Facebook would be nothing without its Ivy League roots. But now a new Ivy League study could mean big trouble for Facebook, along with Instagram and Snapchat for that matter.

That's because this is the first study to show a "clear causal link" between using these three sites and being lonely and depressed.

Other studies have certainly found that heavy users of Facebook and other social media sites suffered mental health issues.

But that was about correlation, not causation. Those studies mostly found that it could simply be that people who are depressed and lonely to begin with wind up using Facebook and similar sites more often--as opposed to the sites themselves causing the issues.

This new study from the psychology department at the University of Pennsylvania, however, says it's made the crucial link.

Here it is in their own words, in what's probably the most important passage in their published research:

[O]urs is the first study to establish a clear causal link between decreasing social media use, and improvements in loneliness and depression. It is ironic, but perhaps not surprising, that reducing social media, which promised to help us connect with others, actually helps people feel less lonely and depressed.

Emphasis added, because it's so important.

The research is due to be published in the January edition of the peer-reviewed Journal of Social & Clinical Psychology (opens as .pdf).

The study, conducted by professors Melissa Hunt, Rachel Marx, Courtney Lipson and Jordyn Young, focused on 143 University of Pennsylvania undergraduates, who were tested over a period of weeks on seven different scales that measure moods and psychological well-being.

Half of the students used Facebook, Instagram and Snapchat just as they normally would over the time period.

The other half restricted their social media use to 10 minutes per day for the course of the study. (This was verified by using data from their phones.)

In the end, the more students used Facebook, Instagram and Snapchat, the more their mental heath deteoriated.

"[L]imiting social media usage on a mobile phone to 10 minutes per platform per day for a full three weeks had a significant impact on well-being. Both loneliness and depressive symptoms declined in the experimental group," the study reported.

The participants could see the positive way that cutting back was helping them. Among their comments:

"Not comparing my life to the lives of others had a much stronger impact than I expected, and I felt a lot more positive about myself during those weeks."

"It was easier than I thought to limit my usage. Afterwards I pretty much stopped using Snapchat because I realized it wasn't something I missed."

"I ended up using less and felt happier and like I could focus on school and not (be as) interested in what everyone is up to."

Of course, it's the empirical data showing that people were happier when they cut back on social media that is probably most important scientifically. And there's lots of room for more research to be done.

(One almost comical aside in the article notes that many participants didn't contribute to a follow-up data effort, because they'd been incentivized to participate by getting extra credit for a class, but then the class ended.)

But like the students involved, you probably can figure out the answer yourself. If you're worried that your use of social media is having a detrimental effect on your mood and well-being, science now says you're probably right.