Time Travel

So far we have established that although PDOS is not defined in conventional quantum mechanics, it is well defined in functional analysis as a winding number of the AD. For a closed loop the winding number is an integer while for a part of the loop the winding number is a fraction that can be represented by a real number. It becomes clear that PDOS as a winding number can be also negative. This definition coming from functional analysis is thereby mathematical and does not rely on the questionable physical idea of spin precession. We will show in this chapter that negative PDOS will also lead to transmitting a physical signal in negative time. Once again the detail of the proof depends on BC and is independent of the potential or model. The only requirement is that the system should sustain Fano resonances and around such a resonance the stationary phase approximation is also analyzed to show that time travel is natural. We will comment on different notions of time and relate them to signal propagation time. We end the chapter with a small section called “reflections” which intends to imply that we are aware of the philosophical consequences but we are not willing to engage in a philosophical discussion at the moment. But we have hinted on what would be a physicists approach to such a philosophy. In the next chapter we will provide much more practical suggestions on how negative PDOS can manifest in the laboratory.