How can I send some message from contract to address

Question

Is it possible? And if it is, how can I send some data from contract to address.
Something like

msg.sender.send.data("0x0")(value)

Answer 1

There is something specifically for this purpose, which is called Whisper

In a nutshell whisper is a communication protocol for DApps to communicate each other.

Example Usage

var shh = web3.shh;
var appName = "My silly app!";
var myName = "Gav Would";
var myIdentity = shh.newIdentity();

shh.post({
  "from": myIdentity,
  "topic": [ web3.fromAscii(appName) ],
  "payload": [ web3.fromAscii(myName), web3.fromAscii("What is your name?") ],
  "ttl": 100,
  "priority": 1000
});

Read Whisper Overview