The consensus among the poskim is that activating light-emitting diodes (LEDs) on Shabbat is not a Torah-level prohibition, but a Rabbinic-level one.[1] The way LEDs work is that one connects a circuit, and light is thereby emitted (by the transfer of electrons through junctions of semi-conductors). It is not simple to pinpoint what Rabbinic injunction is violated by such action (in cases in which the diodes do not form letters or pictures[2]). Some maintain that any activity that creates electric circuits is prohibited as molid (creating something new),[3] even though there is no explicit Talmudic precedent of molid of this sort.[4] Other authorities discuss a prohibition of creating or fixing the electric device.[5]
In the case of a child’s shoes, there are various grounds for leniency. One point is that despite the initial excitement of watching himself light up his shoes, a child eventually walks without even thinking about the lights, making this, on a certain level, a davar she’eino mitkaven (an unintended violation). Since, regardless of intention, the lights definitely will go on, this is a case of p’sik reishei, in which one wishes to perform a permitted act (e.g., walking) but a forbidden result (e.g., activating LEDs on Shabbat) will definitely occur. While p’sik reishei is forbidden,[6] the Terumat HaDeshen[7] rules that if the violation that will occur without intention is only a Rabbinic one, even a p’sik reishei is permitted. Although we accept the opinion of the Magen Avraham,[8] who forbids p’sik reishei even if it entails only a Rabbinic prohibition,[9] the fact that some permit it is still a mitigating factor.[10]
Within the realm of p’sik reishei, there are possible distinctions. The Aruch[11] rules that if the person who performs the p’sik reishei has no interest in the forbidden result (d’lo nicha lei), it is permitted. Although the Aruch’s opinion is not generally accepted,[12] there are quite a few opinions that maintain that a p’sik reishei d’lo nicha lei on a Rabbinically forbidden result is permitted.[13] While many are stringent despite the multiple grounds for leniency, in cases in which refraining from the matter at hand causes particular hardship, it is quite accepted to be lenient.[14] Thus, if an adult were to ask about wearing the LED shoes you describe, we would not allow him to do so in the absence of a special need, but this strict ruling would not be a definite one if he did not care at all about the lights.
When we turn to the question of a child wearing such shoes, the situation becomes much more lenient. If the child is a toddler, who is too young for his parents to train in any serious way about observing Shabbat, they are not obligated to distance him from violations of Shabbat. On the other hand, it is prohibited for them to actively facilitate the prohibition for the child by “feeding him by hand” or the like (and putting shoes on him is certainly considered active facilitation).[15] The Rashba and the Ran rule that this prohibition does not apply to “feeding him” Rabbinic prohibitions.[16] Although the Shulchan Aruch[17] does not accept their opinion, many are lenient in certain cases of need,[18] at least with regard to small children.[19] In the case of an action that is not even unanimously agreed to be forbidden for an adult, such as walking in these shoes without interest in activating LED lights, it is much easier to be lenient for a child. If the child is old enough to be trained in the halachot of Shabbat, it is somewhat more difficult to permit such shoes, but if he wears them of his own volition, there is additional room to argue that one need not stop him.[20]
We will emphasize, however, that despite all the technical grounds for leniency, it is very much not in the spirit of Shabbat to have a child wear such shoes, and it therefore generally should not be done. That being said, if a one-time, unique situation arises in which these are the only shoes a small child is able to wear, and the child does not think about activating the lights, it is possible to combine the different indications for leniency to allow him to wear such shoes (and, if necessary, to even put them on for him).