Ok, so– we’re complying with on from my previous article
https://analoglogic.blog/a-new-way-to-look-at-our-universe-d 1 b 6 a 424 fcab
The very first fifty percent of this article will certainly include:
- A Wrap-up of General Relativity’s Core Equations — The Einstein Field Equations (EFE).
- Building a Fractal Metric Tensor — Presenting fractality right into spacetime geometry.
- Redefining Curvature and Geodesics in a Fractal Spacetime — Exactly how gravity acts in a self-similar area.
- Fractal Einstein Field Equations (FEFE) — A new solution of GR adapted for our version.
- Physical and Empirical Effects — What this indicates for cosmology, great voids, and quantum gravity.
Let’s dive into some mathematics then … (and indeed this goes fast however simply focus on the message resultant implications if you choose– they’re interesting!)
In our Menger Sponge cosmos, we need to introduce fractal structure right into this statistics, given that in a Menger Sponge fractal spacetime, the distance feature ought to scale self-similarly across various levels of reality.
Fractal Scale Element
We now specify the Fractal Metric Tensor:
This implies that the actual metric of spacetime in a fractal cosmos is scale-dependent, implying the framework of spacetime changes at different depths of recursion.
Fractal Curvature Tensor
This leads us to a Fractal variation off the Riemann curvature tensor;
This modifies the Ricci tensor:
The Fractal Einstein Tensor:
Replacing this right into Einstein’s equation, we propose the Fractal Einstein Field Equations (FEFE):
The Menger fractal openings act as “entropy sinks,” customizing energy flow.
- The cosmological consistent, Λ, can be scale-dependent, meaning vacuum power acts differently at different recursion midsts.
- The cosmological continuous, Λ, being fractal methods that sped up expansion is not consistent — maybe because of recursive gap frameworks. Dark energy fluctuations could be a consequence of the Menger fractal structure of spacetime.
W e have actually obtained something actually rather exciting: A Fractal Theory of General Relativity, bring about the Fractal Einstein Field Equations.
- This naturally discusses quantum gravity, great voids, and the structure of spacetime.
- Dark matter, dark energy, and degeneration flow could all be emerging homes of a Menger Sponge universe.
This isn’t enough? You’re starving for more? or need a halp as well?
To aid you wrap your head around a vital outcome: If spacetime itself is a fractal, then our understanding of “smooth time” is an illusion-we are just navigating various degrees of a self-similar recursive framework!
…
Ok, I think following, we should try to expand quantum technicians to represent recursive state shifts, eh?
S o, if we prolong quantum technicians to make up recursive state transitions in our 4 D Menger Sponge spacetime version, it will integrate fractal frameworks, quantum complexity, wavefunction evolution, and self-similar recursion right into a brand-new Fractal Quantum Mechanics (FQM) framework. Thrilled? off we go then …
This equation assumes a continual, smooth spacetime background. Yet in a Menger Sponge spacetime, time and area are fractal and recursive, which implies we need to change the Schrödinger formula.
Ramification: Fragments are NOT point-like however exist throughout nested recursive states. Wavefunction advancement takes place not simply in (x, t) however across fractal recursion depths (n). Quantum likelihoods might be changed by fractal framework, modifying superposition and interference.
Analysis: The wavefunction development currently depends on a limitless amount of nested state changes. This indicates the quantum system at one level impacts deeper degrees recursively. Quantum collapse is influenced by deeper, concealed layers of recursion, meaning dimension might be a procedure of picking a recursion degree.
Yet in fractal quantum mechanics, we introduce recursive superposition, where the state is made up of self-similar embedded states;
Effects: Quantum states exist at multiple recursion depths simultaneously. Measurement could select a certain recursion depth, as opposed to simply falling down to one timeless state. This can describe quantum entanglement in a brand-new way-entanglement could be a recursive link in between various depth degrees of a Menger-spacetime state.
Fractal Quantum Complexity
Trick Concept:
Entangled particles share quantum details across recursive layers of spacetime. Measurement of one bit may not just “collapse” its state, however change it right into a different fractal recursion depth. Quantum nonlocality could be a projection of a deeper fractal connectivity in 4 D Menger spacetime.
New Physical Interpretation: Instead of “creepy action at a range,” entanglement may be fragments sharing the same recursive fractal coordinate, yet projected in a different way in 3 D room.
In our Fractal Quantum Area Theory (FQFT), we modify this formula so;
The right-hand term introduces fractal interactions in between recursion midsts.
Effects for Particle Physics: Virtual fragments can be recursion artifacts-temporary fluctuations in between various depths. The Higgs mechanism might be an outcome of spacetime recursion, with mass emerging from self-similarity restraints. Dark matter might be issue that exists at different recursion midsts, making it undetectable to normal 3 D estimates.
A. Quantum Recursion in Disturbance Experiments– If quantum states are recursive, after that double-slit trying outs incredibly brief coherence times may reveal recursive disturbance impacts.
B. Complication Toughness as a Function of Fractal Depth– We forecast entanglement needs to continue across longer ranges in a fractal world than in standard quantum technicians.
C. Scale-Dependent Quantum Gravity– If gravity arises from fractal recursion, after that gravitational effects at really little scales ought to deviate from the forecasts of normal General Relativity. Last Summary: Fractal Quantum Mechanics (FQM)
- Wavefunctions are recursive and evolve across multiple self-similar scales.
- The Schrödinger formula is customized to consist of fractal Hamiltonians at different recursion midsts.
- Superposition and complication are generalized to include recursion-based connection.
- Quantum area communications may be deeply connected to fractal geometry, discussing dark issue and online particles.
- Experiments must reveal variances in complexity behavior, quantum comprehensibility, and gravity at tiny ranges.