Comments on Loop Quantum Gravity by Carlo Rovelli Page 1

I am commenting upon the work in:

http://igpg.gravity.psu.edu/people/Ashtekar/articles/rovelli03.pdf

Carlo Rovelli's work uses String Theory to create the Quantum Loops and this feature is the one that I alter using my Complex Strings.

String Theory in Complex Quantum Mechanics

An exact definition of what strings actually are as not been put forward until now. I am going to describe stings as being both particles and waves.

In Complex Quantum Mechanics strings and loops (closed strings) can exist as real or complex strings and can translate between these two types.

They manage to exist in this new state of matter as being a combination of mass and energy. That combination may vary but real strings are subject to the geometry of real space and so they tend to behave in a circular manner creating helix patterns as they increase in length with the addition of extra mass and energy (see figure 4 below in Quantum Loop Hypothesis 1).

If we think of these real strings as starting to form just with the formation of two particles then their mass and energy can be thought of as being in balance (if they truly lie into that plane with co curvature) and lying in a 2D plane so that they vary sinusoidally.

Now suppose we add either extra mass or energy. If it is not exactly in the same proportions the string is naturally going to want to form a helix as a result of the circular forces that drive the mass to energy exchange. I suggest that the formation of a helix creates a closed string or loop creating equilibrium for this mass to energy exchange.

In Loop Quantum Gravity these loops are considered as interlocking (see figures 1 to 3 in Quantum Loop Hypothesis 1). I am going to extend the theory of Loop Quantum Gravity by showing how this interlocking operates. I consider the loops to act like Magicians Rings except that they do not have a very fine cut but the crossing points of the helix serve this purpose (see figures 5 to 7 in Quantum Loop Hypothesis 2).

In figures 5 to 7 the loops are actually shown passing through each other. For them to form interconnecting loops as in figure 2 the addition of more helix of the same wavelength would help the first loop to rotate around the surface of the second loop and complete this operation.

The momentum from the pivoting action may explain how this happens or we can attribute it to random movements that will eventually cause the loops to interlock.

continued on page 2

Now we can create a Weaving Space as shown below. If we do not have a nucleus already but only a Weaving Space then I expect that as more and more closed strings or loops are added they begin to align and form a spherical nucleus by the conditions I have already described.

Once they happens I see the effect, theoretically, as increasing exponentially as this influences loops at the edges of the Weaving Space to align themselves in helix patterns around a spherical

‘grid’.

 

This only leaves me to show how the loops can then wrap around a sphere. I have already explained this process in extending Dr Mills theory of the Orbitsphere by using topology but I will give a method using String Theory here.

If we consider the sphere like Dr Mills Orbitsphere (see figures 8 and 9 in Quantum Loop Hypothesis 3) then the surface of the sphere can be considered as wrapped by strings in great circles around it. This is shown schematically in figure 9.

You can either consider the yellow loop as being rotated to form a great circles around the sphere or that it is broken at the point of contact and tries to restore itself by forming a new circle around the sphere. This is debatable and may exist as two different situations in reality.

It is not possible to come to a better conclusion at present given that I am hypothesising.

One remaining feature of strings I would like to add is that strings can come in many shapes and sizes according to current String Theory. I am not suggesting that this is incorrect but that whatever the shape of a string it will have an inherent tendency to behave as I have described above.

I can now approach the subject of complex strings. These exist not as loops but around complex cylinders (zylinders). I have dealt with the complex wrapping of real space at my yahoo site.

So they are surprisingly similar and can quite easily translate between real and complex states.

I can now comment on the article by Carlo Rovelli.

Energy to Mass Conversion in Complex Quantum Mechanics

I can now present, here, the first complete explanation and description for the nuclear energy to mass exchange and conversion.

I have previously described the behaviour of the energy to mass exchange in a photon as acting spherically. It is now possible to see that this process involving photonic energy (energy that is in a fluctuating state between mass and energy) is controlled as a spherical process whether or not we are describing the photon.

 

In the diagram Photonic Energy 1 the F wave is shown determining the actual balance between mass and energy. In figure 3 the F wave is shown more clearly acting orthogonally and it transpires that if the F wave was not orthogonal this system would not work!

In figure 4 the F wave is shown schematically as being connected to the zeelix (complex helix). To create a crossing point that consists of only energy we have to carefully choose the correct phases for each zeelix (see figure 5 in diagram Photonic Energy 2).

 

In the diagram Photonic Energy 2 the F wave does not actually need 4 phases to create a crossing point that consists of entirely energy and acts in effect like a gap in the loop.

The F wave just needs two phases with points A and B to rotate 180 degrees between points A and C (for example).

This is a good model as a second string might be attracted to that point and self align itself to interlock with the first. This is because energy and mass concentrations tend to act like north and south polarities in magnetism.

In reality the loop will have multiple zeelix (for complex strings and helix for real strings) and they can be configured to create a suitable crossing point for interlocking. To arrange the F waves so that they create a crossing point that consists of pure energy then we need to revise figure 4 below in Quantum Loop Hypothesis 1 with figure 5 below in Quantum Loop Hypothesis 2). The way we can best achieve this is to have two F or Fathers waves exactly the same but in opposing rotations. I hypothesise that since these zeelix have to occur in such pairs them the pairs themselves will form crossing points that distribute themselves evenly around the circular cross section of the cylinder.

So if a crossing point occurs at point A, say, at the 360 degree position an additional crossing point occurs at a point directly opposite A, in the 180 degree position. Now it is debatable whether a third crossing point would occur either at a point at the 90 or 270 degree position or if there is a complete re-alignment and they all become separated by an angle of 120 degrees.

The fact that we need the F wave to rotate may be explained by saying that, perhaps, if we have just one zeelix the F wave does not have to form around a zylinder. However if we have just two zeelix as in figure 4 this rotation allows them to interact by following the same line of action along the centre of the zylinder.

If we imagine the loop being broken at any point we can see that the energy and mass process will attempt to reconnect in as a closed string or loop so it plays an important role in String Theory according to Complex Quantum Mechanics.

This also shows why the process of converting energy to mass should act with spherical forces as these loops combine in a three dimensional framework.

This hypothesis agrees with my real wrapping of a complex particle in Dr Mills’ Classical Quantum Mechanics and my complex wrapping of a real particle in my Complex Quantum Mechanics and so combines all four theories.

A comparison with Complex Quantum Mechanics

Article Statement >

The most appealing aspect of loop quantum gravity is that it predicts that space is not infinitely divisible, but that it has a granular structure.

Alex Comment >

Real space is not infinitely divisible but you can continue into complex spaces that are smaller.

To do this we need to revise Newton’s Calculus and rewrite Complex Numbers. This may seem like taking a sledge hammer to crack a nut but it is absolutely necessary. It also comes to the rescue of Loop Quantum Gravity here.

Article Statement >

 

Weaving space – the 3D structure of space in loop quantum gravity can be visualized as a net of intersecting loops. The simple model above was built by the author using key-rings, before spin networks and the physical significance of the nodes were discovered.

Alex Comment >

There do not seem to be any conditions or situations in which these loops align.

This is possibly due to the concept that space itself does not exist as a fabric.

Loop QG has to dismiss the possibility of the geometry of space and I would suggest the introduction of some form of geometry would improve the theory. Loop QG does however use the geometry of the cylinder to create Spin Foam and the loops themselves are shown as circular. This may be an unintended interpretation in the article titled "Loop quantum gravity" by Carlo Rovelli.

No matter how hard Loop QG tries not to use geometry it seems unable to do so and I believe that is for good reason. I would say if Loop QG is telling us one thing then that is that a geometrical framework is essential.

 

Article Statement >

The Newtonian picture of the world is therefore a background space on which matter moves.

A small but momentous change in the Newtonian picture came from the visionary work of Michael Faraday and James Clerk Maxwell at the end of the 19th century. Faraday and Maxwell introduced a novel object that could move in space. This object was called the field, and Faraday visualized it as a set of lines that fill space.

The lines start and end on electric charges, but they can exist and have independent dynamics even when no charges are present. In this latter case the field lines have no ends, and therefore form closed loops. Maxwell then translated Faraday’s intuition into equations, in which these lines and loops became the electric and magnetic fields.

Alex Comment >

These loops are similar to my Complex Horse Shoe Strings and Stephen Hawking's strings.

I intend to focus on this area, in the near future, to show how a Real Horse Shoe String can become a Complex Horse Shoe String.

Article Statement >

Today our basic understanding of the material world is entirely in terms of fields. The fundamental forces in nature are described by Yang–Mills fields, which are similar to the electromagnetic field. Fundamental particles, such as quarks and electrons, are described by “fermionic” fields, and Higgs particles, which endow particles with mass, are described by

“scalar” fields.

Alex Comment >

Yes, and at the same time there is no reason why a complex field may not exist. I have described this elsewhere in the transfer of matter between stars.

Article Statement >

Spin Network

Elementary grains of space are represented by the nodes on a “spin network”(green dots).The lines joining the nodes, or adjacent grains of space, are called links. Spins on the links (integer or half-integer numbers) are the quantum numbers that determine the area of the elementary surfaces separating adjacent grains of space. The quantum numbers of the nodes, which determine the volume of the grains, are not indicated. The spins and the way they come together at the nodes can take on any integer or half-integer value, and are governed by the same algebra as angular momentum in quantum mechanics.

 

Alex Comment >

I believe that it is possible to re-identify these links as the pathways for the inclination of the complex plane albeit in a generalised manner. Perhaps it may be easier to think of the links as the centre lines of potential or actual black holes.

In Complex QM I had envisaged black holes and white holes working to balance each other.

I conjecture that if this network is combined with the mathematics of Organisational Methods then the most economic pathways can be found and perhaps the whole system made to conform to desirable parameters.

In Complex QM the white holes tend to return matter from the edges of the universe to its centre and if we could examine a large enough Spin Network we may be able to prove or disprove this.

Article Statement >

As long as we stay within the classical regime, rather than the quantum one, the gravitational field defines a 4D continuum. We can therefore still think of the field as a sort of space–time, albeit one that bends, oscillates and obeys field equations. However, once we bring quantum mechanics into the picture this continuum breaks down. Quantum fields have a granular structure – the electromagnetic field, for example, consists of photons – and they undergo probabilistic fluctuations.

Alex Comment >

This difficulty is removed with Complex QM as the Heisenberg Uncertainty Principle

is invalidated. Probabilities become movements or displacements into complex space.

These fields can not only be thought of as describing space-time but space- complex displacement.

Article Statement >

The conventional mathematical formalism of quantum field theory relies very much on the existence of background space. There are therefore two possible strategies that we can adopt to construct a quantum theory of gravity. One is to undo Einstein’s discovery and to reintroduce a fictitious back-ground space. This can be done by separating the gravitational field into the sum of two components: one component is regarded as a background, while the other is treated as the quantum field. We are then left with a background space that is available for all our calculations, after which we can hope to recover background independence. This is the strategy

adopted by those who do not regard the general-relativistic revolution as fundamental, but as a sort of accident. And this is the strategy adopted in string theory.

Alex Comment >

This concept background space (is the one of the two options I prefer and) can be replaced with complex space except that we do not intend to discard the results from it at the end of the calculations.

Article Statement >

The key input that made the theory work was an old idea from particle physics: the natural variables for describing a Yang–Mills field theory are precisely Faraday’s “lines of force”. A Faraday line can be viewed as an elementary quantum excitation of the field, and in the absence of charges these lines must close on themselves to form loops. Loop quantum gravity is the mathematical description of the quantum gravitational field in terms of these loops. That is, the loops are quantum excitations of the Faraday lines of force of the gravitational field. In low-energy approximations of the theory, these loops appear as gravitons – the fundamental particles that carry the gravitational force.

This is much the same way that phonons appear in solid-state physics. In other words, gravitons are not in the fundamental theory – as one might expect when trying to formulate a theory of quantum gravity – but they describe collective behaviour at large scales.

Alex Comment >

Why must the fields close in on themselves? I thought it precisely because they had charge and thus polarity they should close. In a Complex Horse Shoe String the uneven cylindrical forces create the flexing and as you balance the cylindrical forces the string closes into a circle or loop.

I believe that Real Horse Shoe Strings can wrap around a real cylinder in much the same way but perhaps need a spherical space to exist upon. So in either case I believe the situation is more complicated than suggested by Loop QG. This is not a natural focus for Loop QG that is more mathematical in its approach. I suppose from a purely mathematical point of view I would agree as it seems to comply with Cauchy’s Theorem. The difficulty I foresee is explaining this within physics.

Article Statement >

The second strategy uses Feynman’s version of quantum field theory, in which the behaviour of a quantum particle can be calculated by summing all the possible classical paths of the particle. Misner suggested that calculations in quantum gravity could be performed by summing over all possible space–times – an idea that was later developed by theorists that included

Steven Hawking at Cambridge University and Jim Hartle at the University of California in Santa Barbara.

Alex Comment >

This is the main drawback with Loop QG at present. The loops have no coherent framework.

By using complex space as a differential plane I provide backbone and a frame to hang Loop QG upon.

 

Alex Comment >

While the diagram shows a five fold branching and not three or four fold branching the elevation does appear to represent a ztar pattern. So I would suggest that the mathematics of Loop QG could replicate the situation in Complex QM. The structures used for Loop QG are also polygonal as I would expect but this does conform to my hyper-geometry (at least as shown here).

Loops on Loops

Alex Comment >

This concept appears a weakness in Loop QG to me and a stronger case seems to be for Complex Loops on Real Loops and vice versa. The ordering of the loops seems to be a persistent problem. In what circumstances would the loops ever act in conjunction? If the answer is never than how can you have a geometry that is truly random and yet have an ordered universe?

Article Statement >

Smolin and I teamed up with Ashtekar to try and understand the physical meaning of the nets of loops that had emerged from the equations. Through various steps we slowly realized that the loops did not describe infinitesimal elements of space as we had first thought, but rather finite elements of space.

Alex Comment >

This was my main objective in rewriting complex mathematics. The concepts of calculus and complex mathematics have not been radically changed since their conception and I saw the need to do so to remove such confusions.

 

Article Statement >

The idea that there cannot be arbitrary small spatial regions can be understood from simple considerations of quantum mechanics and classical general relativity. The uncertainty principle states that in order to observe a small region of space–time we need to concentrate a large amount of energy and momentum. However, general relativity implies that if we concentrate too much energy and momentum in a small region, that region will collapse into a black hole and disappear. Putting in the numbers, we find that the minimum size of such a region is of the order of the Planck length – about 1.6 ×10 –35 m. that had already been studied.

Alex Comment >

I had estimated the size of the differential particle to be approximately between 10^–35 m or 10^–40 m so it is nice to have a formal figure. I agree with most of this comment except that: can we sure about the 'disappearance'? I suggest a wormhole is a better term than a black hole.

I suppose it is hard to explain if there was a single black hole at the time just after the Big Bang then why has not all space and time been consumed?

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Article Statement >

It was not until about 1994 that Smolin and I really understood what we had stumbled upon, thanks to a calculation that is routinely performed in quantum theory. By quantizing a theory, certain physical quantities take only discrete values, such as the energy levels in the hydrogen atom. Computing these quantized values involves solving the eigenvalue problem for the “operator” that represents a particular physical quantity. We studied the volume of a region of space – or a certain number of loops – which in general relativity is determined by the gravitational field. By solving the eigenvalue problem of the volume operator, we found that the eigenvalues were discrete – that is, there are elementary quanta of volume, or elementary “grains of space”. Furthermore, these quanta of space resided precisely at the nodes of the nets.

Alex Comment >

I cannot be certain of the scales being used here but the possibility of space (mathematically at least) becoming quantised may be due to the limit for the diameter of a differential particle. The centre of any ztar at a smaller scale would lie precisely at the nodes of the nets.

These nets thus provide a mathematical framework for tying two spatial geometries together and that need not necessarily involve complex space, although it does. Spin Networks endorse why my hyper geometry, using polygons, can work effectively.

Article Statement >

Spin Foam

In loop gravity, space is replaced by a spin network and space–time is therefore described by a history of spin networks. This history of spin networks is called “spin foam”, and it has a simple geometrical structure. The history of a point is a line, and the history of a line is a surface. Spin foam is therefore formed by surfaces called faces, which are the histories of the links of the spin network, and lines called edges, which are the histories of the nodes of the spin network.

 

Alex Comment >

I see Spin Foam as a purely mathematical device. Spin Foam could be adapted, perhaps, to describe the history of a particle moving, say, from 4D into 3D. To do this the Spin Foam would not to be projected around a cylinder but a zunnel. I suppose a zylinder or complex cylinder could describe a similar situation in complex space.

The Convergence of Quantum Theories

There are similarities between String Theory and Loop Quantum Gravity (LQG). First of all the obvious fact that both theories start with the idea that the relevant excitations at the Planck scale are one dimensional objects (call them loops or strings).

In Complex QM these strings can be complex and real. They also possess the characteristic or tendency of winding as a helix. I suggest that when these strings or loops attach themselves to a spherical nucleus they probably unwind and it is this unwinding that creates a surface binding force.

The random interlinking of LQG loops is now doubtful. In fact I consider that Complex QM will have a major effect on LQG.

If the helix is considered straight then it is open but perfectly balanced. When it is horse shoe shaped I agree with Stephen Hawking that it would emit a force at its ends. I expect that this is the surface binding force that tends to make the string close around a circle and form a doughnut torus.

The doughnut torus is now compressive around the inner circle and tensile around the outer circle. So another doughnut torus may not be able to fit around the outer circle but it could act

perpendicular to the first. In this way the three main axes can be constructed for a sphere.

If we allow for these torii to cross when their helix cross then a system of loops can be created at intervals equal to the wavelengths for the helix and the sphere is mapped as an Orbitsphere. This model seems to compliment the one I have already constructed for Dr Mills Orbitsphere.

By this means I am showing that QLG loops are not random as a rule but tend to coalesce around a cylinder, torus, or sphere. In this way Classical Quantum Mechanics, Complex Quantum Mechanics, String Theory, and Loop Quantum Gravity are all converging.

Energy Mass Conversion in Strings

The string changes from a linear state and wraps around a cylinder because the string is not composed of mass nor energy but fluctuates between the two states. The process controlling this is basically spherical in real space and probably inversely spherical in complex space.

When the string forms a closed loop then inner circle side can be considered as having the equivalent of a wave with a shorter wavelength than the outer side. It is questionable whether the equivalent wave on the inner circle can also increase its amplitude.

This seems to be an energy to mass system that is operating inversely to what I have previously described for the photon. In the photon the energy to mass system expands and contracts spherically. This creates a complicated picture for this process that will require more study to determine the spread of this process. The inner and outer wavelengths seem fixed restricting the energy to mass process but this should only be the case if the overall system is balanced.

If we add or subtract some energy there is an inbuilt energy gradient that will direct this process, say, in the photon.

I also consider it very likely that these strings can be composed from many smaller strings as long as they share the same wavelength and amplitude. The part that Brownian Motion plays to allow for this mechanism to adjust itself helps to complete a comprehensive mechanism that is translatable between real and complex space.

The only missing situation for these strings is if a smaller closed string comes into proximity with a string fixed around a nucleus. If it does not match the wavelength of the outer side of the fixed string then it may break and be added to the nucleus to upset the energy-mass balance and create a movement of energy to mass in the nucleus however small.

The only reason for the neighbouring string to break seems to be if it aligns itself adjacent to the centre line of the torus and tries to spread around its smallest circumference. This string is not just subject to these forces in one dimension but two and the forces are tensile. At the very least, then, this smaller string must try and deform into an ellipse.

Conclusion

Without revising Loop QM to have some geometric framework it will not be possible to delve into smaller and smaller lattices of Spin Foam. Thus an orderly result will remain elusive until Complex QM or some similar theory is developed.

My approach to gravity in Complex QM is still being formulated. I have some suggestions as how gravity operates but it is difficult to deal with gravity as it is nearly always abstract. The investigation of gravity requires from a perspective offered by in Complex QM a more daunting task. It is necessary to examine how all the new multi–dimensional forces, complex forces, and fractal forces may play their part. A moment’s reflection will show that this is necessarily the case as gravity can be considered as operating in all these domains.

I have made headway with gravity without using Complex QM and I am therefore cautious in making any suggestions that may be unintentionally misleading in the long term. I do however believe that Complex QM can help to see and understand gravity more clearly.

Complex QM has not been seriously challenged since first announcing it in1999.