quantum nature of the
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kinetic energy matter of the particles with rest mass and the gauge
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bosons that transfer momentum and energy between them and force-field
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matter. Both the changes in the locations of the particles and the
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changes in the motion of the particles occur in a step like way,
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because they both involve quantum events. That can explain the
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structure of the atom, because those quantum events must fit together
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neatly in the spatio-temporal geometry determined by the inherent
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motion in space in order for them all to coincide with the same part
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of space. It is as if the quantum events constituting the atom were
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spatio-temporal bricks, and the existence of an atom were a result of
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their fitting together both spatially and temporally like a brick
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wall being built into the future. The masonry is so neat and well
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organized that the wall can be built indefinitely high, making the
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atom stable. </font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif">The quantum
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nature of kinetic energy matter means, as we are conceiving it in our
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possibly too crude way, that electrons (and nucleus) change location
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in a step-like way, that is, covering some whole distance in a period
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of time as a single, indivisible event. It is as if the electron must
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first complete an entire quantum kinetic cycle before it can change
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its momentum, and when it does change momentum, it must complete
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another complete quantum cycle before it can change again. Thus, only
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at certain locations and at certain moments does the electron change
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how it is moving. </font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif">Any changes
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that occur in an electron’s motion depends on the electric forces
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being exerted by all the electrons and protons, that is, on the field
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||
that they jointly constitute (because they are all made partly of
|
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force-field matter). These forces cause electrons to change how they
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move (that is, change their momentum), and that depends on some kind
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of (virtual) photon which gives the electron momentum and energy or
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||
takes it away. But on this model, such interactions occur only at the
|
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end of each quantum kinetic cycle, and it is a step-like change that
|
||
determines the nature of the next quantum kinetic cycle. The quantum
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||
nature of the process makes the quantity of the change clear, because
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according to Newton’s laws of motion, the amount of energy and
|
||
momentum that is transferred to the electron each time would depend
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||
on how much of energy and momentum the electron picked up from the
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||
force field matter in space during its previous quantum kinetic
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||
cycle. The change in the electron’s kinetic energy would depend on
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||
the <i>distance </i>it covered in the force field during the last
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kinetic event, and the change in the electron’s momentum (including
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||
its change of direction) would depend on the period spent being
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subject to the force field during the last quantum kinetic cycle. (Or
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||
more precisely, since the strength of the force varies over that
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distance and period, the change in energy would be the integral of
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the force over that distance, and the change in the electron’s
|
||
momentum would be the integral of the force over that period of
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||
time). </font></font>
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||
</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif">This way of
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thinking about the quantum nature of the kinetic cycles may be an
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||
overly crude way of portraying the electromagnetic interactions, but
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the step-like changes bring out how the interaction involves not just
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the electron, but a complete quantum event making up its kinetic
|
||
matter. The change occurs in a cyclic fashion, in which the last
|
||
quantum kinetic cycle combines with the force-field matter to
|
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determine how much the next quantum kinetic cycle differs in momentum
|
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and energy. Such electromagnetic interactions are geometrically
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||
complex, because changes in electric forces cause changes in <i>magnetic
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</i>forces, which affect their motion, and what is more, these
|
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particles also have magnetic moments due to their intrinsic spin,
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which affects them in a different way. The way that these forces work
|
||
is what is described by the gauge field theory for electrodynamics.
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The transfer of matter from force-field matter to kinetic matter or
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back is mediated by the gauge boson for the electromagnetic field,
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that is, by the exchange of a particle between them. This particle is
|
||
like a real photon, because it is constituted by electric and
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magnetic forces interacting in some way. But it is unlike the photons
|
||
that constitute light, because the momentum and energy it carries is
|
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not related by <i>E = pc</i>. They cannot have a constant
|
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proportion, because the energy and momentum needed to change the
|
||
motion of objects with inertial mass as required by Newton’s laws
|
||
do not have the same proportion in every case. (That is, momentum is
|
||
a function of velocity, whereas energy is a function of the square of
|
||
velocity, and so the proportion between them will vary with the
|
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velocity involved.) But this is just the nature of virtual photons,
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||
as opposed to real photons, which can exist independently and make up
|
||
ordinary light. The matter constituting virtual photons can come from
|
||
the force-field matter included in the rest masses of the particles,
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||
but they must have whatever unit-like nature is required to transfer
|
||
all of the momentum and energy picked up from the force-field matter
|
||
during the last quantum kinetic cycle at the moment that cycle ends,
|
||
whatever the real nature of this possibly crude representation may
|
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be.</font></font></p>
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<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">[When
|
||
electrons do finally exchange a photon with the nucleus and their
|
||
next quantum kinetic cycle is changed, they have a different location
|
||
from where they were at the end of the last quantum kinetic cycle and
|
||
their motion is changed for the next quantum kinetic cycle. This
|
||
step-like change in their motion is the effect of virtual photons on
|
||
the electron, but since the electron is a charged particles, it is
|
||
also helping to impose the force field from which the virtual photons
|
||
arises. And that is something that we must assume the electron does
|
||
constantly, not just at the end of each quantum kinetic cycle, for as
|
||
we shall see when we take up the gauge field theory, the electric
|
||
charge is explained ontologically as a pulsation of electric forces
|
||
emanating from the center of rest mass that is synchronized with
|
||
electric charges throughout the universe. That is, all negative
|
||
electric charges exert their maximum electric force at the same time
|
||
in a cyclic way, and what makes positive electric charges opposite is
|
||
that they exert their maximum electric force 180</span></font></font><font color="#000000"><sup><font face="Times New Roman, serif"><span lang="en-US">0</span></font></sup></font><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
out of phase. (The synchronization of their pulsations is what is
|
||
represented by their "orientation in complex vector fields,"
|
||
and the virtual photons of the gauge filed theory are the forces that
|
||
must be exerted on charged particles as a result of their motion in
|
||
order to conserve electric charge, that is, to keep their pulsations
|
||
in synch with the universal pulsation of electric charges everywhere
|
||
despite their motion.) In any case, in order to be able to explain
|
||
quantum electrodynamics in this way, we will assume that electron is
|
||
exerting its electric force in synch with the universal pulsation,
|
||
and thus, it must occurs constantly during each quantum kinetic
|
||
cycle. And that means that we are assuming that the electron has a
|
||
determinate location at each moment during each quantum kinetic
|
||
cycle. (For furthere discussion, see </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/Lo/L/LoOtkCaLeCosGaugeField.htm" target="Lo"><font color="#0000ff"><font face="Arial, sans-serif"><span lang="en-US"><u>Change:
|
||
Basic Objects: Gauge Field.</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">)]
|
||
</span></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">If the
|
||
interactions among these forms of matter must have the unit-like
|
||
nature that we are assuming explains Planck’s constant
|
||
ontologically, the structure of the atom can be explained as a result
|
||
of how all the kinds of quantum events involved fit together in the
|
||
spatio-temporal geometry determined by the inherent motion in the
|
||
part of space where they exist. This means that the interactions
|
||
between the electrons and the nucleus would have a cyclic character,
|
||
and all the interactions between electrons and the nucleus (as well
|
||
as between the electrons themselves) would give them quantum kinetic
|
||
cycles that are synchronized and related spatially, so that they fit
|
||
together neatly in space and time like spatio-temporal brick in the
|
||
atom as a brick wall being built into the future. But since there are
|
||
slightly different combinations of momentums (quantum kinetic cycles)
|
||
and positions (the locations where one quantum kinetic cycle ends and
|
||
another begins), there is no way to say precisely where any
|
||
particular electron is at any time. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Without
|
||
trying to explain the orbitals in detail, it is clearly possible that
|
||
the electrons are following determinate pathways as a result of
|
||
interactions of this kind, changing their quantum kinetic cycles in a
|
||
step-like way while all the time helping constitute the
|
||
electromagnetic force field by way of their (pulsating) electric
|
||
charges. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Though
|
||
electrons in the <i>s </i>orbital are most likely to be found in the
|
||
nucleus, that does not mean that they do not have a regular motion at
|
||
all. Assume that each such electron is in a cyclic interaction with
|
||
the nucleus in which it is accelerated first in one direction across
|
||
the nucleus and then back in the opposite direction. The changes in
|
||
how it moves come at the end of each lap when it is maximally far
|
||
away from the nucleus, and it does not change its velocity during the
|
||
trip, because it is a single quantum kinetic cycle (at least in the
|
||
lowest energy state). That is, where one quantum kinetic cycle ends
|
||
and another one begins, the electron changes its momentum all at
|
||
once, without slowing down or speeding up. The reason it is most
|
||
likely to be found at the center of the nucleus is that it can have
|
||
any direction of back and forth motion through the nucleus, and the
|
||
nucleus is the one part of space traversed by every possible pathway.
|
||
At higher energy levels, the electron would be moving faster, and
|
||
thus, it would have quantum kinetic cycles that are shorter and
|
||
quicker, and at the <i>n=3</i> energy level, it means that the
|
||
electron has a good chance of being located either with the nucleus
|
||
or at a distance from it, but not in between. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Electrons
|
||
in the <i>p </i>orbital at the <i>n=2 </i>higher energy level have an
|
||
orbital angular momentum. But it may seem that they cannot have a
|
||
circular orbit around the nucleus in the relevant plane, because its
|
||
orbital is usually represented as being a sphere located mostly on
|
||
opposite sides of the nucleus. But the regions on opposite sides of
|
||
the nucleus are just the real component of the amplitude its
|
||
Schrödinger wavefunction, and the complex component puts it on
|
||
opposite sides of the nucleus in the same plane, except for being
|
||
rotated by 90<sup>0</sup>. The <i>p </i>orbital could, therefore, be
|
||
a result of two quantum kinetic cycles, each trying to pull it back
|
||
and forth across the nucleus in perpendicular directions (as in the <i>s
|
||
</i>orbital), but perpendicular to one another. The quantum
|
||
interactions with the nucleus that keeps changing their quantum
|
||
kinetic cycles would have to be synchronized to occur 90<sup>0</sup>
|
||
out of phase to have this result, but that could be just the
|
||
condition of such quantum events being able to coincide with the same
|
||
part of space at all. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Even though
|
||
different <i>p </i>orbitals are rotating electrons in independent
|
||
planes of three dimensional space, they may also be synchronized in a
|
||
certain way so as to keep the electrons from exerting too great a
|
||
repulsive force on one another. (The general synchronization of these
|
||
quantum kinetic cycles and changes in them is evident in the <i>s
|
||
</i>electron at the third energy level, for its probable location is
|
||
either outside the lower level shell or at the nucleus, suggesting
|
||
that it is continually moving through those shells in some way.)</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The reason
|
||
that two electrons can fit into each orbital is that, with opposite
|
||
orientations of spin, they can be synchronized in exactly the same
|
||
way, but 180<sup>0</sup> out of phase or in the opposite directions.
|
||
Their opposite orientations of their intrinsic spins would exert a
|
||
force (a "magnetic moment") that lines them up in opposite
|
||
ways in the magnetic field, and that suggests that the magnetic
|
||
fields plays the central role in making it possible for the exchange
|
||
of virtual photons to generate such a neat pattern in the
|
||
spatio-temporal geometry of the inherent motion. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Much more
|
||
needs to be worked out in order to show how all the electrons in the
|
||
orbitals could be following determinate trajectories determined by
|
||
quantum kinetic cycles, but there seems to be no reason to deny that
|
||
they have such step-like trajectories, even if they cannot be
|
||
measured precisely. And it could be extended to include the other
|
||
orbitals of atoms and the molecular orbitals that explain chemical
|
||
bonds among atoms and groups of atoms. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><i>Quantum
|
||
jumps.</i> Finally, the puzzle about the electron jumps entailed by
|
||
the step-like changes in the energy level of atoms would be solved.
|
||
All the changes in momentums of electrons, even those within its
|
||
energy level, are step-like jumps. They occur at the end of one
|
||
quantum kinetic cycle (in our possibly crude way of thinking about
|
||
it) and before the next quantum kinetic cycle begins. It is clear
|
||
that the change in energy state is a change in the orbital occupied
|
||
by an electron is a step-like change, because it occurs with the
|
||
absorption and emission of a single photon of the appropriate energy
|
||
(and momentum). But that is just what would be expected, if the atom
|
||
has a structure that is determined by the way that the quantum events
|
||
of the various forms of matter constituting the atom must fit
|
||
together in order to coincide with the same part of space given the
|
||
spatio-temporal geometry determined by the inherent motion in space.
|
||
The electron absorbs or emits a real photon, which changes its next
|
||
quantum kinetic cycle so that it is part of a different orbital. The
|
||
only possible changes are step-like changes, because they are changes
|
||
in the structure of the atom. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The
|
||
structure I have tried to describe here is the same structure that is
|
||
determined by the “quantum potential” that David Bohm found in
|
||
the Schrödinger wavefunction by mathematically separating out the
|
||
classical forces. That left a force with a localized effect that did
|
||
not decline with distance in the way electric forces do, but spread
|
||
throughout space. Though Bohm thinks of it as “active information”
|
||
which tells the electron how to play out its classical role, it can
|
||
be explained, as I have suggested here, by recognizing that kinetic
|
||
energy exists as a form of quantum matter by which objects with rest
|
||
mass coincide with space, because that determines the same structure
|
||
in the inherent motion in space. Quantum kinetic cycles and the
|
||
inherent motion in which they are fit together are, in other words,
|
||
another ontological explanation of Bohm’s quantum potential.</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><i>Lorentz
|
||
distortions.</i></span></font></font></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">
|
||
By the way, this explanation of the structure of the atom affords an
|
||
of the inevitability of the Lorentz distortions. In explaining the
|
||
truth of Einstein’s special theory of relativity, I showed that the
|
||
Lorentz time dilation and length contraction would be inevitable in
|
||
the atom, if the electrons were bound to its nucleus by a unit-like
|
||
two-way electromagnetic interaction. (See </span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/Lo/L/LoOtkCaLbStrLorentzDist.htm" target="Lo"><font color="#0000ff"><font face="Arial, sans-serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Change:
|
||
Special theory of relativity</u></span></font></font></font></a><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">.)
|
||
That is apparently the implication of the Schrödinger wavefunction
|
||
that describes the motion of such an electron subject to the positive
|
||
charge of the nucleus, as can be seen in the </span></font></font></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><i>s
|
||
</i></span></font></font></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">orbital.
|
||
</span></font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The <i>s
|
||
</i>orbital corresponds to a standing wave (as in a plucked string)
|
||
without a node, and that means that the path of the electron is only
|
||
half the total Schrödinger wavelength. (A standing wave of the
|
||
complete cycle would have a node, because one half would be positive
|
||
amplitude and the other half would have negative amplitude.) Since
|
||
the momentum of an electron cannot change during a quantum kinetic
|
||
cycle, it seems that either a single cycle of the wavefunction must
|
||
be responsible for both legs of its trip across the nucleus, or else
|
||
a complete cycle of the wavefunction is responsible for each leg. In
|
||
either case, the electromagnetic interaction between the electron and
|
||
the nucleus involves a two-way motion across the <i>s </i>orbital. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Such a
|
||
two-way, unit-like interaction would cause Lorentz distortions in the
|
||
atom, as explained in the discussion of special theory of relativity,
|
||
because the inherent motion is what mediates changes in the force
|
||
field (and quantum potential) caused by the electron motion. Thus,
|
||
when the atom has a high velocity relative to the inherent motion,
|
||
the periods of the cyclic interactions between the electrons and the
|
||
nucleus increases (causing a time dilation), and the difference
|
||
between the one-way velocity of light in opposite directions in space
|
||
changes in the longitudinal distance across which they act (causing a
|
||
length contraction). </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">As we have
|
||
seen, the relativistic increase in inertial mass is simply the
|
||
addition of quantum kinetic cycles to the rest mass cycles, which
|
||
determines the scaling factor for quantum kinetic cycle and
|
||
determines the force required to change its momentum. Thus, the
|
||
quantum nature of matter affords an ontological explanation of the
|
||
Lorentz distortions, which should eliminate the suspicion that they
|
||
are simply ad hoc assumptions contrived to defend classical physics
|
||
from the Einsteinian revolution. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font face="Verdana, sans-serif">H<img src="data:image/png;base64,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" name="TtsOtkCLQm_19" align="right" hspace="5" width="200" height="31" border="0">eisenberg’s
|
||
uncertainty principle. </font>The Heisenberg uncertainty principle
|
||
holds that it is not possible to measure both the position and
|
||
momentum of a particle, or indeed both members of any pair of
|
||
complementary variables, with arbitrarily high precision. According
|
||
to the Copenhagen interpretation, this is because these classical
|
||
properties do not describe the real nature of what exists at the most
|
||
elementary level. Position and momentum are just properties we read
|
||
into the world by using instruments designed to measure material
|
||
objects according to principles of classical physics. Since both
|
||
position and momentum are needed to predict what a classical particle
|
||
will do, the Heisenberg uncertainty principle entails, at least, a
|
||
limitation in what can be known, and it can be taken to mean that
|
||
what exists at one moment does not determine what happens the next
|
||
moment, or the denial of determinism. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
Heisenberg uncertainty principle is equivalent, as mentioned above,
|
||
to the non-commutability of operators on the Schrödinger
|
||
wavefunction: </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">When the
|
||
Schrödinger equation is set up for a given situation, such as an
|
||
atom or the two-slit experiment, the time-dependent Schrödinger
|
||
wavefunction is a complete description of how interactions unfold
|
||
over time. They unfold in a completely deterministic way, just like a
|
||
classical wave function, except that the Schrödinger wavefunction
|
||
uses complex numbers to describe the wave and it describes a wave in
|
||
a configuration space with as many dimensions as three times the
|
||
numbers of particles involved. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">In order to
|
||
make predictions from the Schrödinger wavefunction, mathematical
|
||
operators must be applied. They generate real numbers as expectation
|
||
values for the relevant property. But what is predicted is either
|
||
just a mean value for many such measurements, that is, a
|
||
probabilistic prediction, or if it does predict a precise value for
|
||
the property involved, that property is one of a pair of
|
||
complementary properties, and the other member of the pair cannot be
|
||
predicted precisely. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">In other
|
||
words, classical properties come in complementary pairs that do not
|
||
commute. The values predicted for such properties depend on which
|
||
complementary operator is applied first. The application of an
|
||
operator changes the wavefunction, so that the next operator is
|
||
actually applied to a different wavefunction. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">When
|
||
a measurement is actually made, the quantum system turns out to have
|
||
a property with a determinate value. The standard interpretation of
|
||
what happens in such an measurement is called the “collapse of the
|
||
wavefunction.”</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">What
|
||
actually exists in the system represented by a Schrödinger
|
||
wavefunction is assumed to be a superposition of all the states that
|
||
might be revealed by a measurement. That is, states corresponding to
|
||
all possible outcomes of measurements actually exist at the same
|
||
time. Thus, what happens when a measurement is actually made is that
|
||
the wavefunction collapses into one of those superposed states. The
|
||
system is changed, and then another wavefunction describes the
|
||
system, representing a different superposition of states. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Since there
|
||
is nothing to determine which way the wavefunction collapses, this
|
||
view denies determinism. In effect, it explains the truth of the
|
||
Heisenberg uncertainty principle by the actual indeterminacy about
|
||
what happens. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">There
|
||
is, however, no collapse of the wavefunction, according to
|
||
ontological explanations of quantum mechanics along the lines
|
||
presented here. In any quantum system, every particle with rest mass
|
||
has a determinate position and momentum and follows a classical
|
||
trajectory, and measurements reveal properties that the system
|
||
actually has. Instead of <i>giving </i>the system the measured
|
||
property, as the “collapse of the wavefunction” interpretation
|
||
implies, measurement discovers which property the system already had.
|
||
</font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">This
|
||
way of interpreting measurements of quantum systems is entailed by an
|
||
ontological explanation, because it explains the properties and
|
||
regularities described by physics as aspects of the substances
|
||
constituting the world (and if it is to be genuinely explanatory, it
|
||
cannot depend on any randomizing factor assumed as part of the basic
|
||
nature of the substances constituting the world). But the price of
|
||
holding such a view is explaining why the Heisenberg uncertainty
|
||
principle is true. And that can be accomplished by explaining why the
|
||
operators corresponding to complementary variables are
|
||
non-commutable. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The
|
||
ontological explanation of complementarity is just the quantum nature
|
||
of matter. What “quantum” refers to ontologically are the
|
||
elementary events of which everything but space is composed. Each
|
||
quantum event is a unit, which either occurs as a whole or not at
|
||
all, and every such quantum event has the size of a single quantum of
|
||
action, denoted by <i>h,</i> Planck’s constant. This explains, as
|
||
we have seen, both the particle-like nature of photons as well as the
|
||
wave-like nature of particles with rest mass. In the case of such
|
||
particles, the complementarity comes from the quantum nature of their
|
||
kinetic energy, that is, from the nature of the form of matter that
|
||
changes the locations of particles with rest mass. Kinetic energy is
|
||
constituted by quantum kinetic cycles, implying that the motion of a
|
||
rest mass involves a series of cyclic quantum events, each of which
|
||
is a unit of action that moves the rest mass across space a certain
|
||
distance during a certain period of time. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">What
|
||
ultimately causes the Heisenberg uncertainty is the quantum kinetic
|
||
cycle. The velocity of a particle with rest mass moving through space
|
||
depends on the wavelength of its quantum kinetic cycle, but the
|
||
particle can have a range of different positions in space at the
|
||
beginning and end of each quantum kinetic cycle. That is, each
|
||
quantum kinetic cycle involves a certain <i>phase </i>as well as a
|
||
certain <i>wavelength</i>. But since the particle is located in a
|
||
potential field, in order for its energy level to be fixed, a
|
||
different location at the end of each cycle may require a slightly
|
||
different wavelength the next cycle. Thus, the quantum state of the
|
||
particle is some combination of wavelength and phase at its energy
|
||
level, but there are many combinations that might satisfy those
|
||
conditions. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Both
|
||
complementary properties cannot be measured with arbitrary precision
|
||
at the same time, because they are different aspects of the same bit
|
||
of matter, which is a series of cycle of quantum events, each of
|
||
which can interact only as a whole. Either it interacts in a way that
|
||
reveals the wavelength of quantum kinetic cycle, which leaves its
|
||
phase undetermined, or else it interacts in a way that determines its
|
||
phase (that is, the position of the rest mass at the beginning or end
|
||
of a quantum kinetic cycle), and its wavelength is undetermined. But
|
||
both cannot be measured at the same time, because a quantum event
|
||
interacts only as a whole. And complementary aspects cannot be
|
||
measured is succession, because such interactions change the cycles
|
||
of quantum events. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
Schrödinger equation describes the motion of particles with rest
|
||
mass in a potential field where there is a continual exchange between
|
||
kinetic energy and potential energy, and on this ontological
|
||
explanation, the wavefunction that holds for any given system
|
||
describes the quantum kinetic cycles that result for such an
|
||
interaction. I have suggested what such an explanation implies about
|
||
the atom and the two-slit experiment, but it can be generalized.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">One way
|
||
that the Schrödinger wavefunction is different from a classical
|
||
wavefunction is that it is complex. There are complex numbers,
|
||
involving the square root of minus one, that cannot be eliminated,
|
||
and that makes its relationship to the actual world problematic. On
|
||
this ontological interpretation, however, they represent the
|
||
different possible phases of the quantum kinetic cycles constituting
|
||
the momentum of the rest mass cycles. That is, on our crude
|
||
interpretation, the starting points and ending points of the quantum
|
||
kinetic cycles can have different locations in space and time and
|
||
still be quantum kinetic cycles of the kind that can exist under
|
||
those circumstances. The complex numbers are a mathematical device
|
||
for representing all those different possible phases and keeping
|
||
track of how they affect one another. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The other
|
||
way in which the Schrödinger wavefunction is different from a
|
||
classical wavefunction is that it describes a wave in a configuration
|
||
space with three times as many dimensions as there are particles in
|
||
the system, and that also makes its relationship to the actual world
|
||
of three dimensions problematic. On this interpretation, however,
|
||
each of the 3-dimensional spaces is used to keep track of how the
|
||
phases of the quantum kinetic cycle a particle involved in the system
|
||
unfolds in time. Though the quantum kinetic cycles of all the
|
||
particles depend on classical forces and laws, each particle needs a
|
||
3-D space of its own in order to represent all its possible phases
|
||
separately. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">When a
|
||
mathematical operator is applied to the wavefunction and a prediction
|
||
is made about the value of some property, the different possible
|
||
phases for all the particles are all reconciled with one another,
|
||
working out the interference effects they have on one another. And
|
||
the prediction is still usually just a mean value for many
|
||
experiments, because there is a range of different states in which
|
||
the system might be at that point, depending on which precise phases
|
||
and wavelengths the quantum kinetic cycles actually had. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The reason
|
||
that operators on the Schrödinger wavefunction do not commute is
|
||
that they predict two aspects of the same quantum event, such as the
|
||
wavelength and phase of the quantum kinetic cycle (as in the
|
||
explanation of the Heisenberg uncertainty above). It is possible to
|
||
predict a property precisely when it has already been measured once.
|
||
But the wavefunction that represents the quantum system as having
|
||
that precise property cannot be used to predict the complementary
|
||
property of the particle precisely. For example, when a measurement
|
||
of the momentum has been made, there is an operator that can be
|
||
applied to the wavefunction that will predict the momentum precisely.
|
||
But then the phase cannot be predicted precisely, because quantum
|
||
kinetic cycles with that wavelength can have different phases. The
|
||
same holds in reverse if the phase of the cycle is measured.</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The “hidden
|
||
variable,” on this explanation, is space and how bits of matter
|
||
coincide with it, because the quantum nature of the kinetic energy of
|
||
the particles is the factor that determines what happens to the
|
||
particles. They need a complete quantum kinetic cycle to get from one
|
||
place to another, and thus, at the end of each quantum kinetic cycle,
|
||
the forces picked up during that cycle are what determines the next
|
||
complete quantum kinetic cycle. The interaction is step-like, and
|
||
though I may be portraying it too crudely by thinking of the quantum
|
||
events as having definite beginning points and ending points, the
|
||
requirement that particles travel across space by such cyclic quantum
|
||
kinetic events is what needs to be added in order to see how what
|
||
happens to the particle is determined. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">On
|
||
this ontological explanation, therefore, the quantum system is
|
||
deterministic, and we can understand in principle how it is
|
||
determined. But it is not possible to overcome the Heisenberg
|
||
uncertainty because of the nature of the quantum kinetic cycles that
|
||
constitute the motion of particles with rest mass. They exist only as
|
||
a whole or not at all, and thus, they are the smallest unit that can
|
||
interact with other bits of matter as a unit, which means in only one
|
||
way at a time. That is, the uncertainty comes from an incompleteness
|
||
about the representation of the Schrödinger wavefunction: it
|
||
represents quantum kinetic cycles, but it does not reveal which of
|
||
all possible combinations of wavelengths and phases is actual.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">This
|
||
incompleteness interpretation of the Heisenberg uncertainty solves
|
||
the problem of Schrödinger’s cat. Such cases arise when the phases
|
||
of the quantum cycles interfere in such a way that the system can
|
||
unfold in radically different ways. For example, in one case
|
||
Schrödinger’s cat is alive and well, and in the other case it is
|
||
dead. On the collapse of the wavefunction view, the Schrödinger
|
||
wavefunction is a complete description of the situation, implying
|
||
that what exists is a superposition of all the possible outcomes, and
|
||
thus, since it turns out one way or another when someone looks, which
|
||
one actually happens must depend on the measurement. But if which of
|
||
the radically different alternatives is actual depends on the phases
|
||
of their quantum cycles at the beginning, it is determined, and the
|
||
uncertainty about what happens comes from that information not being
|
||
included in the wavefunction representing the system. The
|
||
incompleteness is inevitable, but that does not mean that it is
|
||
indeterministic. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
phenomenon of tunneling can also illustrate the uncertainty. In
|
||
tunneling, a charged particle moves past a force field that is
|
||
classically strong enough to contain it. It occurs, for example, when
|
||
there is a potential barrier separating electrons from protons
|
||
attracting them that is just large enough to overcome the attractive
|
||
force between them. But different electrons have different quantum
|
||
kinetic cycles, setting up different patterns of spacetime cells in
|
||
the inherent motion, and depending on whether they reinforce or
|
||
cancel out the waves set up by the kinetic cycles of the protons, the
|
||
force of attraction will sometimes be great enough for the electron
|
||
to tunnel across the barrier.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">The
|
||
situation can be described by a Schrödinger wavefunction, which
|
||
represents it as a packet of waves, each standing for a different
|
||
possible combination of positions of the particles. As the situation
|
||
evolves, however, the packet splits into two different parts, one in
|
||
which electrons escape and one in which they do not. Thus, the
|
||
equation represents two distinct channels, which subsequently do not
|
||
interact. Which member of the packet is actual depends on precise
|
||
locations and kinetic cycles of the particles (both wavelengths and
|
||
phases). But they behave in a way described by the Schrödinger
|
||
wavefunction because they follow the wave pattern set up by their
|
||
kinetic cycles (See </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Bohm"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Bohm</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
Ch. 5).</span></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font face="Verdana, sans-serif">B<img src="data:image/png;base64,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" name="TtsOtkCLQm_20" align="right" hspace="5" width="200" height="29" border="0">ell
|
||
correlations.</font> The final quantum puzzle is the violation of the
|
||
“Bell inequality” by certain quantum systems. John Bell pointed
|
||
out that quantum theory predicts that there are correlations between
|
||
distant events that cannot be explained without supposing that there
|
||
is a causal influence of some kind that travels between them faster
|
||
than the velocity of light. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Bell
|
||
correlations occur when symmetrical particles, with opposite spin
|
||
orientations, travel apart from one another in opposite directions
|
||
and the spin of each is measured far away from the other. They always
|
||
have opposite spin orientations when measured by imposing a magnetic
|
||
field in the same direction in space. When one is up, the other is
|
||
down. But the spin orientation they have in one direction of three
|
||
dimensional space should not affect the spin orientation in either of
|
||
the other two independent directions of space. And thus, the
|
||
measurement of the spin of one of the separated particles in one
|
||
direction should not affect the spin measured in the other particle
|
||
in a different direction. Nevertheless, it is possible to use the
|
||
measurement of the spin orientation of one of the particles in one
|
||
direction to predict better than expected what spin the other
|
||
particle will have when it is measured in an independent direction.
|
||
That would be impossible, if spin orientation is a property that each
|
||
particle has from the moment they separate and carry with them. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The greater
|
||
than expected correlations are predicted by quantum theory. The
|
||
prediction is made by applying the appropriate operators to the
|
||
Schrödinger wavefunction for the system, and so the measurements are
|
||
usually interpreted as involving a collapse of the wavefunction. That
|
||
makes it seem as though the measurement of the spin of one of the
|
||
particles helps determines which orientation of spin the other
|
||
particle will have. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The Bell
|
||
correlation is not only a prediction of quantum mechanics, but it has
|
||
been confirmed by experiments. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Bohm
|
||
(1993, Ch. 7) treats Bell correlations like any other puzzling
|
||
phenomenon predicted by quantum mechanics, that is, as an indication
|
||
of the quantum potential. Bohm is also giving an ontological
|
||
explanation, but on his theory, the quantum potential is just a
|
||
“non-local” aspect of the processes themselves, as if the common
|
||
pool of information were broadcast faster than the velocity of light.
|
||
Indeed, Bohm takes the world as a whole to have such a non-local
|
||
aspect to it. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Non-locality
|
||
seems to deny substantivalism about space, and that would make it
|
||
incompatible with spatiomaterialism. If space is a substance, then
|
||
what separates one part of space (and what happens there) from any
|
||
distant part of space (and what happens there) are parts of space
|
||
between them that have an existence that is distinct from both of
|
||
them. Thus, the only way that this real separation between the parts
|
||
of space can be overcome is by something traveling across space as
|
||
time passes. To put it negatively, immediate action at a distance
|
||
would seem to deny that there really is any substance between the
|
||
distant points of interaction that is enduring through time distinct
|
||
from them. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The
|
||
inherent motion in space is a dramatic way of representing this fact
|
||
about space as a substance. It is, perhaps, conceivable that Bohm’s
|
||
non-locality is compatible with spatiomaterialism, because I have
|
||
been speaking of the inherent motion in a more realistic way than may
|
||
be necessary. That is, instead of thinking of space as containing an
|
||
inherent motion, we can think of space as having a spatio-temporal
|
||
geometry. Thus, what I have described as waves laid out in space by
|
||
the inherent motion could likewise be just an aspect of the essential
|
||
nature of space everywhere that always exists at the moment. That is,
|
||
when the quantum kinetic cycle of a rest mass coincides with space,
|
||
it has a certain wavelength and phase, and that wavelength and phase
|
||
give it a different relationship to other parts of space with the
|
||
same wavelength that are in phase with it than it does with those
|
||
that are not in phase. Thus, what I have described as a particle
|
||
“broadcasting” its wavelength and phase throughout space would be
|
||
just a relationship that always already exists in the spatio-temporal
|
||
geometry of space. If that were how the quantum potential is
|
||
mediated, as Bohm assumes, it would explain the Bell correlation in
|
||
the same way as other quantum phenomena.</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">I doubt
|
||
that any such ontological explanation is adequate, however, because
|
||
in order to explain interference phenomena in the two-slit
|
||
experiment, for example, the quantum potential at any point in space
|
||
would have to depend not only on the wavelength and phase of the
|
||
particle, but also on the geometrical structure of the wall with
|
||
two-slits. The waves laid out by the inherent motion that guide the
|
||
particle to one of the fringes of the interference pattern must be
|
||
singled out from all the other spacetime cells by the structure of
|
||
the apparatus and how it fits together with the wavelength of the
|
||
particle, and that would also have to be something about each
|
||
location in space that always already exists for each possible
|
||
arrangement of particles and wall with two-slits. This would be to
|
||
attribute an enormously complex structure to the essential nature of
|
||
space at every moment of its existence, and the complexity of such an
|
||
explanation makes it look rather ad hoc. It would be a much simpler
|
||
ontological explanation if the quantum potential were determined by
|
||
an actual wave from the moving particle in the inherent motion that
|
||
interacts with the two-slit wall, but that is not action at a
|
||
distance. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">There
|
||
is, however, another explanation of the Bell correlations which is
|
||
compatible with the principle of local action. Contrary to what many
|
||
philosophers and physicists assume, what is actually known about this
|
||
phenomenon does not force us to believe that the principle of local
|
||
action is violated. There is a way of interpreting these phenomena
|
||
that is compatible with explanation of the quantum potential by waves
|
||
laid out in space by the inherent motion. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
predictions from quantum mechanics have to do with measurements of
|
||
spin orientation, and they cover only those cases in which both
|
||
events are actually measured. As a matter of fact, however, every
|
||
experiment that can test Bell’s theorem involves many, many runs in
|
||
which a measurement is simply not successfully made of one or the
|
||
other particle (or of both particles). It is possible, therefore,
|
||
that the cases in which both measurement are made are a biased
|
||
sample. That is, if we could know the spin orientations in <i>all </i>the
|
||
cases in which two particles split, it could turn out that their spin
|
||
orientations in different directions were indeed independent and
|
||
there is no Bell correlation.<sup><a class="sdendnoteanc" name="sdendnote1anc" href="#sdendnote1sym"><sup>i</sup></a></sup>
|
||
</font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Such a bias
|
||
in the experiment cannot be just an accident. The many cases that
|
||
must be ignored because no measurement was made must, for physical
|
||
reasons, be mostly of a kind that, if included, would wipe out the
|
||
improbable correlation between the distant events. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">It may not
|
||
seem like there can be any such factor, because the Bell correlations
|
||
are predicted by quantum theory. That makes it seem that the Bell
|
||
correlations are just another puzzling quantum phenomena, which
|
||
manifest the same underlying mechanisms (whatever they are) as in any
|
||
case of measurement. This is the assumption that is made in taking
|
||
the correlation to involve the collapse of the wavefunction, except
|
||
that unlike the other puzzling phenomena, it cannot be explained by
|
||
the kinds of ontological causes described above, because Bell
|
||
inequalities show that the collapse of the wavefunction involves
|
||
action at a distance. That is, the hidden variable cannot be a local
|
||
property, but must be a property that somehow holds of the whole
|
||
system, including both particles, regardless how far they are apart
|
||
at the time. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
prediction of the Bell correlation by quantum mechanics shows,
|
||
however, only that some quantum phenomenon is involved. It may not,
|
||
however, be the kind of phenomenon it is seems to be. The nature of
|
||
intrinsic spin is not well understood, and it is treated as though it
|
||
were completely described by the outcome of a measurement. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">In the case
|
||
of fermions, of particles with ½ spin, such as electrons, spin is
|
||
measured by imposing a magnetic field and measuring the magnetic
|
||
moment, that is, the force. The orientation of spin is simply the
|
||
sign of that force, positive or negative: if the force is in one
|
||
direction, it is spin up, and if it is in the other direction, it is
|
||
spin down. Though that is how spin is measured, it is possible that
|
||
particles have a more determinate spin orientation that is not
|
||
measured in that way. An electron, for example, could have a precise
|
||
orientation in three dimensional space, and though that is what
|
||
determines the result of the measurement in the one direction that is
|
||
singled out by the magnetic field applied, it also has other, more
|
||
subtle effects on how the particle interacts.</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">In the case
|
||
of photons, which are what has been used in the experiments that
|
||
confirm the Bell correlations, spin is even more puzzling. Since the
|
||
photon is a boson with a spin of <i>1</i>, it should have three
|
||
different possible orientations in a magnetic field, but since it
|
||
moves through space with the velocity of light, one theoretically
|
||
possible way of interacting is eliminated, leaving two possible
|
||
orientations of spin. Opposite orientations of spin in the case of
|
||
photons can be understood as opposite ways in which their electric
|
||
force rotates as they move across space, one clockwise in the
|
||
direction of motion and the other counterclockwise. However, it is
|
||
usually measured by the polarization of the photon as it passes
|
||
through a polarizer which is at rest and in which perpendicular
|
||
directions, usually called vertical and horizontal, correspond to the
|
||
two orientations of spin. But it is not clear why a rotation through
|
||
a right angle would change whether a photon with, say, a clockwise
|
||
rotation of its electric force, would pass through the polarizer. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">In
|
||
the case of both electrons and photons, there is enough uncertainty
|
||
about the nature of spin and what is being measured that it is
|
||
possible that the Bell correlations depends in some way on how spin
|
||
orientation is measured. In either case, the three independent
|
||
directions in which spin orientation (up or down or vertical or
|
||
horizontal) can be measured are measured by an apparatus that is
|
||
rotated in a two-dimensional plane perpendicular to the pathway of
|
||
the particle. Thus, what may be a three-way symmetry among spins in
|
||
three dimensional space is, in effect, reduced to a three-way
|
||
symmetry in a two-dimensional plane. It is possible that in
|
||
projecting that the three dimensional structure of spin orientations
|
||
onto the two-dimensional plane of the measuring apparatus, some
|
||
orientations of spin are more likely to pass by undetected than
|
||
others, and they could be ones that would destroy the Bell
|
||
correlation. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The
|
||
selectivity may depend, furthermore, on an interaction between the
|
||
actual orientation of spin in three dimensional space and the phase
|
||
of its quantum kinetic cycle. Though the quantum potential that is
|
||
responsible for interference and other real quantum phenomena
|
||
requires a real effect propagating through space with the inherent
|
||
motion, there could be an aspect of the waves set up in space by the
|
||
inherent motion that makes all wavelengths with the same size and
|
||
phase, wherever they exist in space, relate in a special way to the
|
||
three dimensions of space. For example, the two particles have
|
||
quantum kinetic cycles that are not only of the same wavelength, but
|
||
also in phase with one another, and thus, if certain phases make it
|
||
easier for them to interact from certain directions in
|
||
three-dimensional space than others, the direction used by the
|
||
detectors to test for spin orientation could result in a biased
|
||
sample, making it appear that distant events are correlated. Such a
|
||
factor would bias the sample in a way that makes it seem there are
|
||
effect traveling faster than the velocity of light. And it would be
|
||
local, because it depends only on the two particles having kinetic
|
||
cycles that are in phase.</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">There
|
||
is reason to think that some such explanation is correct, because
|
||
Bell correlations occur only with measurements of spin orientation
|
||
and the non-locality exhibited by the Bell correlations in
|
||
measurements of spin is not an essential part of any other quantum
|
||
phenomena. If it really were a result of action at a distance, it
|
||
should be possible to make what happens at one location determine
|
||
what happens elsewhere. But Bell correlations are not of a kind that
|
||
can be used even to send signals from one place to another. In short,
|
||
the Bell correlations are such a limited, subtle and questionable
|
||
violation of the principle of local action that it would be foolish
|
||
to use it as a reason for denying that spatiomaterialism can be used
|
||
as an ontological foundation for a new way of doing philosophy,
|
||
especially when that foundation works out so well in every other way.
|
||
</font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Though
|
||
much more would have to be said to show that this kind of ontological
|
||
explanation of the nature of matter and space accounts for all the
|
||
phenomena described by quantum mechanics, including quantum field
|
||
theory and what it says about the nature of spin, this is enough to
|
||
show <i>that there is no good reason to believe that it is impossible
|
||
</i>to reduce quantum mechanics to spatiomaterialism. What is known
|
||
by physics does not force us to give up the principle of local action
|
||
entailed by this ontology, because neither experiment nor quantum
|
||
mechanics is sufficient to demonstrate that the principle of local
|
||
action does not hold. But this particular ontological theory is just
|
||
a possibility introduced in order to speculate about a deeper
|
||
explanation of the nature of matter and space, and what is relevant
|
||
here is that, even this first approximation shows that there is no
|
||
reason to believe that anything established empirically by quantum
|
||
physics forces us to give up spatiomaterialism. There is at least one
|
||
way that a two-substance ontology like ours can account for the
|
||
quantum mysteries. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Let
|
||
me emphasize, however, that it is not necessary to believe that what
|
||
has been described here is completely accurate. It is only one of a
|
||
family of ontological interpretations of quantum theory. What is
|
||
common to the family is that the essential nature of matter involves
|
||
the ability of bits of matter (of the same form) to exist
|
||
independently of one another so that they can acquire spatial
|
||
relations by being contained by different parts of space. There may
|
||
be reasons for preferring another member of that family to this one.
|
||
But this explanation of the quantum mysteries is enough to show that
|
||
we do not have to give up the belief that space and matter are
|
||
substances that exist continuously over time. </font></font></font>
|
||
</p>
|
||
<div id="sdendnote1">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdendnotesym" name="sdendnote1sym" href="#sdendnote1anc">i</a>
|
||
Abner Shimony (1989, p. 31) points out that many pairs tested for
|
||
correlation in Bell’s experiment are not detected and so a (local)
|
||
hidden variable could “not only determine passage or non-passage
|
||
or a particle through an analyzer but also detection or
|
||
non-detection.” This possibility is also recognized by Bohm (1993,
|
||
pp. 144-5).</p>
|
||
</div>
|
||
</body>
|
||
</html> |