## 1 Introduction  
We have previously published data on the parameters of the magnetic field or electromagnetic treatments that control the physical properties of water [1; 2; 3; 4; 5; 6]. Changes in the physical properties of water can affect biological processes, i.e., they can exhibit biophysical effects. One of the models most sensitive to changes in the physical properties of solutions after magnetic field treatment is the respiratory burst of neutrophils [5; 6]. The respiratory burst is manifested during phagocytosis or in response to soluble mediators (e.g., the bacterial peptide N-formyl-Met-Leu-Phe (fMLF) or the phorbol ester, phorbol 12-myristate 13-acetate (PMA)) by a rapid release of ROS. One of the most sensitive methods for detecting ROS is based on the measurement of chemiluminescence that occurs during the oxidation of luminon (luminol-enhanced chemiluminescence). Using luminon-enhanced cellular chemiluminescence, we have previously shown the effect of weak and very weak combined magnetic fields (CMF) with static and variable components at the micro- and nanotesla scale directly on neutrophil suspensions and, indirectly, through aqueous solutions. The addition of a water sample pre-treated with CMF (60 uT static magnetic field (SMF) and 100 nT alternating magnetic field (AMF), 12.6 Hz) to a neutrophil suspension increased the production of ROS by approximately 70% [7; 8]. This property, which was originally characteristic of a water sample pre-treated with CMF, was maintained after a series of dilutions that were performed in combination with mechanical treatment. Namely, a water sample pre-treated with CMF was mixed with deionized water at a ratio of 1:100 and shaken intensively by hand with an approximate frequency of about 4 Hz (21 strokes in 4.8 s) to produce the first centesimal dilution. All subsequent dilutions consisted of one part of the previous dilution and 99 parts of the solvent with intensive shaking performed identically after each successive step. However, if a similar dilution process was performed in a \"magnetic vacuum\" or without mechanical action, then the ability of the sample to increase the production of ROS did not differ from the control [5,6]. This indicates that a magnetic field with certain controlled parameters, as well as a mechanical effect, represent factors that determine the activity of a water sample. When testing the effect of various substances (including HD forms of proteins and low molecular weight regulators of neutrophil functions) on such exposure to a magnetic field, we concluded that the result of CMF treatment to a certain extent could depend not only on the field parameters, but also on the way that these experiments were carried out. The production of ROS changed by orders of magnitude if various types of samples were subjected to CMF treatment simultaneously inside a controlled magnetic field generation device, possibly indicating a contactless interaction between the samples. The possibility of such contactless or distant interaction between samples was initially treated by us with skepticism, but since such an assumption appeared, we decided to conduct experiments to confirm or disprove this phenomenon. It was clear that if the results of these experiments could not be reproduced, or they were consistently negative, then it would be pointless to continue studies in this field. Phenomena similar to the ultra-weak photon emission ability of biological objects or the ability to interact distantly have been extensively studied and described earlier [9, 10, 11, 12, 13]. However, it had not been possible to reach a consensus on this matter, since the effects in some cases were too unpredictable, not always reproducible, and could often be caused by other processes (e.g., absorption of atmospheric gases). Therefore, some researchers still doubt the existence of such effects, including distant interactions [13]. Probably, this can happen if the researchers do not know or do not observe all the necessary conditions for the realization of these effects.