ॐ पूर्णमदः पूर्णमिदं पूर्णात्पुर्णमुदच्यते
 पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते ॥

Meaning

This much detail is important to understand the depth and subtleties of the meanings that are necessary before one attempts to contemplate on this “mantra” – this “mantra” is part of 2 main “upaniṣad” – “īṣāvāsyopaniṣad” and “bṛhadāraṇyakopaniṣad”

With respect to Continuum Theory or Quantum principles – you may relate or not. Because modern scientists keep changing hypothesis and verbal definitions almost every day !. Also, I am not against mixing Science and Religion – but it should be done after a careful and thorough analysis of both. Therefore for the moment, I leave the conclusion of similarity to the reader.

Note 1: The translations of many complex Sanskrit words below are given in English. They are meant for quick surface-level understanding purpose. The meanings given are neither exact meanings nor in-depth meanings for those Sanskrit words. It is to be always kept in mind that, many Sanskrit words are not translatable to any language, especially “Veda” / “Vedānta” can’t be translated.

Note 2: My answer is just a free-flowing answer and not based on Traditional commentaries of “upaniṣad” (“śrī. ādi śankarācārya” has written “bhāśyam” for both these “upaniṣad” and that gives the correct “vedānta” meaning)

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शान्तिपाठः (मन्त्रः – ईशावस्योपनिषद् बृहदारण्यकोपनिषद च)

This “mantra” is the “śāntipāṭha” (Shanti Mantra) in “īṣāvāsyopaniṣad” and “bṛhadāraṇyakopaniṣad”

पूर्णमदः पूर्णमिदं पूर्णात् पूर्णमुदच्यते ।

पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते ॥

ओँ शान्तिः शान्तिः शान्तिः ॥

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Splitting of this as “pada-pāṭha”(the text in “sandhi” split word format)

पदपाठः

पूर्णम् अदः पूर्णम् इदम् पूर्णात् पूर्णम् उदच्यते । पूर्णस्य पूर्णम् आदाय पूर्णम् एव अवशिष्यते ॥

(With “sandhi” split)

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प्रकृति-प्रत्यय-वियोगः अर्थः च (Morphology)

The Root /Nominal Stem and the affix split – This is for Morphological meaning for better understanding at the root level.

पूर्ण = पुर् (धातुः) + क्त (प्रत्ययः) निँ (आदेशः) = पूर्ण (कृदन्त-प्रातिपदिकम्) = Complete, Full, Whole, Entire, Infinite (गणितशास्त्रम्), Pervasive, etc.

अदः [अदस् – प्रातिपदिकम् (नपुं)] = That

इदम् = (इदम् – प्रातिपदिकम्) = This

उदच्यते = उत्+अचुँ (भ्वादि) गतौ याचने च + य + तिङ् (कर्मणि = स्वयमेव उदञ्जनत्वात्) = Raises and manifests itself

आदाय = आ+दा + घञ् (भावे) = separated, presented, inherited, etc.

अवशिष्यते = अव+शिषॢँ (रुधादि) विशेषणे = especially remaining

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Now the full verse meaning in English (free-flowing):

• ‘That’ (the absolute) is full /complete /whole / pervasive /infinite, ‘This’ (the life-force) is full /complete /whole /pervasive /infinite.
• From ‘That’ ‘This’ raises and manifests itself.
• From ‘That’ when ‘This’ is separated /inherited /presented, what especially remains is ‘That’

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This “śānti-pāṭha” (“Mantra”) appears in Two main Upanishads of “śukla-yajurveda” . Thus this “veda-mantra” (“vedānta-mantra”) is quite significant in its meaning(s) for deep contemplation.

Every “veda-mantra” has meanings at 3 levels – this is as per the Traditional “veda-paramparā” method, in addition, to strictly following the methods prescribed by मीमांसा (“mīmāṃsā” – somewhat similar to exegesis /hermeneutics from a western PoV).

[Note: There are also other points of reference for meaning derivation for “Veda mantra” such as याज्ञीक (ritualistic) नैरुक्त (etymological) पारिव्राज्यिक (mystical) and नैदान्य (causal or diagnostic?), etc… By Sri. Ram Gopal, The history and principles of Vedic interpretation]

1). अधिभौतिकम् = अधि [“upasarga” (loosely prefix) meaning “in” / “within”] + भौतिकम् -In (within) Physical plane/phenomenal world level. This is for our objective understanding.

2). अधिदैविकम् = अधि [“upasarga” (loosely prefix) meaning “in” / “within”] + दैविकम् – In celestial plane /astral level. This is for using the Veda mantra as a method to invoke celestial forces – such as “parjanya-devatā” (rain god ), etc. This is chiefly for “upāsanā” and “yajña” / “yāga”, etc. – This can be said as, for subjective understanding.

3). अध्यात्मिकम् = अधि [“upasarga” (loosely prefix) meaning “in” / “within”] + आत्मिकम् (related to आत्मा / “Self”) – In spiritual level /state. This is to explain to us the deepest purport of the “mantra”) – this is for contemplation and meditation.

[Note: One should not get confused between 1). “अधिभौतिक” (“adhibhautika”) and 2). “आधिभौतिक” (“ādhibhautika”). the first one is about the ‘root of existence’ at physical, astral, causal planes and the second one is about the ‘root of disease’ at physical, astral and causal planes. While writing in English both are written as “Adhibhautika” (without the diacritical marks) – this causes confusion, the same problem applies to many other similar words where the difference between “अ” and “आ” (“a” and “ā”) etc. are not clear – काल and कला – both are written as Kala].

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How we can look at 3 levels of meanings ? let us look at the word “vāyu“, in a “Veda mantra”. If the mantra refers “Vāyu“, then it is to be looked at 3 levels:

1) “Vāyu” as Air (अधिभौतिकम् – level) – in today’s context (objective science – chemistry) containing various gases like oxygen at 20.95%, Carbon-di-oxide, Nitrogen, etc.,

2). “Vāyu” as a natural phenomenon (अधिदैविकम् – level) The one (personified as a god) who is responsible for maintaining the Air-cycle. (read about ‘Air-cycle’ in the Web)

Thus this phenomenon “vāyu”, without an innate intelligence within, can’t be one of the forces that maintain the ‘cyclical order’ (part of ऋतम् – Cosmic cyclical order). Such as maintaining the number of factors for sustaining life on earth such as Seasonal winds, Monsoons, Drying up moisture, Transporting moisture, Precipitation, Supporting Fire, Maintaining the balance of gases – 20.95% oxygen, etc. Thus in Veda (“Sanātana Dharma”) – every single Being – live elemental thing (“भूत” – “पञ्चभूत” ) has life principle within it. Therefore “vāyu” is also a live thing and hence it is a “devatā” (personified) and fit for “upāsanā” (worship). This part of Veda mantra’s meaning helps us in “yajña”, etc.

3). Vaayu as ‘PraaNa’ the Vital breath (अध्यात्मिकम् – level) not only sustains life in the body of beings, it is also the bridge between Body /Mind (“क्षेत्र” – Locus) with “ātmā” (क्षेत्रज्ञ – Locator) – using “vāyu” as a bridge to attain “mokṣa” is the purpose of “vāyu” at अध्यात्मिकम् – level. “prāṇāyāma” (extending “prāṇa”) and Breath-watching, etc.

Note: Vedānta texts, as well as Ayurveda texts (“caraka saṃhita” – one of the main Ayurveda text), say that both our mind and breath are from the same root. [“upadeśasāram”: “चित्त-वायवः चित्क्रियायुताः शाखयोः द्वयी शक्तिमूलका” = ‘mind and breath’ as ‘thought and action’, the two branches spring out from the same root of “śakti” = “ātmā”]. This is why our breath changes depending on our mental state /mood.

[With respect to अधिभौत, अधिदैव, अध्यात्म, अधियज्ञ, (“adhibhūta, adhidaiva, adhyātma, adhiyajña”), etc. In Bhagavadgita, 8th chapter has clear explanations for all these, such as who is – “adhibhūta, adhidaiva, adhyātma, adhiyajña” (the ordainer), etc. – It is necessary to study this chapter deeply with appropriate traditional commentary to understand the three levels of Vedic meaning concept. Keeping the “vedānta paribhāṣā” / “tatva bodha” also for ready reference].

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A Vedic “ṛṣi” is called as “मन्त्रदृष्टा” Mantra Drishtaa (the one who has seen the Mantra – in his/her “cit-ākāśa”…

In Sanskrit the words “dṛṣṭā” , “dṛśya”, “darśana”, “dṛk”, etc. – all these come from the same “dhātu” (verb root) – “दृश्” (“dṛś“_ – This root has 5 primary meanings – corresponding to – eye, act of seeing, cognition, illumination, and sight).

“दृश्” (“dṛś“) – “means to indriya-artha” (act of seeing),
“दृश्” (“dṛś“) – “means to grasp/capture – roopa grahaNam” (the eye),
“दृश्” (“dṛś“) – “means to observe” (the sight as a faculty for focus /observation),
“दृश्” (“dṛś“) – “means to insight” (cognitive ability /contemplation),
“दृश्” (“dṛś“) – “a flash/a vision” (illumination power).

[Note: The word “Veda” itself can be derived from 5 different verb roots, whereas here one verb root itself gives us 5 different meanings]

Thus a Vedic “ṛṣi” is a visionary – who got visions and based on that he/she revealed the absolute truth.

(There are other Sanskrit words for the ‘act of seeing’ from the verb roots (dhātu) such as “ईक्ष्” (“īkṣ”), for meanings such as glance, view, look, etc. – many of these apt usages have diluted over time and words are being interchangeably used nowadays. However, we have to locate the precise meaning for each and every single word in “Veda mantra” to arrive at the correct meanings )

[If the mathematician Sri. Ramanujan, can see (gets the vision) complex mathematical equations as shown by Devi Namagiri (Sri. Lakshmi). Then it is no wonder that the ancient Vedic “ṛṣi” were seers of Mantra].

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The same way this “pūrnam” in this “mantra” should be looked at three levels – Physical, Cognitive and Spiritual, corresponding to भौतिकम् (Physical), दैविकम् (Celestial), आत्मिकम् (Spiritual).

“Pūrnam” as ‘Infinite’ (अधिभौतिकम् – level)

If we remove infinity from infinity what remains is still infinity

For a better understanding of this concept, I have given below the picture explaining the infinity of finite things

“Pūrnam” as ‘Complete’ (अधिदैविकम् – level)

Only “The Absolute” is complete or that which is complete without the need for anything else for eternal existence is “Absolute” and since we are all part of that “Absolute”, it is worshipful. Therefore this mantra is chanted and used for worship (not prayer).

The “Absolute” manifests and takes many many forms (मूर्त – formed) = infinite no. of forms – असङ्ख्या (countless). Yet the “Absolute” is actually (अमूर्त = formless) – अपरिमित (immeasurable /indefinite) or Infinite. Thus in a sense, both मूर्त (form) अमूर्त (formless) is infinite!

मूर्तत्वम् = अवच्छिन्नपरिमाणवत्त्वम् (The technical definition of “Form-ness”)

Thus infinity is reflected in Finite things and Finite-ness is also part of infinity.

“Pūrnam” as ‘Whole’ (holy) – (अध्यात्मिकम् – level)

It is to be understood here that, “pūrnam” as a whole at आत्मिक level…, being cognized means, the cognizer absolves (or) merges with “That” “pūrnam” (in the stateless state of “Samādhi”).

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“pūrnam” at one level is “ऋतम्” – which is at one level the manifested (manifolded) “Absolute” /”One” – which is spread in countless forms (infinity). At another level, the “pūrnam” itself is “सत्यम्” – the “unmanifest” / “absolute” = infinite.

“ऋतात् सत्यम् उपागाम्” — ब्रह्मयज्ञम् (I attain from the manifested truth to the absolute truth – “bṛhmayajña”)

Thus “ऋतम्” is indeed manifolded “सत्यम्”

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Krishnamurthi CG, Ph.D. Sanskrit, University of Hyderabad