If airplanes' highest speed depends directly on the air it is moving through and not the ground,

If airplanes' highest speed depends directly on the air it is moving through and not the ground, does it mean we can build a time machine if only the air moves near the speed of light?

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The downvotes are a bit unfair since you ask a good question. You're really asking about the relativistic addition of velocities i.e. if the plane is moving at 0.9$c$ and the air is moving at 0.9$c$ then is the plane moving at 1.8$c$ relative to the ground?
You probably won't be surprised to find that the answer is no (Einstein was right!) because the simple rule for adding velocities $v = v_1 + v_2$ does not work for velocities near the speed of light. You need to use the relativistic formula for adding velocities.
@LelaDax: oops, sorry. Making the air travel at near $c$ seems considerably harder than making some form of craft travel at near $c$. How would you do it? A big fan? – John Rennie Jan 11 '13 at 9:27