This can be seen from two perspectives: 1) lower or empirical, and 2) higher or spiritual (I try to avoid the word ‘metaphysical’). I am not going to consider what Christianity or Islam hold about any of these two perspectives, only the non-duality of Advaita Vedanta (Buddhism does not contemplate individual existence per se). According to the Advaitic tradition the individual self (jiva) can be considered as a reflection of the higher Self and then his/her faculties (basically memory, mind, and sense of self) as well as all bodies are separate and individual – this pertains to ordinary, transactional life. This is the realm of ignorance (avidya).
Seen from the individual’s essence (the higher vision), there is no distinction and thus no separation between a purported individual and ‘another’ purported individual – there is just no ‘other’; the Self (Atman-brahman) is the sole reality -how can there be a relationship of the Self with what? Once this is realized the former viewpoint is stultified, drops away as being illusory, though not completely false – it is simply ‘mithya’, a relative reality. This, as stated above, is the higher vision, Self-realization properly so called.
2) Evidence for eternity.
Physical bodies are finite, corruptible, but are human beings just their bodies (and their finite minds)? There is an indefinable and unmeasurable entity called consciousness which appears to pervade all sentient beings and nature in general — nature, all life, is conscious – dare we say? This entity – consciousness – is undeniable, for it is our most direct and unfalsifiable experience. Consciousness – by consensus of a majority of physicists – escapes all parameters of physics, neurophysiology, and brain studies. But not only consciousness, so-called matter is in the same category of the intrinsically unknowable, even if there are methods for measuring and experimenting with such entity as matter-energy.
Again, no one knows what eternity might be, such are the limitations of our means of understanding ‘external’ reality, even though physics and mathematics come to our aid in this and also with the phenomenon of space (space-time). What is more, philosophy and metaphysics have a better grasp of the extra-physical dimensions of reality aided and abetted as they are by (universal) intuition. For metaphysics time does not exist outside of our minds, and, rather than eternity-(duration), timelessness – or what is the same, that only the PRESENT exists – is what, as a concept, gives a semblance of reality to reality (all that is and ever has been) – incomprehensible to the unaided mind.