The unified theory of wave-particle duality has been used to derive the Schrödinger equations.
The Schrodinger equations are generally accepted, by postulate rather than derivation, to be laws
of physics.
The Schrodinger equations provide a basis for analyzing many kinds of systems (molecular,
atomic, and nuclear) in a particular inertial reference frame. The success of the Schrödinger
equations constitutes a basis for accepting them, their derivations, and the unified theory of
wave-particle duality which makes such derivations possible. This acceptance is completely
justified in the favored inertial reference frame.
In accord with the principle of relativity, all physical laws must be the same in all inertial
reference frames, i.e., all physical laws must be Lorentz invariant.
Recall, the relationship:
$$\nabla^{2} \psi = \frac{\partial^{2} \psi}{\partial t^{2}}$$ ...........(1)
Equ (1) is Lorentz
invariant
and reduces, by means of the procedure presented in the previous posts, to the Schrodinger
equations. As a result, equ (1) constitutes a unique Lorentz invariant form of the
Schrodinger equations. Consequently, the Schrödinger equations are relativistically invariant.
Conservation of the number of massive quantum objects present occurs when the Schrodinger
equations are applicable. This happens when positrons are absent, nuclei are stable, and energy
transfers lie below the threshold for electron-positron pair production. These low-energy
conditions are often considered to be non-relativistic. Correspondingly, the term relativistic is
often restricted for use when the energies involved are high enough to permit non-conservation
of the number of massive quantum objects present. This use of terminology does not change the
fact that the Schrodinger equations are relativistically invariant.
Relativistic invariance does not imply covariance. Relativistic invariance of the Schrodinger
equations is based on reduction from a covariant law. Because of their relativistic invariance and
their success in analyzing many kinds of systems in particular inertial reference frames, the
Schrodinger equations constitute laws of physics. These laws of physics are applicable when
energies are low enough to assure that the number of massive quantum objects present is
conserved.
In accord with the unified theory of wave-particle duality, quantum objects are linked to particle-
like properties, but not to particles. This is consistent with Blood’s finding that there is no
evidence for particles and with Hobson’s finding that there are no particles, only fields.
The Schrodinger equations are field equations, not particle equations. Rather than describing
particle motion, the time-dependent Schrodinger equation describes a time-dependent field \(\Psi (r,t)\)
throughout a spatial region. Following Hobson, the Schrodinger field is a space-filling physical field whose value at any spatial point is the probability amplitude for an interaction to
occur within an infinitesimal region surrounding the point.
The Schrodinger equations are generally accepted, by postulate rather than derivation, to be laws
of physics.
The Schrodinger equations provide a basis for analyzing many kinds of systems (molecular,
atomic, and nuclear) in a particular inertial reference frame. The success of the Schrödinger
equations constitutes a basis for accepting them, their derivations, and the unified theory of
wave-particle duality which makes such derivations possible. This acceptance is completely
justified in the favored inertial reference frame.
In accord with the principle of relativity, all physical laws must be the same in all inertial
reference frames, i.e., all physical laws must be Lorentz invariant.
Recall, the relationship:
$$\nabla^{2} \psi = \frac{\partial^{2} \psi}{\partial t^{2}}$$ ...........(1)
Equ (1) is Lorentz
invariant
and reduces, by means of the procedure presented in the previous posts, to the Schrodinger
equations. As a result, equ (1) constitutes a unique Lorentz invariant form of the
Schrodinger equations. Consequently, the Schrödinger equations are relativistically invariant.
Conservation of the number of massive quantum objects present occurs when the Schrodinger
equations are applicable. This happens when positrons are absent, nuclei are stable, and energy
transfers lie below the threshold for electron-positron pair production. These low-energy
conditions are often considered to be non-relativistic. Correspondingly, the term relativistic is
often restricted for use when the energies involved are high enough to permit non-conservation
of the number of massive quantum objects present. This use of terminology does not change the
fact that the Schrodinger equations are relativistically invariant.
Relativistic invariance does not imply covariance. Relativistic invariance of the Schrodinger
equations is based on reduction from a covariant law. Because of their relativistic invariance and
their success in analyzing many kinds of systems in particular inertial reference frames, the
Schrodinger equations constitute laws of physics. These laws of physics are applicable when
energies are low enough to assure that the number of massive quantum objects present is
conserved.
In accord with the unified theory of wave-particle duality, quantum objects are linked to particle-
like properties, but not to particles. This is consistent with Blood’s finding that there is no
evidence for particles and with Hobson’s finding that there are no particles, only fields.
The Schrodinger equations are field equations, not particle equations. Rather than describing
particle motion, the time-dependent Schrodinger equation describes a time-dependent field \(\Psi (r,t)\)
throughout a spatial region. Following Hobson, the Schrodinger field is a space-filling physical field whose value at any spatial point is the probability amplitude for an interaction to
occur within an infinitesimal region surrounding the point.
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