Must all women cover their hair?

Halachic Basis:

(יח) וְהֶעֱמִ֨יד הַכֹּהֵ֥ן אֶֽת־הָאִשָּׁה֮ לִפְנֵ֣י יְהוָה֒ וּפָרַע֙ אֶת־רֹ֣אשׁ הָֽאִשָּׁ֔ה וְנָתַ֣ן עַל־כַּפֶּ֗יהָ אֵ֚ת מִנְחַ֣ת הַזִּכָּר֔וֹן מִנְחַ֥ת קְנָאֹ֖ת הִ֑וא וּבְיַ֤ד הַכֹּהֵן֙ יִהְי֔וּ מֵ֥י הַמָּרִ֖ים הַמְאָֽרֲרִֽים׃

Numbers 5:18

(18) After he has made the woman stand before the LORD, the priest shall bare the woman’s head and place upon her hands the meal offering of remembrance, which is a meal offering of jealousy. And in the priest’s hands shall be the water of bitterness that induces the spell.

כתובות ע״ב א:ט׳-י׳

מתני׳ ואלו יוצאות שלא בכתובה: העוברת על דת משה ויהודית. ואיזו היא דת משה? מאכילתו שאינו מעושר, ומשמשתו נדה, ולא קוצה לה חלה, ונודרת ואינה מקיימת. ואיזוהי דת יהודית? יוצאה וראשה פרוע, וטווה בשוק, ומדברת עם כל אדם...

גמ׳ "ואיזוהי דת יהודית? יוצאה וראשה פרוע:" ראשה פרוע דאורייתא היא, דכתיב (במדבר ה, יח) "ופרע את ראש האשה" ותנא דבי רבי ישמעאל אזהרה לבנות ישראל שלא יצאו בפרוע ראש.

רש׳׳י: "אזהרה" - שמע מינה אין דרך בנות ישראל לצאת פרועות ראש וכן עיקר:

Ketubot 72a:9-10

MISHNA: And these are examples of women who may be divorced without payment of their marriage contract: A woman who violates the precepts of Moses, i.e., halakha, or the precepts of Jewish women, i.e., custom. The Mishna explains: And who is categorized as a woman who violates the precepts of Moses? This includes cases such as when she feeds him food that has not been tithed, or she engages in sexual intercourse with him while she has the legal status of a menstruating woman, or she does not separate a portion of dough to be given to a priest [ḥalla], or she vows and does not fulfill her vows. And who is considered a woman who violates the precepts of Jewish women? One who, for example, goes out of her house, and her head, i.e., her hair, is uncovered; or she spins wool in the public marketplace; or she speaks with every man she encounters. Abba Shaul says: Also one who curses his, i.e., her husband’s, parents in his presence. Rabbi Tarfon says: Also a loud woman. And who is defined as a loud woman? When she speaks inside her house and her neighbors hear her voice.

Why would a women cover her hair?

משנה תורה, הלכות אישות כ״ד:י״ב

(יב) וְאֵי זוֹ הִיא דָּת יְהוּדִית? הוּא מִנְהַג הַצְּנִיעוּת שֶׁנָּהֲגוּ בְּנוֹת יִשְׂרָאֵל.

Mishneh Torah, Marriage 24:12

...

ברכות כ״ד א

אָמַר ר׳ יִצְחָק: טֶפַח בָּאִשָּׁה עֶרְוָה. לְמַאי? אִילֵּימָא לְאִסְתַּכּוֹלֵי בַּהּ*... אֶלָּא בְּאִשְׁתּוֹ וְלִקְרִיאַת שְׁמַע... אָמַר רַב שֵׁשֶׁת: שֵׂעָר בָּאִשָּׁה עֶרְוָה, שֶׁנֶּאֱמַר: ״שַׂעֲרֵךְ כְּעֵדֶר הָעִזִּים״ (שיר השירים ד:א).

*רש׳׳י: ’לאסתכולי בה’ – אם אשת איש היא

Berakhot 24a

Because whatever offers more protection is preferable even at the cost of deprecation. And where under his head does he place them? Rabbi Yirmeya said: He places them between the pillow and the mattress, not directly aligned with his head but rather a bit to the side. The Gemara asks: Didn’t Rabbi Ḥiyya teach a baraita that in that case he places them in a pouch used for phylacteries, directly under his head? The Gemara replies: He does so in a manner that the bulge in the pouch, where the phylacteries are, protrudes out and is not beneath his head. On this note, the Gemara relates that Bar Kappara would tie them in his bed curtain and project their bulge outward. Rav Sheisha, son of Rav Idi, would place them on a bench and spread a cloth over them. Rav Hamnuna, son of Rav Yosef, said: I was once standing before Rava and he told me: Go and bring me my phylacteries. And I found them in his bed, between the mattress and the pillow, not aligned with his head. And I knew that it was the day of his wife’s immersion in the ritual bath for purification from the ritual impurity of a menstruating woman, and he certainly engaged in marital relations in order to fulfill the mitzva, and he did so, he sent me to bring him his phylacteries, to teach us the practical halakha in that case. Rav Yosef, son of Rav Neḥunya, who raised a dilemma above, raised a dilemma before Rav Yehuda: Two individuals sleeping in a single bed, given that it was standard practice to sleep without clothing, what is the halakha; is it permissible for this one to turn his head aside and recite Shema and for that one turns his head and recites Shema; or is it prohibited because they are unclothed and are considered unfit to recite Shema even though they are covered with a blanket? He said to him: Shmuel said as follows: This is permitted even if his wife is in bed with him. Rav Yosef strongly objects to this response: You say that he is permitted to recite Shema in bed with his wife, and needless to say he is permitted to do so when in bed with another. On the contrary, since his wife is like his own flesh, and he will not have lustful thoughts of her, it is permitted; another is not like his own flesh and it is prohibited. The Gemara raises an objection to this from the resolution of an apparent contradiction between two baraitot. It was taught in one baraita: Two unclothed individuals who are sleeping in a single bed, this one turns his head aside and recites Shema and that one turns his head aside and recites Shema. And it was taught in another baraita: One who is sleeping in bed and his unclothed children and members of his household are beside him, may not recite Shema unless a garment separates between them. If his children and the members of his household were minors, it is permitted to recite Shema even without a garment separating between them. Granted, according to Rav Yosef, the apparent contradiction between the two baraitot is not difficult, as this baraita is referring to a case where his wife is in the bed with him, while this other baraita is referring to a case where another person is in bed with him and there is concern lest he will have lustful thoughts. However, according to Shmuel, who permits one to recite Shema regardless of who is in bed with him, it is indeed difficult. How would he interpret the baraita that prohibits? The Gemara replies: Shmuel could have said to you: And according to Rav Yosef’s opinion, does it work out well? Wasn’t it taught in that same baraita that one who is sleeping in bed and his children and members of his household are beside him, may not recite Shema unless a garment separates between them? Doesn’t Rav Yosef hold that his wife is like his own flesh and no separation is necessary? Rather, what have you to say in response? Rav Yosef holds that there is a tannaitic dispute in the case of one’s wife; I, too, hold that it is a tannaitic dispute, and I accept the ruling of one of the baraitot. The Gemara reverts to clarify something mentioned above. The Master said in a baraita: This one turns his head aside and recites Shema. The Gemara notes a difficulty: Aren’t there bare buttocks? This supports the opinion of Rav Huna, as Rav Huna said: Buttocks do not constitute nakedness. Let us say that the following mishna supports Rav Huna’s opinion: A woman sits and separates her ḥalla naked, despite the fact that she must recite a blessing over the separation of the ḥalla, because she can cover her face, a euphemism for her genitals, in the ground, but a male, whose genitals are not covered when he sits, may not do so. The mishna teaches that exposed buttocks do not constitute nakedness. Rav Naḥman bar Yitzḥak interpreted the mishna as referring to a case where her face, genitals, was completely covered in the ground such that her posterior was covered by the ground. Therefore, proof for Rav Huna’s opinion cannot be brought from this mishna. The Master said in a baraita: If his children and the members of his household were minors, even though they are unclothed, it is permitted to recite Shema even without a garment separating between them. The Gemara asks: Until what age is one still considered a minor? Rav Ḥisda said: A girl until she is three years and one day old, and a boy until he is nine years and one day old, for these are the ages from which a sexual act in which they participate is considered a sexual act. Some say: A girl eleven years and one day old and a boy of twelve years and one day old, as that is the age at which they are considered adults in this regard. This age is only approximate, as the age of majority for both this, the boy, and that, the girl, is at the onset of puberty in accordance with the verse: “Your breasts were formed and your hair was grown” (Ezekiel 16:7). Rav Kahana said to Rav Ashi: There, with regard to the law of phylacteries, Rava said: Despite a conclusive refutation of the opinion of Shmuel, the halakha is in accordance with the opinion of Shmuel. Here, what is the ruling? He said to him: Were all of them woven in the same act of weaving? Are there no distinctions between different cases? Rather, where it is stated, it is stated, and where it is not stated, it is not stated, and there is no comparison. Rav Mari said to Rav Pappa: Does it constitute nakedness if one’s pubic hair protruded from his garment? Rav Pappa said about him: A hair, a hair. You are splitting hairs and being pedantic over trivialities. Rabbi Yitzḥak stated: An exposed handbreadth in a woman constitutes nakedness. The Gemara asks: Regarding which halakha was this said? If you say that it comes to prohibit looking at an exposed handbreadth in her, didn’t Rav Sheshet say: Why did the verse enumerate “anklets and bracelets, rings, earrings and girdles” (Numbers 31:50), jewelry that is worn externally, over her clothing, e.g., bracelets, together with jewelry worn internally, beneath her clothing, near her nakedness, e.g., girdles? This was to tell you: Anyone who gazes upon a woman’s little finger is considered as if he gazed upon her naked genitals, for if his intentions are impure, it makes no difference where he looks or how much is exposed; even less than a handbreadth. Rather, it is referring even to his wife, with regard to the recitation of Shema. One may not recite Shema before an exposed handbreadth of his wife. Along these lines, Rav Ḥisda said: Even a woman’s exposed leg is considered nakedness, as it is stated: “Uncover the leg and pass through the rivers” (Isaiah 47:2), and it is written in the following verse: “Your nakedness shall be revealed and your shame shall be seen” (Isaiah 47:3). Shmuel further stated: A woman’s singing voice is considered nakedness, which he derives from the praise accorded a woman’s voice, as it is stated: “Sweet is your voice and your countenance is alluring” (Song of Songs 2:14). Similarly, Rav Sheshet stated: Even a woman’s hair is considered nakedness, for it too is praised, as it is written: “Your hair is like a flock of goats, trailing down from Mount Gilead” (Song of Songs 4:1). The Gemara resumes its discussion of phylacteries. Rabbi Ḥanina said: I saw Rabbi Yehuda HaNasi hang his phylacteries. The Gemara raises an objection: It was taught in a baraita that one who hangs his phylacteries will have his life hang in the balance. Moreover, the Symbolic Interpreters of the Torah said that the verse: “And your life shall hang in doubt before you [minneged]” (Deuteronomy 28:66), that is the punishment of one who hangs his phylacteries. The Gemara replies: This apparent contradiction is not difficult, as this baraita, which condemns one who hangs his phylacteries, refers to one who hangs them by the strap, allowing the leather boxes into which the parchment is placed to dangle in a deprecating way, which is certainly prohibited. That baraita, which relates that Rabbi Yehuda HaNasi would hang his phylacteries and that it is clearly permitted, refers to when one hangs them from the box with the straps dangling. And if you wish, say another explanation instead: There is no difference whether he hangs the phylacteries from the strap and there is no difference whether he hangs the phylacteries from the box; both are prohibited. And when Rabbi Yehuda HaNasi hung his phylacteries, he hung them in their pouch. The Gemara asks: If so, what is the purpose to relate that incident? The Gemara replies: Lest you say that phylacteries would require placement atop a surface, as is the custom with a Torah scroll. Therefore, it teaches us that this is unnecessary. Since Rabbi Ḥanina related a story involving Rabbi Yehuda HaNasi, the Gemara cites another such story. Rabbi Ḥanina said: I saw Rabbi Yehuda HaNasi, while he was praying, belch, yawn, sneeze, spit,

משנה תורה, הלכות איסורי ביאה כ״א:י״ז

לֹא יְהַלְּכוּ בְּנוֹת יִשְׂרָאֵל פְּרוּעֵי רֹאשׁ בַּשּׁוּק. אַחַת פְּנוּיָה וְאַחַת אֵשֶׁת אִישׁ.

Mishneh Torah, Forbidden Intercourse 21:17

(17) Jewish women should not walk in the market with their hair uncovered. [This applies to] single women and married women. Additionally, a woman should not walk in the market with her child following behind her. [This is] a decree (gezera) enacted to prevent the child being abducted, and her following after them to bring him back and being molested by the wicked people who capriciously abducted him

אורח חיים ע״ה:ב׳

(ב) שער של אשה שדרכה לכסות אסו' לקרות (קריאת שמע) כנגדו: הגה (אפי' אשתו) אבל בתולות שדרכן לילך פרועות הראש מותר: הגה וה"ה השערות של נשים שרגילין לצאת מחוץ לצמתן (covering) (ב"י בשם הרשב"א) וכ"ש שער נכרית (wigs) אפי' דרכה לכסות (הגהות אלפסי החדשים):

Shulchan Arukh, Orach Chayim 75:2

(2) The hair of a woman that it is the practice (lit. way) to cover is forbidden to recite [the Recitation of the Sh'ma] in front of it. Rem"a: Even his wife . But unmarried women for whom it is their way to go with an uncovered head, it is permitted. Rem"a: And so too is the law with the hairs of women that regularly come out of their covering (Beit Yosef in the name of Rashba) and certainly foreign hair (i.e. a wig) even if it is her practice to cover (Hagahot Alfasi haChadashim).

If we follow that women cover their hair for modesty, like we saw with עֶרְוָה in Brachot and how the Rambam defines דָּת יְהוּדִית as modesty, then why do only married women cover their hair (like we saw in the Shulchan Aruch)?

משנה כתובות ב׳:א׳

(א) הָאִשָּׁה שֶׁנִּתְאַרְמְלָה אוֹ שֶׁנִּתְגָּרְשָׁה, הִיא אוֹמֶרֶת בְּתוּלָה נְשָׂאתַנִי, וְהוּא אוֹמֵר, לֹא כִי אֶלָּא אַלְמָנָה נְשָׂאתִיךְ, אִם יֵשׁ עֵדִים שֶׁיָּצָאת בְּהִנּוּמָא וְרֹאשָׁהּ פָּרוּעַ, כְּתֻבָּתָהּ מָאתָיִם.

Mishnah Ketubot 2:1

(1) With regard to a woman who was widowed or divorced, and is now claiming payment of her marriage contract that is not before the court, and she says: You married me as a virgin, who is entitled to two hundred dinars, and he says: No; rather, I married you as a widow, who is entitled to one hundred dinars, then, if there are witnesses that she went out of her father’s house to her wedding with a hinnuma or with her hair uncovered, in a manner typical of virgins, payment of her marriage contract is two hundred dinars. Rabbi Yoḥanan ben Beroka says: Even testimony that there was distribution of roasted grain, which was customary at weddings of virgins, constitutes proof that she is a virgin.

ראבי”ה חלק א – מסכת ברכות סימן עו
וכל הדברים [שהזכרנו למעלה] לערוה דווקא בדבר שאין רגילות להגלות, אבל בתולה הרגילה בגילוי שער לא חיישינן, דליכא הרהור

אבן העזר כ״א:ב׳-ג׳

(ב) לא תלכנה בנות ישראל פרועות ראש בשוק אחת פנויה ואחת אשת איש:

(ג) מותר להסתכל בפנויה לבדקה אם היא יפה שישאנה בין שהיא בתולה או בעולה, ולא עוד אלא שראוי לעשות כן, אבל לא יסתכל בה דרך זנות.

Shulchan Arukh, Even HaEzer 21:2-3

(2) Jewish women may not go with uncovered head in the marketplace, whether married or not.

(3) It is permissible to gaze at an unmarried woman to determine if she is attractive, in order [to decide whether] to marry her, whether she is a virgin or not, and moreover it is fitting to do so. But he may not look at her in a promiscuous way, and about this it is said (Job 31:1): "I made a covenant with my eyes, and how can I look upon a virgin?"

בית שמואל כ״א:ה׳

(ה) א' פנויה. היינו אלמנה או גרושה אבל בתולה מותר

Beit Shmuel 21:5

...

Final views on who should cover their hair today:

Michael J. Broyde, "HAIR COVERING AND JEWISH LAW: BIBLICAL AND OBJECTIVE OR RABBINIC AND SUBJECTIVE?"
The conventional binary analysis of Berakhot 24a divides between those activities or areas that must never be revealed (including all three mentioned in Berakhot 24a, being a women's thigh, singing voice and hair) and those which may always be revealed (such as hands, face, or speaking voice). According to Rashi’s view, there are actually three categories within the obligation not to reveal immodestly— not two. At one extreme, the first group contains things that are so sexually charged that no woman should ever reveal them outside the confines of a marital relationship.
At the other extreme, the second category includes those things that can always be revealed by all women, such as hands, face, or speaking voice, as they are never erotic. But, for Rashi, between these two poles is a middle area comprising those aspects listed in Berakhot 24a. These areas of women’s bodies or activities are sufficiently erotic that men look at them and ponder matters of sexuality, yet are not so erotic that single women may not reveal them. In this view, the restrictions found in Ketubot 72a-b are specifically marital breaches because, for example, revealing hair is a sign of being single and thus exceedingly immodest for married women and a breach of the marital obligation.
Rashi’s school of thought (which has essentially disappeared from our common conversation with regards to tsni’ut in the last 50 years) has a certain halakhic insight to it. First, it explains the historical practice with regard to hair: unmarried women did not cover their hair, notwithstanding the apparently clear directive of Berakhot 24a that uncovered hair is immodest. Second, it recognizes that when one is single, somewhat enticing conduct of various sorts is part of the process of courting (as we saw in the Shulchan Aruch Even Ha'Ezer).
...Rashi’s view with regard to hair would thus be that if hair covering is one of the indications of being married (which it historically was), then uncovering hair by a married woman violates the category of dat yehudit.

ערוך השולחן, אורח חיים ע״ה:ז׳

(ז) ועתה בואו ונצווח על פרצות דורינו בעוונותינו הרבים, שזה שנים רבות שנפרצו בנות ישראל בעון זה והולכות בגילוי הראש. וכל מה שצעקו על זה – הוא לא לעזר ולא להועיל. ועתה פשתה המספחת, שהנשואות הולכות בשערותן כמו הבתולות. אוי לנו שעלתה בימינו כך!

מיהו על כל פנים לדינא נראה שמותר לנו להתפלל ולברך (קְרִיאַת שְׁמַע) נגד ראשיהן המגולות, כיון שעתה רובן הולכות כך, והוה כמקומות המגולים בגופה, וכמו שכתב המרדכי בשם ראבי"ה בסוף פרק שלישי, וזה לשונו: "כל הדברים שהזכרנו לערוה – דוקא בדבר שאין רגילות להגלות. אבל בתולה הרגילה בגילוי שיער – לא חיישינן, דליכא הרהור." עד כאן לשונו. וכיון שאצלינו גם הנשואות כן, ממילא דליכא הרהור. (והרי"ף והרמב"ם השמיטו לגמרי דין שיער וקול, משום דסבירא להו דלאו לקריאת שמע איתמר. עיין בית יוסף.)

Arukh HaShulchan, Orach Chaim 75:7

...