Thank you for all replies and I forgot to say: My intention was not "Oh, you are to stupid, and I got the solution in just a few hours", but rather "I'm still to stupid to get it".
@deepceleron
It is clear to me, that my client always have to update to receive new bitcoins from transactions. That is a problem, too, if you just not frequently use bitcoins. One month of blocks is not downloaded in a second. The main problem is to download all the first time after you installed the client.
So you can trace back ever bitcoin to the coinbase transaction, but for what? Some competing nodes or firms can offer that information, but not every node has the intention to do that. That is/was my problem.
But I get the idea of lite clients. So can I imagine the analogy, that there will be some banks, whom I trust and they will store and update the block chain, so a user don't have to do that. The bank would be some kind of
client software and the
client humans of the bank would be the user of the client software? Hm, that would be a good solution! Maybe not exactly matching with the bitcoin ideology, anyway. Thanks for the input
@Sukrim
One then only would need the chain headers (a handful MB), the set of unspent transaction outputs (currently ~170 MB afaik) and all full blocks since the last set was created to update this set to the most current state. Once a new set gets released, you verify its integrity and after a few blocks discard the old set and the content of the blocks leading up to the new set.
Hm what "set of full blocks" do you mean there? Just maybe the last 1000 full blocks. And if a client gets started and there are 300 new blocks, the old 300 get discarded and the new 300 gets downloard?
And can you tell me something about the enforcing. Who finanlizes? Is it just a matter of the developers of the competing client softwares? So for example I could come up with my own software that will do the things, like you (and others) suggested?