Resources for Chagigah daf 20
1. The גמרא says that if someone’s hat falls and another person picks it up it is considered a היסח הדעת and the item is considered טמא. The reason is אין אדם שומר מה שביד חברו. The way רש"י explains it in ד"ה טמאה is that the owner cannot watch his item when it is in his friend’s hand. However, see the רמב"ם in פּרק י"ג הלכות מטמאי משכב ומושב הל' ו who says that the issue is the person who is holding the item does not assume he has to watch it, so he doesn’t. However, if you tell him to watch it for you then it works.
This brings us to a question: at the top of עמוד ב, the גמרא tries to bring a proof that a person is שומר מה שביד חברו. The proof is that if you hire workers and they go out of sight, your טהרות are still טהור. According to the רמב"ם the proof is easy to understand as it shows that people can watch something for you. However, according to רש"י it seems very difficult as the owner is obviously not watching the item as he is a מיל away, so how can that prove that an owner can watch something in their friend’s hand? Isn’t it obvious that the ברייתא is just saying that the reason the items are טהור is because the workers are afraid of the owner catching them but not that the owner is watching it in their hands? See the חזון אי"ש in או"ח סימן קכ"ט on our דף who says that the מקשן understood that the worker’s fear of the owner is considered like the owner is watching it himself, and if חז"ל were מבטל שימור ביד חבירו from working, then it shouldn’t work in this case either. To that the גמרא answers that since the workers were טהור, they don’t need שמירה for themselves at all but they can watch that other people don’t touch.
2. The גמרא said that אין אדם שומר מה שביד חברו. There is a fascinating מנחת חינוך in מצוה י אות י who wonders why the ראשונים take it as a given that when it comes to מצות for פּסח the person kneading the מצות himself needs to do שמירה לשמה (and therefore debate whether a נכרי can knead the מצות if there is a ישראל עומד על גביו). Why do you need the one kneading to do שמירה לשמה? Why can’t anyone standing nearby do the שמירה לשמה? He suggests that our גמרא is the answer! Our גמרא says that you can’t watch something in someone else’s hands. Consequently, only the person kneading can do the שמירה. See also the מאירי here in the name of קצת מפרשים who says that based on our גמרא one cannot allow a נכרי to knead your מצות for פּסח since מצת מצוה needs שמירה and אין אדם שומר מה שביד חבירו. The מאירי himself disagrees with the קצת מפרשים and says that one cannot learn anything from טהרות to מצה as we often are more מחמיר by טהרות. Also, see the מקראי קדש on פסח ח"ב ס"ג where רב צבי פּסח פראנק asks whether machine matzos could be considered having שמירה לשמה since אין אדם שומר מה שביד חברו? He answers that we can be מדייק from the word “חבירו” that only another person is an issue but a machine would not be a problem.
3. The גמרא says that if a person thought his Shabbos clothes were his weekday clothes it is considered a היסח הדעת and the Shabbos clothes are טמא since a person watches his Shabbos clothes better. The question is obvious—he still did the שמירה of בגדי חול to his Shabbos clothes so why should the clothes be considered טמא? See the חזון אי"ש here in או"ח סימן קכ"ט on our גמרא who explains that since there is no defined שיעור for שמירה, any lessening of what the person would have done is considered by חז"ל as a היסח הדעת. See the תוספות רי"ד who says that when the person sees he mixed up his clothes, he is upset that he didn’t watch his Shabbos clothes to the level they should have been watched and gives up watching them entirely.