May one wear a reflective armband on Shabbat where there is no eiruv so cars will be better able to see him at night?
There are two categories of objects/situations one can have on his body without violating carrying on Shabbat without an eiruv: 1. Begadim derech malbush (clothes worn normally); 2. Tachshitim (adornments or accessories) (see Shulchan Aruch, Orach Chayim 301 at length). The category of tacshit includes things that are placed on the body to help the body function properly (see Shemirat Shabbat K’hilchata 18:11), including slings, arch supports, glasses, etc.
The first thing we need to see is whether decreasing the chance of danger is a positive use regarding these halachot. The mishna and gemara (Shabbat 60-61) discuss the circumstances under which one can wear an amulet in the public domain. Rashi (ad loc.) explains that when used appropriately, an amulet "is a tachshit for an ill person, like one of his garments." Not only is that true when used for healing, but warding off illness from those susceptible to it justifies wearing it as well (Shulchan Aruch, Orach Chayim 301:26). Thus, wearing something that can reduce the chance of getting hit by a car, Heaven forbid, e.g., in a dark area without traffic lights and/or sidewalks, is legitimate. On the other hand, two distinctions challenge the proof from this and similar sources.
One distinction is that the amulet protects a person from within, whereas a reflector helps in regard to an external danger (cars). Nevertheless, logic dictates that the source of the danger should not make a difference in this regard (L’horot Natan VIII:18).
A stronger distinction is that regarding the amulet, one is "using" the amulet on an ongoing basis. In contrast, sometimes one wears the reflector for a long walk in which only a short time will be in a dark, dangerous place. What is the status of the reflector the rest of the time? The Shemirat Shabbat K’hilchata (18:16) and Yalkut Yosef (301:32) say that one should not wear reading glasses, which one often carries in his pocket, because of the rabbinic concern that he may take them off and carry them. Why not state an intrinsic problem – reading glasses are not used while on the street – as the Orchot Shabbat (28:127) claims? Apparently, the fact that they are generally usable and/or will be used later is sufficient. Even the Orchot Shabbat may agree that it is sufficient for it to be useful sometime during this walk.
44 - Making Up the Money Absconded by a Middleman
45 - Wearing a Reflective Armband on Shabbat Without an Eiruv
46 - Hamapil for Those Who Take a Long Time to Fall Asleep
There are indeed many cases of tachshitim that, intrinsically, should have been permitted to wear, but the Rabbis were concerned that people would take them off in the middle or they might fall and be carried. It is difficult to determine when we apply this rabbinic concern and when not, and there may be additional reasons for leniency here (see below).
Our case is somewhat reminiscent of the badges Jews were required to wear by law (centuries before the Nazis y"s). The Rama (OC 301:23, based on the Ohr Zarua II:84) says they could be worn but only if they were attached (not necessarily sewed) to the clothes. The reason given for leniency is that one wears them all week long and would not dare take it off (see Mishna Berura ad loc.) – logic that does not fully apply here. The Shemirat Shabbat K’hilchata (new edition18:25), says that one is permitted to wear reflective belts on Shabbat, as it is considered a normal mode of dressing, and the Rabbis did not forbid because it is for protection. It is not clear, though, if an armband is considered a normal mode of dress.
We would certainly not tell someone who needs a reflective band for safety to not wear one. However, from a halachic perspective it is better to either: have one permanently attached to a real garment; to wear a reflective vest, which is a normal garment (even if it looks funny); or at least use a reflective belt (belts are semi-clothes, semi-accessories of necessity (see sources related to Rama OC 301:36)). If only an armband is available, one can be lenient.