I have heard everything from 1683(siege of Vienna) , to the late 1500s, & the 19th century .
So, what date is it & most importantly why can't the internet agree upon a answer.
People can’t agree on the beginning of the decline of the Ottoman Empire partly because the decline was not linear. There were periods of decline and periods of resurgence. The definitions of “decline” and “begin” might also be different for different people. Finally, perspective matters. The “beginning of the decline” of the Ottoman Empire might look different from Persia or Russia, or Egypt, or Austria, or Rome, or Portugal, or Constantinople.
I suggest that one possible “beginning” of the relative decline of the Ottoman Empire might have been when they (together with allies) lost the naval battle of Diu to the Portuguese, in 1509, and failed to regain control of the Indian Ocean.
This allowed the Portuguese to set up an alternative trade route (by sea around the Cape of Good Hope) between Europe and the East, which bypassed the routes controlled by the Ottomans. This deprived the Ottomans of a source of income and wealth, and increased the wealth of the Europeans (through profits made by the Portuguese and later others, and because Eastern goods became cheaper in Europe, and less wealth flowed out of Europe towards obtaining them). This might be seen as the start of a long shift in relative wealth and power, which led eventually to the decline and downfall of the Ottoman Empire.
Since Vasco da Gama arrived in the Indian Ocean in 1498, the Portuguese had been fighting Calicut and allying with the Kingdom of Cochin, to establish a spice trade back to Europe around the Cape of Good Hope and undercut the old trade routes through the Mediterranean which were controlled by Mamluk Egypt, the Ottoman Empire, and the Venetians.
In 1507, the Ottomans sent disassembled galleys to Egypt, which were reassembled on the red sea coast. These Turkish galleys, together with Mamluk vessels ventured into the Indian Ocean and surprised a small Portuguese fleet at Chaul in 1508. They captured one of the Portuguese ships and killed the Portuguese commander, Lourenco de Almeida. The rest of the Portuguese ships escaped.
The Muslim fleet then sailed to the port of Diu.
The Portuguese viceroy in the Indian Ocean was Francisco de Almeida, father of the commander who had been killed at Chaul. He was determined to defeat the Muslim fleet, both for strategic reasons, but also for revenge. He sent the Muslim fleet a message saying that he was going to revenge himself on them, and that if they did not fight he would take the City of Diu.
Such was Francisco’s thirst for revenge that he threw his replacement as Portuguese Viceroy in the Indian Ocean into jail so he could not interfere with or take command of Francisco’s naval war.
The combined fleet of the Mamluks, the Ottomans, the Sultan of Gujarat and the Zamorin of Calicut, amounted to 12 major ships (6 carracks and 6 galleys) and over 80 smaller local dhows.
Franciso assembled 5 large ‘naus’, four smaller ‘naus’, four ‘caravelas redondas’, two ‘caravelas’, two galleys and one ‘bergantim’, and sailed these 18 ships to Diu.
The Muslim fleet decided not to come out to attack the Portuguese, but to defend the harbor of Diu, protected by the cannon of the harbor forts.
Francisco sailed straight in with all guns blazing. The entire Muslim fleet was destroyed or captured with great losses of sailors and soldiers. The town of Diu was taken.
The strongly built, seaworthy, and powerfully cannon-armed Portuguese ships were the key technology which enabled the Europeans to dominate the Indian Ocean. No other power in the vast area could compete with this technology. No other power proved able to rapidly copy or duplicate this technology.
Franciso said, “as long as (we) may be powerful at sea (we) will hold India…If (we) do not possess this power, little will avail a fortress on the shore.”
The Ottomans made several subsequent attempts to reverse the defeat at Diu and re-challenge Portuguese control of the Indian Ocean. In 1538, they sent 54 ships to besiege Diu, but suffered a crushing defeat. In 1547, Suleiman the Magnificent sent another fleet to attack Diu, but this was also defeated, marking the end of Ottoman attempts to gain control of the Indian Ocean.
http://forum.worldofwarships.eu/index.php?/topic/2462-naval-battle-of-diu-indian-ocean-1509/
http://en.wikipedia.org/wiki/Battle_of_Diu_(1509)
Of course it was not very obvious at the time that this might have been an inflection point for the Ottoman Empire. It continued to expand and trouble its neighbors for a long time.
After the Battle of Diu, the Ottomans were heavily involved in expanding into Europe. In 1521 they captured Belgrade. In 1522 they conquered Rhodes. In 1526, at the battle of Mohacs, Suleiman the Magnificent defeated Hungary and Bohemia. In 1529 The Ottomans besieged (failed) Vienna. In 1533, they conquered Iraq (taking a break from European operations). In 1541 they conquered Budapest. In 1551 they took over Libya.
In 1571, however, the Ottomans lost the great naval battle of Lepanto in the Mediterranean against the forces of Venice, the Pope and the Hapsburgs. Although it would not be readily apparent for another 100 years, this is often seen as the beginning of the decline of the Ottoman Empire.
It might be possible to assert that the beginning of the decline was even earlier in 1509, when the Ottomans lost the battle of Diu and could not regain control of the Indian Ocean from the Portuguese. This gradually reduced Ottoman wealth from controlling the spice trade, and increased Western European wealth.