Randomised Control Trials, Placeo Effect, and the Many-Worlds interpretation of quantum mechanics

If the Many-Worlds interpretation of quantum mechanics is real, which some view as a valid interpretation of quantumn mechanics, it would theoretically be impossible to test if it were true, unless these universes affected one another.

Many times, in randomised controlled trials, there is often a noticeable effect in control groups which recieve a placebo, reffered to as the placebo effect. It is normally thought that this difference comes from the person believing that they are reciving treatment. If these groups were being selected randomly, then according to the Many-Worlds interpretation of quantum mechanics, some fraction of each of the participants would be participating in experiments where they were recieving the treatment, with another fraction of each indiviual participant would be participating in experiments where they were reciving the placebo. These fractions would be approximately half.

I propose an experiment to explore if the placebo effect which occurs in randomly controlled trials (RCTs) is the product of multiple universes being created when patients are randomly selected, as the Many-Worlds interpretation of quantum mechanics states would happen, and the interactions from the universes where participents are recieving treatment are affecting the universes where participents are recieving placebo:

Set up experiments that would test the affect of some medicine on the sample. Then create three psuedo-identical versions of each experiment with:

(A): A control and treatment group where there is random selection between treatment and control groups, with the control recieving a placebo.

(B): A control and treatment group where there is random selection between treatment and control groups, with the control not recieving a placebo.  After everyone that signed up for the treatment has been finalised, tell the control group that they have not been selected to recieve the treatment, asking them if they would come and take readings at the same times for the same period as the treatment group.

(C): A control and treatment group where the control group is selected by population matching (finding, for every treated person, one (or more) people with similar observable characteristics against which the covariates are balanced out)  with those in the general population that could qualify for the experiment.

Then, if these psuedo-identical versions of each experiment, repeated across many different experiments, showed a consistent skew towards a larger difference between treatment and control in the order of (C)>(B)>(A).  Or if there was a significant difference in the difference between treatment and control between groups (A) and (B), compared to group (C). Then the results could provide evidence towards the hypothesis that existing in a reality where treatment could have been recieved might affect the outcome, even if that person did not recieve treament and was not under the impression that they had been recieving treatment.