return to homepage WHY THE SINGULARITY CANNOT EXIST
Some have still not understood my contention that mass cannot exist at a point, and that the point cannot exist in physics. Since this contention is at the heart of my critique of the calculus, General Relativity, QED, and string theory, I thought it best to give it a paper of its own.
This is of utmost importance in modern physics because these modern mathematical spaces treat the point as the unit. In trying to create a field as the generator of the motions of mass points, Einstein was trying to assign zero to the unit in his math. His mass points are his units, you see. The numbers we find in solutions apply to them, so they are the units. But points as units is a pre-Stevin idea: it is a 16th century idea. Modern physicists and mathematicians are not more sophisticated than Galileo and Copernicus, they are less sophisticated. The same can be said of QED, which does the same thing. As in GR, QED lets mass act as a unit. When QED finds mass at a point, it has assigned zero to its unit. This is why its equations have been rebelling from the beginning. This is why QED requires renormalization. When you assign zero to the unit in your math, your math will implode. It will start spitting out zeros and infinities, and this is what causes the need for renormalization. Renormalization is the getting rid of these pesky zeros and infinities, by a sort of mathematical conjuring. As I have shown, GR has equations that rebel in the same way. The field equations often implode, giving zeros or infinities as solutions. This is precisely what is happening in the math applied to black holes or to the big bang. The math is imploding, just as in QED. But rather than renormalize the field equations, physicists prefer (for some reason) to accept the infinities and zeros, giving them mystical interpretations. In QED, they don't like the singularities and infinities, so they renormalize them away. But in GR, they have found a use for them. In GR, they have made a physical object out of the mathematical failure, selling the singularity as the nut of all massive objects. Singularities are now found all over the place, in many new theories. They are said to explain magnetic monopoles, cosmic strings, domain walls, and even “fuzzballs”. The singularity is even given various dimensions! A domain wall is a two-dimensional singularity, for example. That is somewhat like a three-dimensional line, a unicycle with three wheels, or a ten-armed octopus.
Loop quantum gravity, developed by Abhay Ashtekar, Carlo Rovelli, and Lee Smolin since 1986, is the attempt to show that singularities cannot exist. The attempt is praiseworthy, but the method is not. These physicists are correct to excise the singularity, but the way they go about it is very incorrect. Rather than correct the math at the foundation like I have done, they have done as all modern physicists do, piling more new bad math on top of old bad math. They basically renormalize the field equations of GR. Although they do not renormalize with the same tricks as QED, they do renormalize, since renormalization can be defined (broadly) as removing zeros and infinities from imploding field or space equations. One trick used in loop quantum gravity is the spin network (see diagram top of page). I mention it because I want to start by showing you why this trick cannot work. At Wikipedia we find this:
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