# A New Class of Retrocausal Models

## Abstract

**:**

## 1. Introduction

## 2. Conceptual Framework

## 3. Constrained Classical Fields

#### 3.1. Classical Photons

#### 3.2. Simple Model Example

- The a priori probability distribution on each unknown field intensity is given by Equation (1)—to be updated for any given experiment.
- The unknown field values are further constrained to be equal as pairs, $\{{I}_{1},{I}_{2}\}=\{{I}_{A},{I}_{B}\}$.
- ${I}_{1}$ is non-negligible because it accompanies a known “photon”.
- The probability of each diagram is given by ${P}_{0}\left({I}_{1}\right){P}_{0}\left({I}_{2}\right)$, or equivalently, ${P}_{0}\left({I}_{A}\right){P}_{0}\left({I}_{B}\right)$.

#### 3.3. Discussion

## 4. Averaged Fields and Weak Values

#### 4.1. Beamsplitter Analysis

#### 4.2. Interferometer Analysis

#### 4.3. Weak Values

## 5. An Improved Model

- The unknown field values are constrained to all be equal: ${I}_{1}={I}_{2}={I}_{A}={I}_{B}$.
- The $apriori$ probability distribution on each unknown field intensity is given by Equation (22)—but must be updated for any given experiment.
- The relative phase between the incoming fields is a priori completely unknown—but must be updated for any given experiment.

## 6. Summary and Future Directions

- Distributed classical fields can be consistent with particle-like detection events.
- There exist simple constraints and a priori field intensity distributions that yield the correct probabilities for basic experimental geometries.
- Most unobserved field modes are expected to have zero intensity (unlike in SED).
- The usual retrocausal account for maximally entangled photons still seems to be available.
- The average intermediate field values, minus the unobserved background, is precisely equal to the “weak value” predicted by quantum theory (in the cases considered so far).
- Negative weak values can have a classical interpretation, provided the unobserved background is sufficiently large.

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) A classical photon analog encounters a beamsplitter, and is divided among two detectors, in contradiction with observation. (

**b**) A classical photon analog, boosted by some unknown peak intensity ${I}_{1}$, encounters the same beamsplitter. Another beam with unknown peak intensity ${I}_{2}$ enters the dark port. This is potentially consistent with a classical photon detection in only detector A (“Y" for yes, “N" for no), so long as the output intensities ${I}_{A}$ and ${I}_{B}$ remain unobserved. (The wavefronts have been replaced by dashed lines for clarity.) (

**c**) The same inputs as in (

**b**), but with outputs consistent with classical photon detection in only detector B, where the output intensities ${I}_{A}$ and ${I}_{B}$ again remain unobserved.

**Figure 2.**A classical photon analog encounters two beamsplitters, and is divided among three detectors. The CPA is boosted by some unknown peak intensity ${I}_{1}$, and each beamsplitter’s dark port has an additional incident field with unknown intensity.

**Figure 3.**(

**a**) A classical photon analog, boosted by some unknown peak intensity ${I}_{1}$, enters an interferometer through a beamsplitter with transmission fraction T. An unknown field also enters from the dark port. Both paths to the final 50/50 beamsplitter are the same length; the intermediate field intensities on these paths are ${I}_{X}$ and ${I}_{Y}$. Here, detector A fires, leaving unmeasured output fields ${I}_{A}$ and ${I}_{B}$. (

**b**) The same situation as (

**a**), except here detector B fires.

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Wharton, K.
A New Class of Retrocausal Models. *Entropy* **2018**, *20*, 410.
https://doi.org/10.3390/e20060410

**AMA Style**

Wharton K.
A New Class of Retrocausal Models. *Entropy*. 2018; 20(6):410.
https://doi.org/10.3390/e20060410

**Chicago/Turabian Style**

Wharton, Ken.
2018. "A New Class of Retrocausal Models" *Entropy* 20, no. 6: 410.
https://doi.org/10.3390/e20060410