nāsato vidyate bhāvo
nābhāvo vidyate sataḥ
ubhayor api dṛṣṭo ‘ntas
tv anayos tattva-darśibhiḥ

Translation of Bhagavad Gita 2.16

Those who are seers of the truth have concluded that of the nonexistent [the material body] there is no endurance and of the eternal [the soul] there is no change. This they have concluded by studying the nature of both.

Commentary by Sri A.C. Bhaktivedanta Swami Prabhupada of Gaudiya Sampradaya:

There is no endurance of the changing body. That the body is changing every moment by the actions and reactions of the different cells is admitted by modern medical science; and thus growth and old age are taking place in the body. But the spirit soul exists permanently, remaining the same despite all changes of the body and the mind. That is the difference between matter and spirit. By nature, the body is ever changing, and the soul is eternal. This conclusion is established by all classes of seers of the truth, both impersonalist and personalist. In the Vishnu Purana (2.12.38) it is stated that Vishnu and His abodes all have self-illuminated spiritual existence (jyotimsi vishnur bhuvanani vishnuh). The words existent and nonexistent refer only to spirit and matter. That is the version of all seers of truth.

This is the beginning of the instruction by the Lord to the living entities who are bewildered by the influence of ignorance. Removal of ignorance involves the reestablishment of the eternal relationship between the worshiper and the worshipable and the consequent understanding of the difference between the part-and-parcel living entities and the Supreme Personality of Godhead. One can understand the nature of the Supreme by thorough study of oneself, the difference between oneself and the Supreme being understood as the relationship between the part and the whole. In the Vedanta-sutras, as well as in the Srimad-Bhagavatam, the Supreme has been accepted as the origin of all emanations. Such emanations are experienced by superior and inferior natural sequences. The living entities belong to the superior nature, as it will be revealed in the Seventh Chapter. Although there is no difference between the energy and the energetic, the energetic is accepted as the Supreme, and energy or nature is accepted as the subordinate. The living entities, therefore, are always subordinate to the Supreme Lord, as in the case of the master and the servant, or the teacher and the taught. Such clear knowledge is impossible to understand under the spell of ignorance, and to drive away such ignorance the Lord teaches the Bhagavad-gita for the enlightenment of all living entities for all time.Commentary by Sri Vishvanatha Chakravarthi Thakur of Gaudiya Sampradaya:

This verse describes the results for those who have attained the level of discrimination. Actually as sruti says, the soul is not attached to matter: asango hi ayam purusah. (Brhad Aranyaka Upanisad 4.3.15) Thus, the jiva does not have a relationship with the subtle or gross bodies and its products such as lamentation and bewilderment. This relationship is caused by ignorance. This is explained in this verse.

There is no existence (bhavah) of the body (asatah), the shelter of lamentation and bewilderment, because of its opposite nature to the soul, in which these do not exist. And there is no destruction of the jiva with its real form (satah). The conclusion (antah) about both of these—the body and the soul – is seen by the seers of truth. By this, there will be no lamentation or bewilderment arising from seeing body and things related to the body because of the eternal, indestructible soul in Bhisma and others of the opposing party as well as you and your allies. How can Bhisma and others be destroyed, and why do you lament for them?

Commentary by Sri Ramanuja of Sri Sampradaya:

2.16 ‘The unreal,’ that is, the body, can never come into being. ‘The real,’ that is, the self, can never cease to be. The finale about these, the body and the self, which can be experienced, has been realised correctly by the seers of the Truth. As analyis ends in conclusion, the term ‘finale’ is here used. The meaning is this: Non-existence (i.e., perishableness) is the real nature of the body which is in itself insentient. Existence (i.e., imperishableness) is the real nature of the self, which is sentient. [What follows is the justification of describing the body as ‘unreal’ and as having ‘never come into being.’] Non-existence has, indeed, the nature of perishableness, and existence has the nature of imperishableness, as Bhagavan Parasara has said: ‘O Brahmana, apart from conscious entity there does not exist any group of things anywhere and at any time. Thus have I taught you what is real existence — how conscious entity is real, and all else is unreal’ (V. P., 2.12.43 – 45). ‘The Supreme Reality is considered as imperishable by the wise. There is no doubt that what can be obtained from a perishable substance is also perishable’ (Ibid., 2.14.24). ‘That entity which even by a change in time cannot come to possess a difference through modification etc., is real. What is that entity, O King? (It is the self who retains Its knowledge)’ (Ibid., 2.13.100). It is said here also: ‘These bodies … are said to have an end’ (2.18) and ‘Know That (the Atman) to be indestructible’ (2.17). It is seen from this that this (i.e., perishableness of the body and imperishableness of the self) is the reason for the designating the Atman as ‘existence’ (Sattva) and body as ‘non-existence’ (Asvattva). This verse has no reference to the doctrine of Satkaryavada (i.e., the theory that effects are present in the cause), as such a theory has no relevance here. Arjuna is deluded about the true nature of the body and the self; so what ought to be taught to him in order to remove his delusion, is discrimination between these two — what is qualified by perishablenss and what, by imperishableness. This (declaration) is introduced in the following way: ‘For the dead, or for the living’ (2.11). Again this poin is made clear immediately (by the words), ‘Know that to be indestructible …’ (2.17) and ‘These bodies … are said to have an end’ (2.18). How the imperishableness of the self is to be understood, Sri Krsna now teaches:
Commentary by Sri Sridhara Swami of Rudra Sampradaya:

It may be submitted that the objects of the sense like excessive heat and cold are extremely difficult to endure. Sometimes it is seen that exposure to elements like heat and cold can even cause the destruction of the body. In answer to this to convey that it is possible to endure anything with the correct discrimination of the truth the Supreme Lord states this verse. The unreal being of the nature of the impermanent is not reality having no existence in the self. The real of the nature of the eternal has no destruction being always existent. Thus the conclusion about both of these the real and the unreal has been determined. By whom? As the verse states by the knoweres of the Ultimate Truth who understand the true nature of things. So the conclusion is that by such discrimination one must learn to tolerate and endure them.
Commentary by Sri Madhvacharya of Brahma Sampradaya:

The soul is eternal as verified in the Vedas. Why is the soul eternal? Is there anything else eternal as well? Hence it is stated in the verse beginning nasato vidyate. There is no annihilation of a-sat meaning prakriti which is the material substratum or sat referring to the Ultimate Truth because it is declared in the Visnu Purana that prakriti, purusa and kala or time are eternal. Because the word vidyate has been seperately used in relation to sat and a-sat and because it has been said in Srimad Bhagavatam also known as Bhagavat Purana that a-sat is the physical manifestation and sat is of the subtle form the Ultimate Truth of reality, a-sat is known as manifestation of sat, the unmanifest. This understanding for both a-sat and sat and is confirmed by the word anta meaning summation.

Now begins the summation.

The actual sorrow expressed by Arjuna is not being felt because the consequences of war lead to misery in the next life. The rule in the material existence is that every action has its corresponding and equal reaction, thus it is seen that by unrighteous actions there is no happiness and by righteous actions there can be no unhappiness. The words referring to sat bhavah are all connected to happiness and the words connected to a- sat abhava are those which are connected to sorrow.

Thus it is stated in Shabda Nirnaya that sat bhava is sadhu bhava, having meritorious disposition and we will see this word used again further in the Gita. Therefore for whatever is in righteousness the word sat is used. Whoever has thought they have become a-sat, asat brahmeti, for this person their personal conceptions have become a-sat and consequently they become sorrowful.

It should not be misconstrued that the purpose of this verse is to deny the existence of what is appearing now in the present, was non-existing before creation and would be non-existent after destruction. This would be a contradiction in itself. The statement nasato vidyate bhavo is specifically used to emphasise a spiritual truth. Although in normal everyday life people relate to the material manifestation as if it did not exist before and will also cease to exist hereafter. For example a flower to be offered to the Lord which blossomed today, did not exist last week and by next week it will have ceased to exist but still it is utilised while it is here. So there is no reason to reflect that any of this is due to delusion.

Thus it is stated in the Brahma Tarka :

All acts prior to creation and all acts after the dissolution of creation cease to exist is the Vedic statement. If in each action the specific form was not manifest before it was born but came to be formed only later, then wisdom and normal circumstances would not justify such a statement. If according to wisdom and normal circumstances an archetype existed before the form came to exist then before anything is born it did not, in fact exist. Even due to the experiences of modification there is action and its result. Because of these modifications the experiences of the physical body become apparent. Normal affairs in this world take place on the basis of these modifications and the experience connected with these modifications solely.

It is not correct to accept that this world is made up of special attributes such as sat the Ultimate Truth due to its perception of modification and a-sat as the physical manifestation by its being self evident. Both the experiences are subjected to delusion. The physical manifestation is spoken as such because it is evident not because it is understood. If it is non-existent then its knowledge is without purpose even if it is non-manifesting.

A falsehood can never be validated by another falsehood. In delusion the false appearing as truth can never be accepted as real. In normal life the unreal cannot cease to be in any case. That which exists as its form may also appear as real and the same is the case with delusion.

Even though it is indescribable, when what is real appears as truth verily such appearance of truth cannot be accepted as false on the assumption that it is delusion. Thus the truth which appears as unreal should also be accepted then there is no contradiction.

In the Vedic scriptures it is stated the cosmic manifestation is truth. What is created is the truth. The sages and rishi’s who contemplating deeply describe the Ultimate Truth as Self evolved and Self evident and by such words declare the eternal existence of all things created.
Commentary by Sri Keshava Kashmiri of Kumara Sampradaya:

It is seen that one feels extreme discomfort due to bodily experiences of excessive heat and cold and the like; if this is the case then what is the experience for one who remains unconscious of the soul even unto the moment of a very painful demise. How can they realize that heat, cold and pain to be impermanent and how can they imagine the eternal reality of the souls immortality. Such questions and bewilderment is clarified by Lord Krishna with the words in the impermanent like heat, cold, pleasure and pain there is no duration and in the permanent as the eternal soul there is no cessation. It must be understood that this nature of the duration and cessation of things in this world cannot be ascertained by one lacking spiritual intelligence. Lord Krishna emphasizes the point that the reality of the duration and cessation in the material existence has been perceived by those elevated souls who have attained the Ultimate Truth. The eternal reality of the souls immortality is revealed in various places in the Vedic scriptures and this has been realized by those who have achieved this understanding.
Commentary by Sri Adi Shankaracharya of Advaita Sampradaya:

2.16 Since ‘the unreal has no being,’ etc., for this reason also it is proper to bear cold, heat, etc. without becoming sorrowful or deluded. Asatah, of the unreal, of cold, heat, etc. together with their causes; na vidyate, there is no; bhavah, being, existence, reality; because heat, cold, etc. together with their causes are not substantially real when tested by means of proof. For they are changeful, and whatever is changeful is inconstant. As configurations like pot etc. are unreal since they are not perceived to be different from earth when tested by the eyes, so also are all changeful things unreal because they are not perceived to be different from their (material) causes, and also because they are not perceived before (their) origination and after destruction. Objection: If it be that [Here Ast. has the additional words ‘karyasya ghatadeh, the effect, viz pot etc. (and)’.-Tr.] such (material) causes as earth etc. as also their causes are unreal since they are not perceived differently from their causes, in that case, may it not be urged that owing to the nonexistence of those (causes) there will arise the contingency of everything becoming unreal [An entity cannot be said to be unreal merely because it is non-different from its cause. Were it to be asserted as being unreal, then the cause also should be unreal, because there is no entity which is not subject to the law of cuase and effect.]? Vedantin: No, for in all cases there is the experience of two awarenesses, viz the awareness of reality, and the awareness of unreality. [In all cases of perception two awarenesses are involved: one is invariable, and the other is variable. Since the variable is imagined on the invariable, therefore it is proved that there is something which is the substratum of all imagination, and which is neither a cause nor an effect.] That in relation to which the awareness does not change is real; that in relation to which it changes is unreal. Thus, since the distinction between the real and the unreal is dependent on awareness, therefore in all cases (of empirical experiences) everyone has two kinds of awarenesses with regard to the same substratum: (As for instance, the experiences) ‘The pot is real’, ‘The cloth is real’, ‘The elephant is real’ — (which experiences) are not like (that of) ‘A blue lotus’. [In the empirical experience, ‘A blue lotus’, there are two awarenesses concerned with two entities, viz the substance (lotus) and the quality (blueness). In the case of the experience, ‘The pot is real’, etc. the awarenesses are not concerned with substratum and qualities, but the awareness of pot,of cloth, etc. are superimposed on the awareness of ‘reality’, like that of ‘water’ in a mirage.] This is how it happens everywhere. [The coexistence of ‘reality’ and ‘pot’ etc. are valid only empirically — according to the non-dualists; whereas the coexistence of ‘blueness’ and ‘lotus’ is real according to the dualists.] Of these two awareness, the awareness of pot etc. is inconstant; and thus has it been shown above. But the awareness of reality is not (inconstant). Therefore the object of the awareness of pot etc. is unreal because of inconstancy; but not so the object of the awareness of reality, because of its constancy. Objection: If it be argued that, since the awareness of pot also changes when the pot is destroyed, therefore the awareness of the pot’s reality is also changeful? Vedantin: No, because in cloth etc. the awareness of reality is seen to persist. That awareness relates to the odjective (and not to the noun ‘pot’). For this reason also it is not destroyed. [This last sentence has been cited in the f.n. of A.A.-Tr.] Objection: If it be argued that like the awareness of reality, the awareness of a pot also persists in other pots? Vedantin: No, because that (awareness of pot) is not present in (the awareness of) a cloth etc. Objection: May it not be that even the awareness of reality is not present in relation to a pot that has been destroyed? Vedantin: No, because the noun is absent (there). Since the awareness of reality corresponds to the adjective (i.e. it is used adjectivelly), therefore, when the noun is missing there is no possibility of its (that awareness) being an adjective. So, to what should it relate? But, again, the awareness of reality (does not cease) with the absence of an object.. [Even when a pot is absent and the awareness of reality does not arise with regare to it, the awareness of reality persists in the region where the pot had existed. Some read nanu in place of na tu (‘But, again’). In that case, the first portion (No,…since…adjective. So,…relate?) is a statement of the Vedantin, and the Objection starts from nanu punah sadbuddheh, etc. so, the next Objection will run thus: ‘May it not be said that, when nouns like pot etc. are absent, the awareness of existence has no noun to qualify, and therefore it becomes impossible for it (the awareness of existence) to exist in the same substratum?’-Tr.] Objection: May it not be said that, when nouns like pot etc. are absent, (the awareness of existence has no noun to qualify and therefore) it becomes impossible for it to exist in the same substratum? [The relationship of an adjective and a noun is seen between two real entities. Therefore, if the relationship between ‘pot’ and ‘reality’ be the same as between a noun and an adjective, then both of them will be real entities. So, the coexistence of reality with a non-pot does not stand to reason.] Vedantin: No, because in such experiences as, ‘This water exists’, (which arises on seeing a mirage etc.) it is observed that there is a coexistence of two objects though one of them is non-existent. Therefore, asatah, of the unreal, viz body etc. and the dualities (heat, cold, etc.), together with their causes; na vidyate, there is no; bhavah, being. And similarly, satah, of the real, of the Self; na vidyate, there is no; abhavah, nonexistence, because It is constant everywhere. This is what we have said. Tu, but; antah, the nature, the conclusion (regarding the nature of the real and the unreal) that the Real is verily real, and the unreal is verily unreal; ubhayoh api, of both these indeed, of the Self and the non-Self, of the Real and the unreal, as explained above; drstah, has been realized thus; tattva-darsibhih, by the seers of Truth. Tat is a pronoun (Sarvanama, lit. name of all) which can be used with regard to all. And all is Brahman. And Its name is tat. The abstraction of tat is tattva, the true nature of Brahman. Those who are apt to realize this are tattva-darsinah, seers of Truth. Therefore, you too, by adopting the vision of the men of realization and giving up sorrow and delusion, forbear the dualities, heat, cold, etc. — some of which are definite in their nature, and others inconstant –, mentally being convinced that this (phenomenal world) is changeful, verily unreal and appears falsely like water in a mirage. This is the idea. What, again, is that reality which remains verily as the Real and surely for ever? This is being answered in, ‘But know That’, etc.
Commentary by Sri Abhinavagupta of Kaula Tantra Sampradaya:    

2.16 Nasatah etc. And then, also following the common worldly practice [the Lord] says this : There is no [real] existence for what is non-existent i.e., the body [etc.], that is continuously perishing; for it is changing incessantly by stages. Again, never there is destruction for the ever existing Supreme Self, because of Its unchanging nature. So says the Veda too : ‘Lo ! This Soul is of unchanging nature and [hence] is destructions’ (the Br. U, IV, v. 14). Of These two : of what is existent and what is non-existent. Finality : the point of boundary where they come to an end. But is this permanent or transient which is perceived by persons who are prone to see the truth ? Having raised this doubt, [the Lord] says :
Sanskrit Shloka Without Transliteration Marks:

nasato vidyate bhavo
nabhavo vidyate satah
ubhayor api drsto ‘ntas
tv anayos tattva-darsibhih
Sanskrit to English Word for Word Meanings:

na — never; asataḥ — of the nonexistent; vidyate — there is; bhāvaḥ — endurance; na — never; abhāvaḥ — changing quality; vidyate — there is; sataḥ — of the eternal; ubhayoḥ — of the two; api — verily; dṛṣṭaḥ — observed; antaḥ — conclusion; tu — indeed; anayoḥ — of them; tattva — of the truth; darśibhiḥ — by the seers.