Directly doesn't work over the internet, because the internet doesn't work like that. You'd be restricted to bluetooth, wifi direct or similar.
If you allow for forwarding in between, there are p2p messengers. Messages are stored - if at all - using store & forward techniques. They can use the internet, but also bluetooth and other communication technology to transmit messages. The most popular ones would be Briar and Jami.
Matrix P2P exists at an experimental stage as well (moving servers onto devices).
The problem with them you give up convenient things, even though there are often are workarounds.
For instance, plain p2p you cannot communicate with offline devices, but store and forward techniques exist, either storing messages on random people or dedicated store and forward servers.
Battery drain, lack of reliability. It's just extremely simple, quick and reliable to send messages to a defined server and receive Push Notifications via push service.
Want a reliable storage of your messages (encrypted) such that you can always access them when you wish? well...
> Directly doesn't work over the internet, because the internet doesn't work like that. You'd be restricted to bluetooth, wifi direct or similar.
That is how "the internet" has worked forever.
People have been running servers on their own home machines, for a long time. If you really want you can setup a webserver/sshd/etc. on your own machine and access it from the outside if you don't care about DNS and static IP. Will also probably need to port forward at the router, though.
Its less common nowadays due to the cloud, and security issues, etc. sure. And I'm not sure to what extent its possible over mobile.
But for two people who are on PCs/Macs, it should definitely be possible. And it would be much lower latency because you don't have to bounce it off another server.
If you allow for forwarding in between, there are p2p messengers. Messages are stored - if at all - using store & forward techniques. They can use the internet, but also bluetooth and other communication technology to transmit messages. The most popular ones would be Briar and Jami. Matrix P2P exists at an experimental stage as well (moving servers onto devices).
The problem with them you give up convenient things, even though there are often are workarounds. For instance, plain p2p you cannot communicate with offline devices, but store and forward techniques exist, either storing messages on random people or dedicated store and forward servers.
Battery drain, lack of reliability. It's just extremely simple, quick and reliable to send messages to a defined server and receive Push Notifications via push service.
Want a reliable storage of your messages (encrypted) such that you can always access them when you wish? well...