Effects in this sense is a synonym for movable goods, that is, physical property. The text of the fourth amendment protects your property. This and other rulings are saying that the records your phone company produces of what calls they've connected are not yours, but the phone company's property. If Verizon gives its own property to someone, government or otherwise, you have no standing to claim any violation of your rights.
A web analogy: the records of who called whom (i.e. "phone metadata") are just like web server access logs. You would like the court to say that the web server access logs you produce are the property of all the individual people that visit your website. The judge is saying those logs, produced and held by your server, are your property alone.
I still don't get it. There's equivocation with the verb to produce.
I'm going to play Socratic Advocate here. When a music producer produces a record of an artist, who owns it? How do we conceptualize this relationship of artist to market? Do we argue for record companies or for artists? What motivates the moral structure of this debate? Are we sympathizing with record companies or artists? It's a record of the artist's musical activity.
Now, a phone company is a producer of our records. We're its content producers. But if the record company re-uses its artist's work without that artist's permission...?
If I tell you I murdered someone, should the government have to get a warrant to get that information from you? What if they asked you if I visited your bookstore last week? What if you kept a journal indicating each time I visited your store, or bought a book? What if they asked Amazon for a list of when I visited their site, or bought a book? (Keep in mind Amazon has the right to refuse to give that information without a court order...the question is whether I can protest that subpoena, or only Amazon can).
At some point, there needs to be a line drawn. The 4th amendment has been interpreted to protect "reasonable expectations of privacy" in order to draw that line. If I tell you I murdered someone, or if you tell the police when I visited your store, that's over that side of the line. I have no reasonable expectation of privacy. I freely gave up this information to a third party.
The copyright law has an entirely different history, text, and history of interpretation.
I agree that the third party doctrine is no longer workable in the digital age (people probably have just as much of an expectation of privacy in their DropBox as their C: drive), but I don't think the other viewpoint is entirely unreasonable, especially during the pre-digital age.
A web analogy: the records of who called whom (i.e. "phone metadata") are just like web server access logs. You would like the court to say that the web server access logs you produce are the property of all the individual people that visit your website. The judge is saying those logs, produced and held by your server, are your property alone.