Would Rabbeinu Tam Wear "Rabbeinu Tam Tefillin"??

I love Judaism!!

There is a famous machlokes between Rashi and Rabbeinu Tam concerning the order of the parshiyos of the tefillin. Rashi says that the correct order is as they appear in the Torah - Kadesh, Vihaya ki yiveeacha, Shema, Vihaya im shamoa. Rabbeinu Tam argues that the correct order is Kadesh, Vihaya ki yiviacha, Vihaya im shamoa, Shema [called "Havayos ba-emtza" because the "vihaya's" are in the middle]. There argument is rooted in a differing understanding of a gemara in Menachos 34.

There is another machlokes between Rashi and Rabbeinu Tam - whether the parshiyos must be laying flat or standing up. Rashi holds that they must lay flat while Rabbeinu Tam says that must be standing upright. What is so fascinating is that in our Rabbeinu Tam tefillin where the parshiyos are according to his order, the parshiyos lay flat like Rashi.

So it emerges that according to Rabbeinu Tam one is not yotzei with Rabbeinu Tam tefillin:-).

The reason we follow Rashi even for Rabbeinu Tam tefillin is explained by the Noda Bi-yehuda in a teshuva [ח"ב סי' ד].