Two men in the desert disagree about the qiblah

The questioner : Now, if we disagree about the qiblah, and we are in the desert now, and there is no compass or qiblah indicator, and I say the qiblah is here on the right, and you say it is on the left, do we pray in congregation?

The Shaykh : No, it is not permissible. Each person prays according to his own ijtihad.

The questioner : Do you understand? Some scholars say that the imamah is not valid, not because I believe that your prayer is valid, but because I believe that if you agree with me, your prayer is invalid.

The Shaykh : I believe that your prayer is valid, do you understand? But they tell me that this is not valid due to the contradiction. How can I fulfill my obligation and you fulfill your obligation, and you become my imam? Yes, where is the agreement? This is different from circling the Ka'bah. It is true that in circling the Ka'bah, their faces are not all facing the same direction, but each person is facing the other.