The Sanskrit word "puja" means "to honor;" it doesn't mean "to worship"—it is not a prayer. The puja procedure is a traditional performance of Vedic or Indian culture, used for many circumstances and occasions throughout India: people perform non-religious or secular pujas to honor teachers, guests, elders, musicians, literary figures — anyone who inspires respect. For example, on Mahatma Ghandi's birthday, secular pujas are performed all over India, with elements of invocation and offering, and attended by people of all religions and no religion. During India's Independence Day celebrations, candlelight may be offered and ceremoniously waved before a map or flag of India — another example of a non-religious, secular puja.
There are also religious pujas used for honoring deities; the language and offerings are similar to the secular pujas, but the context and intention is very, very different.
Nowadays, people seem more respectful and willing to accept ceremonies and protocols from other traditions — and that's what the puja is: an ancient, traditional ceremony from another culture, which uses some of that culture's traditional language of adoration. You might say that the TM program puja is performed in a sense similar to doctors taking the Hippocratic oath* — no worship is involved, it's traditional and ceremonial.
Yet the ceremony serves the vital function of keeping the TM technique connected to its source in the Vedic tradition. This timeless tradition of knowledge and the comprehensive understanding of consciousness that Maharishi revived from this tradition is the basis of the TM technique's effectiveness. TM instructors teach the technique in the way that has proven effective, using the ceremony as a preparation to teach.
If you're into ceremonies, you'll enjoy it. If you're not, it's very brief.
Religious leaders on the TM technique
More about the TM program's instruction ceremony (puja)
More about science, religion, and the Transcendental Meditation program
Myth #2: Meditation and relaxation practices are basically all the same and produce the same effects.
Myth #5: The research studies were conducted only by “TM scientists” and are not impartial scientific studies.
Myth #6: Independent scientific reviews show that Transcendental Meditation practice produces no significant health benefits. (On the AHRQ report.)
Myth #7: Yikes! It's a cult!
Myth #8: TM began as a religion, then became scientific to reach more people.
Myth #11: When learning Transcendental Meditation you undergo a religious ceremony.
Myth #12: Transcendental Meditation is a form of Hinduism
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*The Hippocratic oath, still used by many Western medical schools as part of the symbolic ceremony of becoming a medical doctor, begins, "I swear by Apollo, Asclepius, Hygieia, and Panacea, and I take to witness all the gods, all the goddesses, to keep according to my ability and my judgment, the following Oath...."