Maybe tryptophan, an ingredient in turkey makes you sleepy. Maybe not. I suspect it is has either no effect or a small effect. But when people say “the turkey makes you sleepy because it has tryptophan in it,” they are repeating an easily disprovable myth.
Let’s say tryptophan makes you sleepy. Why does turkey take the rap? Other things with tryptophan: Cattle, swine, chickens, fish. Pretty much, animals. Plants too. Tryptophan is a basic building block, aka amino acid, in your basic biological protein.
So if turkey makes you sleepy because of tryptophan, then when you mix up that whey protein super shake, to up your protein intake on a gym workout day, you should pass out. If you consume 120 grams of protein in your workout juice, that’s 2,160 mg of tryptophan.
If you look at a USDA list of nutrients, and search for tryptophan, you’ll find that pork, steak, hamburger, turkey breast, etc. etc. all have almost identical amounts of the amino acid, because the are, after all, almost identical animals (all tetrapods) at the 20,000 foot level (but don’t drop your turkey out of a helicopter at any altitude). But turkey breast has a tiny bit more than the other, for random reasons.
I think the real reason you take a nap is because you need a nap and the turkey takes the rap for your nap. The turkey is none the wiser, so go for it.