Why will or will not the bitcoin infrastructure become unsustainable? I am new to bitcoins, but as I understand the technology:


All transactions must be downloaded to the client machine (say, Grandma's Windows XP machine from 2003)
New transactions are also sent to all clients


Is that correct?

If 1 billion people adopted Bitcoin as their primary currency, and performed an average of 1 transaction per day each, this would be 11,000 transactions per second every day on Grandma's Windows XP machine.  I think it would catch fire!
I will let Satoshi Nakamoto answer this:


  Long before the network gets anywhere near as large as that, it would
  be safe  for users to use Simplified Payment Verification (section 8)
  to check for  double spending, which only requires having the chain of
  block headers, or  about 12KB per day.  Only people trying to create
  new coins would need to run  network nodes.  At first, most users
  would run network nodes, but as the  network grows beyond a certain
  point, it would be left more and more to  specialists with server
  farms of specialized hardware.  A server farm would  only need to have
  one node on the network and the rest of the LAN connects with  that
  one node.
  
  The bandwidth might not be as prohibitive as you think.  A typical
  transaction  would be about 400 bytes (ECC is nicely compact).  Each
  transaction has to be  broadcast twice, so lets say 1KB per
  transaction.  Visa processed 37 billion  transactions in FY2008, or an
  average of 100 million transactions per day.   That many transactions
  would take 100GB of bandwidth, or the size of 12 DVD or  2 HD quality
  movies, or about $18 worth of bandwidth at current prices.
  
  If the network were to get that big, it would take several years, and
  by then,  sending 2 HD movies over the Internet would probably not
  seem like a big deal. 
  
  Satoshi Nakamoto


Link: http://www.mail-archive.com/cryptography@metzdowd.com/msg09964.html