How did the gold of the new world cause the Spanish Empire to collapse?

No use having an advanced army if you can not keep it in time . It was also expensive, was a proffessional army, which forced to have a healthy economy. The fact of not having it brought to Spain several economic cracks at the second half of XVI. century. A proffessional army with gun artillery since XIV. century and firearm since XV. century. Those advances werent seen in other european country until XVII. century.

If the gold was the real problem of Spain the Spanish empire will no take long far from XVI. century. The real problem of were from 1780-1876.

1º When French bourbons arrived to Spain he drove the textile industry and modernized the army and navy as the same level as European country. While the mining and agriculture industry was still outdated. From 1714-1780 maintained its empire and even recovered Italy from Austrian hands and defied English power. However, it was only a shadow and in 1780 the political and economical crisis started. Nor Agriculture nor Mining was updated and the production was too small for that years and furthermore, there was the mentality of politicians to go forward to the liberal and parliamentary monarchy.

2º 1792-1814: The War against Napoleon ended with 2-4% population killed, textile factories destroyed, the navy nearly complete destroyed and the political crisis between liberals and absolutist started. 1814-1876: Civil wars and political instability provoked a great chaos and Latin-america take advantage of the empty power. That marked the lost of the most part of the American colonies. Between 1876-1929 was the rapid recovery, the 1st industrial revolution done it and the start of the Second one (battleships, machine guns, destroyers, submarines, radio, pharmaceutic, automotive, aeronautic etc...). However, the new innovations not arrives to the army until the first decade of the XX.century. Spain couldn't hold the American colonies but the African colonies just in time.

From a monetary stand point gold is always deflationary. Silver being inflationary. Contrary to the idea of Spanish gold. Spain never received a surplus amount of gold. It wasn't until the mid 16th century that Spain discovered large deposits of silver in Peru, Mexico and Bolivia. These deposits largely fuelled a wave of trade in china. The escudo or the gold coins were very rarely minted because gold was not the greatest deposit found- silver was. Silver coins were struck making the price of currency cheaper. Thus driving the gold prices up. Gold will always be a rarer commodity than silver and that is a fact. In turn Spain was disappointed in the amount of gold recovered. However all the Spanish silver coins fuelled trade with the orient. Silver for silk was the trade. Inflation was due to the surplus of silver not gold.

John Maynard Keynes indirectly answered this question in his 1930 essay "Economic Possibilities for our Grandchildren," http://www.econ.yale.edu/smith/econ116a/keynes1.pdf, in which he traced the development of Britain's capital account directly to the capture of Spanish Treasure by Sir Francis Drake. Essentially Queen Elizabeth I was able to pay off the (remaining) national debt and invest 40,000 pounds. Given the "typical" one-fifth royal share, the total amount was somewhere over 200,000 pounds for British investors in Drake's "venture," with even greater losses for the Spanish.

Basically, gold shipments made Spain feel wealthier than they actually were. Or put another way, they had budgeted for X, and were X-200,000 pounds poorer after Drake's depredations. Overspending (or losing) a large part of one's budget is a sure way to economic decline.