No way. 

But you can detect what coins transferred from one address and what coins transferred from another.


Look for example at the first address in the network:

12c6DSiU4Rq3P4ZxziKxzrL5LmMBrzjrJX

http://blockchain.info/address/12c6DSiU4Rq3P4ZxziKxzrL5LmMBrzjrJX

https://blockexplorer.com/address/12c6DSiU4Rq3P4ZxziKxzrL5LmMBrzjrJX

Nobody can stop people to send bitcoins to Satoshi's address, first bitcoin address in the network.