Search teams have reportedly found the boots and helmets belonging to two Turkish aviators whose plane was shot down by Syrian forces last week, but there's still no sign of the pilots themselves.

Top Turkish officials announced today the helmets were found among the two-seat Air Force plane's wreckage, Turkey's prominent Hurriyet Daily reported. No parachutes have been found but the flyers' boots were discovered days before, Turkish Prime Minister Recep Tayyip Erdogan said.

Erdogan said it was unclear whether the pilots had been able to eject before the plane went down.

But that might not have mattered, according to former fighter pilot and ABC News consultant Steve Ganyard. The plane that was hit, reportedly a reconnaissance version of the F-4 Phantom fighter, is an old but extremely fast aircraft, capable of flying at over twice the speed of sound. Ganyard said that even if the pilots managed to eject, it would've been difficult for them to survive the ejection alone and it's possible the sheer wind blast could have ripped the helmet and boots from them. If the pilots were unable to eject, Ganyard said, a plane as fast as the Phantom could have hit the water "as if it were concrete" - spreading debris wide and leaving little intact.

Still, the search continues.

In addition to the mystery of what happened to the pilots, Turkey and Syria continue to disagree about what led to the shoot down in the first place. In a letter written to the United Nations early this week, the Turkish government claimed the unarmed plane had been flying in international airspace when it suddenly came under fire from Syrian air defenses. After being hit, the plane turned and entered Syrian airspace before crashing, the letter said.

But a day before that letter was sent, a top Syrian official told the Syrian State News Agency that the plane had "blatantly" violated Syrian airspace and the shooting was a defensive and sovereign act. J. Makdessi, a spokesperson for Syria's Foreign and Expatriates Ministry, said the jet had gone deep into Syrian airspace before it triggered an automatic air defense system.

The incident prompted a stern warning from the Turkish government about future military action and NATO condemnation, but the father of one of the pilots urged restraint from his leaders.

"It is not appropriate to go to war over a pilot, an airplane or 50 airplanes," Ali Erton, father of missing pilot Capt. Gokhan Ertan, told a Turkish television station. "What matters is that my son serves his country… I am a man of faith and do not believe martyrs ever die."