The difference is that people would not send messages to PAY other people. Instead, they would send messages to say that they OWE them money. We could call the system Owem - for "Owe 'em".
I just tried simulating how the system could work with a group of 10 different people in a community - a Baker, a Builder, a Carpenter, a Cleaner, an Electrician, a Farmer, a Gardener, a Hairdresser, a Nurse and a Teacher.
Suppose they all start of with a balance of zero. Then, during the first week, they note the following set of IOUs.
For example, the Baker emitted two IOUs : one to the Electrician for €8 and another to the Farmer for €7. This makes a total of €15 that you can see in red in the IOU column.
At the same time, the Baker was given IOUs by the Builder, Carpenter, Cleaner, Electrician, Gardener, Hairdresser, Nurse and Teacher (they all went to the Baker to get some bread!). That gives him a total in UOIs (you owe I) of €26, which is the number in green at the bottom.
This means that the Baker has a Net status of +11 euros - which you can see in the right hand column.
Adding up all the IOUs (or all the UOIs - it comes to the same) gives a total amount of "money" in circulation of €384 - the number highlighted in blue.
Note also that the sum of all the "Net" values in the right hand column is Zero. It has to be - because every IOU emitted is matched by an equivalent UOI.
Now, while all this economic activity may look complicated, you can actually cancel out most of the activity. Some of the IOUs were between the same two people. Thus while the Baker emitted an IOU to the Electrician for €8, the Electrician also emitted an IOU to the Baker for €3, meaning that the Baker now owes the Electrician €5.
But there are more complicated chains involving three or more "players". Thus, while the Baker still owes the Electrician €5, we can note that the Electrician owes the Carpenter €10, and the Carpenter owes the Baker €5. The result is that all that can be cancelled out, leaving just the Electrician owing the Carpenter €5.
Once you have done all the cancelling out, you are left with the following highly simplified table.
And all this money creation and removal was done without the need for a bank! It could all be done with a simple bit of software that could be provided for free.
Seriously, I think that this can be done. We don't need to borrow euros from banks. And we don't need to pay interest to the banks for lending us their tape measure. All we need is a bit of software that allows people to keep a tally of who owes who what.
If, after several months of running the system, the Carpenter still owes money to the Cleaner, it might be necessary to ask him to make the payment with "real" euros. But in the meantime, everyone has been getting on just fine using their IOUs. Business will have been booming, bread will have been baked, buildings built, farms farmed, gardens gardened, hair dressed, the sick nursed and the children taught - and no need for debt-based money at all.
I really do think that there is a way out.