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Quantum Interference and the Limits of Separability

Sebastian Horvat

Abstract

Quantum theory implies, and empirical evidence confirms, that while particles $\textit{can}$ exhibit wave-like behavior in interferometric experiments, this behavior is so limited as $\textit{not}$ to allow for third- and higher-order interference. The article at hand shows that this possibility-impossibility structure suggests the universal validity of a principle that regulates statistical correlations between spatiotemporally localized events, $\textit{independently}$ of the nature of the objects that may or may not partake in these events. Roughly, the said principle mandates that $\textit{any}$ joint influence of $m$ mutually spacelike separated events on $\textit{another}$ event, be such, that it can be separated by $\textit{at least}$ $\lceil \frac{m}{2} \rceil$ mediating events, and in some cases, by $\textit{no more}$ than $\lceil \frac{m}{2} \rceil$ mediating events. The structure of quantum interference thus teaches us that events can influence each other in a non-separable fashion, but that this non-separability has a certain exactly quantifiable limit.

Quantum Interference and the Limits of Separability

Abstract

Quantum theory implies, and empirical evidence confirms, that while particles exhibit wave-like behavior in interferometric experiments, this behavior is so limited as to allow for third- and higher-order interference. The article at hand shows that this possibility-impossibility structure suggests the universal validity of a principle that regulates statistical correlations between spatiotemporally localized events, of the nature of the objects that may or may not partake in these events. Roughly, the said principle mandates that joint influence of mutually spacelike separated events on event, be such, that it can be separated by mediating events, and in some cases, by than mediating events. The structure of quantum interference thus teaches us that events can influence each other in a non-separable fashion, but that this non-separability has a certain exactly quantifiable limit.
Paper Structure (16 sections, 102 equations, 5 figures)

This paper contains 16 sections, 102 equations, 5 figures.

Table of Contents

  1. I. The Double-slit and Multiple-slit Experiments
  2. II. Semi-general Interference Experiments
  3. III. General Interference Phenomena
  4. IV. Reaching for the Principle
  5. V. The Principle
  6. VI. What have we learned?
  7. Funding Information
  8. References
  9. Appendix 1: Discussion of Example 2
  10. Appendix 2: Proof of Lemma 1
  11. Appendix 3: Proof of Theorem 1
  12. Appendix 4: Proof of Theorem 2
  13. Appendix 5: Further observations on the case of odd $m$

Figures (5)

  • Figure 1: The double-slit experiment.
  • Figure 2: The $m$-slit experiment.
  • Figure 3: The semi-general interference experiment of order $m$.
  • Figure 4: Spatiotemporal diagram of a general interference phenomenon of order 3. The dashed lines represent the future or past lightcones of their pertaining locations. Events $(a_1,a_2,a_3)$ (occurring at mutually spacelike separated locations $(x_1,x_2,x_3)$) are so correlated with event $b$ (that occurs at future location $y$) as to generate $I_3 \neq 0$.
  • Figure 5: A 2-local-completion (right figure) of a $\text{GIP}_{\text{3}}$ (left figure). The 2-local completion contains two additional mutually spacelike separated events $(b_1,b_2)$ that mediate and preserve the correlation between $(a_1,a_2,a_3)$ and $b$. The yellow lines indicate that the events in the causal past of $(a_1,a_2,a_3)$ are equally distributed in both phenomena.