Disclaimer: I watched only the anime. (And read Toarupedia)
In season 2 of Index we are introduced to Kihara Amata, one of the scientists who worked on researching Accelerator's ability. He attacks him head on which usually proves fatal for the attacker depending on their attack strength and punches Accelerator. Then Accelerator creates a wind tornado and attacks Amata. However, Amata dispels the attack into thin air.
Now the thing that bugs me is how he managed to punch Accelerator and the anime's explanation. Amata narrates what he is deeply knowledgeable about the inner workings of Accelerator's ability and points out that his redirection shield switches the directions of objects which come in contact with it and the trick to bypass it is to pull back your fist just at the moment of contact and the shield will switch direction of the fist which would be backwards right into Accelerator (or somehow the momentum of the punch and not the fist it is not perfectly clear to be honest).
The problem in this explanation is that we are quite often told that Accelerator's shield's speed is equal or faster than the speed of light because his ability reflects UV and other radiation (at least UV travels in speed close to speed of light) which means that to bypass the shield and trick it into letting through an attack Amata would have to move at speeds which are faster than the speed of UV rays or the speed of light, which is absurd even given the fact that he apparently replaces his hand with artificial one.
To illustrate, imagine what you are standing before a big Vector field which is slightly visible. It is of a size of a wall or something. You see Kihara Amata on the other side running at the wall going for a punch. There are few things what could happen here:
Amata moves faster than the shield can react and punches you in the face.
The shield's reaction time is much much higher than Kihara's time (and that includes calculations to determine whether the vector brings harm/no harm, as shown wth UV), Kihara moves his fist close to the edge of the field and then pulls back. Nothing happens, as the fist did not make contact.
The shield's reaction time is still higher than Amata's punch,but this time Amata goes for the punch-pullback on the edge of the field, entering it slightly. As shield is too fast for him, Amata breaks his arm moment he even makes contact with the field, and there is no time for him (as per his relative slowness of movement) to even begin to pullback, as the shield already made calculations and reacted with at least speed higher than UV.
The only way the punch bypasses the shield is if it's movement speed is faster than the field's reaction. This way, it is possible to just ignore the shield as it does not even have time to make calculations if it is slower than the vector's speed.
Even if for a moment we imagine that Amata invented a way for his hand to harmlessly move at the speed of light or rather faster than the shield can react as we are never told in the anime whether the shield has any speed limits, his punch would just go through the shield, and if Amata pulls back, shield still would not have time to react and nothing happens. However that Amata can give a punch that travels at the speed of light is highly doubtful, so we can assume that the trick is something else and he bluffs. But what is it? Did the guy who wrote the script decide to include plot induced stupidity or is there an in-verse explanation which actually makes sense?
Edit: @Ryans comment's about with theory of possible exploit of the the shield got me thinking. If the field decides whether to reflect or not, and let's some things in, perhaps it could be exploited by first just moving slowly and entering the field. The field would mark the vector "non-harmful" and allow the hand in. Then the hand would suddenly accelerate into opposite direction of the shield's emittor (i.e. Accelerator) and the shield would mark the vector as "harmful" and switch the directions of the hand. Though this seems odd now that I think about it more, because the moment shield would switch direction of the fist it would become "harmful" again, would not it switch the direction of the vector again this time away from the field emittor? Now, one other things I wonder about is why Kihara's hand when he punches Accelerator does not fly towards him and instead the momentum of the punch does? This is certainlynot the case with bullets, when the field switches their directions, they fly away, not the momentum of theirs. But in anime it is shown that when Kihara sends a punch to Accelerator, when he executed his trick, it's not his fist what goes towards Accelerator after being switched by the shield, but the momentum. Thois seems to leave much room for speculation (for example, would the field even classify a hand, of any velocity "non-harmful"? We never see in the anime and in other materials as far as I can tell from Indexpedia anyone touch Accelerator in a non-harmful way (aside from when Accelerator magines what a normal childhood would be like in Railgun S, but this is obviously in his head).
So far, it seems there is not enough information but as far as I see, @Ryan's theory seems to be the most plausible one.