TIL Super Saiyan 2 Goku's hair is the same length of his normal hair, but when he transforms into SSJ3, his hair starts growing and becomes pretty long.
Even if the hair grows while in SSJ3, it should not shrink back when he's returns to normal. The growth could be the result of the pressure exerted from his body, but shouldn't shrink back when he's normal.
Is there an explanation for that or is it just the way it is?
Before we begin an answer:
I prefer honestly saying that there is no answer for this (or I personally never saw something that answers that on the web), but we can use some deductions from what we know and experienced from the long series of the anime.
As we already know from Dragon Ball, the trademark characteristic of the transformation is the user's hair, it goes golden yellow at the Super Saiyan 2 level as a representation of achieving a higher level of energy.
I guess you could also ask:
why does his hair goes golden yellow at the first place ?
For me I know no reason of getting hair color changed when rising the energetic level, but by assuming that saiyans are a different race than humans, we could explain it as a result of the rise in Ki consumption, for example in SS3 :
The rigid hair of the Super Saiyan 2 state becomes flowing and smooth again, and grows down to or sometimes passes the user's waist. The eyebrows vanish completely, making the forehead and eye ridges appear larger and revealing a more prominent brow ridge. A small increase in muscle mass is evident, and muscle tone is sharply defined. Energy radiation is so great that the aura pulses at an extremely high frequency, almost to the point where it seems static; the sound of the aura is also pitched even higher than that of Super Saiyan 2. Bio-electricity, like in the Super Saiyan 2 form, is again constant, and may reach further outward from the body than before. The Saiyan's voice may become slightly deeper, though this is obviously a feature only found in the anime. If the user of the Super Saiyan 3 form has a tail, it turns yellowish gold.
So as a personal explanation:
I can say that just like when you eat a lot you get fat (as a human), when you open your body for a perfect Ki consumption (as in SS3 level) your hair will grow as long golden yellow (as a Saiyan).
And as a remark:
The body must change the morphological shape to achieve a higher efficiency in using the current level of energy for combat (for example largest muscles in SS3, tallest in SS4 .. etc), and as one can deduce: hair has no effect on the combat course, but personally again, I think the complete opposite: the hair style may cause more effect than muscles, it have an impact on the moral and psychic state of the enemy, to make it even clear:
Just like the lion is scary with large hair, so is the saiyan in SS3, he looks stronger sometimes more than what he really is. Unlike what was the small evil Boo, his physical appearance didn't show his strength therefore it had no impact on his enemies (Goku and Vegeta).
I have to say that the bulleted answer that I just read was incredible, and a lot can be taken away from that to understand the Saiyan race. In my eyes, the Saiyan's hair is a very key part of their ki control, their physical stature, and their own understanding of themselves. I believe it was Vegeta who said to Bulma that a Saiyan's hair never grows, it never changes (to paraphrase, of course).
Saiyan's hairstyles and strengths
It does not seem that the length of a Saiyan's hair is immediately related to the base power of the Saiyan. The Saiyan saga made it quite clear that Raditz is weaker than Nappa is weaker than Vegeta, and the lengths of hair do not grow shorter or longer in that sequence, as Nappa is bald and is stronger than Raditz (according to Team Four Star, Nappa is 5Raditz, lol). It's possible that I'm wrong, and Raditz had unrealized potential to be unrelentingly strong but was too mentally weak to achieve it. However, I don't believe this to be the case.
Supers and their hair
Now onto the relationship between the hairstyle and Super Saiyan abilities. To make a note, all the Saiyans we know to have achieved a true Super Saiyan form, had hair. This is minor, but makes the analysis a whole lot easier. Goku and Bardock were the first two Saiyans in known history to transform and they had the same fairly short, spiky hairstyle. Vegeta's early SS form was a bit invalid in my opinion, as he forced his way in, like achieving full meditation with help from drugs. However, his hairstyle is in many ways very similar to Goku's, which I will comment on in my next point. Goten, same hairstyle as Bardock and Goku, and as far as Trunks, that's just a different story, I'll make a side point in the end for that.
Goku vs. Vegeta
So what is the difference between Goku's hairstyle and Vegeta's (in base form)? If you look closely, their hairs are actually quite identical. I've never counted the spikes, however. If Goku's hair was forced upward I feel that they would be the same length and style. This opens up to my real idea of what the hair represents. On Earth, martial artists have the ability to suppress their power, not hide, but suppress. Vegeta learns this, proving he never had this ability before coming to Earth. So while Goku spent his life only bursting his power at the moment he needs it, Vegeta has always pushed himself to the limits at all time. I believe their hairstyles resemble this. Goku is always at peace and relaxed, so I believe his hair is relaxed and does not flow as much ki. When Goku uses the Kaio-ken, his hair rushes up for just a moment.
A channel for ki
So all in all, my theory is that a Saiyan's hair has no cosmetic value, and is a direct representation of their average ki consumption. When Goku and Vegeta transform, their hair is passing far more ki than normal, and this causes it to stand up and resemble their aura. For all known Super Saiyans, there is a gold aura, however we do not know that this is always the case. Perhaps the SS of legends, thousands of years ago, had a green or red aura. However, Goku and Bardock have a golden spirit aura and Vegeta learned to transform by watching Goku, resembling his technique and passing it to his son Trunks (again, not getting into that little bastard). Broly's final transformation had more of a green aura as well, but I'm not an expert on the movies.
SSJ1-SSJ2-SSJ3
The typical first transformation involves the hair turning from black to gold, and the eyes turning bluish-green. The next transformation involves the hair to flow even more forcefully upward, the aura to grow sometimes with lightning, and muscle growth. Then the transformation to SSJ3, which I have only seen done by Goku in the greatest scene ever, involves the obvious growth of hair, more muscle growth, and some major facial changes.
SSJ3 analysis
Now I think I'll get to my opinion on the question that was asked. In the SSJ3 form, not only do the eyebrows disappear, but the entire forehead grows severely. It seems to me that the top of the head and base of the hair is the last biological point in the body which passes ki, and the growth of his cranium is no doubt to accommodate the intense flow of ki. The eyebrows may serve as an auxiliary port for key to enhance vision and the senses, or even just to project ki in different directions. However, when the body must focus enough energy to reach such a high level, such accessories are pointless, therefore they vanish into the flow of ki. When I watch Goku transform for the first time on Earth, I see him not only intensify his own energy, but taking it in from the world, like a slowly expanding spirit bomb in a way. The clouds fly towards him, the grasses bend his way and all the trees shake immensely. His body is at that point holding far too much energy to handle and he must adapt his physical body to survive and use that energy. This is where the hair reacts and becomes much larger to allow him to hold the energy a little longer and direct his power much more finely. This doesn't answer the question how hair could just grow and shrink, but the idea is, maybe instead of calcium and proteins, a Saiyan's hair is made of raw ki.
Trunks
I promised to make a side note on how Trunks' hair works, so here it is. Trunks can go screw because I don't want to think about the one hole in my entire theory. Bulma is ruining it YET AGAIN and I'm sick of her s**t. SICK OF IT!
Maybe it is because a saiyan's eyebrows disappear due to the increase of muscle around the eyes, there for increasing their sight ability furthermore.
The hair length though. I'd say it's half cosmetic just for intimidating purposes but also because it has a deeper meaning. The hair styles with saiyan's personally, going off human hair, means nothing. But the increase of hair length of a Saiyan hair being that it increases in length through base form - SSJ3 (yes it does increase slightly). This maybe a way of cooling the body down or an outlet for excess energy that the body needs to exile or does naturally. I don't believe it to be an energy channeler as there isn't any evidence and it make no sense, but that's clearly my opinion.
As to the original question as to why the hair increases and why this change is not permanent maybe due to the fact that the body undergoes mass physical changes to adapt to the physical and physiological needs to the present form, or even just a simple side effect of the transformation in which the changing of the hair could all just be a coincidence and an unintentional argumentation.
When the user "retreats" (and I use that term loosely) the side effects or the augmentations due to the transformation are reversed due to the transformation "retreating" and no longer in effect.
I.e. Like when a smoker starts after a while their lungs get worse but as they start to quit, their lungs become better. Same theory applies. Not being in that state returns the body back to its original form.
Hope that solves your question and others as well, I hope someone finds my theory to be interesting.
This isn't an answer, but rather a theory:
Just like when your hair becomes charged from static buildup and begins to rise, when a Saiyan goes Super Saiyan, their hair becomes super charged with Ki energy to such an extent that it literally begins to glow, resulting in a blond appearance.
As this charge is pushed to greater extents, the focused charge pulsing from root to tip not only glows outward from the shaft, but also fires a visible laser like beam of light from the tip, resulting in the apparent lengthening of the hair.
As this charge is pushed to EVEN greater extents, the visible distance of this light is amplified, and the space around the hair begins to distort, further "lengthening" the hair, as well as amplifying it's volume.
