Is it permissible for women to wear jewelry in a public domain on Shabbat?
On the level of Torah law, wearing jewelry in a public domain Shabbat does not entail any prohibition. Jewelry is considered akin to garments, and just as wearing clothing does not constitute "carrying," so does wearing jewelry not transgress the prohibition against carrying in a public domain on Shabbat.
However, as the Gemara discusses in the sixth chapter of Masechet Shabbat, the Sages enacted a prohibition forbidding wearing jewelry in a public domain on Shabbat, out of concern that a woman might remove her jewelry and carry it. Women would customarily remove their jewelry to show it to their peers, and thus the concern arose that women may forgetfully remove and carry their jewelry in a public domain on Shabbat. The Rabbis therefore issued a decree forbidding wearing jewelry in a public domain on Shabbat, as a safeguard against the Torah prohibition of carrying.
The Sefer Ha'teruma (Rabbi Baruch of Worms, Germany, 1170-1211) ruled that this prohibition does not apply nowadays, because public areas today do not meet the criteria of a Halachic "public domain" with respect to the prohibition of carrying on Shabbat. For an area to become a public domain, the Sefer Ha'teruma claimed, it must be 16 Amot (approx. 32 feet) wide and be passed through by 600,000 people each day. Since public areas today do not see this kind of traffic on a daily basis, he contended, women may walk in public areas with jewelry on Shabbat.
The Ran (Rabbenu Nissim of Gerona, Spain, 1290-1380), however, disagreed, arguing that a public area sixteen Amot wide qualifies as a Reshut Ha'rabim (public domain) regardless of how many people pass through it each day. According to the Ran, therefore, the prohibition against wearing jewelry in a public domain on Shabbat indeed applies nowadays in principle. However, he adds, since women would most likely ignore such a rule, it is preferable not to inform them of this prohibition, so that they transgress inadvertently, and not intentionally.
The Shulchan Aruch (303) rules in accordance with the Sefer Ha'teruma's position, that one may wear jewelry in a public domain on Shabbat nowadays, because our public areas do not qualify as a Halachic "Reshut Ha'rabim." Many later writers were puzzled by this ruling, in light of the Shulchan Aruch's own ruling later (345) that an area does not require 600,000 pedestrians each day to qualify as a "Reshut Ha'Rabim." Chacham Bentzion Abba Shaul (Jerusalem, 1924-1998), in his work Or Le'tziyon, Helek 2, Perek 23:11, and also Helek 1, siman 30, reconciled these rulings by explaining that the Shulchan Aruch distinguished between laws involving a Torah prohibition, and those that were enacted by the Rabbis. With regard to Torah law, the Shulchan Aruch held that we must follow the stringent view and classify any area 16 Amot wide as a "Reshut Ha'Rabim." With regard to laws enacted by the Sages, however, we may rely on the lenient position, according to which our public areas do not meet the criteria of a "Reshut Ha'rabim." Therefore, with regard to the Rabbinic enactment forbidding walking in a public domain wearing jewelry, we may follow the lenient position whereby our public areas do not qualify as a "Reshut Ha'rabim."
As for the final Halacha, although some authorities forbid wearing jewelry in a public domain Shabbat even nowadays, Chacham Bentzion Abba Shaul held that this is permissible, in accordance with the ruling of the Shulchan Aruch.