# The Weak Reality That Makes Quantum Phenomena More Natural: Novel Insights and Experiments

^{1}

^{2}

^{3}

^{4}

^{5}

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## Abstract

**:**

## 1. Introduction

## 2. How “Void” Are the Wavefunction’s Non-Observed Parts?

## 3. Can a Particle Be Where It Never Went?

_{1}splits the beam into 1/3 and 2/3, and the last, BS

_{4}, splits the 1/3 of the original beam into 1/9–2/9. On the right, 2/3 arm E, goes past a smaller, standard MZI with two 50/50 BSs dividing the beam into two equal parts.

_{1}and never goes through F to the final beam splitter BS

_{4}and the last two detectors D

_{2}and D

_{3}.

_{1}did not click are selected. This entire part of the wavefunction now becomes “void” based on the introduction of the previous section: the photon seems to have never gone through this E arm, but takes the C arm.

_{3}has clicked are selected. This amounts to post-selection of

## 4. In Search of Validation: Weak and Strong Measurements

_{1}has failed to click, one would regard this part of the wavefunction completely ruled out, “collapsed” into nothingness. Lo and behold, when D

_{3}later clicks, then, within the middle segment of this never-traversed trajectory, the particle is revived.

_{3}has clicked, apparently implies that the nested MZI has never been traversed. Because the mirrors’ momenta are subject to quantum uncertainty, it is necessary to repeat the experiment many times to overcome the noise. The predicted result offers the first affirmation to the TSVF prediction; moreover, the right-hand mirror indicates a recoil upon the photon’s overall hits, while the left hand undergoes a negative recoil, namely a “pull” rather than a “push”.

- (i)
- at t
_{1}: to a mirror placed just behind the trajectory E leading to the nested MZI; - (ii)
- at t
_{2}: to the nested MZI’s right-hand path A where the mirage photon is expected to be; - (iii)
- at t
_{2}: to the large MZI’s left path C where the photon is simultaneously expected to be; - (iv)
- at t
_{3}: to a mirror placed behind the exit trajectory F from the nested MZI towards BS_{4}.

_{5}of all the probe’s wavepackets returning from E, A, C and F with their original amplitudes ${\alpha}_{i}$, that is

_{4}and detectors D

_{2}and D

_{3}. The photon is not expected to pass there by the basic laws of optics, and indeed the probe photon’s 4th part is expected not to find it there. However, this segment should remain open, that is, any obstruction along it would make the experiment fail [17], for the future effect of the post-selection at D

_{3}. This account, while demanding a great conceptual sacrifice, is the most intuitive for us.

## 5. The “Spooky Particle” Experiment

- (i)
- in A and C at t
_{1}; - (ii)
- only in C at t
_{2}; - (iii)
- in B and C at t
_{3}; - (iv)
- and then again in A and C at t
_{4}.

_{1}when the two mirage particles coexist in A and C (as already implied by the Okamoto–Takeuchi experiment [36]). The nega-photon is now in B. At this instant, the following retrodiction holds: had we joined B with C rather than with A, the particle would have vanished from C and “collapsed” into A.

## 6. On Negative Weak Values: Can a Mirror be “Pushed” Inwards?

## 7. Generalizing: Interaction-Free and Positive Measurements as Sums of Weak Values

_{1}and no detection turns out to be a self-cancelling pair of mirage particles, of which one is a nega-particle. The nested MZI, then, enables a momentary resolution of this “nothing”. Suppose, for example, that detector D

_{1}is a movable mirror, which, by not recoiling, indicates that the particle does not go that way. According to the TSVF, the mirror’s non-recoil is simply the sum of positive and negative recoils. Similarly, if detector D

_{1}is a photographic plate, the “no dot” would be a mirage photon accompanied by a nega-photon, as implicated in the above “negative absorption” experiment [14]. Indeed, Quantum Oblivion [41], which underlies several quantum phenomena from the quantum Zeno to the Aharonov–Bohm effects, has shown, also with pre- and post-selections and “strong” measurements, how each of these apparent non-events can be decomposed into its occurrence followed by “un-occurrence” [21,22]. Nega-particles may thus become a common currency in quantum transactions. A profound time-symmetry of quantum reality seems to underlie the (in)famous asymmetry of measurement and classical reality.

## 8. Discussion: Time-Symmetric Causality and the Particle-Based Heisenberg Representation

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**A particle split by a beam splitter is predicted to go through one out of two possible paths and eventually be detected in one, with the other becoming “void” (

**a**). Similarly to the time-reversed retrodiction (

**b**): the wavefunction splits again towards the past, with one half leading to an obviously void “origin”.

**Figure 2.**Vaidman’s nested MZI [16,17]. From BS

_{1}, the path goes to a smaller MZI between BS

_{2}and BS

_{3}. The path emerging from the nested MZI in case of constructive interference goes to detector D

_{1}, of which non-clicking cancels the entire right-hand path, implying that the photon never passes through BS

_{1}but is rather reflected to the left towards BS

_{4}and detectors D

_{2}and D

_{3}.

**Figure 3.**The backward evolution from the actual detection. Again, a void branch goes to the nested MZI and exits towards an obviously void source.

**Figure 4.**The purple trajectory is the overlap of the blue and red lines of the earlier forward and backward state vectors. A momentary additional particle appears on the right path’s middle segment.

**Figure 5.**A probe photon (drawn in blue), superposed in both space and time, interacts via quantum routers with the photon traversing the nested MZI in three moments at four places, where the shutter photon is expected to be either present (the probe being reflected by the shutter) or absent (the probe being reflected by a mirror). Correlation between probe and shutter detectors emerges only if the probe photon is reflected by the mirage shutter photons where they are expected to pass (D

_{2}, and D

_{5}), and by the mirrors where no shutter photon is expected (D

_{3}, and D

_{4}).

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**MDPI and ACS Style**

Aharonov, Y.; Cohen, E.; Waegell, M.; Elitzur, A.C.
The Weak Reality That Makes Quantum Phenomena More Natural: Novel Insights and Experiments. *Entropy* **2018**, *20*, 854.
https://doi.org/10.3390/e20110854

**AMA Style**

Aharonov Y, Cohen E, Waegell M, Elitzur AC.
The Weak Reality That Makes Quantum Phenomena More Natural: Novel Insights and Experiments. *Entropy*. 2018; 20(11):854.
https://doi.org/10.3390/e20110854

**Chicago/Turabian Style**

Aharonov, Yakir, Eliahu Cohen, Mordecai Waegell, and Avshalom C. Elitzur.
2018. "The Weak Reality That Makes Quantum Phenomena More Natural: Novel Insights and Experiments" *Entropy* 20, no. 11: 854.
https://doi.org/10.3390/e20110854