Not only will I mess with Riemann’s famous Z-func, today I will straighten out his geometry. To begin with, his correction of Euclid is excellent. I agree with Riemann on that.
Riemannian geometry, also called elliptic geometry, one of the non-Euclidean geometries that completely rejects the validity of Euclid’s fifth postulate and modifies his second postulate. Simply stated, Euclid’s fifth postulate is: through a point not on a given line there is only one line parallel to the given line. In Riemannian geometry, there are no lines parallel to the given line. Euclid’s second postulate is: a straight line of finite length can be extended continuously without bounds. In Riemannian geometry, a straight line of finite length can be extended continuously without bounds, but all straight lines are of the same …
In essence; Riemann rejects the idea of linearity. He says all extensions are basically circles. Thank you R, that’s definitely it. All of my space is of circular surfaces extended by pole frequencies. These pol extensions IS what we measure as “space”. Don’t let your mind fool you here, and assume there is:
Wrong Wrong and Wrong!!!
There is: Extensions.
Riemann had it perfectly right in building a geometry out of such extensions, and to have them being circular. They are. The pole extension is circular and of finite area. It is a disc. This is not really a problem if we want to build a 3D reality. We simply stack those surfaces in whatever way we like and, lo and behold, 3D space.
Now, how can we make both being right? It is much related to the problem with making both QM and GR equally correct. It seems they are, but we cannot figure out how that can be since they sort of contradict each other in a disturbing way.
I thought we could approach this academic problem with a little help from one of the academic superstars, Edward Witten of String Theory fame. I’m being a monopole guy, I found a paper on ST and singularities from which I quote:
Here we run into a problem. One can read a textbook recipe for quantization in Dirac’s old book or in more modern texts on quantum ﬁeld theory. But these recipes, applied to the Einstein-Hilbert theory, do not work. Because of the highly nonlinear nature of Riemannian geometry, these methods fail to give a consistent and meaningful result.
So if I read Prof. Witten right, he detects a problem in that quantization seems a fact while Riemann’s geometry also seems true. On one hand, quantization and Riemann agrees on the finiteness of geometry. Unlike Euclid, both say that extension is not infinite in space, but rater in rotation. The closed circle, string, surfce can in priciple spin forever without going anywhere in space. I can draw a 2 km long line on my A4 paper by curling it up in a circle. I can thus “bend” space into a particular Place. Then we ask, is it still a line?
Of course it isn’t, but the energy spent on drawing it can be exactly, has to be exactly, same as if drawing a true line. And please don’t get hung up on the energy expenditure and definitions of “energy”. Try getting the point instead. Thank you.
The problem Witten finds is likely that Dirac’s quantizing recipe will generate a real geometry/space with gaps in it. Reality might ultimately be quantized and dot-like, but it is also true that it acts in accordance with the smootheness of General Relativity, and however discrete Riemann’s infinite dots look like, when put to work they generate a manifold of smooth complexity. Riemann gets there by adding a tensor to his circles. This is the same trick as Einstein used to wrap up spacetime. A metric tensor is a mathematical function that aids in measuring and dimensioning, but it is not a real part of reality.
It simply is not there to look at. I will replace that device with the internal frequency of the geometry since it is pole spin that both extends to a surface and which keeps it in shape. More on that later.
Now I will tell you how to make a continous line from discrete dots that goes on and off like pixles on a screen. This is important, because Dirac’s recipe is a good one, but the “string” he imagined to have it work properly can be replaced with my viscoelastic point of spinning contraction. I reality, the Dirac string is the circular currency of 2 monopole surface extensions spinning in opposite directions. That my friends is what a photon looks like. The string is the photon’s helical twist of transversed waves. It is the 2 poles frequencies that does the twisting extensions, and we get a photon wavelength from that. But that’s off topic.
So…how should I phrase this…? Let the extensions be reality because they are reality. Really make a mental effort to let this sink in: Only the extended sufaces are real, as in empirically measurable. It is not because we cannot look close enough to see the poles in their middles. It is because there is only spin frequency there. It is as visible as a black hole. The Riemann geometry of a closed circle prevents outsiders from looking in. It is like having an Euclidian line “bent” around it. That’s excellent, and it should have put an end to ideas of infinite space….I wish.
We see that the Euclidian geometry applied to quantum systems just ends up in infinities. Especially conceptual infinities. However academically rewarding that might be, it won’t take us further around the road. Let’s settle for Riemann’s infinity instead. An infinity that allows a process, like for example universal evolution, to keep going, but prohibits infinities of space. I suggest the arrow of time goes around the clock and not like a hand of time that keeps stretching out the face. If the hands reach out too far, they will lose frequency/momentum and the turning of time will stop. It doesn’t. So if we look at the chart below and realize the monopole itself is a first harmonic string/circle, then it will not have a complete basic unit of space. The minimum circles needed for space to emerge is a pair of monopoles, and that’s a photon. The first harmonic singularity (initial state) is a circular surface of 1 wave. By the way Prof. Witten, that’s the cosmic string soon about to be 2 strings. But in this particular case, it is not a nice and wavy surfers wave, but an instant pulse when the spin of the pole makes it shrink inwards as to press its great circle outwards to extension. The spheroid point flattens out, just like that. Boom.
|Harmonic||Pattern||# of Loops||Length-WavelengthRelationship|
|1st||1||L = 1 / 2 • λ|
|2nd||2||L = 2 / 2 • λ|
But we still have only half a space, right. No matter how fearful and gigantic we assume this entity to be, with one single loop there’s zero space. It simply cannot achieve “space” on its own. Was it not alone we could assume its existence by looking at what’s external to it, as we do with Black Holes in our already banged up universe. But looking at one single solitaire of a monopole, there is nothing external to prove it existing at all.
It is just frequency/rate of oscillating contraction/extension. We should also be careful with the notion of frequency, because at this point we don’t know the frequency of what. We don’t have a clock to say “It rotates 300 000 000 times in a second”.
Come on guys, “time” is just as not-there as “space”.
So how do we quantize a la Dirac to make a nice wave out of this monster of a dimensionless oscillator? Witten of course wants an electromagnetic wave out of this, and that it should be smoothe, and able to, in multiples, build a Riemann manifold of continous complexities without those crazy quantum gaps in it. I suggest we let the monopole oscillate itself in half. The twist from spin is likely to break it at some point in the sequence, and until further notice, I will set that point at 3. 3 full contractions and extensions and it is suddenly 2 monopoles. By that, we have played the first second harmonic and now we have 1 basic length of space and it took a frequency of 3 times. When you stop laughing at the paradox of having created 1 dimension of space from 3 dimensions of time, you can open your eyes an have yourself a Big Bang of light.
I’m not sure yet how the next breaking plays out so there’s a few options available to this uneducated mind at least. For a pro there may not be so many. Hopefully only one according to what we know of electromagnetism. The important thing to note is that once the monopole singularity is broken in two, we can have a sequence of multiple oscillations. That will bridge the quantized gap so we now face a reality that is no longer black or white, as in on/off quantum flickering, but relatively smooth and continous.
This means we can throw away the tensors and keep the Dirac monopole(s) binary nature intact and build a Riemann manifold. The tensor effect is now inherent in the combined contractions of the multiple spinning poles. It is what gives the space extensions their frequencies and holds them together as “waves” and not Euclidean straight lines.
That we cannot directly measure the quantum jumping with out probes without getting tunnel-vision should not be a problem if you know how it’s done and what it is. The reality of the many lights being momentarily “off” is shadowed by the many which are always “on”. The pre-reality of what is real will show up in the real measurements however we go about doing them.
We’re swimming in the Dirac Sea as we speak, it’s just that we are the clouds hoovering above it. When we cool down, we fall down into the ocean of insides.
Count to C and we’re up and flying for real again.
Sorry to mess with String Theories, but the opens strings are not neccesary. The math is probably spot on, but I suspect it is way more complex than is actually called for. I believe we can keep the single closed string/surface as it is with wavelength 1, and then we just break it down in as many legos/points we like to fit with the data. I’m sure the flow of currency appearing smooth and continous can be achieved by letting the “off” poles be what they are supposed to be i.e. non interfering with measures of space qualities.
“Flow” is exactly one such quality, and if the silent 1’s are not real is space, they will not affect how space evolves. But they will indeed affect the frequency/timing of space.
The timing is of how that which is linear is curved and folded into complex geometries. Space extension doesn’t do that.