The Rapture: Do we really leave the earth for heaven, or what?

In my last post, we looked at Matthew 24:40-41 which is often used to support the rapture but as we saw, those who will be caught up in the air are the evil, wicked ones, not the righteous believers. Now, what about 1 Thessalonians 4:13-18 which is often cited as Paul's description of the rapture. This passage has more to do with the message of hope for believers who have died, that they too will be resurrected from the dead.
1 Thessalonians 4:14-17 (ESV) 
¹⁴ For since we believe that Jesus died and rose again, even so, through Jesus, God will bring with him those who have fallen asleep.
¹⁵ For this we declare to you by a word from the Lord, that we who are alive, who are left until the coming of the Lord, will not precede those who have fallen asleep.
¹⁶ For the Lord himself will descend from heaven with a cry of command, with the voice of an archangel, and with the sound of the trumpet of God. And the dead in Christ will rise first.
¹⁷ Then we who are alive, who are left, will be caught up together with them in the clouds to meet the Lord in the air, and so we will always be with the Lord.

Notice that Paul does not mention believers leaving, but rather says we are caught up together to meet the Lord in the air. The word meeting here is apantesis which means going out to meet a newly arriving dignitary. This passage's emphasis is on Jesus' triumphant return, not our departure from the earth. Paul seems to be invoking Jesus' triumphal entry into Jerusalem when the crowds went outside the city to welcome Him.

1 Thessalonians 4 deals with the coming of a king and in the Roman Empire there was a way a King was to be welcomed. According to scholars like N.T. Wright, if Caesar decided to visit a Roman city, He would take his imperial ship to the nearest bay and ride from the boat on his chariot surrounded by the Roman legions. He would journey to about a mile outside of the city and then he would command his chief soldier to shout the command to his trumpeteers to alert blow their trumpets to alert the city of the King’s presence. All of the city’s residents would then file out to meet the king and then escort him back into the city.