PaulCDaiber

The process of discovery involves the violation of established axioms and principles such that human inventiveness replaces derivation. Years later, retroactively applied rigor teaches the discovery in reverse, as if logical application of known fundamentals led to it. The excitement gets lost, along with the stress and celebration, and most importantly, what is forgotten is the reluctance to transition from the old ideas to the new with all the heartache caused by change. The bumpiness of this process is what I tried to capture in the book Seeking Infinity: A Desperate Hunt for New Applied Math by Paul C Daiber.

@Math_files If you really want to learn what infinity is, read Seeking Infinity: A Desperate Hunt for New Applied Math by Paul C Daiber

A well-known mathematician, the son of one of the most respected mathematicians of the century, taught at a large public university. To protect his privacy, let us call him “Professor X.” One day, he was teaching a calculus class when a student raised a simple but deep question: “Professor, what is infinity?” Professor X paused for a moment, then nodded thoughtfully. “Infinity,” he said, “is like a line that never ends.” To explain, he turned to the blackboard and began drawing a long straight line with a piece of chalk. As he continued, he slowly walked across the room, extending the line further and further. The students watched with curiosity as he moved past the edge of the board—yet he did not stop. Still drawing, Professor X kept walking… straight toward the window. Before anyone could react, he stepped right through it and disappeared. The classroom fell into stunned silence. No one spoke. The students looked at each other, unsure of what had just happened. After a few moments, one student cautiously approached the window and looked down. There, two floors below, lay Professor X—spread out in the bushes, but fortunately unharmed. His lesson, it seemed, had gone a little too far… just like infinity itself. Source: Mathematical Apocrypha by Steven Krantz

Correct. Set up a radial fourth dimension from the Big Bang and through our universe as if our universe is the 3-d surface of a 4-d sphere. By assuming validity of this fourth spatial dimension, there is something, not nothing outside the universe, as if the universe is the shockwave of an explosion. Shockwaves do not rotate, conforming to Gödel’s model of a rotating universe having time loop to its beginning. Also, there is group and phase properties in a shockwave. The group is phonons so that particles in our universe are analogous to phonons, and that means there must be a material outside the universe. Thinking 7-d, this model incorporates even more items familiar to us, like quarks.

@AstronomyVibes The universe cannot expand into NOTHING, which has neither spatial properties nor time. Hubble's law is the radiiluminescence of hydrogen. sbkaravashkin.blogspot.com/2019/03/blog-p… selftrans.narod.ru/v3_1/hubblerus…

If the Universe is expanding, What is it expanding Into?

When Schrödinger’s Equation was first discovered, it was noticed how similar it was to the ideal fluid mechanics equations for mass and for energy conservation. Into Schrödinger’s original equation assume a wave of psi = sqrt(density)*exp(phi - omega*time) with phi the potential for velocity and with the potential energy equal to pressure times the volume of a fluid element. Derive the unsteady form of Bernoulli’s equation.

d’Alembert’s Paradox: The 1752 Paradox That Stood in the Way of Real Aerodynamics In 1752, d’Alembert found a result that still feels wrong at first sight: An ideal fluid can flow around a body and produce no drag at all. In the first animation, viscosity is set to zero. The fluid bends around the object, accelerates, slows down, and stitches itself back together downstream. You get no wake, no loss and no scar in the flow. The equations have removed the very thing that would let the body leave a trace. That is Euler flow: ρ(∂u/∂t + (u · ∇)u) = −∇p ∇ · u = 0 For steady irrotational flow, u = ∇φ and ∇²φ = 0. The pressure field stays perfectly symmetric front to back, so when you integrate pressure over the body, the drag cancels: D = 0 The second animation changes one thing: viscosity is allowed back in. ρ(∂u/∂t + (u · ∇)u) = −∇p + μ∇²u ∇ · u = 0 Now, the surface can grip the fluid. A boundary layer forms. It can separate, vorticity rolls off the body and wake appears. Drag is now built by the flow. Therefore, making viscosity tiny is not the same as deleting it. ν → 0 still has a boundary layer. ν = 0 has no memory.

Per Gödel’s solution for a rotating universe, time loops around back to its beginning. Because that violates cause-and-effect, it appears that the universe should have no rotation. But Friedmann’s 1922 balloon visualization of the universe can also rotate. Therefore perhaps the balloon visualization should be replaced with a shockwave visualization because a shockwave cannot rotate. The implication from a shockwave visualization is that there is material inside (at a smaller radius) and outside the universe, and that violates the null hypothesis popular today that there is nothing, not even void, beyond what can be measured in our 4-d time-space universe.

Kurt Gödel, who was one of Albert Einstein's best friends in his later years, found a solution to general theory of relativity that modelled a strange, unusual and rotating universe allowing for backward time travel.

Maxwell’s Equations can be derived from the Dirac Equation. This is quite simple by setting mass and electric charge to zero, introducing a column spinor for electric charge density, and using all three rotations of the Pauli Spin Matrices. The real insight from this derivation is that it suggests specific properties for infinity that are different from establishment pure math in that infinity cannot be the quantity of a set.

the dirac matrix is not just math it is a compression of relativistic quantum mechanics it encodes: • spin as a fundamental property, not an add-on • compatibility between quantum mechanics and special relativity • the existence of antimatter as a consequence, not a hypothesis. • linearization of the relativistic energy equation at its core are the gamma matrices: • they enforce the structure needed for the dirac equation to work this leads to: • a wave equation that predicts electron behavior correctly and forces negative energy solutions → interpreted as antimatter this is what happens when physics is constrained by symmetry and consistency reality becomes an output of the math

The axis of rotation of a 7-d object corresponds mathematically to the radial direction from the Big Bang through our universe as if our universe is a thin surface of a 4-d spacial sphere. The math uses the three quaternions in the Pauli Spin Matrices and for multiplication every other product has factors reversed. The three quaternions relate to red, green, blue and form six 2x2 matrices, and the seventh using 1 in the matrix is the axis of rotation with the 1 corresponding to the radial direction.

A neutron fits nicely into 7-d because of analogous features to a 7-d object. There is an axis of rotation, and rotation speed appears analogous to electric charge, split -1, -1, 2 between the three planes. There are three planes of rotation, each a cross product of two directions, and those paired directions appear analogous to red, green, blue. Octonion algebra removes a connection from the axis to which pair so that the plane is ambiguous to the pairs, and that is analogous to gluon transfers. Also, because rotation speed is disconnected from the pair, speed can jump to split to decompose to form an electron. This might all sound confusing but the nice thing about it is that it is geometry and so can be easily illustrated. This is presented in the second half of the book The 5th Dimension: Math for Physics Outside Our Universe by Paul C Daiber.

A new theoretical proposal attempts to connect two of the deepest open problems in physics: the black hole information paradox and the origin of particle mass through the Higgs field. The paradox arises because quantum mechanics requires that information is never destroyed, while black holes, through Hawking radiation and evaporation, appear to erase it, creating a fundamental inconsistency in our understanding of nature. The study suggests that this conflict might be resolved if spacetime has more structure than we normally assume, specifically by extending it into a seven-dimensional geometric framework. Within this approach, black holes would not simply evaporate into nothing, but instead leave behind stable remnants that preserve the information that fell into them. Rather than being lost, that information could be encoded in subtle quantum properties of these remnants, potentially restoring consistency with quantum theory. What makes this idea particularly interesting is that the same underlying geometry might also be linked to the Higgs mechanism, which is responsible for giving mass to fundamental particles. In this picture, the Higgs field and its associated mass scale would not be arbitrary parameters but could emerge naturally from the deeper structure of spacetime itself. This creates a conceptual bridge between gravity, quantum mechanics, and particle physics, areas that are usually treated separately. Although still highly speculative, the proposal illustrates a broader trend in theoretical physics: attempts to unify seemingly unrelated phenomena by embedding them in higher-dimensional or more fundamental frameworks. If correct, it would imply that black holes are not just endpoints of gravitational collapse but key probes of the underlying geometry of the universe, with implications that extend all the way down to why particles have the masses we measure. 👉 share.google/WMaPkrNNQUn2Oz…

The Poynting vector as e-field cross m-field was discovered through measurements, and similarly, energy density as e-squared plus m-squared is also only known by experiment and cannot be derived from Maxwell’s equations. The problem is that e-m theory is scattered into many different mathematical equations that were empirically discovered, with the non-relativistic force equations being a few more. Uniting them all into one quantum equation for dynamics of a photon requires a useable mathematical infinity which pure mathematics has not provided to applied math. But small pockets of people have those properties of infinity defined, for example, infinity cannot be the quantity of a set.

@PhilosophyOfPhy Another important layer is how energy moves in these waves. The flow of energy is described by something called the Poynting vector, which shows that energy travels perpendicular to both the electric and magnetic fields.

Electromagnetic waves are self-sustaining patterns of change in electric and magnetic fields that move through space. Start with something concrete. An electric field tells you how a charged particle would be pushed or pulled. A magnetic field tells you how a moving charge would curve. These fields are not just abstract ideas, they are measurable influences that exist in space. Now the key point: changing fields create each other. A changing electric field produces a magnetic field, and a changing magnetic field produces an electric field. This is captured in Maxwell's equations. When these changes are arranged in the right way, they sustain each other and move forward through space. That moving, self-maintaining pattern is an electromagnetic wave. No medium is required. Unlike sound, which needs air, these waves propagate because the fields continuously regenerate one another. The speed at which this happens is fixed by fundamental constants of nature, and it turns out to be the speed of light. So instead of thinking “light is made of something unknown,” think of it this way: light is a traveling structure of fields, where energy and momentum flow through space as a coordinated oscillation of electric and magnetic influences. Photons come later, when we describe how this wave interacts with matter at very small scales. But at its core, an electromagnetic wave is not a thing moving through space. It is a pattern that moves through space.

If the magnetic field wave and the electric field wave were two components of the same wave, then they would both be included in one mathematical model rather than being in two cause-and-effect models as two separate equations in Maxwell’s equations. Yes, e-m theory can be reformulated to unite Maxwell’s equations into one Dirac equation for a quantum model of e-m but it requires dismissing establishment pure mathematics’ countable and uncountable infinities to create an infinity that cannot be the quantity of a set by being unknown and unknowable place-value digits far to the left of the decimal point, and then performing a Lorentz Transformation to the speed of light. But that radical change to fundamental math and the continuum is too deep and so will not happen anytime soon.

@PhilosophyOfPhy So, rather than each generating the other, the electric field and magnetic field are simply orthogonal components of a single electromagnetic field, aren’t they?

@PierceLilholt The bigger question is: What portion of what a person thinks they understand is actually incorrect? Pursuing this question is probably more important for a person.

How much of the universe can a sovereign mind understand before it hits a hard boundary?

@PhilosophyOfPhy Time is the rate at which place-value digits change from unknown and unknowable to known or knowable both before and after the decimal point for a unitless real number, an example of which is the hyperbolic angle between the time and space directions for a moving particle.

What is time ? ✍️

I recommend reading Seeking Infinity: A Desperate Hunt for New Applied Math by Paul C Daiber. It had to shoot for the lower bar of mathematical beauty in the consolidation of the many e-m theory equations, because there is not much new to measure in e-m theory but perhaps an application to quarks/gluons by someone smarter than me will reach that bar. The book has a story line to keep a reader’s interest and so is not boring.

It only looks like a “mess” if you’re mixing formalisms. Maxwell’s equations are already fully consistent and Lorentz-covariant. Energy/momentum come cleanly from the stress–energy tensor, and when you move to QED the connection to Dirac is well-defined. Different pieces showing up in different formulations isn’t a flaw it’s how physics scales across regimes. If you’ve got a “fix,” it should reproduce standard results and make a new testable prediction. That’s the bar.

What’s the most mind-blowing concept in science you’ve come across recently? No explanations needed just drop the topic 👇

If our universe is a computer simulation, then the question is why. Unlike the big and powerful quasars and magnetic neutron stars and such, it is small and physically insignificant life that is likely the reason, because life, especially human life, is not only self-aware, but humans team together to build AI robots and space ships. But for what purpose? It would not be for entertainment. Rather, perhaps people create ideas and technologies the outside entity needs, or our minds interface with a control system. It’s hard to imagine how religion factors in, but maybe that’s how humans are made cooperative.

Many people subscribe to the Theory that the most likely outcome is that we’re all living in a Simulation. If we’re living in a simulation… who’s running it — and why?

@YuDai_Tsai I have two books on reversing the divergence of math from physics, and both are quite entertaining because of unconventional ideas. The 5th Dimension: Math for Physics Outside Our Universe, and Seeking Infinity: A Desperate Hunt for New Applied Math by Paul C Daiber.

幾世紀以來，數論與粒子物理看似沿著兩條截然不同的道路發展。 一者研究純粹的數字規律，一者探索構成宇宙的基本。 然而，它們之間其實潛藏著出人意料的深層聯繫。 量子規範理論的一致性條件，將粒子電荷分配的問題轉化為一個經典的數論難題, 並預示一個全新的輕粒子質量譜 arxiv.org/abs/2603.12320

Photon theory is a disaster because it is spread out into several different empirically derived equations for its theory. And none of them is a quantum model of photon dynamics. The problem is that an infinity is needed in applied mathematics. The infinity that is needed is to restrict the quantity of zeros before the decimal point for the hyperbolic angle between time and space dimensions to a largest number so far counted to, and further than that the zeros do not yet exist, to cause large-scale imprecision. This large-scale imprecision is infinity, but it cannot be the quantity of a set. Use it in a Lorentz Transformation to the speed of light in the Dirac Equation and the result unites all those different empirical models.

When we think about energy in everyday life, we often imagine it as smooth and continuous. But in quantum physics, energy is not continuous—it comes in small, discrete packets called quanta. These packets of energy are known as photons. Instead of a smooth flow, energy is exchanged in tiny, separate units. At a fundamental level, the universe is made up of particles, not continuous substances. So the classical idea of continuous energy is replaced by quantum physics—the study of how these energy particles interact with one another.

The debt we owe ancient astrologers who sought to understand God’s entry into our container of a universe is that perfecting those observations led to astronomy. Similarly, the numerology of the Pythagoreans led to Hellenistic mathematics. And Newton’s alchemy led to today’s chemistry. Before the science existed, curious minds used superstition because it was all they had. The supernatural had not yet separated from the natural. And today there are many beliefs that will appear just as insane to future generations. I call these today’s null hypotheses.

I don't have to be an expert in astrology to know that astrology is bullshit.

Never ask how .999… equals 1 because the answer is dependent on belief in the establishment pure mathematics of countable/uncountable infinities and the Dedekind cut, and the supporting incomplete bijection proofs. “It’s called real analysis”. “Infinity is not a position”. If a person learns enough to be included in that belief, then perhaps they have been indoctrinated rather than taught. Cruel as that sounds, reactions are expected to be crueler, because beliefs are defended with mockery and insults, and because rational arguments are boring in comparison, beliefs win. Obviously, this observation has its roots in frustration.

In mathematics, I'm always amazed by how often people are afraid to ask questions, like in lectures and seminars. You aren't born knowing this stuff. It takes a long time to learn, and questions are one shortcut to knowledge

@pickover If 99^100 > 100 ^99 and since 2^3 < 3^2, then at what sequential pair of integers does the < change to a <?

Math: "Exponent Showdown." Which is larger: 100⁹⁹ or 99¹⁰⁰? At first glance it looks like a simple comparison… but it’s a beautiful little trap that reveals how our intuition may fail with exponents. Take a guess, then try to prove it without a calculator.

The null hypothesis is that math is only a language for physics. This null hypothesis is based on no need to combine the two. But people should not be so closed minded that they say it is impossible to combine math and physics to make math more than a language. Eventually people will find the two are combined because to dispose of the baggage of Cantor’s two infinities a real number becomes a rational number that has precision improve as time advances. And when that reconstruction of numbers leads to a prediction for a measurement in a clean model of the strong force, data will support a new null hypothesis.

“Mathematics exists independently of us, yet the way we express and use it is a human creation. Nature follows its own rules whether we understand them or not; mathematics is the language we have invented to discover, describe, and make use of those rules. In that sense, it lies somewhere between discovery and invention—a kind of ‘discovention.’” — Terence Tao ✍️

I did not comprehend how the complex conjugate models time in reverse or how it relates to e-m. But I can contribute. The e-m field can be written as a Dirac spinor by changing real numbers to be rational numbers that become more precise as time advances, because the imprecision portion of a real number pertains to the e-m field. The math is in each of my latest two books that are given in the pinned tweets on my profile.

🪞 Every quantum probability you've ever calculated has a wave running backward through time. Nobody talks about it. P = ψψ*. Two factors. One propagates forward. The other propagates backward. Every overlap integral. Every matrix element. Every expectation value. Since 1926. Wigner proved it: the time-reversal operator IS complex conjugation. ψ* runs backward through time. That's not interpretation. That's the formalism. In 1945, Wheeler and Feynman showed the time-symmetric version of electrodynamics is fully consistent. Dirac showed in 1938 that using half retarded plus half advanced fields kills the electron's infinite self-energy. No renormalization. The "unphysical" solutions fixed what the standard ones couldn't. Then Cramer connected the two: ψ* is the advanced wave. Measurement is a handshake across the light cone. Here's the part that got under my skin. The time-symmetric sector that Heaviside and the Lorenz gauge deleted from classical EM in the 1880s was smuggled right back into quantum mechanics through the one symbol nobody questions. The complex conjugate. Today's article traces how Act 2 of the deletion connects to the Born rule, and why the "measurement problem" might be partly an artifact of refusing to read ψ* literally. 👉 open.substack.com/pub/drxwilhelm… 📬 Article 5 of 10. This article is free. Subscribe to get the next one delivered to your inbox — the physics that textbooks skip. Paid subscribers also get The EED Playbook — from the three deletions to the experiment you can build yourself: news.advanced-rediscovery.com/p/thank-you-20…