^ Jump up to: a b Fox, Kieran C.R.; Nijeboer, Savannah; Dixon, Matthew L.; Floman, James L.; Ellamil, Melissa; Rumak, Samuel P.; Sedlmeier, Peter; Christoff, Kalina (2014). "Is meditation associated with altered brain structure? A systematic review and meta-analysis of morphometric neuroimaging in meditation practitioners". Neuroscience & Biobehavioral Reviews. 43: 48–73. doi:10.1016/j.neubiorev.2014.03.016. PMID 24705269.

Entrainment is a phenomenon seen is a wide variety of different natural circumstance. In the field of chronobiology, the study of biological rhythms in living organisms, entrainment is the synchronization of a circadian rhythm with the rhythm of an external pattern, such as the synchronizing of women’s menstrual cycles with the phases of the moon or with one another in a group.
Alpha waves unlock your imagination, bringing creative inspiration from deep within the currents of your own mind. In the Alpha state, awareness expands and fresh creative energy begins to flow. Alpha training helps you tap into higher levels of creativity and is excellent for problem solving, finding new ideas and practicing creative visualization. In Alpha, you can access the wealth of creativity that lies just below your conscious awareness - it is the gateway that leads into deeper states of consciousness.
Theta waves have a frequency between 4 and 7.5 hertz, making them slower than more wakeful alpha but faster than the dreamless slumber of delta. Theta brainwaves are the frequencies of nighttime dreams and REM sleep when the brain goes through bursts of activity and eye movement. People also experience theta waves in a state of light sleep, deep relaxation, during meditation and prayer, and when daydreaming. Theta waves produce an experience of inward wakefulness where we become disengaged from the outside world while engaging in inner activity. At the lower frequencies of theta, sleeping states are experienced, and at the higher range of frequency, awake relaxed states are experienced. 
In addition to potentially boosting sleep-promoting hormones, binaural beats may also reduce our perceptions of pain. A 2017 study found binaural beats used in combination with visual stimulation led to reductions in patients’ perception of acute pain. Other recent research showed binaural beats helped improve pain perception in patients with chronic pain.
The review by Cahn also notes findings describing a heightened emotional state of meditators. A more complex study, conducted in 2008 by Lutz et al., focused on emotional response during meditation.[9] This investigation involved the creation of a “compassion meditation” state by novice and experienced meditators and testing the meditators response to emotionally charged sounds. fMRI results indicated heightened activity in the cingulate cortex but also in the amygdala, temporo-parietal junction, and right posterior superior temporal sulcus in response to the emotional sounds. The authors of this study believe this indicates greater sensitivity to emotional expression and positive emotion due to the neural circuitry activated.[9]
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Studies have shown binaural beats may affect levels of dopamine, a hormone that plays a broad role in cognition and a particular role in creative thinking. This has scientists examining the possibility that binaural beats can be used to stimulate creativity. (If you’re looking to be more creative and innovative in your thinking, keep in mind that sleep itself is a powerful tool!)
There’s an aesthetic element to the music and there are a lot of drone-based sounds and time-stretched sounds, deep, rich bass sounds—there’s a spectrum of sounds within there—and what’s more, there’s a load of 3D processing that goes on to ensure that the mind doesn’t become habituated to them. There’s also a constant, subtle sense, a slow and gradual sense, of the sounds shifting around. And, there are layers of binaural beats.
Resonant entrainment of oscillating systems is a well-understood principle within the physical sciences. If a tuning fork designed to produce a frequency of 440 Hz is struck (causing it to oscillate) and then brought into the vicinity of another 440 Hz tuning fork, the second tuning fork will begin to oscillate. The first tuning fork is said to have entrained the second or caused it to resonate. The physics of entrainment apply to bio-systems as well. Of interest here are the electromagnetic brain waves. The electrochemical activity of the brain results in the production of electromagnetic wave forms which can be objectively measured with sensitive equipment. Brain waves change frequencies based on neural activity within the brain. Because neural activity is electrochemical, brain function can be modified through the introduction of specific chemicals (drugs), by altering the brain's electromagnetic environment through induction, or through resonant entrainment techniques.
Belief and faith, argue believers, are larger than the sum of their brain parts: "The brain is the hardware through which religion is experienced," said Daniel Batson, a University of Kansas psychologist who studies the effect of religion on people. "To say the brain produces religion is like saying a piano produces music." At the Fuller Theological Seminary's school of psychology, Warren Brown, a cognitive neuropsychologist, said, "Sitting where I'm sitting and dealing with experts in theology and Christian religious practice, I just look at what these people know about religiousness and think they are not very sophisticated. They are sophisticated neuroscientists, but they are not scholars in the area of what is involved in various forms of religiousness."

Most of these websites give some brief explanation of entrainment. The example you hear most often is that of Dutch polymath Christiaan Huygens, who in 1665, hung two pendulum clocks next to each other on a wall. He noticed that the pendulums eventually matched each others' frequency, but always in antiphase, opposite to each other, as if canceling each other out. He'd try disturbing one or setting them in sync, but they'd always return to the same antiphase synchronization. Huygen's experience is widely touted on binaural beat websites as a demonstration of how systems can become spiritually connected through some energy field. However, they misunderstand what happened, and have not read the full story. Huygens also tried taking one clock off the wall, and as soon as they were no longer physically connected to one another via the actual wall, the effect disappeared. It was not the proximity of the clocks to one another that created the entrainment; it was their physical, mechanical connection to one another. As each pendulum swung it imparted an infinitesimal equal and opposite reaction to the wall itself. With two clocks on the wall, the system naturally sought the lowest energy level, according to the laws of thermodynamics; and both pendulums would thus swing exactly counter to each other, minimizing the system's total energy.