How Can Eliyahu Attend Every Bris?

How Can Eliyahu Attend Every Bris simultaneously everywhere?

On Mount Carmel, Eliyahu proved himself by bringing fire from heaven, and the multitudes responded, Hashem hu ha’Elokim, Hashem is the God, Hashem hu ha’Elokim, Hashem is the God. R. Elimelekh of Lizhensk says, because he brought the entire nation to repent, he merited to have a neshama, a soul, that encompasses all of Klal Yisrael. When a baby boy is being circumcised, a spark of Eliyahu’s nefesh flies off and reveals itself at the bris to the baby. Each baby gets his share. When he grows up and leads a good life this part of Eliyahu reveals itself in him.

The Tur (Orach Chaim, 295) writes that after Shabbos we mention Eliyahu because the prohibition against crossing the Techum Shabbos prevented him from attending any bris on Shabbos. Once Shabbos is over, Eliyahu can come, and so we mention him at that time. If that is the case: How could Eliyahu ever attend any bris on Shabbos anywhere outside the techum?

According to the answer offered by R. Elimelekh the problem is solved. However, the Chasam Sofer offers another answer: There are two types of revelations of Eliyahu. One is where he appears in bodily form. In that form he is required to observe the mitzvos and the issur of techumin apply. The second type of revelation is in the spiritual form in which he appears at a bris. In this spiritual form he is not obligated to observe the mitzvos, just as a dead person is exempt from mitzvos. Therefore, Eliyahu can attend every bris everywhere, even on Shabbos.