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Samadhi a State of Physical Transcendence
With modern science being skeptical about Samadhi and sometimes finds itself helpless to explain the physical state of a yogi in Samadhi, there is ample information available in the ancient scriptures which has been observed to be true in case of many saints in the recent history. The modern Hindu saints/scholars have also written extensively to guide modern scientific community on the phenomenon of Samadhi.

While talking about the Pranas, Swami Vivekananda says “There are persons who can train themselves in such a manner that the body will live on even when their lungs, the most obvious manifestation of Prana in the human body, have stopped and there are some persons who can bury themselves for days and yet live without breathing”. Throwing some more light on this, Swami Sivananda states "When the Kundalini is awakened, it takes the mind and Prana along with it upwards towards Sahasrara Chakra through Sushumna and the Yogi is shut out from the physical consciousness of the world and is practically dead to the world".

Scriptural References
Shiv Puran

Shiv Puran, one of the early and ancient Indian scriptures, clearly states that in state of Samadhi, the vital forces and the consciousness recede back from every iota of the Being to get confined in the inner or outer cosmic space where a Being seems to be standstill. It further states that at the time of Samadhi, one neither hears anything, nor smells any odour, nor does he taste or see anything; one is unable to identify any feeling of touch, neither does can one determine anything in mind, and nor does he believe in anything. The person becomes stiff like a log of wood. In this manner, when the soul force of the person merges with the Brahm (the super cosmic force), one is said to be in the state of Samadhi.

Hath Yog Pradipika

It states that the one who is in Samadhi, his body transcends the sphere of experiences of smell, taste, touch, speech and consciousness”, implying that even the unconsciously regulated vital senses come to a state of hibernation. For a yogi in the state of Samadhi, his inner-self and outer-self nullifies to zero state, thus establishing in Absolute stillness. This zero-state or absolute stillness of Samadhi appears identical to that of a life-less body. The state wherein the life-force declines and the mind rests in it (divine element) - such a unification of the soul and the Supreme is known as Samadhi

Patanjal Yogdarshanam and Mahopanishad

Mahopanishad states that when the state of Samadhi arrives, all thoughts and ambitions come to peace, there is no effort of any form. The way a rock is motionless, likewise the state of yogi comes to rest. The yogi becomes independent of Waking state, Dream state and Deep Sleep state, and gets established in Supreme Self. According to Patanjal Yogdarshanam, where the entire Self or existence appears to be still, it is known as Samadhi.

Scientific Case Studies
Flat ECG during Samadhi : A Research on Yogi Satyamurti

A research paper documenting the ECG patterns of Yogi Satyamurti during his week long Samadhi demonstrated a flat line in ECG when the yogi was in state of Samdhi inside the pit. This research paper named - An Unusual Demonstration “The yogic claim of voluntary control over the heart beat - was published in 'A letter to the American Heart Journal – 1973,'  and describes the finding in detail.

Yogi Satyamurti, a sparsely built man of about 60 years of age, remained confined to a small underground pit for 8 days. An ECG was continuously monitored during these 8 days and various other laboratory investigations were carried out before and after. The 12-lead ECG increased progressively, reaching a heart rate of 250 per minute on the second day. At 5:15 pm on the second day, when the yogi had been inside for about 29 hours, a straight line replaced the ECG tracing. There was no electrical disturbance of any sort even at higher amplification and with different leads. There had been no slowing of the heart or signs of ischemia preceding this.

The straight line on the ECG persisted till the eighth morning. Electrical activity returned about half an hour before the pit was scheduled to be opened. After some initial disturbance, a normal configuration appeared. The Yogi had informed beforehand that he would begin to come out of his Samadhi after nearly 7 days. When the pit was opened on the eighth day, ECG repeated in the laboratory subsequently was found again within normal limits.

The researchers conclusively stated that although it was obviously difficult to believe that the Yogi could have completely stopped his heart or decreased its electrical activity below a recordable level, there was still no satisfactory explanation for the ECG tracings