We need a new mechanics to derive quantum mechanics, thus far, attempts were made to derive quantum mechanics, from classical mechanics, giving a twist in imaginary time and eliminating the concept of an energy barrier. Classical events could happen in an imaginary time and then you reach quantum mechanical observations, which happens in null time. So, we allowed time required for an event to happen to satisfy our classical need and at the same time we made sure that a quantum observation is fit. Similarly we know very well that in quantum mechanics, energy barrier is not supreme, a particle with a very less energy could cross a high energy barrier. To meet that need, we again took the help of uncertainty principle which acts like a universal receipe added to every classical observables and turning them into the imaginary domain. We knew very well, while creating a theory for quantum concepts that position, mass, momentum, velocity, time could be coupled to imaginary time and then shocking quantum observations could be derived.

When we argue for a new mechanics (see our nanobrain book https://www.amazon.com/Nanobrain-Making-Intelligent-Molecular-Machine/dp/1439875499), definitely the transition from classical concepts to quantum analogs via imaginary route would not be the case. Imaginary time acts as a transfer function to complete the journey from classical to quantum but that’s the inclusion of additional features unseen in classical mechanics. If we want to invent a new mechanic that is one step higher than quantum mechanics, then there will be a reduction of more shocking features. This transition from fractal mechanics to quantum mechanics would be losing something just like we lose the concept of imaginary time when we transit from quantum to fractal.

We proposed the concept of 12 nested layers of invariants, that defines fractal mechanics. In the classical world our observables are real data that we see. In the quantum world, it’s about delivering classically impossible observations, when we move from the classical world, but from fractal mechanics, losing out key features. What is that?

The first key factor of fractal mechanics is a transition from space-time to space-time-topology-prime metric. It means, every single point in the universe, should not be seen as space alone, or space-time alone. It should be seen as a space-time-topology-prime. In the year 1915, when we talked about space and time together, it brought a new sensation in the philosophical world. We learnt about space that is changing the flow of time, and time is changing the configuration of space. Now, change in symmetry of a particular topology due to SRT (projection, transformation and bonding) features would regulate time and so would be changing the space. Now, pattern of primes would change the topologies, so the space and time. The problem is that space and time could be sensed physically, but the role of topology is not that straightforward.

Lets imagine we are creating the universe and trying to create a temporal scale, then can we create any time of our choice? No, we build systems with times like discrete energy orbitals of a molecule. We do not get all possible times. Maharshi Ganita was the first to calculate the orbital like discrete time levels, thats intimately connected to the allowed topologies. It is amazing to see that since topologies need to be symmetric at the very core, we cannot allow any time to be a possibility. Finally, ordered factor metric of primes talk about singularity and creation of a point that vibrates with all possibilities. It means, every single point is a complete phase prime metric, or the complete temple like architecture of the universe. Therefore, universe is a journey through singularity, it is an self operating mathematical universe, SOMU. Three dimensions, 10-11-12 are responsible for primes, 7-8-9 for topology, 4-5-6 responsible for time, 1-2-3 regulates space. 86% probabilities are covered by a few primes, SOMU explores the rest 14%.

We have a habit of looking at everything spatially, and considering it as an absolute. However, when we see everything as singularity and metric generated absolute possibilities of singularity points as space.

What is information then in such a SOMU? Space-time-topology-prime metric is a system, undefined because it has no beginning and no end, the mathematical probability for the existence of singularity points is the constituent that builds SOMU. It is not a matter, space, time, or even a topological property, its simply, undefinedness of a point.

Once we have undefined points and a probability of arranging the undefined points, we can think of invariants. The concept of invariance takes us beyond the domain of normal data points that we measure using instruments. We have to change the narrative and start looking at the universe as if invariant data production is the new normal, a fundamental property of the universe. Imagine two spheres overlap and a new sphere is generated in the middle, a new clock is born. We say that this new clock is born in the orthogonal space. Moreover this clock is invariant with respect to the two clocks.

The journey that begins at the elementary level, to find an orthogonal dataset, continues, 12 times. It means we find an orthogonal space and from the derived dataset we find another orthogonal dataset, the same process of finding invariants is repeated many times to find the higher level dynamics. One of the advantages of reaching higher dimensions is that we follow the space-time-topology-prime metric pathway accurately. Therefore, fractal mechanics is all about dynamics of invariants in a SOMU.

When we want to derive quantum mechanics from fractal mechanics, first we need to restrict ourselves in one of the 12 invariant datasets, preferrably 6D, where space and time are integrated. Then, 4D, 5D and 6D invariants would work together in implementing events with less energy barrier, and imaginary time. Here are seven basic principles of Fractal mechanics.

**Space-time-topology prime metric**of 12 dimensions is the minimum requirement of a system to implement the fractal mechanics. Space, time, topology and prime, all four are periodic and repeats in their own way. Instead of saying fractal like, we say PPM like, we need to replace the word fractal.**12 layers of invariant network**in the orthogonal space build the dataset. Nowhere in this universe real direct data are taken, always an orthogonal space transformation is required.**Eighty six percent wants to learn 14%**: The dynamics are governed by eternal quest to achieve 14% of the probability space, in SOMU, an architecture of singularity.**Origin of uncertainty**,**metric of metrics**: is 12, 16, 20, 30 universes of different dimensions above 12, which becomes independent and begins to form an independent singularity network or universes. Fractal mechanics begin at 12D but it has many versions. They all work together.**Quantization of space, time, topology and prime**. Entanglement, superposition are derived from 6D alone, similarly, we get unique properties of world line bonding, transformation, projection and in those universes we find grouping following primes. It may appear that they are not as exciting as superposition or entanglement, but, imagine, mathematical similar of dataset deciding where to collapse and how.**Ten classes of phase prime metrics**to regulate time polycrystals in the orthogonal space: 10 PPMs govern dynamic features including fundamental constants and plank constant like various constants one each in a dimension.**Multinion algebra**operations for infinite series returning invariants: Higher dimension algebra where dot products of multinions returns null or constant number. Arithmetic of circles and continued fractions geometric algebra.**Sixty dynamic elements**: 5×12=60 elements of SOMU are dynamic elements that define the constituents of fractal mechanics (find them in our previous blog post).**Superstructure of manifolds**: Multinion manifold dynamics are all embedded locally building a nested architecture of manfolds, one manifold is a subset of another. The architecture of manifolds is the regulator of all dynamics in a SOMU universe.**Action and plank constants and fundamental constants**: Plank constant like several actions form a network to hold invariant network and network of fundamental constants hold the quantization of space time topology prime metric, two kinds of constants are eventually one and unified.