Commentary for Tahorot 6:2
אַרְבָּעָה סְפֵקוֹת רַבִּי יְהוֹשֻׁעַ מְטַמֵּא וַחֲכָמִים מְטַהֲרִין. כֵּיצַד. הַטָּמֵא עוֹמֵד וְהַטָּהוֹר עוֹבֵר, הַטָּהוֹר עוֹמֵד וְהַטָּמֵא עוֹבֵר, הַטֻּמְאָה בִרְשׁוּת הַיָּחִיד וְטָהֳרָה בִרְשׁוּת הָרַבִּים, טָהֳרָה בִרְשׁוּת הַיָּחִיד וְטֻמְאָה בִרְשׁוּת הָרַבִּים, סָפֵק נָגַע סָפֵק לֹא נָגַע, סָפֵק הֶאֱהִיל סָפֵק לֹא הֶאֱהִיל, סָפֵק הִסִּיט סָפֵק לֹא הִסִּיט, רַבִּי יְהוֹשֻׁע מְטַמֵּא, וַחֲכָמִים מְטַהֲרִין:
There are four cases of uncertain impurity which Rabbi Yehoshua declares impure and the Sages declare pure. How so? If an impure person stood [in a covered area, such as under a tree, constituting a "tent" or area of impurity,] and a pure person passed by; or a pure person stood [in a covered area] and an impure person passed by; or if something impure was in a private domain and [it was next to] something pure in the [adjacent] public domain; or if something pure was in the private domain and [it was next to] something impure in the [adjacent] public domain; if there is an uncertainty as to whether one touched [the impure object] or did not touch it, or whether it [i.e. the covered area] covered over [both the impure and the pure person at once] or did not cover over, or whether someone moved [the impure object, even indirectly] or did not move it; [in all these cases of uncertainty] Rabbi Yehoshua declares it impure, and the Sages declare it pure.
Bartenura on Mishnah Tahorot
English Explanation of Mishnah Tahorot
How so? If an unclean man stood and a clean man passed by or the clean man stood and the unclean one passed by; or if an unclean object was in a private domain and a clean one in the public domain or the clean object was in the private domain and the unclean one in the public domain, and there is doubt whether there was contact or not, or whether there was overshadowing or not, or whether there was shifting or not: Rabbi Joshua rules that the clean becomes unclean, But the sages rule that the clean remains clean.
There are four cases here:
1) An unclean man is standing and a clean man passes by him and he may have been defiled by contact, overshadowing or shifting.
2) The same situation but the clean man is standing and the unclean one is moving.
3) There is an unclean object in the private domain and an clean one in the public domain and the clean one may have had contact with the unclean one.
4) The same situation but the positions are reversed.
Rabbi Joshua says that since at least one of the elements was in the private domain, the doubt is impure.
The other sages say that for impurity to occur both elements have to be in the same situation within the private domain both must be moving or both must be standing. Since in all of these cases one element is either not in the private domain or one element is moving and the other standing, there is no impurity.