Timely answers to academic e-mails and internet addiction After lots of struggles with the internet, almost overcoming an addiction to Facebook and a compulsive obsession to check my e-mail, I have finally reached an equilibrium that allows me to concentrate and be productive. My strategy is simple: I check and answer e-mails only three times a day: when I get to the lab in the morning, after lunch, and before leaving at night. 

During the rest of the day, I use the computer just for work (I’m a bioinformatician) and keep my e-mail locked with an app. At home, I fully disconnect from my computer. Also, I don’t have a smartphone. I know this strategy seems a bit extreme these days when most people is connected 24/7, but it’s the only way I found to control myself and get my things done. I have the impression that everybody (especially in bioinformatics and including my PI) assumes I’m catching up with my e-mail almost instantly (for real, it isn’t rare to get answers from coworkers in matter of seconds). 

For instance, one day my PI came kind of angry to my desk asking why I hadn’t gone to his office (or cancelled) if he had sent me and e-mail asking me to. Of course, the message had been sent but I hadn’t checked the e-mail.  The follow up message “Could you please answer my previous e-mail?” isn’t uncommon in my inbox. So I’m starting to get worried that some people may get upset at me for being a late responder, especially people outside my lab, but at the same time I have to level out my internet usage to keep my addiction tamed. 

In that context, I would like to known what is considered a timely response to an academic e-mail? If I can’t use my e-mail all the time, what strategies to use so I don’t miss crucial information? Should I let my PI and coworkers know about my previous problems with the internet?
What's considered a timely response depends on context.  A response could be expected within hours, days, or weeks, depending on the email.  What I think is important is that both parties are clear on expectations.  

For normal academic activities, I would say checking emails twice a day is generally sufficient.  Academics are often busy with classes and meetings throughout the day, so it's generally understood (at least between faculty, though not always by students) that you might not read or respond to an email within an hour.

However, it sounds like your PI expects you to check email more frequently than you do, so it's probably worthwhile mentioning that you only check email a few times a day (if asked why, just say so it doesn't distract you too much from your work).  Then you can see if your PI is happy with calling you or seeing you in person if it's something urgent.  If not, and PI really wants you to check email constantly, maybe you can set up something where you will only see emails from your PI (e.g., forward them to another email that you use for nothing else).

Similarly, if there are other people that seem to be expecting immediate responses from you, just maybe add a "PS" in your reply about how often you check email.  I don't think most people will be upset if they know your habits.