From Hertz to Heaviside and Harmuth

[Henry_Yang]

Ultrawideband, also known as pulse radio, was once a viable candidate to replace Wi-Fi. Although that did not happen, the low energy requirement allows for batteries to last longer, meaning the technology is making a comeback in other sectors of the technological world. It sends messages only in short-range communications and uses radio waves, and was implemented in smartphones only a few years ago.

Hertz and Marconi where early pioneers of Ultrawideband. But due to the inability of the wide bandwidth to share signals, narrowband communications technologies won out and ultrawideband was temporarily forgotten. In the late 1980s, DARPA and the USAF took an interest in developing radar technology with Ultrawideband systems.

Conventional radio systems work by varying the power level of a sinusoidal wave. Meanwhile, Ultrawideband works by generating signals at specific time intervals. Pulses at unique timeframes encode a message and the signals allow for time modulation. Orthogonal pulses can modulate information.

The earliest form of Ultrawideband radio was one of Hertz's Spark-gap transmitters. Raymond Lavas essentially built a modern version of one of these and hooked a METC unit to it. By electrostatically cooling the apparatus to quench the spark, the Shannon entropy was reversed, because the speed of which information can flow is naturally limited by the time it takes for the spark to be extinguished. The plasma must be cool enough to turn off the spark, or the device becomes unstable and the spark circuit breaks.

If the arc is broken on purpose, the system still allows for oscillations of the capacitor, but only in the time it takes until the circuit is quenched. This is why Raymond Lavas left the ends of the filament of the arc lamp on. If he shut the entire thing off, the plasma would not modulate any signals at all.

Gabriel Kron developed a way to solve Kirchhoff's circuit laws using the topology of the circuit itself. David Bohm's Holomovement of plasma has been likened to Kron's method by Dr. Keith Geoffery Bowden. Bowden has generalized the theory to make it converge with the work of Tom Etter. As I mentioned before, Etter is the founder of Link Physics, which Raymond Lavas said is the foundational framework of the RASP computer system. A boundary contains all the information in its interior due to the holographic principle. In potential theory, this is called the "balayage" idea.

The Kron-Bohm-Etter idea needs to be researched more. Etter worked with Ray Solomonoff on Algorithmic Probability, which was inspired by Korzybski's' General Semantics. Solomonoff solved the information packing problem, a solution that I believe will be very relevant when linking Etter's Link Physics with category theory and with Bohm's plasmons.

I have even been so bold as to claim a connection from the Amplituhedron of Yang-Mills fame to Kron's polyhedron model, although the latter does not live in a positive Grassmannian space. Kron uses orthogonal electrical networks to create higher-dimensional simplexes that have electromagnetic waves propagate through their hyper-volumes. Advanced problems in thermodynamics, fluid flow and statistical phenomena can be generalized and solved. Yang-Mills theory deals with particle scattering, however, but the structure of the operads that make up the Amplituhedron is similar to the Kron polyhedron, with the main difference being that the spacetime the Kron polyhedron exists in is real and the spacetime of the Amplituhedron is abstract and its integral gives rise to the real spacetime after the probability amplitude is observed.

Henning F. Harmuth contributed greatly to Ultrawideband communications and modified Maxwell's equations to do so. Boundary value problems from conducting mediums and dielectric materials result in the magnetic field diverging and needing a function like the Heaviside step function to be obtained correctly. Only the Soviet Union was open to this idea at the time it was proposed. The symmetry group of Maxwell's equations is U(1). Harmuth, however, modified it to SU(2). This crashes the Standard Model of Particle Physics because SU(2) is also the symmetry group of the Weak Nuclear Force.

Mendel Sachs noted that Maxwell's equations do not have a discrete spacetime reflection group of symmetries, and neither does the Klein-Gordon equation. This led him to incorrectly remove the discrete symmetries from Einstein's equations and toss the Poincare group in the trash. This is wrong because the bivectors he related to the electromagnetic field vanish in a vacuum, and thus should not be used to represent any kind of force. Einstein was right that they where trivial.

Harmuth moves the other way. He introduces those same discrete symmetries into the Maxwell equations. Now they respect the one-way arrow of time in this universe. He also applied finite differences to the spacetime continuum to remove the infinities that the regular model so often obtains. This discretizes spacetime further and has interesting results in terms of information theory.

I suspect that Kitselman's work on classifying orthogonal functions is related to Harmuth's same work on orthogonal functions in discrete spacetime and information transfer. But I have not yet had the chance to review Kitselman's work.

I have taken an interest in both Kron and Harmuth because their work is the most advanced electrodynamics I have ever seen. I believe that alternatives to the Maxwell theory are essential for moving forward with our understanding of the universe. I have looked at Weber's electrodynamics, and the Ampere-Neumann electrodynamics of Peter Graneau. Both imply that Ampere's law is the correct foundation, the Grassmann made several mistakes, and that the Coulomb law should be relativistic in terms of velocity and direction of charge transfer. Naturally there are many problems in these models and Maxwell's model wins out in the end. But that may not last forever.

Mikado mentioned work by Riconosciuto about interactions with standing waves and the electromagnetic waves in the METC unit that appear to be gravitational. These papers appear in the red notebook that Raymond Lavas gave to Mikado.

My hope is that this notebook and its contents can be retrieved. Riconosciuto's theory is said to be the foundation of modulated gravity waves that carry electro-gravitic communications signals and represents an alternative communications and power system then the one that we've always known. Maybe the secrets of interstellar travel are in there as well.

[Henry_Yang]

May I point out also that Harmuth's SU(2) electrodynamics implies the existence of spin-2 photons. The ordinary U(1) QED theory only permits the spin-1 photon.

spin-2 photons would be gravity like in nature. Whereas the spin-1 particles attract and repel (+ and - charges), the spin-2 particles only attract. Gravity itself is an attractive force and contains no repulsion. The electromagnetic field attracts and repels based on sign of charge.

"Specially Conditioned EM Fields to Reduce Nuclear Fusion Input Energy Needs"
By: H. David Froning, Terence Barrett, and George H Miley
https://www.researchgate.net/publicatio ... ergy_Needs

Now the above paper caught my attention because Dr. Barrett is a co-author of Dr. Harmuth. In this paper, written with two other co-authors, he realizes that spin-2 photons can be used to complete a fusor device similar to Philo T Farnsworth's version. A spin-2 photon, with its always-attractive force, will mediate the reaction in the central electrode and confine the energy in the cage with an efficiency high enough to achieve over-unity.

"Understanding Retrocausality -- Can a Message Be Sent to the Past?"
By: Richard Shoup
https://cs.uwaterloo.ca/~ijdavis/qic890 ... oup011.pdf

Now Raymond Lavas called Link Physics the foundation of the RASP computer setup, despite the fact that Link Physics was invented by Tom Etter in 1996, and RASP by Michael Riconosciuto in or before 1983. However, assuming a dual processing system like RASP did in fact use a system like Link Physics, it is entirely possible that some messages traveled backwards in time and that retro-casual communications are possible.

There is a theorem that a computer using closed time-like curves will be as powerful as a quantum computer. Quantum computers can never outpace the former system. Despite being super powerful, closed time-like curves and multi-sheeted spacetimes gave computers even more power. I believe David Deutsch proved this theorem.

"Quantum Time Travel"
By: John G. Cramer, "Alternate View Column AV-45"
https://www.npl.washington.edu/av/altvw45.html

There is another paper, "Superposition of Time Evolutions of Quantum System and a Quantum Time Translation Machine" by Y. Aharonov, J. Anandan, S. Popescu, and L. Vaidman. Called the AAPV paper by Dr. Cramer in the above article, it details a quantum computer doing calculations in a multi-sheeted spacetime. However, if the probabilities correspond to the size and shape of a gravitational field, and that gravitational field exists in every parallel dimension in a different state, the oscillating motion of said gravitational field will enter the system into a super-position of universes, in which other probabilities, also on the macro-scale, can be affected.

A spin-2 photon field may provide the same effect. And it may be far more powerful. Perhaps Harmuth's SU(2) spin-2 photon can bring the AAPV computer into fruition. spin-2 gravitons are way smaller and weaker and cause the wavefunction to collapse in a different dimension each time, ruining the time travel prospects for us in our own dimension.

We must also not forget Kron's work on a pocket sized crystal computer, something that he actually built, completed, and carried around with him. He began to believe that it was a universe just like ours, and that our universe would ultimately be described in the same way, with the same equations. After he died, the device disappeared, although glass computers and voxels are now apparently arising as interests of some certain corporations...

[Henry_Yang]

Trickfox mentioned that there was a link between Peter Wright and Marcus Kuhn. At least, he said, that as he was googling the technologies that Peter Wright described in the book "Spycatcher", he found Kuhn's thesis in his search results, and then merely speculated openly that Wright and Kuhn both had knowledge of non-sinusoidal waveforms aka square waves.

Peter Wright was an MI5 agent who discovered The Thing. This was a hidden microphone in a wooden carving of the great seal of the United States, a trojan horse gift from the Soviet Union. The microphone was remote activated and had no internal power supply and is sometimes credited to Léon Theremin.

Wright also worked on Operation RAFTER and worked on decrypting Soviet messages and finding agents receiving transmissions decoded through a one-time pad. Wright later accused Roger Hollis and Graham Mitchell of working with Kim Philby, although both accusations where denied.

Now a word on "white noise" and "choas"... These subjects where popular only in the Soviet Union, until Joe Ford brought them to the Western world. Joe Ford also discovered himself the "Ford Paradox", which says that because chaos does not exist at the quantum level, quantum mechanics must not be an adequate model of reality AT ALL... As noted by his GT page:

Significant and outstanding contributions included his work in the field of chaotic dynamics. In 1963 he discovered a new phenomenon, a transition from regular motion to what was later called dynamic chaos. Working with the concept that the exponential instability of motion was the most important property of the new dynamics, he isolated it from other characteristics of nonlinear phenomena and established an empirical criterion for chaos that later became standard. He was a co-organizer of the First International Conference on Classical and Quantum Chaos in 1977 .

In the 1980s until his death, he worked on the exploration of the deeper consequences of deterministic chaos. Again in the role of pioneer, he realized that the concept of chaos transcends the domains of mappings and differential equations. He used "algorithmic complexity" as a means of defining and assessing the fundamental limits of human ability to deal with chaotic systems. He was challenging the very basis of quantum mechanics by questioning the assumption that chaos should enter microscopic descriptions of nature when he died, cutting short his research in this area.

Before he died from cancer, he suggested an experiment that could be done to prove the validity of the paradox:

Joe Ford was a scientist’s scientist who understood that “the true method of knowledge is experiment.” He suggested we go build one of these crazy things and see what happens, rather than simply yakking about it. Why not build a set of small and precise double pendulums and see what happens? The double pendulum is pretty good, in that its classical mechanics has been exhaustively studied. If you make a small enough one, and study it on the right time scales, quantum mechanics should apply. In principle, you can make a bunch of them of various sizes, excite them to the chaotic manifold, and watch the dynamics unfold. You should also do this in simulation, of course. My pal Luca made some steps in that direction. This experiment could also be done with other kinds of classically chaotic systems; perhaps the stadium problem is the right approach. Nobody, to my knowledge, is thinking of doing this experiment, though there are many potential ways to do it.

Trickfox admitted to knowing Douglas Kendall, a friend of Robert Booth Nichols and former MI6 agent. Trickfox claims that Peter Wright's devices are related to the research of Marcus Kuhn. Trickfox also ridicules Kuhn for dismissing Riconosciuto. All the relevant quotes on those matters are quoted in the Trickfox quotes thread.

The connection to TTBrown and the Phasorphone still escape me but I can see clearly that frequency modulation (FM) is a common theme, and that the SE Harris / Riconosciuto work on that subject is tied intimately to the work of G Kron "diakoptics" and to T Etter "Link Physics".

[Henry_Yang]

From "General relativity theory explains the Shnoll effect and makes possible forecasting earthquakes and weather cataclysms"...

So, in 1944 Abraham Zelmanov published his massive theoretical study [3], where he first determined physical observable quantities as the projections of four-dimensional quantities onto the line of time and the three-dimensional spatial section of the observer's reference frame. His mathematical apparatus for calculating physically observable quantities in the space-time of General Relativity then became known as the theory of chronometric invariants [4, 5]. Roger Penrose, Kip Thorne, and Stephen Hawking as young researchers visited Zelmanov in Sternberg Astronomical Institute (Moscow), and listened to his presentations about physical reference frames and observable quantities at his seminar. In particular, Zelmanov showed [3] that an absolute reference frame is allowed in a finite closed universe, if such a reference frame is linked to the global rotation or the global deformation of the universe.

We showed that zero-space is inhabited by light-like particles which are similar to regular photons. We called these particles zero-particles. Zero-particles travel in zero-space with the speed of light. But their motion is perceived by a regular observer as instantaneous displacement. This is one of the effects of relativity theory, which is due to the space-time geometry. We only see that particles travel instantaneously while they travel at the speed of light in their home space (zero-space), which appears to us, the external observers, as the space wherein all intervals of time and all three-dimensional intervals are zero.

We also showed that the regular relation between energy and momentum is not true for zero-particles. Zero-particles bear the properties of virtual photons, which are known from Quantum Electrodynamics (i.e., they transfer interactions between regular particles). This means that zero-particles play the role of virtual photons, which are material carriers of interaction between regular particles of our world.

Zero-space as a whole is connected to our regular space-time in every point: at every point of our regular space-time, we have full access to any location inside zero-space. Once a regular photon has entered into such a zero-space "gate" at one location of our regular space, it can be instantly connected to another regular photon which has entered into a similar "gate" at another location. This is a way for non-quantum teleportation of photons.

We also showed that zero-particles manifest themselves as standing light waves (stopped light) while zero-space as a whole is filled with the global system of the standing light waves (the world-hologram). This matches with what Lene Hau registered in the frozen light experiment [18,19]: there, a light beam being stopped is "stored" in atomic vapor, remaining invisible to the observer until that moment of time when it is set free again in its regularly "travelling state". The complete theory of stopped light according to General Relativity was first given in 2011, in our presentations [20,21], then again in 2012, in the third edition of our book [14]. The obtained theoretical results mean that the frozen light experiment pioneered at Harvard by Lene Hau is an experimental "foreword" to the discovery of zero-particles and, hence, a way for non-quantum teleportation.

Therefore, we arrive at the following conclusion. In terms of relativity theory, the Shnoll effect means that the reference frame of a terrestrial observer is somehow synchronized with remote cosmic bodies. This synchronization is done at each moment of time with respect to coordinates connected with stars (cycles of the stellar day and the sidereal year), and with respect to the coordinates connected with the Sun (cycles of the solar day and the calendar year). Also, the synchronization condition (the form of the histogram) is repeated in the reversed mode in time at each of two opposite points in the Earth's orbit around the Sun, and at each of two opposite points of the observer's location with respect to stars (due to the daily rotation of the Earth): this is the "palindrome effect", including the half-year and half-day palindromes.

Now the second question arises. How is this synchronization accomplished? Regularly, and according to the initial suggestion of Einstein (which was introduced in the framework of Special Relativity), reference frames are synchronized by light signals. But in the case of experiments where the Schnoll effect was registered, the noise source and the measurement equipment were located in a laboratory building under a massive roof. So the laboratory is surely isolated from light signals and other (low-magnitude) electromagnetic radiations which come from stars ... The answer comes from General Relativity.

Second. Synchronization is possible not only of light signals or other electromagnetic signals moving at the speed of light. Instant synchronization of remote reference frames is possible in the space-time of General Relativity [14,17]. This can be done through zero-space--the fully degenerate space-time. It will appear to a regular observer as a point; that is the necessary condition of non-quantum teleportation at any distance in our world. Therefore the "non-quantum teleportation channel" is constantly allowed between any two points of our space. Zero-particles--the particles that are hosted by zero-space --are material carriers in non-quantum teleportation. Zero-particles are standing light waves (i.e. stopped light), thus zero-space is filled with a global system of standing light waves--the world-hologram of non-quantum teleportation channels. According to space topology, there is univalent mapping of zero-space (the world-hologram) onto our regular space (our universe). This means that the local physical reference frame of a terrestrial observer, travelling together with the Earth in the cosmos, "scans" the world-hologram of teleportation channels.

Randomness is due to a choice of coordinates only?

[natecull]

Hi Henry. This big spicy stew feels like a condensed summary of everything I've read in the "weird physics" subculture from the 1980s on. Points for including Gabriel Kron! I remember the Antigravity Handbook crowd being obsessed with him.

Sadly I don't really have any General Relativity mathematics. In fact my brain rebels at even Special Relativity because it always insists on asking "but what is the actual time and velocity of the primary particles, down at the level of the actual ether? Because surely the space-time fabric of the universe doesn't run an infinite number of computations in every possible reference frame, there must just be one really-existing physical thing that's crunching the actual numbers by which the actual Universe does actual physics; describe the time and space coordinates of that thing for me, please". This is because I was exposed to computers at a very young age, running spatial physics simulations in BASIC (aka "video games") and so I have an irredeemably numerical rather than symbolic approach to equations.

What you're talking about with all these GR extensions is interesting, but I don't entirely trust towers of exotic physics speculations. At some point we need to touch experimental data. The Standard Model is ugly, and I hope we replace it with something cleaner, but I don't yet see which of these many possible alternate physics paths is the actual way forward.

We must also not forget Kron's work on a pocket sized crystal computer, something that he actually built, completed, and carried around with him.

Must we not? I particularly remember that very spicy Kron story from the 1980s, and my eyebrows remain raised at it. I think it came via Tom Bearden, who was very excitable but not what I would consider an entirely reliable source.

No, I don't believe that Kron actually did build a "crystal pocket computer" in the 1930s. At least not by the standards of what we now consider a "computer" (a digital von Neumann processor), and not if we're thinking in the sense of "a transparent chunk of glass".

On the other hand, Kron was very interested in analog computers - eg his "Network Analyzer", which like every "computer" before WW2 was analog. So it seems very possible to me that Kron might have scaled his Network Analyzer concept down, and built a small handheld similar device on what passed for semiconductors in the 1930s, in the pre-transistor era ("The Day after Roswell" to the contrary, transistors didn't come out of nowhere). Some kind of "cat's whisker crystal" or diode-based circuit network, that solved equations that could be reduced to voltages and/or oscillations. The sort of thing that might resemble, in its circuit diagram, something like an analog music synthesizer.

Then digital computers (running on vacuum tubes) came out after ENIAC and whipped all the analog computers so hard that that entire field of development vanished. Then we finally got transistors good enough to out-compete tubes (1953 for the first very flaky one of them: https://en.wikipedia.org/wiki/Transistor_computer ) and semiconductors became the foundation of our network society.

But quantum computers are essentially just analog computers come back again (i think particularly the "D-wave" concept is often accused of being literally just a conventional analog computer and not even quantum) - so maybe there's more gas in the "Crystal Computer" tank than we realised, and Kron might turn out to be ahead of the crowd.

Regards, Nate

[natecull]

A few more notes:

The symmetry group of Maxwell's equations is U(1). Harmuth, however, modified it to SU(2). This crashes the Standard Model of Particle Physics because SU(2) is also the symmetry group of the Weak Nuclear Force.

Interesting. I don't know Harmuth (and will start looking), but naively, from a 10,000 foot persective, wouldn't unifying electromagnetism with the Weak Nuclear Force by using the same symmetry group be something similar to Electroweak Unification, which far from "crashing" the Standard Model, is now an accepted part of it? Or is Harmuth's approach to this completely different and unresolvable with the SM, mathematically?

Edit: Yikes! A quick Google on Henning Harmuth and yeah, he's a Very Radar Guy isn't he? Has that deep black military feel all over his stuff. So there's probably some "explosive potential" there.

https://www.nwfdailynews.com/obituaries/ppan0046732

Henning F. Harmuth, age 93, died peacefully at his home in Destin, FL on August 5, 2021. He is survived by his wife Anne Spragins-Harmuth, and daughter, Ursula Harmuth and granddaughter Carlotta Fabian, both of Berlin, Germany.

Dr. Harmuth was born in Vienna, Austria on July 27, 1928. He received his Diplom-Ingenieur degree in telecommunication engineering in 1951 and the Doctor of Technical Sciences degree in 1953, from the University of Technology Vienna. He also studied in Vienna University and University of Paris, France. Dr. Harmuth is the holder of some 30 patents, author of more than 150 journal publications and of 16 books. His last book "Dirac's Difference Equation and the Physics of Finite Differences" was published in 2008. His editor wrote "Henning Harmuth's scientific work always contains explosive potential". Several of his books have been translated into Russian and Chinese. Dr. Harmuth has lectured at universities around the world and as an exchange scientist of the U.S. National Academy of Sciences at various institutes. He retired from the Department of Electrical Engineering at Catholic University of America, Washington D.C., in 1996.

Dr. Harmuth's means of relaxation was as extraordinary as his working life. He and his wife repeatedly enjoyed canoeing adventures in northern Canada exploring rivers of the Northwest Territories in the arctic region.

I guess this book is where he develops his ideas about "sequency" and space-time?

"Information Theory Applied to Space-Time Physics", World Scientific, 1992

https://books.google.com.gh/books?id=1Bwv_v87NMUC

Edit 2: Ok, I've read all the available free chapters of this book. I like where Harmuth's head is at: he's thinking about space-time being discrete and finite because he's thinking from the perspective of a computer/data-transmission person dealing with bits, a viewpoint that (since I am one) I heartily agree with. Would be interesting to see where he goes with that.


However:

Mendel Sachs noted that Maxwell's equations do not have a discrete spacetime reflection group of symmetries, and neither does the Klein-Gordon equation. This led him to incorrectly remove the discrete symmetries from Einstein's equations and toss the Poincare group in the trash. This is wrong because the bivectors he related to the electromagnetic field vanish in a vacuum, and thus should not be used to represent any kind of force. Einstein was right that they where trivial.

Hmm. Again, I'm an idiot where General Relativity is concerned, but I'm aware that Sachs is/was considered very, very far from today's Relativity mainstream, and his idea about removing reflection from the symmetry group so as to use the normally-unused torsion component of the full GR tensor to represent EM, is as you said, generally considered to be extremely unhelpful because (a whole lot of technical issues that I don't understand but I imagine you do). And that's why Sachs is ignored today. It's a sad story but a very common one in physics: the universe just doesn't play fair and use the equations we hope it does.

But.

When you say "Einstein was right that they were trivial" - Wasn't it Einstein, himself, who pursued that particular "trivial" path towards a Unified Field? (The torsion one, I mean). And was interested enough to do that twice? Yes, Einstein pursued a lot of different approaches and abandoned them all. But he came back to that torsion idea at the end of his life, and it's what he was working on with Hlavaty (sorry, can't do the diacritic) and that Sachs then took up. And then the Russian GR crowd, perhaps following Sakharov and his "crystal defects" concept, also picked up torsion and worried at it heavily, and the Psychotronics crowd (with their Townsend Brown obsession) in turn got very interested in what the Russians were cooking.

So while it is indeed probably wrong, because of the universe not playing ball... and Einstein post-1915 having a track record of chasing a lot of futile shadows.... and I don't even understand 1905 Einstein... isn't torsion sort of wrong in a much more Einstein-shaped way than some of the other GR extensions?

I can't run the maths and I don't have any physical intuition for what should look or feel "right" in a GR extension. I still don't even have my head around what makes for a "pseudotensor" vs a genuine tensor (though I know even genuine Einstein-brand vanilla unmodified GR uses pseudotensors - which feels more than a bit odd). But something about "try to find a physical use for every part of the beast, don't throw three-eighths of your numbers away" strikes me as aesthetically pleasing. If the raw geometry of the tensor gives us (something like) 4 distortion vectors in 4 dimensions, so 16 separate numerical quantities by which spacetime can warp, no more, no less... well, isn't that grid possibly telling us something? Why are we insisting on imposing a reflection-symmetry condition on how spacetime must behave - when we don't a-priori know even what spacetime even is? I mean sure we want to reduce the number of unknowns to make the equation more tractable, so more symmetry conditions is better for us - but our computational tractability isn't necessarily what the universe cares about.

Of course, as Sabine H. has pointed out in "Lost In Math" which I just finished reading, aesthetics isn't always a good guide in physics. If it was, good old 19th century Quaternions (not just the vector cross product, but the whole curvy 4D beast) would actually represent something physical and tangible in our macroscopic 4D universe, and not just a throwaway computational tool down at the abstract quantum level.

Nate

[Henry_Yang]

Dear Nate,

When you say "Einstein was right that they were trivial" - Wasn't it Einstein, himself, who pursued that particular "trivial" path towards a Unified Field? (The torsion one, I mean). And was interested enough to do that twice? Yes, Einstein pursued a lot of different approaches and abandoned them all. But he came back to that torsion idea at the end of his life, and it's what he was working on with Hlavaty (sorry, can't do the diacritic) and that Sachs then took up. And then the Russian GR crowd, perhaps following Sakharov and his "crystal defects" concept, also picked up torsion and worried at it heavily, and the Psychotronics crowd (with their Townsend Brown obsession) in turn got very interested in what the Russians were cooking.

If you are referring to Gennady I. Shipov, you may be interested to know that Jack Sarfatti, an American and former member of the FFG is the one continuing that research.

Feynman criticised Einstein in his later years because his new equations "where just math" and "had no physical meaning". Feynman essentially voiced the same criticisms that you are hearing from Hossenfelder.

Even though Hossenfelder was clearly talking about String Theory, not Einstein.

But something about "try to find a physical use for every part of the beast, don't throw three-eighths of your numbers away" strikes me as aesthetically pleasing. If the raw geometry of the tensor gives us (something like) 4 distortion vectors in 4 dimensions, so 16 separate numerical quantities by which spacetime can warp, no more, no less... well, isn't that grid possibly telling us something?

Due to the symmetry of the Gik = Gki tensor, only 10 pieces remain. The other 6 are called "Bianchi identities" and they DO tell us stuff:

http://math_research.uct.ac.za/omei/gr/chap6/node14.html

Of course, as Sabine H. has pointed out in "Lost In Math" which I just finished reading, aesthetics isn't always a good guide in physics. If it was, good old 19th century Quaternions (not just the vector cross product, but the whole curvy 4D beast) would actually represent something physical and tangible in our macroscopic 4D universe, and not just a throwaway computational tool down at the abstract quantum level.

I would like to throw in that Raymond was definitely onto something when he asked where the time = infinitely continuous theory came from. But Minkowski did not use Quaternions because they do not model Lorentz boosts. Complexified Quaternions can, but that is only because of the imaginary i-factor, which was already made use of in the Minkowski vector calculus.

[natecull]

Feynman criticised Einstein in his later years because his new equations "where just math" and "had no physical meaning". Feynman essentially voiced the same criticisms that you are hearing from Hossenfelder.

Yep, I do think that it was Einstein who set the mathematics-first path that the Wittens then later followed with String Theory. I have deeply complicated and ambiguous feelings about Einstein. Especially because I just don't understand what his overall guiding sense of beauty and intuition even was, what it was he was searching for all those years alone. And he was probably very wrong about space being continuous: Harmuth makes a very good case that it can't possibly be because information can't be infinite, and that's an intuition that I do understand.

But Minkowski did not use Quaternions because they do not model Lorentz boosts. Complexified Quaternions can, but that is only because of the imaginary i-factor, which was already made use of in the Minkowski vector calculus.

Perhaps that's true. I've read papers querying that assumption, but I'm not able to judge their merit. I imagine that relativity would have made more use of them if they were useful, so I guess they're not.

The thing about vector calculus though, is that it came from quaternions originally. It took one very important part of quaternions (the cross product), which seemed obviously helpful - but left the other parts which mathematical completeness called for, because they didn't seem (and still don't seem) to map onto actual physical reality. Despite being a very simplest self consistent algebra. One of the earliest ones after complex numbers. It seemed obvious that just like complex numbers, they'd find plenty of uses.. but they didn't. Except in 3D rotation, and then only sort of.

Someone coined the phrase "the unreasonable effectiveness of mathematics in physics" - but quaternions are a very interesting, early, and surprising case of what appears to be the unreasonable ineffectiveness of mathematics. Why doesn't nature like or use them - or stranger still, why does nature like and use part of them but not all of them - even though they're simple and complete and feel like they make a compelling mathematical argument that they ought to exist? That conflict interests me.

Nate

[Jan Lundquist]

Henry, I hope you see this. I am certain that you are off somewhere, doing great things.

Sometimes, when I have a spare hour. I like to stop and reread one of your posts and I always learn something. Thank you for taking the time to write it so clearly.

You and Nate are veritable word wonders, often delivering more than I can absorb in one sitting.

Jan