I drunkenly told a professor something fundamentally wrong about a friend's thesis work. Should I clarify and/or apologize? TL;DR: I told a professor something fundamental about a friends' work that is absolutely wrong, and I should have known, but I was drunk. Will it help the situation if I clarify and apologize via e-mail?  

Yesterday evening I attended a festivity at my old university. I got drunk and talked to a professor who is working in a field related to my studies. 
In particular, I told him that a friend and coworker of mine did his master thesis on a topic that is related to a project the professor is working on. However, I got it mixed up and this is not true. He appeared surprised and said he was going to look into that.

Now I regret getting drunk and I am wondering whether I should email him to clarify (and apologize). Either he did know that I was in the wrong, and did not correct me out of politeness, or he will actually ask around and several people will know that I gave the professor wrong information. The latter option would be very embarrassing to me, since I actually attended my friends' thesis defense and I know what it was about.
I don't see why Germany should be any different from other places, but generally it is a good idea to apologize for stupid things said drunkenly. And since this may have a bearing on the reputation of a third party you probably have an obligation to make sure the record is correct. 

Sooner is better than later in such things, so the professor doesn't spend effort on a lost cause.