Note: This article is open to everyone, as per Wikia. If you disagree with the effects of the initial brief, or want the brief to be slightly more accurate in itself, then please feel free to correct it.
The reality simply titled "No Abraham" reflects the state of the world in which early tribes and settlements around Israel never documented their tales of Abraham, thus eradicating all Abrahamic religions, including Judaism, Christianity and Islam. For the purposes of this page we will use the Common Era dating system, despite the obvious impossibilities of using this system within the reality itself. The page for this reality is under construction.
Scientists in the fields of physics, chemistry, biology and paleontology understand the current scientific theorems on the Big Bang, universal cooling, the formation of the Sun and the Earth that, most believe lead to basic biogenesis and, over three billion years, the evolution of basic cellular life to the Human Era, some 12,010 years ago.
It is believed that "modern man" (Homo Sapiens Sapiens) spread from central Africa outward, replacing more primitive forms of man (Homo Neanderthalensis, Homo Erectus) in Afro-Eurasia and then, through basic exploration, to Australasia and the Americas. The oldest civilisations followed either little to no religion at all or basic pagan religions that varied from area to area. None of these belief systems were what we today would define as an organised religion. The oldest religion known to man developed around around 3000 BCE, and over the course of a millennia became the organised religion we know today as Hinduism, most prominent in a large area of southern Asia.
The Turning Point
In around 2000 BCE, Abraham was born, and the tales around his life promised that a group of chosen people would own a promised land. Unlike Hinduism and practically all other neighboring faiths, this religion believed in a single god, Yahweh. The tales of his life, and the lives of his tribe and his God, are written by many different authors in the Torah, Qur'an and the Old Testament in the Bible. However, in this time line, a young Abraham died in his home town of Ur in Mesopotamia, changing world history forever.
There would have little effect on the development of the world for a good part of the next thousand years, but an area-wide famine would cripple the ancient Egyptians in 1600 BCE for the course of several decades. But that resilient nation survived to face the invasions of later empires to come.
With the absence of the Hebrews and their nation, pagan religions dominated the Fertile Crescent. Tiny tribal groups would vie for the possession of the land on both sides of the Jordan river, but were no match for the invading Assyrian, and later Babylonian, forces that would overrun the land down to the inhospitable Sinai desert. After that, the Persian empire would overwhelm the Babylonians, bringing their organized religion that had many similarities to the ancient roots of Hinduism. This religion, though, was of a more aggressive nature and would prove popular among the masses.
Effects on the Roman Empire
With no Jewish state having arisen, the people of Palestine gave little resistance to the Roman invasion and a vast majority of them ended up embracing the traditions of their invaders who have a far easier time controlling the area. Fast-forward several hundred years, and Jesus Christ never exists. There is no rise of the Christian faith, and the balance of the Empire doesn't have to deal with a religion that would deny the totalitarian claims of the Caesars.
The question of whether the empire would have benefited from the centralisation of its religion by Constantine in the long run is a controversial one. Some claim that Christianity caused enough ill faith amongst the pagan peoples in the empire that it shortened the Western Empire by several hundred years. Others say that the centralisation meant a smaller gap between people and state, and so it lengthened the Empire's run, preventing it from fracturing as it had done during Constantine's life. I agree with the latter, and for the purposes of this study I will assume that the many variations of religion within the state fractured the empire years before its real counterpart. What we are left with is several large ex-provinces that share common concepts along the lines of the same religion, which I shall now name Romanism. A lot of these different groupings are concepts that the Romans had adapted from those regions in the first place.
Effects on the formation of European States
The most prominent difference in the post-Roman European states is that paganism still richly thrived for the following centuries. Rather than the Monasteries and their libraries being Christian, they remained geared towards the Roman faith. There also was never the concept of the absolute monarch (a concept springing from the Abrahamic faiths in OTL) and therefore, somewhat more democratic governments emerged from the ashes of The Roman Imperial fragments. Full fledged democracy managed to arise centuries earlier than in OTL.
The lack of a common central religious authority throughout the continent meant that it was much more difficult to guard the Monasteries, meaning knowledge of the ancient world was constantly fought over by the Romanist and several different pagan religions. Because of this, Europe rather as a whole, different sections of it over a course of many years gradually left the Dark Ages.
With Byzantium in the East acting as a conduit of knowledge, classic style investigation of science was able to grow more rapidly throughout the continent without the resistance of a religion like Christianity and its generally negative reaction towards scientific thinking and discovery. Byzantium's fellow Romanist territories were the first to benefit with great effect and the rest of the continent shared the same experience slowly afterwards.
Due to the Celtic and Germanic paganism being more lenient towards gender equality, men and women among the said people faced a much faster rise in the ideology and it eventually spread into the Romanist territories.
The Middle East and Central Asia
Due to the absence of Mohammed's existence, the Arab people and the Peninsula which they lived was never unified through Islam and therefore the land remained divided under rule by different Empires over the centuries. With no Islam, the duty of securing ancient knowledge was taken up by Byzantium. The ancient knowledge spread much more smoothly and faster into the West than in OTL due to the continuity of thought provided by Byzantium and the unbroken line of Greek and Roman scholarship.
Rather than losing lands to the Arabs, Byzantium itself conquered proportions of the Arab Peninsula, including the Red Sea region which included Mecca and Medina. The two aforementioned holy cities of Islam in OTL simply remained average cities. The result of gaining territory from the Arabs rather than losing territory from them (which lead to Empire's decline in OTL), along with the Turks never being unified by Islam and wanting to conquer Byzantium, caused Roman culture to survive for at least three centuries longer than OTL.
Persia and its conquered territories remain Zoroastrianist, while Afghanistan remains Buddhist. Today, Central Asian countries such as Afghanistan, Kazakhstan, Uzbekistan and others remain divided between both Buddhism, Zoroastrianism and local Animist faiths.
Effects in the New World
Even though they did suffer greatly in number from introduced diseases brought by the European settlers, the aboriginal people of the New World along with their cultures and religions, managed to survive much more completely. This was because the Old world's pagan faiths and Romanism were much more accepting of others than the Abrahamic faiths.
In the absence of the Abrahamic faiths, Romanism, Germanic Paganism, Celtic Druidic faiths, Zoroastrianism and many Native American faiths remain dominant in the spiritual aspect of modern society. Holidays such as Passover, Hanukkah, Christmas and Easter as we know them exist in different forms.
The indigenous people of the Oil-rich Middle East, while still angry over the superpowers ransacking and dominating their lands over fossil fuels can do very little without the unifying effect of Islam and thus, instead of one large faction like Al Qaeda, there are multiple different small rebel groups who are quickly put down.
The lack of the Abrahamic faiths like Christianity establishing their codes for moralizing society resulted in a general more lenient attitude towards nudity and sex.
The calendral system in this timeline is still based around the Roman system of counting with Nones, Ides, etc.
Unfortunately slavery still exists in this OTL for the lack of anti-slavery movements, motivated by the Abrahamic religions during the industrial revolution.