7. Acknowledgements and References

Acknowledgements

This work was supported in part by the Division of Nuclear Sciences of the U. S. Department of Energy. The author would like to acknowledge critical readings and valuable comments and suggestions from Drs. Albert Lazzarini and Eric Norman (University of Washington), from Prof. Riley Newman (University of California at Irvine), from Dr. Ron Burman (University of Western Australia), from Dr. Nick Herbert (Boulder Creek, CA), and from Prof. Paul Davies (University of Newcastle upon Tyne). A very useful discussion with Sir Rudolph Peierls is also gratefully acknowledged. The present version of this paper has profited greatly from their remarks.

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Figures and Captions

  
Figure 1: Minkowski diagram showing an emitter-absorber transaction. The single vertical line indicates emitter or absorber is in a state of low energy, while the double vertical line indicates a higher energy state. Waves produced by the emitter and absorber will lie along the diagonal light-like world line, but here the emitter waves are indicated schematically by the red sinusoidal curves. Similarly, waves produced by the absorber are indicated schematically by the blue sinusoidal curves. Retarded waves are drawn as solid curves, while advanced waves are shown as dashed curves. As indicated, advanced waves before the emission event and retarded waves after the absorption event are 180^o out of phase and will cancel, while the advanced and retarded wave in the interval between the emission and absorption events are in phase and will reinforce.

  
Figure 2: Minkowski diagram showing an open-ended emission transaction. The conventions used here are the same as those used in Fig. 1. The advanced waves propagate backward in time to the T=0 origin, where they are subject to a reflection boundary condition. The reflected wave arising from the boundary condition cancels the advanced wave up to the emission event, and at times after emission it reinforces the retarded wave from the emitter.