Is it technically possible to encrypt the blockchain so the transactions becomes totally impossible to trace for others than the two parts involved in the transaction?
The reason: make it impossible for government to trace how much bitcoins you have, who you have transactions with and so on.
The architecture of the Bitcoin ledger is such that each node can verify that a transaction has not been previously spent. There's no way to verify that the transaction hasn't previously been spent without knowing the address and the transaction details (transaction hash and index).
There is a somewhat related project, Open Transactions, that allows Bitcoin transactions with blinding.
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https://github.com/FellowTraveler/Open-Transactions/wiki