Not only is it rationally possible for the Imams (as) to have knowledge of the unseen, the holy Qur'an also states that God, the Almighty, has granted some of his prophets such knowledge. Being successors of the Prophet (sawa), the Imams (as) were also entrusted with such knowledge so that they would succeed in guiding people to the right path.
It may be argued that whether the Imams (as) have knowledge of the unseen or not. Putting together the following premises, we can conclude that the Imams (as) may acquire knowledge of the unseen: first, it is possible for some humans, like the prophets, to acquire such knowledge; second, the Imams (as) are successors of the prophets and play a similar role, therefore, they must be endowed with the same capabilities including knowledge of the unseen. With regard to feasibilty of such knowledge for the prophets we must mention the following verse, “Knower of the Unseen, He does not disclose His Unseen to anyone, except to an apostle He approves of. Then He dispatches a sentinel before and behind him.” [1]
The abovementioned verse of the glorious Qur'an explicitly states that God, the Almighty, discloses (at least parts of) knowledge of the unseen to the prophets He approves of. In another verse the Qur'an says, “Allah will not acquaint you with the Unseen (in order to tell the believers from the hypocrites, because this is against Allah’s custom), but Allah chooses from His apostles whomever He wishes (and informs them of some of the secrets that are needed for the position of leadership).” [2]
Now the significant question, which must be answered, is: Do the infallible Imams also have knowledge of the unseen or is it only a prerogative of the Prophets? Knowing that after Prophet Muhammad (sawa) the infallible Imams (as) play the same role of guiding mankind to the right path, it is necessary for them to know all issues including the seen and the unseen, which are related to the guidance and leadership of mankind. Hence, on occasions and in cases where they need knowing the unseen, they must be provided with such knowledge. Based on this, if they need, Allah (swt) will grant them the required knowledge. Imam Sadiq (as) says in this regard: “When an imam wills to know something, Allah gives him the knowledge he needs.”[3]
In conclusion, since both the prophets and the Imams are responsible for guiding mankind in all spiritual and physical fields, they must have knowledge of the unseen whenever they need so that they can fulfil their duty properly.
Notes:
[1] Jinn26 and 27 عٰالِمُ اَلْغَيْبِ فَلاٰ يُظْهِرُ عَلىٰ غَيْبِهِ أَحَداً إِلاّٰ مَنِ اِرْتَضىٰ مِنْ رَسُولٍ فَإِنَّهُ يَسْلُكُ مِنْ بَيْنِ يَدَيْهِ وَ مِنْ خَلْفِهِ رَصَداً
[2] Āl Imrān: 179 وَ مٰا كٰانَ اَللّٰهُ لِيُطْلِعَكُمْ عَلَى اَلْغَيْبِ وَ لٰكِنَّ اَللّٰهَ يَجْتَبِي مِنْ رُسُلِهِ مَنْ يَشٰاءُ فَآمِنُوا بِاللّٰهِ وَ رُسُلِهِ وَ إِنْ تُؤْمِنُوا وَ تَتَّقُوا فَلَكُمْ أَجْرٌ عَظِيمٌ
[3] Kuleini, Usul Kāfī, vol. 1, chapter on when the imams wish to know something, they know it, hadith 3. For further information, see: Man and Knowledge of the Unseen, Question 150 (website: 1056)