Can Contract Accounts send Messages to EOAs?

Question

I often hear the following statement:

Contract Accounts cannot send Messages to EOAs. They can only:
  1. send Messages to other Contract Accounts
  2. send Ether to EOAs

... see, e.g., here: Are contracts able to send messages to EOA's?

This statement does not really make sense to me. According to the Ethereum Docs (see http://www.ethdocs.org/en/latest/contracts-and-transactions/account-types-gas-and-transactions.html#what-is-a-message) a message contains: 1. the sender of the message (implicit) 2. the recipient of the message 3. VALUE field - The amount of wei to transfer 4. an optional data field 5. STARTGAS value

So when a Contract Account sends Ether to an EOA, it does so by sending a Message with an empty data field and containing the amount of Ether/Wei to be transferred in the VALUE field, right?

That is, Contract Accounts do send Messages to EOAs but the data field of these messages is empty, correct?

Answer 1

The true is that both statements are correct somehow.

A contract can attach a message when making a transfer to an external owned account. But the message is not easily accessible for an external account to read it.

pragma solidity ^0.4.19;

contract A {
    // Make a transfer to who and attach message m
    function bar(address who, bytes m) public payable returns (bytes32) {
        address a = who;
        uint l = m.length;
        uint v = msg.value;
        assembly {
            if iszero(call(gas, a, v, add(m, 0x20), l, 0, 0)) {
                revert(0, 0)
            }
        }
        return 0;
    }
}

An external account can detect if its balance has changed and from what transaction made the change. But to read the message it will have to execute the transaction.