This is the minimal cost to achieve the experimental aims. Here's why.

Equipment: All equipment is necessary to do the experiment. Previously, a shared double-slit setup was used, which did not allow for recalibration by a single PI when necessary. Now we are purchasing a devoted double-slit setup (the bulk of the cost) as well as our own digital multimeter and oscilloscope -- all of which can be used for future studies. We will purchase our own bulbs, table for the equipment, laptop, and Arduino controller.

Consultant salaries: Minimal salaries for 2 consultants (Daniel Sheehan and Loren Carpenter) are required to reserve their time for this project -- without these consultants the automation (Carpenter) and insights into interpretation by someone who understands quantum mechanics better than the PI (Sheehan) would not be available.

PI salary: PI is on "soft money" and requires salary to set aside time for projects. This project will take about 200 hours spread out over a year.

Additional Information

Methods

In the pilot study, the double-slit optical apparatus was run 36 times with the light source at a low enough level to emit a single photon at a time. In each of these runs, a random-number generator was used to determine the duration that the light source would remain on for that particular run (the on-duration for that run). This determination was made 90 seconds after the photomultiplier was turned on. Two dependent variables were calculated: meanFirstMinute and SDFirstMinute. These were the means and standard deviations of the 24 photon counts taken in the first 60 seconds in each run, recorded at a nadir in the interference pattern.

Results

Both dependent variables appeared to be influenced by the duration the light source would be on after the variables were recorded. Note that one would expect the interference patterns to differ between runs of different lengths, when they recorded after the full duration of each run. The dependent variables, however, were calculated only using data obtained within the first minute of each run, prior to when the quantum-based random-number generator selected the duration of the run.

MeanFirstMinute values increased with on-duration times (Fig. 1, linear regression, R-squared=0.169, p<0.02). SDFirstMinute values showed the same trend: variability increased as on-duration increased (Fig. 2, linear regression, R-squared=0.129, p<0.03). For both dependent variables, significant differences between the longest and shortest durations were also clear (MeanFirstMinute: p<0.005; SDFirstMinute: p<0.008). The only difference in the apparatus between runs at different on-durations was how long the light source would be on after the first 90 seconds; thus both the mean and standard deviation effects were apparently retrocausal.

Fig. 1. Mean of the MeanFirstMinute values at each of the on-durations for the pilot study 1. Black line shows average of all the MeanFirstMinute values, to which the data would be expected to conform if the total on-duration of the light source did not influence the MeanFirstMinute values.

Fig. 2. Mean of the SDFirstMinute values at each of the on-durations for the pilot study 1. Black line shows average of all the SDFirstMinute values, to which the data would be expected to conform if the total on-duration of the light source did not influence the SDFirstMinute values.

An additional 21 runs were performed in which the on-duration was selected by the random number generator after 22 seconds. The trends were similar, but because the on-duration was selected during the time the dependent variables were calculated, these data do not present convincing evidence of retrocausality. However, this second pilot study revealed that periodic recalibration of the equipment is necessary -- a process that was made difficult during the pilot studies as the equipment was shared across experimenters. The proposed experiments eliminate this concern, as a new and solely-owned single-photon double-slit system will be purchased.

Proposed experiments

1. Set up automated version -- working with engineer Loren Carpenter, we plan to create a mechanism for slowly turning up/down the voltage to the light source so the experiment can be automated (at least 2 experiments, ~100 runs each))

2. Replicate using more time points -- to understand potential nonlinearities in the effect and to determine whether the effect of future on-duration times is limited to the minute time range, we plan to sample many more on-duration times, from 60 seconds to 1 hour (at least 6 experiments, ~100 runs each)

3. Examine the influences of…

• Observation rate -- pilot data suggest that the rate at which the photomultiplier records photon counts could influence the effect, so we will run several experiments in which the on-duration remains the same but the observation rate is randomly selected. The transactional interpretation of QM would predict that photon absorption, but not observation, would influence any quantum effect (at least 4 experiments, ~100 runs each).

• Observation location -- if these changes are occurring at a nadir in the interference pattern, what is happening at a peak? We'll run several experiments to find out, using the best times to sample on-durations (revealed by 2, above; at least 3 experiments, ~100 runs each).

• Time of on-duration selection -- it is possible that effects after the time the on-duration is known are diminished. We'll run several planned experiments to assess this possibility by manipulating on-duration selection time while all other parameters stay constant. The transactional interpretation is not consistent with knowledge effects on the system (at least 4 experiments, ~100 runs each).