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:

  1. Amata moves faster than the shield can react and punches you in the face.

  2. 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.

  3. 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.

  • Allow me to edit my theory slightly. Emphasis on a true passive reflection being subconscious, but at the same time its not like a CPU, thus its programming is very simple to allow it to process so quickly (like dealing with UV). The punch would under normal circumstances never hit Accelerator, which is how it bypasses his filter initially. However, once the punch begins accelerating away from him, it triggers the analysis, an accelerating fist at close range. Its deemed a threat, and the filter does what its programmed to do, reverse the vector. SO its more like a bug in the programming. – Ryan Jul 20 '18 at 17:40
  • @Ryan Still, even a normal touch could be classified as harmful. For example, what if a hand was infected wth disease or there was poison on it? Would the shield allow it? This we do not know for now. But, it is possible, so in theory, let's imagine what it is, perhaps, it would act according to your theory. But then I think about it, it is somwhat tricky in a way, i.e. the shield first registers the hand as non harmful (lets say it would for the purpose of speculation), allow the hand in. The hand enters inside the field and begins accelerating towards the shield emmitor. – Moe Epo Jul 21 '18 at 15:00
  • @Ryan The field register the vector as ' harmful " and switches the vector. The hand is now moving at the field emittor. The shield did what it is programmed to do and sits back idle. This is plausible, yes.. But there is one problem, which is whether the field would allow the hand to enter in the first place. Though there is not much place for discussing about this, as it could possibly be either way and we simply does not have enough info. And I advice you turn your theory into an answer, as as the discussion currently stands I think it has highest chance of being correct. – Moe Epo Jul 21 '18 at 15:02
  • (aside from my boring theory xd) It is not really a bug though but rather a missing feature. The point on which your theory stands is what Accelerator's Vector shield misses one feature: knowledge of it's relative position to the shield's emittor [Accelerator]. So, for instance if a punch is directed in Accelerator's way, it mighth have direction of "+150" but if it would suddenly have direction of "-120" it would ignore it even if the vector itself can be classified as "harmful" as it moves away from the position of the shield emmitor. – Moe Epo Jul 21 '18 at 15:02
  • Accelerators filter is powered by his brain. He can't do extensive calculations without slowing the speed down greatly, and more importantly, like a computer, it can only perform that fast because it was told what to do beforehand. Its set to flip vectors, and Accelerator never thought to program for a threat from the inside, figuring it could never get there to begin with. Such costly processing time to cover for a super rare and (in accelerators mind at least) effectively impossible situation, which also slows down the filters processing speed and increases mental burden, not worth it to him – Ryan Jul 22 '18 at 16:01

Incidentally, there's a wikia page for this technique. The fans call it the Kihara Counter.

As far as I can tell, the explanation is meant to be taken at face value. Later on in the light novels, other people have attempted to replicate the technique (or at the very least, demonstrated the potential to replicate the technique) with varying levels of success.

For example, in volume 19, chapter 3, part 8, Sugitani manages to land a hit on Accelerator using this technique, although he injures his hand in the process because his execution of the technique isn't perfect.

Wandering more into speculation territory...

This technique does seem a bit farfetched. However, I don't think the technique involves any light speed shenanigans. Both Kihara and Sugitani are humans without any special augmentations, as far as I can tell (although Sugitani does happen to be a ninja), so the technique ought to be achievable using human-level reflexes and speed (or thereabouts).

Keep in mind that although Accelerator's passive reflection may seem straightforward (just reflect all the things, right?) there is lots of complexity to it that leaves it vulnerable to exploitation. Let's review the details of his passive reflection ability:

  1. His ability can reverse any oncoming vector that comes towards the field.
  2. His ability acts passively and automatically. In other words, his ability can reflect high velocity projectiles such as bullets that he obviously could not consciously react to.
  3. He subconsciously establishes a filter that analyzes everything as harmful or not. This filter reflects any harmful things.
  4. His filter allows certain non-harmful things to pass through out of convenience. This includes gravity, air, pressure, light, heat, and sound.

The main vulnerability here is his harmful/not harmful filter. If his filter doesn't recognize the projectile as harmful, then it will get through. For example, Teitoku's Dark Matter wings manage to bypass Accelerator's redirection during their fight in volume 15 because Accelerator's filter doesn't recognize the exotic matter.

If you think about it, all of the harmful vectors that his ability reflects are incoming vectors. Bullets that go right toward him. UV rays that go right towards him. Shockwaves, explosion fronts, and so on that all go directly towards him. As a result, Accelerator's harmful/not harmful filter is probably very good at recognizing these sorts of threats.

However, a punch that goes right towards him and then stops right on the edge of his AIM field and then reverses is a very unusual edge case. I doubt his filter has much experience with vectors that follow this pattern. As a result, it's not implausible his subconscious filter would misclassify the fist as "not harmful" and then perhaps "harmful" again when the hand suddenly begins to accelerate in a reverse direction, and then perhaps get confused with the outgoing direction and cause it to reflect inwards.

If you're familiar with neural networks, there are lots of models these days that approach superhuman performance in various classification tasks, such as the ImageNet Large Scale Visual Recognition Challenge. However, it easy to construct adversarial data inputs that fool the classifier (for example, see High Confidence Predictions for Unrecognizable Images and One Pixel Attack Defeats Neural Networks).

In a similar vein, with Kihara knowing what he does about Accelerator's powers, I think it's quite plausible that with enough computing power, Kihara could figure out an adversarial vector sequence that could fool Accelerator's harmful/not harmful filter. Or indeed, as Moe Epo's answer suggests, it's also a possibility that Kihara implanted the bug/exploit intentionally.

However, it should be noted that once Accelerator figures out the exploit, he can easily adjust his calculations to take that into account. He has indeed done so with Dark Matter during his battle against Teitoku in volume 15.

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  • Actually sounds really clever, the Ability naturally reflects UV and such, but a punch is so slow by comparison it doesn't trigger. Even better, when the punch enters range, it is slowing down, and thus not a threat and bypasses the filter. Then he stops and pulls back the punch, but at this time, the more active part of his passive filter which decides everything else finishes processing the situation and recognizes it as a punch which must be reversed and automatically reverses it. Thus, the punch which is accelerating away from him is reversed into him, and we get the famous 1 inch punch. – Ryan Jun 26 '18 at 17:30
  • Well, Kihara's attack is obviously not like Kakine's "Dark Matter". The problem with this theory is that it ignores the point of speed of Accelerator's shield. If the shield can react at the speed of light it means Kihara's hand's velocity is switched the instant he comes in contact with Accelerator's shield and sends it away, leaving no room or place for any other 'shenanigan'. Kihara simply can not execute the trick of confusing the shield because he is relatively very slow. – Moe Epo Jul 20 '18 at 11:42
  • @Ryan your comment got me thinking, I will update the OP regarding this. – Moe Epo Jul 20 '18 at 11:43

My theory is that Kihara Amata indeed bluffs and in reality he actually implanted some subtle bug (perhaps activated by a particular soundwave as IIRC Amata mentions something about soundwaves) in Accelerator's power while he developed/researched it. We may ask why he did not just implant a bug which allowed him to disable Accelerator's powers all together and possible answer to that is that Amata could only create a bug subtle enough for Accelerator to not notice while using his ability and the bug could be only extended as far as to bypass Accelerator's redirection shield on contact and his "wind-based powers". This is the only explanation I can come up with which may be in-verse without just damping it on the authors despair to make a match for Accelerator and thus include PIS in his story, though even then I think my theory might be a bit far fetched considering that it's never mentioned again in the anime and as far as I read Toaru wiki, in the source material as well in any form. I admit this might be the only possible theory in-verse.

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Amata is pulling off a Supertask here. (Yes, that is as ridiculous as it sounds).

At every point in time before his fist actually reaches Accelerator, it is still moving forward, though decelerating. At the exact instant his fist actually touches Accelerator, it stops moving - nothing to reflect.

He then pulls his fist back.

Because his fist is touching Accelerator, it gets reflected - but because it's accelerating away from Accelerator, reflecting it causes it to accelerate into Accelerator.

It's not really a punch - more of a hard shove. This is especially obvious in a later scene where Accelerator's collar runs out of charge, and Amata starts 'kicking' Accelerator while he is down. The novel notes that if he was kicking him normally, he probably would have killed him.

(Remember, Accelerator is actually really fragile with his powers off - Touma jabs at him, not punches, because he is terrified Accelerator will grab his forearm and make him explode.)

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