Abstract
Whether it is the crack and snap of an electric shock on a cold winter day or the boom and crash of a lightning bolt on a stormy summer afternoon, we are familiar with electrons because they influence us. Similarly, scientists know about electrons because they influence their measurement equipment .
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Notes
- 1.
If all one can detect is the occurrence of an influence event, how can anything ever be known about the relation between those events and any internal states of the particle?
- 2.
If the particle states were accessible, then we could alternatively describe the particle as a totally ordered chain of particle states.
- 3.
An event z covers an event x if \(x < z\) and there does not exist any y such that \(x < y\) and \(y < z\).
- 4.
As an example, given events \(p_1< p_2< p_3< \cdots < p_{12}\) along the chain \({\mathbf {P}}\), the map \(\phi \) which gives \(\phi (p_1) = \phi (p_2) = \phi (p_3)< \phi (p_4) = \phi (p_5) = \phi (p_6)< \phi (p_7) = \phi (p_8) = \phi (p_9) < \phi (p_{10}) = \phi (p_{11}) = \phi (p_{12})\) is a valid coarse-graining map.
- 5.
The event x is said to be incomparable to the event y if it is true that \(x \nleq y\) and \(y \nleq x\).
- 6.
The two events defining the interval are assumed to be collinear to the coordinated pair of observers. This is precisely defined in [36] in terms of projections.
- 7.
Please see [36] for technical details.
- 8.
Directed distance differs from distance by at most a sign, which indicates the orientation of the interval with respect to the observers \({\mathbf {P}}\) and \({\mathbf {Q}}\).
- 9.
This observation was made by James L. Walsh.
- 10.
It is important to note that the case where both rates are zero would result in not only zero mass but also zero energy and momentum. Such a particle would not influence anything and would therefore be unobserved.
- 11.
By ‘position’ and ‘time’, we mean the directed distance and duration with respect to a defined origin.
- 12.
Our initial studies of influenced particles indicate that one needs four complex numbers and that they appear to take the form of a Dirac spinor with the positive energy components representing the amplitudes for the particle to influence and the negative energy components representing the amplitudes for the particle to be influenced.
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Acknowledgements
I would like to thank Newshaw Bahreyni, Seth Chaiken, Ariel Caticha, Keith Earle, David Hestenes, Oleg Lunin, John Skilling, and James Lyons Walsh for numerous insightful discussions. I also want to specifically thank James Lyons Walsh for his careful proofreading of this manuscript and his invaluable comments.
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Knuth, K.H. (2017). Understanding the Electron. In: Durham, I., Rickles, D. (eds) Information and Interaction. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-319-43760-6_10
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