It is forbidden to pass within four amot in front of a person reciting the Amida, since doing so is likely to disturb her kavana. Others say that the reason for the prohibition is that the person reciting the Amida is standing before the Shekhina, and one who passes before her offends God’s honor (Peninei Halakha: Prayer, ch. 17 n. 16).
The poskim disagree about where exactly it is forbidden to pass. According to Eliya Rabba, the prohibition only applies to passing directly in front of the one reciting the Amida, since only this will be disruptive. In other words, if a person’s width is approximately half a meter, one may not pass through that half meter up to a distance of four amot. According to Magen Avraham, it is forbidden to pass anywhere that the person praying can see within his four amot, since passing there is likely to slightly disrupt his kavana.
They disagree further. According to Eliya Rabba, one may come and stand within the four amot of a person praying and remain standing there; only when one crosses through the four amot directly in front of his face does it disturb his prayer. However, if she approaches from the side and remains standing in front of him, she does not disrupt him as much. According to Magen Avraham, it is forbidden to enter into the four amot in front of a person praying at all.
Le-khatĥila, one should follow Magen Avraham’s strict opinion and not walk anywhere within four amot in front of a person reciting the Amida. In times of need, however, one may adopt Eliya Rabba’s lenient practice and pass alongside a person praying or come to a standing stop directly in front of him. Therefore, one who arrives late to the prayer service may pass alongside a person reciting the Amida in order to pray in her regular seat. Yet, if in order to do so she must pass alongside a number of people praying, she may not pass, since it is almost certain that she will disturb at least one person’s concentration (Peninei Halakha: Prayer, ch. 17 n. 17).
In a case of great need, when there is no other option, it is even permissible to pass directly in front of a person reciting the Amida. Hence, one who must leave to conduct a Torah class may pass in front of a person praying. Likewise, one who is in a great hurry, such as one who fears she will miss her bus or ride, may pass as well.
If one is reciting the Amida while standing in an aisle, since she did not act in accordance with the law and instead stood in a place that blocks the passage of those coming and going, there is no obligation to take her into consideration, and it is permissible to pass directly in front of her when necessary (ibid. note 18).