#### The incompleteness of relativity and quantum theories

So, for me, there’s always been a nagging shortfall of visualization for the major theories of modern physics: Relativity and Quantum theories. Successful theories indeed. But a focus on the mathematics, with some hand-waving surrounding implicit assumptions (or definitions), conveying a flawless formulation in popular presentations.

As discussed elsewhere, in Quantum Mechanics there’s the long-standing “*shut up & compute*” mantra. And legacy characterizations of particles and waves. Like, odd visualizations of huge radio telescope dishes collecting EM “particles.” Or, “force carrying” (fundamental) particles somehow producing attraction and repulsion.

In Relativity, there’s the mantra “*the speed of light (electromagnetic radiation) is the same (constant) in all inertial frames of reference*.” But the long-standing nag’s been how those frames are known to be inertial – sans any acceleration (even a tad) – as agreed upon between all observers.

Elsewhere the incompleteness of the Standard Model of physics has been discussed. And the quest to integrate relativity and quantum theories (a quantum theory of gravity, for example). A presentation below highlights how defects can still lurk in the metaphors and mathematics.

The first article below provides some historical background on how Einstein developed his theory of relativity. The second piece is a YouTube video which discusses an unresolved flaw (*internal inconsistency*) in the conceptual framework of relativity.

#### How we came to understand that electricity and magnetism are linked

Here’s a useful recap of how we came to understand that electricity and magnetism are linked (rather than independent) phenomena. Some seminal experiments. By tinkerers.

• Big Think > “71 years earlier, this scientist beat Einstein to relativity” by Ethan Siegel (June 28, 2023) – Michael Faraday’s 1834 law of induction was the key experiment behind the eventual discovery of relativity. Einstein admitted it himself.

All of these phenomena [demonstrated by Faraday] could be encapsulated by a single physical rule, known today as Faraday’s law of induction.

In the first scenario, you move the magnet into a stationary, conducting coil. …

In the second scenario, where you instead keep the magnet stationary and move the conducting coil down onto the magnet, …

… experimentally, both of these setups [that seem so different on the surface] must be equivalent. In both scenarios, a magnet moves into a coil of wire at the same speed, where they produce the same electric currents of the same magnitude, intensity, and direction in the coils of wire.

And it was this realization, more than any other, that led Einstein to the principle of relativity.

The principle recognizes, first and foremost, that there is no such thing as a state of absolute rest. … Only relative motion within the system matters …

#### On the relativity problem – absolute acceleration is undefinable – ether redux

Here’s a provocative, historical perspective visualizing conceptual inconsistency in relativity (in line with my interest in a theory of space – see paper cited at end of video). Sort of a lesson in having your cake and eating it too (having absolute acceleration in a relativistic paradigm).

• YouTube > Dialect > “Why The Theory of Relativity Doesn’t Add Up (In Einstein’s Own Words)” (June 24, 2023)

Description: Relativity is as successful a theory as it is mind-bending – yet Einstein himself did not believe it was complete, and in a 1914 paper he critiqued its internal consistency at some length. … and so here we find ourselves compelled to ask the same question Einstein did over a century ago: is the theory of relativity truly consistent, and if not, what does this mean for its future?

Video chapters: *Intro, Of Axioms & Absolutes, Einstein Calls Out His Own Theory, Defining “Absolute” Acceleration, What are We Accelerating Relative to, Einstein’s Mistake, Where Do We Go from Here*.

The quest for “a more intuitive and concrete way of understanding the Theory’s formalism” sans mathematical abstraction

[from transcript file]

For that reason in a 1914 paper entitled “on the relativity problem,” Einstein wrote that he felt special relativity suffered from the same

undeniable fundamental defectthat Newtonian physics did – that is, thatit relied on a notion of absolute acceleration in order to complete its formalism.For instance if you say you’re accelerating in a car, you’re implying that you’re accelerating relative to the ground. but if that ground were say actually the deck of a boat accelerating equally and oppositely over a body of water, then relative to someone on the shore you’d actually be at rest.

… the answer to this problem is to define absolute acceleration [non-inertial motion] as meaning acceleration

relative to an inertial frame.But of course inertial frames are defined via an absence of acceleration so this definition is horrifically circular!

[Nope, accelerometers don’t help. Invoking “the rest of the universe” as a frame is no help – the problem of locality ensues. Tensors are just a mathematical repackaging, eh.]

… and special relativity, of course, rejects both these possibilities, telling us that we can have neither absolutes nor ethers.

For the remainder of his life, Einstein would struggle to interpret the meaning of Relativity, changing his mind frequently about its implications and completely reversing his stances on topics such as the existence of the Ether or Mach’s principle.

Indeed, it’s easy to see that this defect comes about because we want to treat acceleration as absolutely real and yet at the same time persist in saying that all the components which go into making up acceleration – time, space, length, velocity – are all relative.

… for all the mystery surrounding what the Ether may or may not be, what our current theories most strongly suggest is the idea that we detect its presence every time we accelerate.[The Lorenzian Axiom (an answer to this question) … in and of itself feels pretty

arbitrary and jarring. Einstein’s Axiom … hardly feels any less arbitrary or jarring.Neither intuitive.]

While checking my list of references today … perhaps this 2019 article provides some background.

• Space.com > “Physicist Lee Smolin On Einstein’s Unfinished Revolution in Quantum Physics: Author Q&A” by Marcus Banks (June 05, 2019) – As a realist, you believe there is a complete story, and there’s a complete description, that we can attain of any atomic process.

While checking my list of references today … this 2019 article provides some useful historical recap (and visualizations) re the quest for a theory of everything.

• Forbes > “This Is Why Quantum Field Theory Is More Fundamental Than Quantum Mechanics” by Ethan Siegel, Senior Contributor (April 25, 2019) – What’s truly fundamental in this Universe? Think about what happens if you put two electrons close to one another. [1]

Notes[1] This article is a reminder of my discomfort with the notion of point particles as “containing” charge and “generating” fields. That is, rather than the notion of topological interactions – in which localized field excitations induce gradients in fields (which manifest classically as forces).

This video about Einstein’s general [vs. special] relativity equations is interesting. Not that I can grasp a higher-dimensional hypergraph, a geodesic ball of a Riemannian manifold, etc. [1] But that the derivation starts from some first principles and obtains Einstein’s formulation – an alternate approach..

Also, this struck me for the non-vacuum derivation – “that particles can be treated as

localized topological obstructions.” (Akin to my comments about so-called particles as “knots.”)• YouTube > The Last Theory > “How to derive general relativity from Wolfram Physics with Jonathan Gorard” (Sep 21, 2023) and hosted by Mark Jeffery – The structure of space-time in the presence of matter falls out of the hypergraph.

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Notes[1] I have a general appreciation of the stress-energy tensor, but hardly these terms / concepts:

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