First some short introduction about infinities and singularities. For example lets imagine some company which is manufacturing computer chips and is planning the increase of production in next years. They have some equation which is producing the increasing number of chips based on some production parameters. And they get number like 150 mil, 180 mil following year, 250 mil and then they get infinity for the next year. They know for sure, that there is some error in the equation or in parameters and they will find it and fix it. On the other hand in physics the situation is not that simple. Some physicist have the opinion, that if you get infinity aka singularity, the equation is wrong and it has to be reworked. For example Dirac was a proponent of this direction. Then there are pragmatic people like for example Feynman, who removed infinities by dividing infinity by infinity, but the usage of such nasty tricks is quite limited. And then there are kind of priests of physics, who preach kind of divine mystery of infinities or singularities and present it like special magic thing to wide audience in popular media. These are people who are perfectly OK for example with the infinite density of black holes. Personally, I think that the main source of infinities in relativity is Lorentz factor: Please Register or Log in to view the hidden image! This equation was tested many times and always passed the tests, so we can be quite confident that it is quite right. But the way it is constructed is always leading to infinities if the speed or the process related to speed reaches c. I think, there could be some better version, which would still be in line with observations/experiments and would not lead to infinities. In such improved version you have to ditch c and replace it with some other value, lets call it X, which would serve as a temporary value until it would be identified if there is some physics meaning of it and converting it to a new constant. The idea is to replace Lorentz factor with new equation which would give almost identical shape of the graph until you reach c, and then it would give some extremely high number, but not infinity. The main question is how to construct a new equation, which would give such shape of graph and deviate only at speed of c and above. Is there some tool out there which could help with such task? I have tried it with GeoGebra, but was not successful yet.