Nutshell 2018
5th February 2019

"So my conclusion is that, the dynamics of the interior of black-holes is governed by the complexity in a way,  which is somewhat similar to the way the dynamics of the exterior of the horizon and so forth, as seen from outside, is dependent on the thermodynamics of entropy."

 - Leonard Susskind, Complexity and Gravity, Prospects in Theoretical Physics: From Qubits to Spacetime, 2018.

 "...but it was a little bit like me and
maybe you know if the anteaters went on a trading mission to the beluga whales
and you might imagine that the beluga whales would say, well thanks, well we'll let you know if we need any ants, but you know we're we're we're you know we're
we're doing okay as it is...."

 - Scott Aaronson describing his initial interaction with Juan Maldacena, Firewalls, AdS/CFT, and the Complexity of States and Unitaries..., Prospects in Theoretical Physics: From Qubits to Spacetime, 2018.

" WHY? are all three forces due to local symmetry? Why is α = 1/137.036999708..?

WHY? are there families of quarks and leptons? Why is Mtop/Mup ~ 100,000?

WHY? is space three dimensional?"

- David Gross, The Coming Revolutions in Theoretical Physics, October 19, 2007.

String theory must answer these questions.  The eventual goal remains the understanding of the life-force, not quantum gravity.  The concept of an infinite source in j-space, is an attempt  in that direction.


    In the year 2018 we discussed some really interesting topics, such as Quantum Computing-III, Knots and DNAs, the equivalence between Lorentz transformation and Möbius transformation, and the Curve of Least Disorder or equivalently the Curve of  Least Energy.  Each of these topics, is of great importance and we will be discussing them in greater details in 2019.

Quantum Computing:  For Quantum Computing (QC), it has always been the case that there is no clear sense of which fundamental problem to solve, if the technical issues causing decoherence are properly addressed, which is very likely in the near future.  In this context, we described the impossible-problem and then the impossible-problem-1, which are "the knowledge of  the outcome of the next instant" and "the resource optimization in a closed system" respectively.  Any other problem that we can think of at present, for example the minimization of the action integral in physics, is a subset of the impossible-problem-1.  Our strategy will be to focus on the impossible-problem-1, and that should be able to provide us with enough understanding of the various issues involved.  The knowledge thus gained, will perhaps allow us a better insight into the "impossible-problem".  The discussion on the curve of least disorder, is an important step in that direction. 

    On the commercial prototyping of QC, currently there seem to be three leading contenders for a working QC.  They are Quantum Annealer from D-Wave, SQUID based QC from IBM, and Anyon based topological QC from Microsoft.  D-Wave Q-annealer is already out in the market with mixed reviews.  IBM's QC will be out, probably in few years time.  Both of these SQUID based solutions are sensitive to the decoherence problem, hence they require strict operational environment control (very low temperature and noise), which is a major drawback.  The Microsoft solution is based on Qbits designed using Anyons or Majorana particles.  Should it come through, the problem of the decoherence will not be an issue, as this solution does not use electrons as carriers.  In fact a working device using  Majorana particles, will be a monumental technological breakthrough, which will change the world-wide manufacturing landscape completely.  Anyon based QC architecture has an distinct advantage over SQUID based QC, as the solution will be independent of the operating environment conditions, it will require a minimal fault tolerant architecture, therefore it should be scalable and the miniaturization of Qbit will be possible.  But there is no prediction as such to if or when, a prototype will be available. 

   If we could ever got our act together and focus more on moving the manufacturing into the space, rather than moving ourselves to Mars or some other fictional planet, then QC combined with some truly advanced concepts such as, evolutionary design and manufacturing, additive manufacturing (3-D manufacturing), digital twins, & Industry 4.0, will result in products of extraordinary quality, reliability, and aesthetics.  Up in the space, extremely low temperature required for QC is available, the effect of gravity is minimal, and the manufacturing activities will have no impact on the earth's environment.  From theoretical physics point of view, the equivalence between the inner mechanism of a black hole and a QC is quite fascinating.  We will be discussing black holes, and what they mean in the discrete measurement space or j-space in 2019.

Knots: Just few points about knots in j-space;

1. The knots in j-space are written so that each configuration is completely distinct from other.  We can introduce symmetries later on, to determine structures which could be equivalent to each other.  But similar structures really do not help us, as we want better and better resolution in discrete measurement space.

2. The equations of knots are written as Laurent polynomials, for example,

Laurent polynomials for knots in j-space, represent the motion alternating between positive and negative time axes, as the knots are formed.  We want low-order exponents of Laurent polynomial, along with the contribution of the term 0j.  The idea here, is to compare the effectiveness of competing mechanisms, which are represented by complex knots and respective Laurent polynomials.

3. If we compare the knot polynomials written for enzymes and DNA, the enzymes corresponding to the polynomials of lower order (t+n, n small) and with high contributions of 0j terms, are more likely to succeed in breaking down DNA which have relatively higher order polynomials, (t+n, n large), and small contributions of 0j terms.  In similar fashion, the DNA with lower order polynomials and with high contributions from 0j terms, should be immune to the effects of enzymes corresponding to higher order polynomials and with little contributions from 0j terms.*

Equivalence between Möbius and Lorentz transformations: We already had a lot of fun with this truly remarkable concept and we ended up designing  a universal translator, just in case Vulcans, Ramulans, Klingons and others happen to descend on the good old blue marble presently inhabited by future Martians.  The equivalence is extremely important, as the structures following these transformations are scalable (z -> 1/z) and conformal (the angles between the intersecting lines are preserved).  We will be using this equivalence extensively in the discrete measurement space we call j-space, which itself is a complex space.

The curve of least disorder:  If we can complete a circuit in discrete measurement space and form a curve of least disorder, then theoretically we can use Stokes' theorem, line-integral to surface-integral, to form the corresponding surface of least disorder.  Next we can use Gauss' theorem, surface-integral to volume-integral, to transform this surface to get the volume of least disorder. What does it really gets us? It gives us:

1. A measure of the origin or 0j in discrete measurement space,

2. The definition of null {} for a given group of objects in j-space,

3. A Qbit for the most efficient Quantum computer in j-space.

All of above three are invariants in there respective descriptions.  More importantly we have an expression for ds rather than ds2, given as:

Therefore, we have ds which is essentially an invariant in discrete measurement space, similar to dswhich is an invariant in general theory of relativity.  The advantage is that we will not need metrics or manifolds, if the criterion for the curve of least disorder ds is precisely established, as is the case here.  We should be able to figure out how to count next**.  Good stuff !


*    <0j|0j> represents the initial state. The polynomial with higher contribution from the initial state is likely to be more effective than the polynomial with smaller contribution from the initial state.  As a simple example, if we compare the knot polynomials for the Trefoil knot and the Figure-8 knot, as they are written in j-space, we will notice that the Trefoil knot is more fundamental in nature than the Figure-8 knot.

**    0j, 0j+0j, 0j+0j+0j...................., {}, { {} }, { {} {{}} }..........and so on.

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