In many anime, comics, movies, etc, we see a lot of super human beings moving and fighting at such high speeds that a regular human being cannot see that they are fighting or moving pass by.
In particular, in the first battle between Goku and Piccolo, those two are able to fight in a confined environment (when Piccolo first appears in the comics, stage fight, if I remembered correctly), and regular audiences are unable to see them when they battle.
Is it physically possible for a "human" (human size object) to move in a confined environment (let's say, $20~\text{m} \times 20~\text{m} \times 10~\text{m}$ ) so fast that a normal person would be unable to see it? If it is possible, how fast must this "person" be?
Assume that this "human" cannot move faster than, or even close to the speed of light.
Some clarifications:
First, please ignore the strength/physicality of the object, and consider it an object that can can move "freely" in this confined space without causing any "side effects" (such as heat, sounds, etc)
Second, please take in note that the object is moving in a confined, rather small 3D space as mentioned in the question, and the observer would be always able to see the entire space.
And last, a blurred image would be considered as "able to see".
Answer
Let me start by clarifying that I assume the question is whether a superhuman or any object of human size can render itself invisible through speed alone. And that the speed of said object must be $v\ll c$. From this, I assume that the object or person being viewed must spend a reasonably long amount of time within the observer's field of view such that invisibility can't be cheated through exploiting blinks or by having too short an exposure time or by hiding behind the observer most of the time.
In short, no, it is not possible for something to move fast enough that a normal human would cease to see it entirely. Firstly, at any velocity, the amount of light that is redirected from the moving object to the observer is reasonably constant. At relativistic velocities, length contraction of the moving object in the observer's frame could reduce the size and, thus, visibility of the object; however, the previously mentioned speed restriction allows us to ignore any contraction of this magnitude. Additionally, the human eye-brain system processes input continuously and uses as-yet not completely understood processes for extrapolating and interpolating motion. In fact, even when presented with rapid images of the same object at different locations, the brain has the ability to assume motion and perceives these images as being continuously linked; something referred to as stroboscopic motion or illusory motion of stroboscopic images. Since the objects moving quickly still have light shining on them, the light that reflects towards the observer would still be captured and processed. However, since image processing is a complex task and due to something called persistence of vision, the images we perceive can include not only the light that recently entered your eyes, but also parts of previously perceived images. Therefore, at higher speeds, the image an observer gets would probably be blurry as it is an amalgamation of the moving object's position at multiple times as well as an effect of small eye movements; this is sometimes called motion blur.
However, while it is not possible to disappear entirely, there are other and cooler things that are possible. Because of the processing speed of the eye-brain system and the illusory effects that can be created from the brain's extrapolation of data, it is entirely possible for an object to move fast enough that it does not appear to move at all. If Goku and Piccolo fight each other at an extremely high speed, but they make sure to periodically spend most of every, say, second in one specific position, then the images your eye captures will be mostly of them in those specific positions. As a result, they will appear unmoving to an observer (except, of course, for mysterious cuts and bruises showing up and their edges may appear slightly more blurred). Additionally, by spending an equal amount of time in two different locations (and with the help of perfect timing) it can appear as if there is two identical and slightly faded/blurry copies of the moving object. This effect works for creating large numbers of copies and can also be used to make the image appear to "jump" from place to place.
Some have argued that an extremely fast moving object can blur so much as to be indistinguishable from the background. This may be true, however it is more dependent on the contrast between the background and the object than on purely its speed. Once camouflage and things of that sort are ruled out, there is simply no non-relativistic speed where a human-sized object in a confined space can become invisible to an ideal, normal human observer for an extended period of time.
Let me further add that at relativistic speeds, it's possible for the light reflecting off the moving object to be red or blue-shifted outside of the visible spectrum (although, in the case of blue-shifting, the object's own heat, ie IR emissions, would be shifted into the visible range). This could make the object invisible (and would be really cool to see happening), but as the question requires speeds "[not] even close to the speed of light", that rules out the possibility in this case. Additionally, since it is in a confined environment and the red-shifting effect only works for when the object is travelling away from the observer, the invisibility effect would not last long enough to be considered sustainably invisible.
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