We normally think the soul is physically situated inside the heart together with Paramātmā, and that both move "physically" to another body at the time of death. This simplistic idea helps us to understand several concepts, starting with the idea that there is a soul and that the soul is dependent on the Supersoul, but in reality, is actually a little more complicated than that.
The first problem is that there is nothing "physical" connected with the soul. Although the soul is described as a particle of consciousness in the Śvetāśvatara Upaniṣad (5.9), it is not a particle in the physical sense, with weight and measurable dimensions. On Bg 2.24, Krsna describes the soul as sarva-gataḥ (all-pervading), sthāṇuḥ (unchangeable) and acalaḥ (immovable). Just like Kṣīrodakaśāyī Vishnu (Paramātmā) pervades the whole universe, being present everywhere, the soul pervades the body, and thus our consciousness is present in all parts of the body. We can feel a pinch in our ear the same way we feel someone steeping on our toe. This shows that the soul is more than just the idea we have of a particle. If the soul was something similar to a grain of sand, for example, it would not be able to permeate the whole body. If we would accept that this particle is dissolved, and thus spreads through the whole body, then we would contradict the principle of the soul being unchangeable. The soul is a "particle" of consciousness means the soul is a portion of consciousness and not a "particle" in the literal sense.
Another idea we may have difficulty conceiving is that the soul is acalaḥ (immovable). How can the soul be immovable if we go from one body to the other? It becomes easier to understand when we understand that the soul is a spiritual being who manifests in the material world in the form of consciousness and not a physical particle. The soul is part and parcel of Krsna and is always situated in his original position together with Krsna. The soul can't be moved from this position. It's not possible to separate the soul from Krsna.
However, our attention may go away to a different place, just like I may be with you, sitting at the same table, but I may look at my phone and my attention may go there. There are uncountable material bodies inside of each universe, divided into the 8,400,000 species of life. Everything is moving according to the dictations of material nature. When a soul "enters" a body, it means that his consciousness, or his attention becomes focused in this body, and thus the soul becomes aware of what is happening in that body, but unaware of everything else. Just like when I become absorbed in what I'm seeing on my phone and forget reality. Focused on the body, we forget who we are and what our original position is and start our unfortunate trip in the material world, going from one body to another.
Another way to understand that is that the soul is like a lamp shining on the ceiling. The light of the lamp is reflected into different material objects, although the lamp is never moved. The light of the lamp is originally white, but when this light is reflected in different objects it assumes the colors of these different objects. When reflected on a red table, the light becomes red, when reflected on a yellow carpet it becomes yellow, and when reflected on a black stone, the light practically disappears, since there is very little reflection. In the same way, the original, pure consciousness of the soul when conditioned to this world is reflected in different bodies and assumes different levels of conditioning according to the three modes of nature. When the soul becomes absorbed in the body of horse, he acts like a horse, and so on.
In this way, liberation doesn't require physical movement, we just need to again focus our attention on Krsna. As soon as our consciousness is again fixed on Krsna, we are with Him, even though we may be still technically living in a material body. The spiritual world is also not a geographical location, but a state of consciousness. As soon as our consciousness becomes fully focused on Krsna's form, names, pastimes, etc. we are in the spiritual world. That's how pure devotees can experience Krsna's pastimes although still present amongst us.
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