Question

I am a rabbi who officiates weddings, usually for secular people from the general public, the thoroughly secular who are not even traditional. The assumption is that a large portion of them, perhaps even most, do not believe at all.
In the past I asked you about the Jewish laws relevant to the wedding canopy ceremony for them; now I would like to ask about the very validity of the betrothal in the case of a person who does not believe in the Holy One, blessed be He, and of course does not accept halakhic obligation.
In light of your view, and I quote: “It follows that in practice, a commandment performed by a Jew who does not believe has no religious value… Moreover, I argued there that for the same reason, a transgression committed by such a person is also not a transgression.”
The essence of betrothal (as you explained well in “Matters of Agency”) is a proprietary legal act that creates a *halakhic* effect. In addition, the custom is to say: according to the law of Moses and Israel. According to Tosafot (Ketubot 3a and Gittin 33a), “according to the law of Moses” means the Torah, and “Israel” means the sages. That is, subject to their authority.
It seems that the whole essence of this legal effect is that they understand and intend, and therefore impose upon themselves the halakhic rules that apply to a married couple according to Jewish law: commandments and transgressions.
If the non-believer is not in the category of commandments, and his transgressions are not transgressions, and it is obvious that they do not intend this (either because they do not want such a legal effect, or because it has no meaning as long as they do not believe in it), then why is a valid betrothal created here?
In the lecture you compared the law of betrothal involving a minor to conversion without acceptance of the commandments. In both cases it is clear that they are not part of the relevant framework, because they are not within the essence of the act. Why is the non-believer not also included under that category?
As for the ketubah, I can understand it more, because in the end he signs a contract with material obligations, and that has force regardless of the religious aspect (civil courts even sometimes enforce the amount of the ketubah as a matter of contract law),
but what about betrothal? Its whole essence is a halakhic legal effect, in the sense of commandments and transgressions, and the non-believer is not part of that framework, so the essential component is missing.