Quantum systems require a new way to think about math.

"IISc physicists discovered that Ramanujan’s classic π-formulas arise naturally in modern theories describing critical phenomena and black holes. The connection suggests his early mathematics may have foreshadowed key structures in today’s high-energy physics. Credit: Stock" (ScitechDaily, Ramanujan’s 100-Year-Old Pi Formula That Hides the Secrets of the Universe)

"A new study reveals that Srinivasa Ramanujan’s century-old formulas for calculating pi unexpectedly emerge within modern theories of critical phenomena, turbulence, and black holes."(ScitechDaily, Ramanujan’s 100-Year-Old Pi Formula That Hides the Secrets of the Universe)

100 years ago, Srinivasa Ramanujan introduced a Pi formula that hides a powerful argument. Pi is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics and physics, and some of these formulae are commonly used. for defining π, to avoid relying on the definition. Of the length of a curve.” Wikipedia, Pi) We know that Pi has a certain value, and we can use that value in mathematical formulae. To use in calculations to determine the area of the circles. 

Pi is also needed. To calculate the volume of things like balls. The ball can be. Determined as a series of circles or rims. So, where is that information needed? What would you do with formulas that can calculate the distance from the ball surface to the layer? That information is useful in the calculations. That is used. For. Calculating the qubit interaction with the receiver. This information is urgent for quantum networking and quantum computing. 

The new quantum systems require new types of calculations. Or those calculations are not. A very new thing. The needed accuracy. The third-degree and higher polynomial functions are very high. The new mathematical formulas must be created. For the quantum systems that require new types of dimensions. And new variables. To make it possible. To simulate quantum systems. For making a complete simulation, the machine requires all information from the system. And the main problem with quantum systems is this. Everything happens in the 3D universe. 

"Choose a point on the circle (blue). You want to map it to a unique point on the straight yellow line. To do this, draw a dashed line between the green point at the top of the circle and your chosen blue point. Then map the blue point to whichever yellow point this dashed line passes through. You can do this for any given point on the circle. (The green point at the top of the circle gets mapped to a special yellow point at infinity.)" (QauntaMagazine, String Theory Inspires a Brilliant, Baffling New Math Proof)

"Unlike in the previous examples, your dashed line sometimes maps two different points on the elliptic curve (blue) to the same point on the yellow line below. You can’t find a map that avoids this, meaning that the elliptic curve has a more complicated set of solutions than the circle or sphere." (QauntaMagazine, String Theory Inspires a Brilliant, Baffling New Math Proof)

A second problem is this. Everything means something in those systems. Things like solar winds, changes in magnetic fields. And other kinds of things. It can have a big effect on systems. There, a superstring travels through a photon. And that turns a photon into a quantum router that shares photonic information into qubits.

Those calculations are needed for models that the systems use for quantum simulations. The millennium problem P=NP (P versus NP) means that checking calculations should be as fast as solving them. Error detection happens. By. Calculating all calculations backward. The problem is in extremely long calculations. If.  The machine uses. Even. Days to calculate some formula. Using backward calculation is a very long process. So if some stage needs more time to check, there should be a problem. But the fact is this. Nobody proved or disproved that problem universally. 

“The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved.”(Wikipedia, P versus NP problem). The idea is that these complex polynomials can be checked by calculating the time. If P=NP. 

Here, "quickly" means an algorithm exists that solves the task and runs in polynomial time (as opposed to, say, exponential time), meaning the task completion time is bounded above by a polynomial function on the size of the input to the algorithm. The general class of questions that some algorithms can answer in polynomial time is "P" or "class P". For some questions, there is no known way to find an answer quickly, but if provided with an answer, it can be verified quickly. The class of questions where an answer can be verified in polynomial time is "NP", standing for "nondeterministic polynomial time” (Wikipedia, P versus NP problem)

The new calculation models give new changes. To solve and check a complex polynomial problem. Things. Like, high-class polynomial functions are new tools. For quantum simulations. New. High-power computers can be used to calculate polynomial functions with new accuracy. This thing requires new accuracy for mathematical constants, like Pi. 

https://www.claymath.org/millennium/p-vs-np/

https://www.quantamagazine.org/string-theory-inspires-a-brilliant-baffling-new-math-proof-20251212/

https://en.wikipedia.org/wiki/P_versus_NP_problem

https://en.wikipedia.org/wiki/Srinivasa_Ramanujan

The brain uses memory Lego to create new behavioral models.

“Princeton researchers found that a primate’s prefrontal cortex reuses modular “cognitive Legos” to solve related tasks, giving biological brains a flexibility that AI still lacks. The insight could help improve AI systems so they retain old skills while learning new ones. Credit: Adapted by Dan Vahaba (Princeton University), from “Brain Silhouette 2” (Littleolred, CC0 1.0, freesvg.org) and “Lego bricks” (Benjamin D. Esham, CC BY-SA 4.0, Wikimedia Commons).” (ScitechDaily, Your Brain Has a Learning Shortcut AI Can’t Copy)

Behavior is the reaction that we see from the outside. And. When an actor notices something, that something acts as a trigger. The trigger launches. A certain behavioral reaction. When we see our friends, we can say “hi”. Or, when we slip on the ice, we put our hands in a certain position, that protects our head from impact with the ground. This means that. When we see something. Hear something, or feel something that causes a reaction. Does something cause a reaction, and what type of reaction is? That depends on the memory blocks connected to that sense. If. There is no memory connection with sense. That doesn’t launch a reaction that we see as behavior. 

The ability to use complete building blocks to create new behavioral models makes human brains more effective than any AI. The AI cannot mimic that ability. Each memory block is like Lego. And. It gives flexibility and effectiveness. To handle memories. And especially the behavior or reflexes. Those are connected with those memories. 

The idea is that there is so-called macro behavior. Behavior is the thing. That. The memory block activates. The modular structure of memories. And actions. What we see from the outside gives humans incredible flexibility. The macro-behavior is like a puzzle, an entirety that includes multiple smaller bits.  Each macro-behavior module can act as a module for larger-scale macro puzzles. 

This means that the human brain handles behavior like a set of modules, which can connect and reconnect with other modules. If we think that. The human brain includes about 100 billion neurons. And each of them has one memory unit. That means there are 100 billion memory units. That gives very high flexibility and morphing ability. For those. Memory structures. The AI cannot mimic those things because that requires the ability to handle so many memory units simultaneously. 

The ability to create new behavioral modules makes human brains effective. The ability to interconnect those modules is unique. One of the reasons. The reason this thing is so unique is that the neuron is not passive. The neuron knows what kind of data it can handle. So it can tell other neurons. That. It's a neuron that processes signals that come from the eye. This means that the neuron that transmits a signal from the retina can ask the routing for data to the neuron that can handle that vision information. 

This saves energy and time because the signal doesn’t disturb other neurons. The transmitter neuron connects a mark. Like a serial number, to the data packet. This information includes data from the transmitter neuron. And if the route that neurons select is wrong. And the receiver neuron cannot handle that information. It can send that information back to the transmitter. Then the routing neurons can ask where the right receiver is. 

https://scitechdaily.com/your-brain-has-a-learning-shortcut-ai-cant-copy/

Gravitational lensing and twist in the universe’s expansion.

“Timing delays in quasar light bent by massive galaxies offer a fresh way to measure the universe’s expansion, and the results deepen the rift between early- and late-universe estimates. This growing tension may be a clue that something fundamental about cosmic physics is still undiscovered. Credit: SciTechDaily.com” (ScitechDaily, Gravitational Lensing Reveals a Twist in the Universe’s Expansion)

When there is a difference between observations and theoretical models, it means. Something is missing from the model. The missing thing. It might be the fifth force or some other large-scale effect. Like a spinning megastructure. Because the material is not homogeneously spread. Through the universe. That means its effects are not homogeneous. The just-found megastructures are like strings throughout the universe, and they should cause interactions. That slows large areas in the universe. 

Things like previously unknown high-energy reactions can also cause unpredictable effects in the universe. When GRB or CRB injects energy into particles, they will not deliver that energy straight away. They glow or. Deliver energy for a while. 

Those megastructures can also form a maser effect inside them. That means. They will collect energy into those massive structures. Like. Metal tubes do. When a magnetic field forms inside it by rolling an electric wire around that tube. Those megastructures act like all other tubes. But they are far larger. So, they might have a stronger electromagnetic effect than previously thought. 

The previously unknown megastructures can cause a need. To re-estimate cosmological principles. An extremely. A large megastructure. It can have a gravitational effect on large parts. Of the universe. Those spinning megastructures that can close chains of galactic superclusters. Inside them can cause previously unknown interactions in some areas of the universe.  That means the universe’s expansion speed might not be the same everywhere

The universe’s expansion is slowing. Or, is it? The question is about the Hubble constant, which is thought to be 73 km/s per megaparsec (km/s/mpc). But in some new measurements, the Hubble constant is slowing down to 67 km/s/mpc. But there is also a possibility. The expansion of the universe. It is not the same everywhere. This means that. There are masses. That. We don’t know in the universe. If something slows the expansion of the remarkable part of the universe, that thing must be very massive. The thing that slows the expansion can be in the universe. Or, outside the universe. Or something else. The expansion of the universe depends on many things. Like, cosmic voids. 

And the differences between quantum field energy levels. Those things cause energy flows. That can have. An unexpected, powerful effect on the universe’s expansion. If. The effect’s area is large enough. It can have. An effect. On the entire universe. There are observations. The universe’s expansion. This is not in line with a young universe. The reason. For It. It can be that the radiation and temperature in the young universe. It was higher than in the modern universe. But that universe caused a stronger redshift in space around it. 

Nobody expected that. Objects were close to each other, and they caused redshift between each other. We can think. About things. Like merging black holes. Those black holes stretch radiation also between them. In the young universe, the scattering effect was stronger. And this caused the idea that the young universe needed. To have components. That is unknown. Some quite common particles. In the young universe. Exist in the modern universe. In very high-energy areas. Also, those exotic particles existed longer in the young universe. This can cause measurement mistakes. If. We use models. Those were made for the modern universe.

“A montage of eight time-delay gravitational lens systems. There’s an entire galaxy at the center of each image, and the bright points in rings around them are gravitationally lensed images of quasars behind the galaxy. These images are false-color and are composites of data from different telescopes and instruments. Credit: ©2025 TDCOSMO Collaboration et al. CC-BY-ND” (ScitechDaily, Gravitational Lensing Reveals a Twist in the Universe’s Expansion)

It’s possible that the hypothetical fifth force is not a new force. It might be some previously unknown interaction between known natural forces. And, maybe EM-fields. If the model doesn’t fit the system, it means something is missing. 

Gravity and light interact. In the same way, new observations show. Electromagnetic fields can also have. A stronger interaction with light. Than predicted. This means the fifth force might not be some new force. It might be a previously unknown interaction. “Scientists have recently discovered an interaction between an electromagnetic wave and its own magnetic component as it passes through a material, updating a 180-year-old assumption that only accounted for the interaction between light and its electric field.” (Science Alert, A 180-Year Assumption About Light Was Just Proven Wrong)

“This phenomenon, the Faraday effect (FE), was first described in 1845 by Michael Faraday, providing some of the earliest evidence of interaction between magnetism and light waves.”(Science Alert, A 180-Year Assumption About Light Was Just Proven Wrong)

“It describes how a beam of light passing through a transparent material is affected when that material is subjected to a magnetic field. Specifically, this changes the direction of polarization of that light beam.”(Science Alert, A 180-Year Assumption About Light Was Just Proven Wrong)

For a simplified perspective, light can be unpolarized or polarized. When light is unpolarized, its electromagnetic oscillations occur in various directions (perpendicular to its plane of travel).”(Science Alert, A 180-Year Assumption About Light Was Just Proven Wrong)

So can some other interaction. Between photons and light remains unknown. Another thing is that. If some particles travel out from the universe faster than the main material. That means those particles can decay or vaporize throughout the universe. This means that those particles release energy, which pushes the universe or even large megastructures back. 

The light and its interaction with gravity mean that the light. Will not necessarily travel on straight routes. Gravitational lenses bend light. Also, things like string gravitational fields can stretch light. This causes an unexpected redshift. Things like cosmic voids can also cause an effect. The wave movement that travels into those voids can jump back from its center. The universe is full of cosmic voids. That means. Those voids can collect and reflect energy. In the same way. Spinning megastructures.  It can bind energy into them. When those megastructures spin, that spin binds energy. And those megastructures can have a large-scale effect on the universe. The previously unknown structures and interactions can affect things. Like, the Hubble constant. 

https://www.sciencealert.com/a-180-year-assumption-about-light-was-just-proven-wrong

https://scitechdaily.com/astronomers-discover-one-of-the-largest-rotating-structures-ever-seen-in-the-universe/

https://scitechdaily.com/gravitational-lensing-reveals-a-twist-in-the-universes-expansion/

Gravitation and beyond.

“A 1977 theory known as quadratic gravity was long left to languish because of its negative-energy “ghost” particle. But the ghost might not be a deal-breaker after all.” (Quanta, Old ‘Ghost’ Theory of Quantum Gravity Makes a Comeback)

Is it possible that gravitation is not one single force? Or is it possible that dark energy forms dark matter when that energy string travels through the particle? The gravity wave is like an energy ditch that travels through the universe. And that pulls objects into them. 

The gravitation model goes like this. The fast-spinning particle binds energy. From around it. And transforms that energy into kinetic energy. If that energy field is lost, that forms a situation. Where the particle or object starts to send energy. Out of it. If we think that there are hypothetical tachyons, faster-than-light particles, those particles will be invisible until they slow their speed. At a speed. That is slower than the speed of light. So are photons the codensation fields? But there is another gravitational model. That could support the existence of tachyons. The tachyon would be a particle. 

That can tunnel through other particles. This phenomenon behaves as a thermal pump. That takes energy. Out of the particle. When energy travels. From a particle, outside energy tries to fill that space. So, are Hawking radiation and gravity the same thing? And are tachyons and gravitons the same thing? The fact is that. The evaporation of particles. It can also occur. Energy fields into it. 

So we have four forms of gravitation. 

1) Quantum evaporation makes that bind energy. That means when the universe expands. Quantum fields in the universe. Turn weaker. That causes an effect. The particle acts like an ice bite that melts in the room. Same way. As ice. A particle that turns into a wave movement. Requires energy for that process. That binds energy from the room. 

2) When the particle spins very fast, it binds energy from its environment. That makes energy fields travel to the particle. That binds energy from its environment. And when the energy field travels to a particle, or gravitational center. That traveling field transports particles with it. 

3) Fast-moving particles like hypothetical tachyons travel through a particle. That makes those particles act like a thermal pump. When those particles. That tunnel itself goes through another particle. They transport energy out of it. The particle acts like a thermal pump. 

That causes an induction thought. 

4) Can dark matter form when dark energy, or an extremely short-wave energy string, travels through a particle? In that model, dark energy is a wave movement that acts like a thermal pump. It takes energy with it. And if it can bind enough energy, it denies the reflection. 

5) The string model. So, can there be a string model of gravity? There is also a possibility. That gravitational effect forms in quantum entanglement. Between two quarks or some other particles, or even between entire atoms, which makes quantum entanglement between them. If that kind of quantum channel forms between two atoms. That effect forms the quantum tornado, or quantum channel, between those atoms. And then outside energy fields push those particles or structures toward each other. 

Cherenkov radiation glowing in the core of the Advanced Test Reactor at Idaho National Laboratory.

"Cherenkov radiation is an electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium (such as distilled water) at a speed greater than the phase velocity (speed of propagation of a wavefront in a medium) of light in that medium.[2] A classic example of Cherenkov radiation is the characteristic blue glow of an underwater nuclear reactor. Its cause is similar to the cause of a sonic boom, the sharp sound heard when faster-than-sound movement occurs. The phenomenon is named after Soviet physicist Pavel Cherenkov."(Wikipedia, Cherenkov radiation)

If somewhere is a sound barrier, could there be a light barrier? The blue-light shockwave or Cherenkov radiation supports that model. Cherenkov radiation forms when a particle travels faster than light travels in water. The particle cannot travel faster than the speed of light. So it must release its energy. So that its speed can decrease. And we see that thing as the blue light shockwave around nuclear reactors. 

"A new theory, that explains how light and matter interact at the quantum level has enabled researchers to define for the first time the precise shape of a single photon. Credit: Dr. Benjamin Yuen. Researchers have developed a new quantum theory that for the first time defines the precise shape of a photon, showing its interaction with atoms and its environment."

Photon. The photon is like a wheel. And that can explain why it has energy stability. There it gets as much energy. As it releases. Energy transfers into a photon from inside and outside. Or, the photon has. A little bit higher energy level. Than the environment.  This can explain why a photon has no mass either. Because a photon cannot release or bind energy. Or the photon has a slightly higher energy level than its environment. Which means energy cannot travel to the photon. Because a photon transmits energy to its environment. That means the photon pushes other particles away. Because a photon conducts energy from its environment. It makes the photon hover above the environment. We can think. If there could be some kind of string. That transmits energy to a photon. That energy pushes fields and particles out from the photon. That explains why a photon has no mass, and that model also works if the photon is stopped. 

Sonic boom. 

Subsonic Mach 1 Supersonic Shock wave. If tachyon exists. It should behave like this. 

Wave movement or an extremely fast particle that tunnels through other particles and systems can take energy with it. That acts like a thermal pump, which can take so much energy with it, that there is no other reflection from the particle. 

The wave movement that tunnels through the particle also acts like a thermal pump. If wave movement travels through a particle, it can make that particle invisible. In that case, the wave, or energy string, can pull energy through the particle so fast that it cannot send a reflection. The thing that makes a particle invisible is the reflection. If there is some kind of quantum flow through the particle. That takes enough energy with it, that denies the reflection. 

In models. A particle is like a whisk. The superstring forms a structure. There is a model. There can be a quantum-sized black hole in every particle. The relativistic jet can transport energy in two directions. And that is one thing that could keep particles in their form. 

There is a small. Quantum low-pressure inside it. Superstrings are extremely thin waves. The spin of a particle forms a small quantum whirl around it. And we see that thing as a particle. When one extremely thin superstring travels through the particle. That thing can transport all the energy. Out of the particle. With it. And that thing makes the particle invisible. Or, the particle is invisible to an observer who doesn’t stand in the line of the superstring that carries energy out from the particle. This makes energy fall. To the particle. And the speed of the energy flow determines. How strongly quantum fields travel to the particle.

There is another thing that can make material invisible. That is the quantum entanglement between two photons. If two photons make some kind of electromagnetic tornado, or channel between them. That thing makes the quantum tube, and if that tube goes through the quantum fields. Energy that travels through that channel can make particles around it invisible. And this can make the ultimate stealth system possible. 

So if we someday could make a tachyon engine. That engine should be the system that sends tachyons forward rather than backward. Those tachyons can make a channel through the space, and that channel pulls craft into it. The confirmation of tachyons is not. A very easy thing. Tachyons are tachyons only if they travel faster than the speed of light. And that means tachyon remains for a very short time. When a tachyon escapes from a black hole. That particle releases its extra energy. 

The gravitational model is hard to make. Gravitation makes particles and fields behave like low-energy particles. Gravitation puts energy. To travel to the gravitational center. And that forms the “shadow” to the side of gravitational centers. That energy shadow causes a situation. Where the field. At the opposite side of the particle that travels to the gravitational center. Pushes the particle into it. The season for why nothing can escape from inside the black hole’s event horizon is this. There is no field or particle that can travel faster than the speed of light. Because particles ride on the field, the effect is similar. As we try to make a boat to travel against the river flow. We must put the propeller spin so fast. It can push water flow backward faster than the river flows. 

The engine should make the electromagnetic wave. Into the energy, or quantum field flow, that it can push against it. If the flow takes that wave away, the object cannot move forward. The problem is: how to make a quantum shadow. To the front of the object. The system should fire particles against the flowing field. That it can turn the field to move past it. The idea of the tachyon engine is that there can be a particle that travels faster than light. 

In modern models.

A hypothetical tachyon. It can be the carrier particle. That carries the Hawking radiation. The thing that supports this model is that. When a tachyon travels through space. It leaves a quantum boom.  That is similar to a sonic boom. Behind it. That quantum sonic boom, or “crossing the light wall,”. Causes a situation.  Where there is a higher-energy wave behind  the hypothetical tachyon that denies other energy, and quantum fields travel to that cone. The photon. It would form when a tachyon slows its speed below the speed of light. So in this model. The photon is the condensation ring of the quantum field. That forms when a hypothetical tachyon releases its kinetic energy to the quantum field around it. 

https://www.quantamagazine.org/old-ghost-theory-of-quantum-gravity-makes-a-comeback-20251117/

https://en.wikipedia.org/wiki/Cherenkov_radiation

https://en.wikipedia.org/wiki/Dark_energy

https://en.wikipedia.org/wiki/Dark_matter

https://en.wikipedia.org/wiki/Fundamental_interaction

https://en.wikipedia.org/wiki/Graviton

https://en.wikipedia.org/wiki/Gravity

https://en.wikipedia.org/wiki/Hawking_radiation

https://en.wikipedia.org/wiki/Sound_barrier

https://en.wikipedia.org/wiki/Tachyon