\(\int^{x}_{0}{\psi}\,dx=-m_{\rho}c^2\)
then,
\(\int^{x}_{0}{\psi}\,dx=m_{\rho}(ic)^2\)
this is possible in a wave where energy oscillates between two orthogonal dimensions, here denoted by,
\(c\) and \(ic\)
Energy oscillations between two space dimensions will not manifest negative \(\psi\) as the total \(\psi\) across both space dimensions, both accessible in our reality, sum to a positive constant.
If energy oscillations are between two time dimensions, a third time dimension is then necessary for the phenomenon to exist, by which all time based calculation are made.
If energy oscillations are between one time dimensions and one space dimension, energy drain from the space dimension will be seen as negative energy as the total energy in 3D space will decrease. This kind of particle will require another time dimension on which to exist and be at light speed, and another space dimension on which it is also at light speed so that particle is a wave.
This particle will take away energy without itself gaining energy (in space). The gained energy is in the time dimension, that is part of a space-time dimensional pair between which energy oscillates. Since it is energy oscillations, the particle can also give energy without itself losing energy.
Both \(t_c\) and \(t_g\) are possible candidates for the space-time dimensional pair; all three space dimensions are also available. This makes two types of such particles as the space dimensions are all equivalent,
\(m_{vc}\) and \(m_{vg}\)
that exist on the \(t_c\) time dimension and \(t_g\) time dimension respectively. And \(v\) is for Vampire.
\(m_{vc}\) is charged and has energy oscillating between \(t_g\) and a space dimension. \(m_{vg}\) is not charged and has energy oscillating between \(t_c\) and a space dimension.
How then to detect such particles? These particles require light speed in space to manifest as a wave, ie \(\dot{x}=c\), which is the difference between them and the particles responsible for charge and gravity. From the post "My Own Wave Equation",
\(\left(1+\cfrac{1}{\gamma^2} \right)\cfrac { \partial \, \psi }{ \partial \, t_{ c } }=2\cfrac { \partial V\, }{ \partial \, t_{ c } }\)
where,
\(\cfrac{1}{\gamma^2}=\left( 1-\cfrac { \dot { x } ^{ 2 } }{ c^{ 2 } } \right)\)
As \(T\) and \(V\) are symmetrical, because \(\psi=T+V\). Given, \(\dot{x}=c\),
\(\cfrac { \partial \, \psi }{ \partial \, t_{ c } }=2\cfrac { \partial V\, }{ \partial \, t_{ c } }\)
if however, the particle is to slow down \(\dot{x}\lt c\), then
\(\cfrac { \partial \, \psi }{ \partial \, t_{ c } }=\cfrac{2}{\left(1+\cfrac{1}{\gamma^2} \right)}\cfrac { \partial V\, }{ \partial \, t_{ c } }\)
which casues
\(\cfrac { \partial V\, }{ \partial \, t_{ c } }\) to increase.
If \(V\) is energy in the time dimension, there will be a
decrease in \(\cfrac { \partial T\, }{ \partial \, t_{ c } }\)
in the space dimension.
because \(\cfrac { \partial \, \psi }{ \partial \, t_{ c } }=\cfrac { \partial T\, }{ \partial \, t_{ c } }+\cfrac { \partial V\, }{ \partial \, t_{ c } }\)
This results in a shift of energy to \(V\) and energy perceived only in space, \(T\) decreases. In other words, the particle cools. The space, denoted by \(x_2\) here, as the particle passes however, cools down. The gain in \(V\) is in the time dimension. The total \(\psi\) however remains a constant, this shift in \(V\) corresponds to a shift in the center of oscillation.
If the particle has a lower velocity to start with (ie. \(\dot{x}\lt c\)) and then is accelerated to \(c\), a decrease in \(V\) will shift the center of oscillation toward \(T\); \(T\) increases. If these changes in velocity of the particles happen across two materials, then we have an energy pump that transfer energy from one material to another.
Have a nice day.
Afternote:
Cooling photons will be oscillating between \(t_T\), the thermal time dimension and one other space dimension. Please refer to later posts on \(t_T\), starting with "3 Space, 3 Time Dimensions And Sesame Street".
