Research on practitioners of the TM-Sidhi program relative to subjects practicing Transcendental Meditation alone has shown increased EEG coherence during "Yogic Flying", one of the components of the TM-Sidhi program, as well as long-term increases in EEG coherence. , differences in reflex, and changes in endocrinological performance. In addition, a study on EEG coherence associated with practice of the TM-Sidhi program is correlated with greater creativity as measured by the Torrance Test of Creative Thinking.
Early promotional posters for program offered TM practitioners powers of Yogic Flying, invisibility, the ability to walk through walls, and the "strength of an elephant." The TM organization eventually stopped talking publicly about these powers, except for the ability to hover and fly; the organization says that TM-Sidhi practitioners (called Sidhas) have already achieved the first of the three stages of Yogic Flying – hopping. Further practice of the technique is said to lead to the second stage, which is hovering, and flying through the air, the third stage. Accounts within the organization of yogic flyers advancing beyond the hopping stage have varied over the years. For example, in 1978, when the host of The Merv Griffin (TV) Show asked Maharishi Mahesh Yogi how many of the 40,000 TM-Sidhi students he taught learned to levitate, he answered, "Thousands."
Researchers associated with Maharishi University of Management have hypothesized that practicing the Transcendental Meditation and TM-Sidhi programs in a group produces a "Maharishi Effect," that is said to influence coherence and positivity in the social and natural environment." According to these researchers, if the square root of one percent of the population (that is, first calculating 1% of the population and then taking the square root of the resulting number) regularly practices the TM-Sidhi program together, the entire population will experience greater coherence - including reduction in violence, crime, disease, deadly storms, and other destructive natural forces.
James Randi, a magician and critic of paranormal claims, investigated the claims of Dr. Robert Rabinoff, a former Maharishi International University physics professor who claimed that a large gathering of TM practitioners had reduced crime and accidents and increased crop production in the vicinity of Maharishi International University in Fairfield, Iowa. Rabinoff made the claims during a talk at the University of Oregon in 1978. Randi spoke with the Fairfield Police Department, the Iowa Department of Agriculture, and Iowa Department of Motor Vehicles and was unable to substantiate the claims.
According to a bibliography on the Maharishi University of Management web site, studies on the Maharishi Effect have been published in journals such as Social Indicators Research, Journal of Mind and Behavior, Social Science Perspectives Journal, Journal of Conflict Resolution, Journal of Crime and Justice, and Psychology, Crime and Law.
At a 1994 press conference to announce the analysis of that study, John Hagelin said that, during the period of the experiment, Washington, D.C. experienced a significant reduction in psychiatric emergency calls, fewer complaints against the police, and an increase in public approval of President Clinton -- all of which was consistent with the hypothesis that a coherence-creating group of practitioners of the TM-Sidhi program can relieve social stress and reverse negative social trends. Overall, there was an 18-percent reduction in violent crime, he told the press. When a reporter asked, an 18-percent reduction compared to what, Hagelin answered, compared to the level of violent crime had the study not taken place. Hagelin said that criminologists have shown that violent crime fluctuates significantly relative to the temperature. Crime goes down when it's cold and up when it's hot. The standard methodology for assessing whether the crime rate changed or not is to compare it with what is expected for that particular season. Hagelin said that by using the standard methodology (time series analysis), they were able to show the level of violent crime in Washington had dropped well below the expected level based on previous data.
In his book Voodoo Science, physicist Robert L. Park called the study a "clinic in data manipulation." Maxwell Rainforth, a coauthor of the Washington, D.C., study says that Park does not support the assertion with either supporting data or analysis, and that Park’s objection to the use of time series analysis isn't based on any scientific argument. The researchers also questioned whether Park had read the published study, since his criticism focused on a preliminary Interim Report released at a press conference in 1994.
Park questioned the validity of the study by saying that during the weeks of the experiment Washington D.C.'s weekly murder count hit the highest level ever recorded. According to the study, statistical analysis suggests that the murder rate, which typically goes up during hot weather, fell within the range of what would have been expected for that time of year.
In 1994 John Hagelin received an Ig Nobel Prize in peace based on this study. This parody of the Nobel Prize is given annually to "honor achievements that first make people laugh, and then make them think."
While Yogic Flying appears to be simply cross-legged hopping, EEG studies comparing Yogic Flyers with a control group voluntarily hopping found that the neurological characteristics were different. Immediately before hopping the yogic flyers showed significant shifts in EEG coherence and power, whereas the controls did not. The differences in EEG spatial distribution and mean amplitude between the two groups suggested that a different biological mechanism underlies the EEG activity in the two groups.
The TM organization has presented a number of public demonstrations of Yogic Flying, such as the one in 1999 described by Robert L. Park, professor of physics at the University of Maryland and author of the weekly science Internet column, What's New. The Yogic Flying demonstration was presented at a press conference at the Washington, DC Press Club by physicist and Natural Law Party Presidential candidate, John Hagelin. Hagelin had called the press conference to offer help in ending the war in Kosovo by sending 7000 yogic flyers to create positive coherence in the violence-torn country. Proponents of Yogic Flying claim that world peace and many other social and environmental benefits can be generated by having at least seven thousand yogic flyers around the world hopping at the same time. This is how Park described the demonstration:
A system of Yogic Flying also exists within the inner tantras (anuttara-tantras) of Tibetan Buddhism as a system to attain enlightenment. In this system the practitioners work at the dissolution of the vital airs, prana, into the centermost part of being, the avadhuti or "central channel". In the initial stages this is used in a system of yogic-running where the practitioner is able to proceed across the ground in large jumps. Some of kings of the Himalayan kingdoms kept speed-runners or practitioners of yogic-running from this Buddhist tradition to carry messages over long distances.
During the 1990s, various Natural Law Parties encouraged the use of Yogic Flying as part of their party platform. Current plans by Maharishi Mahesh Yogi, the founder of the Transcendental Meditation Program and related programs, include building 3000 Peace Palaces in major cities, and creating permanent groups of 8,000 yogic flyers to create permanent world peace. His plan also calls for a group of 1000 Vedic pandits, all flyers, to take up residence at Maharishi Vedic City, Iowa.