For the halachic system, this prompts the question of whether such cars would be permissible on shabbat.
There is no direct action causing the outcome, it is purely thought directed. And, if the car is electric, it is a d'rabannan prohibition alraedy.
There can likely be some debate about this last statement, but R' Shlomo Zalman Auerbach and others have ruled there is essentially no basis for forbidding electricity in and of itself; and beyond that, even though we claim minhag clal yisrael, there are those alive today who remember using electricity in various manners on shabbat and yom tov before Mosheh Feinstein, the Lubavitcher Rebbe and others took up a battle against electricity on Shabbat in the mid-20th century.
One of the Rabbi-PhD's on staff at Bar Ilan University claims thought-driven cars may well be permitted on shabbat. At the 18th Torah and Science Conference, Rabbi Dr. Dror Fixler acknowledges some will want to forbid driving such a vehicle on shabbat, but according to an article in the Jerusalem Post, he argues it isn't so clear that driving it on shabbat would violate halacha:
But there are those who could contend that just thinking does not constitute a “melacha” – prohibited activity on Shabbat that was necessary for the construction of the Tabernacle taken by the People of Israel through the desert after the Exodus from Egypt. There are 39 such types of “work” and their subcategories that cannot be performed on the Sabbath.
The discussion would discuss whether an bionic artificial limb that is moved with brain pulses – which is much closer to actual use than think-only cars – or a bionic eye that could enable the blind see – could be used on Shabbat.
Fixler noted that even without seeing something work such as a remote control it could be argued that the tool was under the user’s control without actually being observed as doing something; it is much more complicated if only the brain is in control, he said.
Only time will tell how the Orthodox community takes in such advances when (and if) they should reach the mass market. There would also be issues of eiruv and tchum shabbat, but we can look at tshuvot regarding bikes on shabbat for precedents there.
In the mean time, it is interesting to think of all the possible tasks that could become thought-driven, and thus possibly permitted on shabbat.
