Potential Currency
Veritasium intersects MMT ... for one paragraph 🤣
Vacua Smack-U-R
During lunch today I was watching the latest Veritasium vid on Lagrangian mechanics and the Aharonov–Bohm effect. There’s a series of these on Lagrangian principles I think. The episode was devoted to how the Potentials have physical effect, so in some sense are 𝕣𝕖𝕒𝕝. Which is to say, our mathematical models which employ potentials as more than pure gauge are capturing something in the natural world.
For the youngin’s, you’d maybe know already that forces are not 𝕣𝕖𝕒𝕝, and energy is not exactly 𝕣𝕖𝕒𝕝 either, these are just words we use for mathematical constructs that organize our knowledge about the world. What appears to be 𝕣𝕖𝕒𝕝 is just particles and spacetime. Though one might substitute their own alternative ontology, e.g., you maybe think some computer is simulating us and so our proximate reality is bit-strings, or whatever representations this fanciful computer is using. I do not want to debate-bro ontology today, I will just assume you can cope with spacetime and particles as fundamental bedrock, without begging the question. Make the dictionary translation to your preferred ontological frame yourself, don’t bug me about it!
While I’d love to expound upon how force and energy are derived from the concepts of particles plus spacetime, that’s for another day. Today I just wanted to comment on Veritasium’s point about the Potentials being “physical.”
To be clear, there are two related concepts, from which a force vector field can be defined,
And, yes, I coined that term “spepential”. These lead to derived quantities called field and force respectively, the two F’s:
Things “specific” in physics are usually “quantity per unit of …”. In this case, per unit of the charge. For all the forces (gravity, electromagnetism, strong and weak) the charge, Q, is just a fundamental coupling constant. Gravity being the unique special case since It’s charge is also the response (inertia).
In classical mechanics the potentials are regarded as fictional constructs, useful devices for getting at computing the “real stuff” which is the force. (The “field” is misnomer, and is more correctly identified as the Specific Force, or Sorce.)
This changes in quantum physics. It is a subtle thing, but provides us with tremendous insights into the nature of physical reality, the 𝕣𝕖𝕒𝕝. But I think few journeying physicists even realize. The “cause” (so-to-speak) of the physical effectiveness of the potentials is entanglement. This “explains” why the potentials have no effect in classical mechanics, since entanglement is not recognized in CM. What it does not explain is the nature of entanglement itself.
What most journeying physicists would perhaps say is that the phase factors are responsible for the interference effects in single-particle quantum mechanics. This is true. It is the phase factor effect which is what we use to model the effectiveness of the Potentials A(x). When a particle takes different paths that have a topological obstruction between them, so one path cannot be continuously deformed to another (without passing across the obstruction) then there is a measurable phase difference between two paths around the obstruction, and the experimentalist who can alter the path length difference will be able to measure shifts in the interference pattern.
Note that this is not a statistical effect of many trials, nor a wave effect. The interference occurs for a single individual particle (even without the interference fringe shift this is already highly non-classical). The point is that we can shift the interference pattern by altering the relationship between the possible paths and the potential A(x).
That’s impossible if the potential A(x) is nothing but a mathematical model artifice. Quantum physics experiments therefore show the potentials A(x) and/or V(x) cannot be mere modelling artifices. For those interested, the seminal experiment was the Aharonov–Bohm effect — that’s wikipedia, here are also some lecture notes: James MacDonald course notes I saw from DuckDuckGo.
It’s Not Wave Interference
The Veritasium crew wrote a script that makes it sound like the electrons are a wave-like beam of ectoplasm. I had to write:
@26:20 why do you write the script like this? It is highly misleading. Sounds like PBS Science dopiness. The “beams” do not interfere. Each single electron interferes with itself, so-to-speak, that’s the quantum mechanics. Beam interference is a purely classical effect at a (statistical) wave approximation. The quantum phase shift effect is no such thing. The wave function being non-physical (it is a Hilbert space construct, hence also, in fact, stochastic).
My guess is the Veritasium physics experts know this, but why dumb it all down? I think the lay audience can grasp the whole wonder of it all more to the wonderful if the explanations were technically correct. No one should bat an eye-lid at actual spacetime waves interfering. that’s what they do for a living. But a single particle interfering with itself is a veritable marvel of our cosmos. So marvelous that it demands a non-classical explanation, because there is no classical mechanics for it!
Modern Turns
There is a wrinkle in this fabric. More recent analyses like those of Pearle ＆ Rizzi show that the potential A(x) does not in the end need to be regarded as 𝕣𝕖𝕒𝕝, and the electromagnetic force suffices to explain the effect — provided the electrons or currents in the solenoid making the obstruction are quantized. Hence the Aharonov–Bohm effect might not truly be an effect of fields and potentials, but can be regarded as a manifestation of quantized charges. In other words, entangled particles.
This view accords with our T4G theory here.
In T4G theory we recognize the fields and potentials as stochastic variables, so indeed they are not 𝕣𝕖𝕒𝕝. The statistical dynamics is however highly non-classical, and can be mathematically modeled only with non-Markov probability transitions. This in turn requires entanglement (see Barandes (2023) ).
That’s REQUIRES do you hear me!? Whatever is responsible for non-Markovianty is likely most responsible for entanglement. Non-Markovianity is pretty awesome, it — in effect — says spacetime itself has a deep memory. The immediate past is insufficient to account for the future. By CPT symmetry this implies, as a near mathematical theorem (with experimental support, CPT is not known to be violated) that the far future also is influencing us today. Albeit in incredibly stupidly insignificant ways perhaps.1
The discussion in the last 10 minutes of the Veritasium episode is pretty good, debating the nub of the issue. There are two sharp resolutions of the non-classical Tonomura Aharanov-Bohm experiment (which proved the quantum potential phase shift is real).
The potential A(x) is a 𝕣𝕖𝕒𝕝ity — hence the physical force-fields can have effects where there is no field, via their underlying spepential.
The force-fields are the only 𝕣𝕖𝕒𝕝ity but they can act non-locally, and the gauge potentials are just accounting for such non-local effects.
I’m “ok” with both these opinions, but T4G goes deeper. Both the forces and the potentials are field-variables, hence accounting tools, neither are 𝕣𝕖𝕒𝕝ity. The field quanta, the gauge bosons, are what are 𝕣𝕖𝕒𝕝 — according to T4G theory.
All the fields are the statistical remnants of stochastic effects in the indivisible structure of the highly entangled T4G spacetime cobordism.
Ultimately this is because the vacuum of spacetime itself is highly entangled. This is something the Veritasium episode failed to discuss. Entanglement, you see, is ubiquitous but fickle, outside of a highly controlled cryogenic and isolated quantum computer qubit array, the vacuum entanglement is completely wild, and it is therefore not hard for an electron or photon to get entangled, with almost anything.
As I remarked at 34 min on the “observation” of gravitational Aharonov-Bohm effects.
Edit, red ink here mate. There are not two atom source particles, there’s only one. It is self-entangled, so-to-speak, hence a wavefunction description is necessary, and also hence the interference. It is not because the atom is a wave, it is because it is pairwise piece-wise entangled. (Just orthodox QM: entanglement is monogamous.)
At least that’s my story.
This leads to an alternative point of view. It is the particles that behave non-locally, due to entanglement, and this gives rise at a statistical level of description to the fields and potentials.
If you are to have any success modelling events in spacetime you’ll need to crutch of the field variables you see, just you go and try without them, it’ll be a nightmare. The field variables, in a sense, help you avoid having to consider time-travel. Ask any film script-writer, the only decent movies about time-travel were Bill & Ted’s Excellent Adventure, and Primer. The former making comedy from the absurdity, the latter making inscrutability.
To respond to the young kid’s comment at about 29 min , who thought ground state levels are arbitrary, one must remark: on the contrary, that in curved spacetime the ground state of the vacuum is non-trivial. The arbitrary ground state vacuum energy is only arbitrary in flat spacetime, which is not the real world. In the real world a cosmological constant, even if it turns out to be ≈0, is measurable.
To respond to that “professors” comment also around 31 min: this “professor” seems to not understand gauge potentials. They are “not real” even before you show they “have effects.” Gravity is the prime example. Just because you can gauge position and rotation and thus must have position and rotation gauge in your covariant derivatives for a non-sick theory, does not mean your gauging is a physical effect per se. The physical effect in gravity being curvature, which is why gauging is required. The underlying physics is that of a dynamic vacuum, or dynamical spacetime vacua. That underpins all gauge theories we know, not just gravity. Electroweak and Electrocolor (chromodynamics) groups are the gauge groups for topology frame change, hence intimately related to entanglement, rather than position and rotation Lorentz frames (not related to entanglement).
Ironically Gravity is a big lesson in this respect.
No one would claim that re-gauging a covariant derivative to account for a position or rotation re-mapping is a “real thing.” It is just gauge. A change in how we map position and orientation in a reference frame necessitates a model-theoretic gauge field. But this is all about our frames of reference, ℕ𝕒𝕥𝕦𝕣𝕖 herself does not care for our POV.
It is our theoretical model which is at fault. We have to use gauge fields to correct for our parochial local observation point-of-view. If we do not do so then we have a sick theory that will not compute for us valid predictions. I hope you can see from this that quantum mechanics is a lot closer to general relativity than you are led to believe in the textbooks.
The gauge principles are vital for removing observer-dependence from our models. The exact opposite of what many quantum new-age hipsters like to pretend (something about the universe being observer-centric or some other nonsense). I have a little koan for this:
Quantum physics has to account for the observer to remove the observer.
The physical reality remaining after gauge is accounted for is not observer dependent. That’s the whole point, to remove the observer.
Why did classical mechanics not need to? The short answer comes back to entanglement. In classical mechanics the observer’s entanglement with a system under measurement is not taken into account, since it is a teeny tiny effect when the characteristic action for a system,
is small compared to ℏ.
This is not unlike state currency systems according to MMT! It is essential to understand currency gauges, if one is to not implement 𖨚𖢧ꚶ𖡮𖥣𖦧 as ꕷꖾꔇꖡꗍ policy. Or, in other words, currency inflation is a complete red herring, the true horror (of unimaginable proportions) is unemployment. Everyone who does not understand this is today guilty of virtual crimes against humanity more horrific than a thousand genocides. Or let’s be generous and say a hundred genocides.
Far more important stuff than nerdy theoretical physics. I am ashamed to be still writing about the theoretical physics.
T4G Musings
This brings me to my own musings from lunch time.
I’ve been thinking about dynamical vacuum recently in relation to our Cℓ(8) T4G model.2
It is possible to regard the coupling of the gauge fields A(x) to the elementary quanta (either the charges or the currents, since they’re the same thing really) as vacuum entanglement mediated. It is a dynamic spacetime vacuum that is most of the non-classical effect.
In T4G theory we can account for Two-Slit interference of a single particle “with itself” by postulating every elementary particle has a wormhole sub-structure, and one end of this structure can get pinned to an aperture, or pinned to “the vacuum” (just a manner of speaking). In fact it does not matter how the wormhole gets pinned, it can be to matter or to vacuum. Either way it can be modeled as coupling to the electromagnetic potential in one way or another.
Note that this is a highly non-local theory in a Minkowski frame point-of-view, if one ignores the wormhole topology. Wormholes, if they have any effect at all, will always appear highly non-local to anyone who does not account for their existence. Taking into account the wormhole topology — non-Minkoswki — recovers local causality.
In T4G theory neither the “it’s all particles” nor “it’s all fields” view is perfectly correct. Firstly, if all were just point-particle we’d be unable to explain entanglement other than mystically, or, just as bad, mereologically (“It’s just the Law!”). But the fields effects are statistical, not fundamental, so they are not a full explanation either. In T4G theory we have wormhole structure responsible for entanglement, and this necessitates a stochastic description.
All phenomenological descriptions of continuum physics that are inherently statistical are fields theories. A probability density function p(x,t) being an example par excellence of a spacetime field.
Another wrinkle is that the converse is not true: just because you have a workable tested field theory does not mean it is necessarily merely statistical. One of the great unresolved experimental questions of our time is an all-or-nothing test, or no-go experiment, for whether 𝕟𝕒𝕥𝕦𝕣𝕖 is fundamentally fields living on spacetime, or particles that merely statistically behave like fields. I think I would be lucky to live long enough to learn of a definitive experimental result convincing us one way or the other.
A test for fundamental fields (other than spacetime) that fails to find them would be one of the greatest negative result experiments in the history of science. Probably more important than negative results for higher dimensional supersymmetry. On a par with the Michelson–Morley experiment.
It is pretty amazing that in our lifetimes we actually have several of these “would-be-famous” negative experiments looming. Here are my top seven:
No primordial gravity waves?
Violation of the Bell Inequalities. ✅
No higher D supersymmetry?
No fundamental graviton?
No fundamental fields other than spacetime?
Nothing beyond the minimal LR-symmetric Standard Model (three generations)?
Existence of a heavy right-handed neutrino — the one positive experiment on my list.
Negative results on the first six of these (the “no” is correct) would be a huge benefit for T4G theory, alternatively a “not no” on any of them would kill T4G theory, at least as I presently conceive the theory. The really hard one here, the one I do not know how anyone could test is, “5. No fundamental fields other than spacetime.” If you think you know of a doable test then you should publish the concept for the experiment.
Was it worth all this to just write one MMT paragraph for the day? 𝕳𝐞𝘭𝐥𝐲𝔢𝖆𝕙.🤣
If you knew reich-wing ℭ𝔘𝔑𝔗𝔰 were not going to be in government power anywhere in the world after 2050, that might cause you to relax and not do a thing about it today? Oh-oh, paradox!
Who is “us” here? I used to think I was alone, but recently I contacted two sympathizers, Niels Gresnigt and Jason Blood. Jason, in particular, really opened my eyes. After Gresnigt alerted me via arXiv majiks to the 8-dimensional Clifford frame, Jason gave me the improved left-right action ℂℓ(8) model, which is so tasty and delicious if it was a pizza I could sell it at $1 million a slice.
Once you know, you can’t un-know: austerity is murder.