Dear Leshan,
''By definition, the velocity is the rate and direction of the change in the position of an object. For example, since light travels a distance ct during the time t, it is in agreement with the definition of the velocity.''
We can only speak about the velocity of an object with respect to objects if and when it interacts with them as it moves. Since the photon has no mass or charge, it cannot express its presence to the objects with respect to which it is supposed to move: having no mass, it cannot have a position. If it doesn't interact, exist to these objects nor the environment to the photon, then it makes no sense to speak about its velocity as there's nothing with respect to which it moves. This is why to the photon itself its transmission is instantaneous: it bridges a spacetime distance in no time at all even though an observer measures a time equal to that space distance. (All interactions the photon is supposed to be involved in as travels, all Feynman diagrams of all possible interactions with virtual electrons, positrons and photons, are actually taken care off at the photon source and receiver.) The idea of a photon as some kind of bullet buzzing from a light source to some random target across spacetime is a classical notion of what in actually is a purely quantum mechanic phenomenon. Since we assume that the universe evolves as a whole with respect to some clock outside of it, we assume the emission of the photon to (causally) precede its absorption elsewhere, according to that clock.
If particle A emits a photon which is absorbed by B, a transmission changing the state of both A and B, then A sees the state of B change at the time it emits the photon, whereas B sees the state of A change as it absorbs the photon. (That is, unless B after absorbing the photon sends back a message to A to confirm the receipt of the photon, a thank-you-note saying that A can from this moment start to see B in its new state). Whereas according to A and B the transmission is instantaneous, having no mass, to the photon there's no space nor time distance between A and B so to the photon its transmission also is instantaneous. Since to a massive observer A and B are separated in space and thus in time, he measures a transmission time equal to their distance. So if there's no time, no clock outside the universe to determine what in an absolute sense precedes what, then we cannot say that either A or B is the cause of the transmission, which is a requisite to be able to speak about a velocity. We can, therefore, only speak about a velocity if it is smaller than c. The difference is that at velocities < c, a bullet may miss the intended target, whereas at the 'speed' of light, the bullet only can be shot if and when it hits the target. For a photon to be emitted, transmitted requires the cooperation of the receiver, so quantum mechanics at heart is non-causal, which is why it seems so strange. The flaw of causality, however, is that if we understand something only if we can reduce it to a cause, and we can understand this cause only as the effect of a preceding cause etcetera, to end at some primordial cause which by definition cannot be understood, then causality ultimately cannot explain anything. More over time and causality you can find in my UPDATE 2 post above (Feb. 8).
Regards, Anton