In Modern Physics, there are two distinct forms of singularities which are (i) Black Hole Singularity and; (ii) Big Bang Initial Singularity. These so called ‘counter intuitive’ notions or concepts of ‘singularity’ are results of mistakes and misunderstandings rather than actual result taken from equations of mathematics. Development of scientific ideas is not outside the regime of epistemological principles. Scientific Knowledge is also evolved as progression of ideas. Ridiculous, non-sense or ‘counter intuitive’ ideas usually come from mistakes and not from genuine observations, deductions, inferences or mathematical derivations.
Ideas of above two kinds of ‘singularities’ are not older than early twentieth century though concept of ‘Black Holes’ can be traced to as early time as year 1783 when John Michell[i] first time pointed out the possibility of massive stars who could be able to trap light. He even provided the method to indirectly identify the presence of such ‘dark stars’ through the type of orbital motion of other visible stars in particular locality. Thanks to John Michell, he introduced genuinely possible concept of ‘black holes’ that was not based on ridiculous idea of ‘singularity’. The ‘super massive black holes’ that are now supposed to exist at center of galaxies are actually this type of non-singularity black holes. According to John Michell such ‘dark stars’ could have diameter as large as 500 times that of Sun. Therefore we see that original concept of black holes did not involve concept of singularities.
Following is a relevant quote from Wikipedia article on John Michell.
It was Michell who, in a paper for the Philosophical Transactions of the Royal Society of London, read on 27 November 1783, first proposed the idea that there were such things as black holes, which he called “dark stars”. Having accepted Newton’s corpuscular theory of light, which posited that light consists of minuscule particles, he reasoned that such particles, when emanated by a star, would be slowed down by its gravitational pull, and thought that it might therefore be possible to determine the star’s mass based on the reduction in speed. This insight led in turn to the recognition that a star’s gravitational pull might be so strong that the escape velocity would exceed the speed of light. Michell calculated that this would be the case with a star more than 500 times the size of the Sun. Since light would not be able to escape such a star, it would be invisible. In his own words:
If there should really exist in nature any bodies, whose density is not less than that of the sun, and whose diameters are more than 500 times the diameter of the sun, since their light could not arrive at us; or if there should exist any other bodies of a somewhat smaller size, which are not naturally luminous; of the existence of bodies under either of these circumstances, we could have no information from sight; yet, if any other luminous bodies should happen to revolve about them we might still perhaps from the motions of these revolving bodies infer the existence of the central ones with some degree of probability, as this might afford a clue to some of the apparent irregularities of the revolving bodies, which would not be easily explicable on any other hypothesis; but as the consequences of such a supposition are very obvious, and the consideration of them somewhat beside my present purpose, I shall not prosecute them any further.
— John Michell, 1784
Then comes the twentieth century where Einstein induced new spirit to mathematicians by giving them opportunity to find ‘solutions’ to his General Relativity equations. One early solution that emerged was by K. Schwarzschild[ii] whose work has now become basis of all the singularity based black hole physics.
The English translation title of his 1916 paper is “On the Gravitational Field of a Mass Point according to Einstein’s Theory”. The paper itself is too complicated to offer solid and consistent sense. But title of the paper is simple. It is talking about ‘Mass Point’ and the first impression that at least I get is that he is going to discuss gravity field in abstract mathematical terms. From the title, I am not getting the impression that he is going to invent brand new idea of a physically ‘massive singularity’. There is also nothing in whole paper that could indicate that he was talking about ‘massive singularity’ type of thing.
Above is a more relevant point in this paper where he was giving an example of ‘point mass’ equal to mass of sun. Well, if I write a book on gravity, I will also use similar examples. But instead of using term ‘point mass’ equal to mass of earth, I will use phrase “hologram earth with nothing solid but real gravity equal to the gravity of earth.” It will make simple for me to explain what should be the behavior of falling body if there is no solid ground capable to stop motion under gravity. Schwarzschild was trying to explain gravity field in this sense. But since his paper was too complex … It was prone to interpretation errors. Apparently same thing happened. He died soon after publication of this paper while some other Physicists, excluding Einstein, started taking this ‘point mass’ with literally real meanings and eventually these concepts became the basis of all the coming singularity based black hole physics. However Big Bang Initial Singularity was going to emerge from a different source.
The Big Bang Theory acknowledges Alexander Friedmann as its founder. Friedmann must be unaware of misinterpreted concept of singularity that emerged in year 1916. In 1922, Friedmann founded a genuine (not misinterpreted) concept of ‘monotonic world’.
The ‘monotonic world’ of Friedmann was not ‘point mass’ at all. Simply, it was radius of universe at time 0. Friedmann’s model is actually consistent with Steady State Model though in the Steady State model there is no time 0. Just like Steady State model, radius of universe is to be increased with increase (creation) of matter such that total density remains the same. According to Friedmann, at time 0, mass was also 0. His monotonic world was not a point mass – it was like a singularity which is not consistent with Big Bang Model. Following point in Friedmann’s 1922 paper clearly shows that radius of universe increases or decreases with increase or decrease of both time and mass content of universe and this thing aligns his model with the Steady State Model rather than with Big Bang Model.
Here ‘M’ stands for total mass contents of universe and x4 is fourth coordinate and denotes time. Its meaning is that with increase or decrease of time, mass content (M) has to increase or decrease. This point is clearly in line with Steady State Model and thus Big Bang Model is actually not supported by Friedmann’s model. And with this setup where mass is getting reduced if we go back in time, then at 0 time there has to be 0 mass. Hence Singularity of Friedmann is not consistent with the singularity of Modern Big Bang Cosmology where there is infinite mass (or density at least) at 0 time, 0 radius. And actually Big Bang model has no other source of initial singularity which means that essentially Big Bang Model’s ‘Initial Singularity’ has come from misunderstanding of Friedmann’s actual model.
By 1927 when Lemaître published his French article, he was not aware of Friedmann’s work. In 1927 article, there is no concept of singularity at all. There is a ‘pre-expansion universe’ which was static Einstein’s universe. But then ‘pressure of radiation’ caused equations to change (cosmological constant modified) and universe came under the rule of revised equations (revised by Lemaître himself). Thus Lemaître was unaware of singularities by 1927. Then it happens that in a meeting at a conference, Einstein told him that Friedmann had already talked about expansion stuff. Now onwards, Lemaître would start studying Friedmann and would misinterpret and absorb his ideas of monotonic world. In year 1931, Lemaître would first time talk about Primival Atom i.e. singularity sort of thing. For further detail, please see A Philosophical Rejection of The Big Bang Theory.