Here's another theory that is missing a few features to make it wholly robust, but work with me here.
Green Bull has a radioactive devil fruit (a 'Radioactive Man', if you will).
I will get to the specifics, later, but now I draw a comparison between scientific thinking prior to and following Columbus' journey to the Americas, the New World.
Prior to this, science was, largely, an attempt to explain the actions of God; whereas, as the Renaissance lurched forward, so did ideas of the Enlightment and rationalism. Effectively, science had become a practice of understanding how the world works. Admittedly, this is a painfully reductive summary of what took place; however, I want you to take the spirit of thoser statements on board.
To roughly translate this into One Piece, pre-timeskip consists of a pre-Columbian thought and perception; post-timeskip refers to the Enlightenment era following the discovery of the New World on the Grand Line, which, obviously, shares its name with its real world counterpart.
The example is best shown through the admirals. Aokiji, Akainu, Kizaru have powers that resemble godly power or fury: Aokiji possesses a DF power that most closely resembles a great deluge, much like in the story of Noah; Akainu, seemingly, summons the fires of Hell; Kizaru embodies the light of God. Moreover, their fleet Admiral is a massive, shining, representation of a godly figure.
It is a very rough translation, but the interplay of powers between Akainu and Aokiji reminds me of the Classical Elements (Fire/Water/Earth/Wind), which embodies that idea of classical thought; whereas, Fujitora's gravity DF represents one of the four fundamental forces (Gravity/Magnetism/Weak and Strong Radiation), which, clearly is a very recent development in the history of science.
Obviously, there are some holes: Akainu becomes Fleet Admiral and Kizaru remains an Admiral, which suggests a continuation of Classical Thought; the Classical Elements DF users do not exist solely amongst the ranks of admirals; the only other Fundamental Force user, Kidd, is a pirate. Let me address these concerns one-by-one.
Regarding Kizaru, I think the perception of light has changed rapidly over the centuries. Once, it was the light of God and now it is a particle and wave, which has led to new developments in Quantum mechanics; effectively, Kizaru's power has come to represent something totally different.
This is supported by Akainu's promotion, or perhaps, Sengoku's resignation/retirement. Essentially, the representation of God, faith and worship stepped away for a walking volcano. On one hand, this could be a symbol for God giving way to the fires of hell; however, it also shows how our perception and understanding of volcanoes has developed. Akainu's power is that which creates new lands and pushes and pulls continents. With greater scientific understanding, magma is no longer something daemonic, but something radically creative and essential to the rock cycle. Fundamentally, once gods stepped aside, we began to understand the true potential or power of magma, we began to become rational, enlightened, scientific. In effect, rational thinking has taken hold of the Navy, as opposed to god worship.
Due to the water weakness of DFs, I am aware how flimsy the 'original admirals represented the Classical Elements' may seem. Explicitly, we haven't encountered a wind user (although, Dragon seems to be the guy); the closest thing to earth would be Caribou with his swamp logia. Therefore, wind bears a question mark; however, I would like to offer Whitebeard as a candidate for 'earth', from his earth shattering DF. I say this because he, like Sengoku, were eclipsed, in one way or another, by a new generation of characters, themes, representations. Despite not being an admiral, Whitebeard typified this classical way of thinking. This is a wild diversion, but he always reminded me of a Confucian 'father of the house' figure, which, of course, is an ancient, pre-Columbian philosophy, although, I am aware that throwing chunks of Western and Eastern ancient philosophy is flawed and perhaps, dangerous, I think that Oda has combined a lot of different cultural perspectives in his work, with differing levels of success, of course.
If Whitebeard represents the 'old way', then Kidd's magnetic DF represents the 'new'. He was always widely tipped as Luffy's greatest rival from his generation; although he was introduced in Paradise, it was at the very end, almost signalling a new chapter. Also, recall the time he crucified those pirates in the New World - they begged to return to Paradise and he chastised them for trying to return to that place, and by extension, that old way of thinking.
To return to Green Bull, however, I want to envision Akainu's navy as a 'house of science', with Fujitora's gravity and Kizaru's quantum mechanical light as constituent figures; whereas, Sengoku's was a 'house of faith', with his admirals able to perform acts of God. Following the fundamental forces reasoning, gravity and magnetism have been taken, so what's left? Strong and weak radiation. I highly doubt these will be fleshed out as individual DFs, and instead rolled into one. I think this would be a totally brutal DF, and that's one of the reasons why I'm sceptical: would Oda really have a character suffer from radioactive poisoning? Of course, there would myriad ways to overcome this and to make this a viable DF. Whatever you say though, it would be very powerful.
This post went on far longer than anticipated. I hope I've addressed most of the holes with relatively reasonable answers, although, trying to balance quantity and quality is really difficult sometimes. Please let me know what you think.