There is a verse in the Śvetāśvatara Upanishad which describes about the dimensions of the soul. The verse is as follows:
bālāgra-śata–bhāgasya śatadhā kalpitasya ca bhāgo jīvaḥ sa vijñeyaḥ sa cānantyāya kalpate.
It says that the dimension of the soul is equivalent to the size of a human hair which is divided into one hundred parts and each such part is further divided into one hundred parts.
There is another verse which describes this. It is as follows:
keśāgra-śata–bhāgasya śatāṁśaḥ sādṛśātmakaḥ jīvaḥ sūkṣma-svarupo ‘yaṁ saṅkhyātīto hi cit–kaṇaḥ
It means that there are infinitely many particles of the spirit soul, one of which is equivalent to one ten-thousandth of the upper portion of the hair. Therefore the spiritual atom is even smaller than the material atom.
The equation is as follows:
Material body – consciousness = dead body
He further explains that the soul is neither the slayer nor the slain.
It is so small that it cannot be attacked by material weapons.
He further explains that the soul is neither ever born nor it ever dies. It is ever-existing and primeval.
He tells that our body is subjected to 6 forms of transformation:
But the soul is never born, therefore it never dies.
Since it is never born, there is no trace in the history of it coming into existence therefore it does not have any past, present and future. Therefore whether a person is in his childhood, adulthood or in his old age, he experiences the same spirit within him.
It even does not have any by-product either.
The by-products of a human body are his children, but since every living being has a different soul therefore everybody is different at a spiritual level.
As the soul never changes, hence the soul is independent of the above 6 changes that our materialistic body goes through.
The consciousness in our body is due to this soul.
He further explains that there are two kinds of souls:
1.) The supersoul (vibhu–ātmā)
2.) The minute particle soul (aṇu–ātmā)
The minute particle soul(us) is forgetful in nature therefore it cannot remember anything about it’s previous births but the supersoul(Shri Krishna) remembers everything.
Lets see the next verse. It is as follows:
vāsāṁsi jīrṇāni yathā vihāya
navāni gṛhṇāti naro ‘parāṇi
tathā śarīrāṇi vihāya jīrṇāny
anyāni saṁyāti navāni dehī
The above lines tell us that as a body accepts new garments giving up the old one’s, in the similar manner, the soul accepts new bodies giving up the previous one’s.
Lets look at another interesting verse:
nainaṁ chindanti śastrāṇi
nainaṁ dahati pāvakaḥ
na cainaṁ kledayanty āpo
na śoṣayati mārutaḥ
The above lines means that the soul can neither be cut into pieces by any material weapon, nor can it be burned by fire, nor can be moistened by water, nor can be dried up by the wind.
One more verse can be found out which goes as follows:
acchedyo ‘yam adāhyo ‘yam
akledyo ‘śoṣya eva ca
nityaḥ sarva-gataḥ sthāṇur
acalo ‘yaṁ sanātanaḥ
It means that the soul cannot be broken down into smaller pieces and is neither soluble. It cannot be burned and dried. It is everlasting and all pervading. Therefore we must not grieve for the body.
This is how Lord Krishna has described what is a “soul.”