Invariance, Covariance, Unity, and Duality

While reviewing some needed math for a paper, I am somewhat embarrassed to discover that in the strictest mathematical sense , I have been equivocating the concept of gauge invariance with the incomparably stronger meaning of the term as it applies to relativity.

Let's first be ABSOLUTELY clear on what I mean by this. In the mathematical parlance of axiomatic geometry of any number of dimensions or topology, there is never a conflict between what is meant by the concepts of a point, a straight line, a circle, or a curved line, nor would one expect there to be a difference between the ratios of numbers representing congruence relationships or anything else that would render a change of references that are ratiometrically congruent when at rest to behave any differently when things begin to move.

In physics, relativistic INVARIANCE of the speed of light is evidently now considered unique by only a spare precious few thinkers and EVEN FEWER MATHEMATICIANS. This seems to have caused more than a few problems for me here and elsewhere. It is not a science problem. It is not a math problem. Both of these fields apparently can remain self-consistent and yet not have the slightest idea what the person(s) in the other field is talking about. I don't think it is even possible to resolve the issue using the terminology of either because they are simply incompatible world views.

When a mathematician learns that unity is the basis of almost everything he or she will be doing for the rest of their lives, and that it can always be renormalized by means of division of itself by itself, the rest of life becomes no more challenging than a table of conversion factors. When systems of linear equations are reduced to matrices, more generalization is achieved. The fundamental theorem of calculus provides templates for understanding changes in anything and everything as a function of time or anything else, and all without caring a whit about what something like time or motion or change actually is.

A mathematician seems to be able to accept there is only one solution or a field of solutions to a math problem of a particular category and that's all there is to it. That's wrong. Moreover, it's the whole world view of mathematics that is wrong, not just an insignificant portion of it.

There is not even one frame of reference in this universe that behaves as a vector field does in math, including and especially 'at rest', unless it is your plan never to allow anything in it to move. The relationship I am talking about cannot be explained by means of any ratio, and that is going to be a problem for anyone who thinks that any math problem that resolves to division by zero means that the only way left to do math is to convert everything or anything to a probability.

You can do you Lagrangian and Hermitian conjugate math until Emmy Noeter herself comes back to tell you, you are doing it wrong. You can add energies and subtract energies all you want, but if you do not realize there is a built in inconsistency in this manner of counting, there is little any other observer will be able to do to convince you, there is a problem inherent in the way you are attacking the problem and there is basically no hope you will ever understand. The quantization of all energy events depends on the state of motion of the observer. Calculate what that means and provide us with a SINGLE answer on which everyone can agree. Now do it without a geometrical origin to work with. The speed of light can do it, so why can't you? You must be very bad at your job. Your ONE job.

But for starters, I do not believe that 'INVARIANT' means what you think it means, or to put it in terms expressable only someplace like a philosophy forum, the definition mathematicians have fabricated for invariance for themselves and their available tools is not even close to the one Einstein intended. No wonder so many of them insist on bringing back the 19th century luminiferous aether, and another round of absolute space and absolute time to go along with it.

The aether is the working definition I have for both unnecessary and insufficient.

 

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http://arxiv.org/abs/hep-ph/0211092

So now there are now actually FOUR theories of relativity where before there was only one. This is what 'gauge invariance' does to the original formulation of relativity and its single foundational assumption of speed of light (REAL, TRUE) invariance. Gauge invariance corrupts inertialess (and also inertia bearing) energy transfer events with absolute space and absolute time for the sake of a consistent mathematical description that suffers no duplicity from the descriptions of the same events by different observers in different states of relative motion or in a gravitational field.

Did it occur to no one that those different descriptions of reality might just be the key to understanding certain interactions, particularly ones involving the transfer of inertial or gravitational mass?

No wonder quantum gravity goes exactly nowhere. Gravitons would need to be nailed to an aether or a stationary rubber sheet to see any gravity. Idiots.

It is truly a miracle that the Higgs mechanism was described the way it was and as accurately as it was.. That description occurred a very long time before any of the gauge corruptions of invariance crept into ideas about QFT and theoretical physics.

This is just sad. For every Newton or Einstein that comes along every 500-1000 years, there are hoards of detractors who work ten times as hard to make certain science progresses as slowly as possible or not at all, or that it does not benefit at all from the ideas that matter most.

It would actually be redundant to curse them. They reward themselves with exactly the lack of understanding they richly deserve.

 

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Or to put it in terms of the popular Princess Bride Meme:

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and the inevitable reply (courtesy of the late Wallace Shawn):

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That appears to be crackpottery from a physics outsider who never understood the relationship between space and time in special relativity. It is likely that the author struggles with simple algebra.

His "innovation", what he calls generic relativity, is of no physical utility as he apparently can't explain the significant of minus signs in the special relativistic metric — they have no absolute significant but serve to separate time from space. Without basis he singles out spatial directions and adds minus signs, effectively moving certain spacial directions into the same bin as time, thus (5a) is (3,1) special relativity and (5c) is also (3,1) special relativity with the Z-direction singled out as time-like and (5d) is 4-dimensional Euclidean geometry.

 

Not just "certain" spatial dimensions. All three of them are simply components of light travel time.

You could also do this in spherical coordinates. This would be more appropriate than Rene Descarte's rectilinear geometric abomination, which commemorates a vector space. An ABSOLUTE vector space. A dead issue. Since 1905. But at least, now I do understand where the actual crackpottery comes from.

The only reason it works even a little is because particle physics actually uses the only coordinate system that makes any real sense; the centers of particles of bound energy AND ALSO BECAUSE gravity works REAL SLOW, relativistically speaking.

But if your plan is to bring these bits of physics together into one theory, you will need to understand what time is, and you don't get there by making a separate relativity for each observer in kinematic and electromagnetic interactions.

And this is something else you also taught me on another forum, rpenner.

I do like your Wallace Shawn impression. It suits you.

 

Again you mistake the choice to use Cartesian coordinates (which necessarily mandate a choice of origin) with statements in geometry (which makes that choice irrelevant).

Both \(A = (0,0), \; B=( \frac{11}{8}, \frac{3 \sqrt{15}}{8}), \; C=(4,0)\) and \(A'=(2,0), \; B' = (0,0), \; C'=(- \frac{3}{4}, \frac{3 \sqrt{15}}{4})\) describe the same triangle with sides of lengths 2, 3 and 4 with the coordinates being related by continuous isometries of Euclidean geometry, rotation and translation.

AB = 2 = A'B', BC = 3 = B'C', AC = 4 = A'C'

\( \begin{pmatrix} 2 & 0 & - \frac{3}{4} \\ 0 & 0 & \frac{3 \sqrt{15}}{4} \\ 1 & 1 & 1 \end{pmatrix} \\ = \begin{pmatrix} -\frac{11}{16} & -\frac{3 \sqrt{15}}{16} & 2 \\ \frac{3 \sqrt{15}}{16} & -\frac{11}{16} & 0 \\ 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} 0 & \frac{11}{8} & 4 \\ 0 & \frac{3 \sqrt{15}}{8} & 0 \\ 1 & 1 & 1 \end{pmatrix} \\ = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} -\frac{11}{16} & -\frac{3 \sqrt{15}}{16} & 0 \\ \frac{3 \sqrt{15}}{16} & -\frac{11}{16} & 0 \\ 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} 0 & \frac{11}{8} & 4 \\ 0 & \frac{3 \sqrt{15}}{8} & 0 \\ 1 & 1 & 1 \end{pmatrix} \\ = \left( \textrm{translation by}\; (2,0) \right) \left( \textrm{rotation by} \; 133.43^{\circ} \; \textrm{counterclockwise} \right) \begin{pmatrix} 0 & \frac{11}{8} & 4 \\ 0 & \frac{3 \sqrt{15}}{8} & 0 \\ 1 & 1 & 1 \end{pmatrix} \)

In both cases we can compute the area of the triangle as half of the absolute value of the cross product of the vectors of any two sides, because those vectors are made of coordinate differences which ignore the origin and the absolute value of the cross product of two vectors is an invariant of Euclidean geometry because the dot product is and:
\( \left| \vec{u} \times \vec{v} \right| = \sqrt{ \vec{u}^2 \vec{v}^2 - \left( \vec{u} \cdot \vec{v} \right)^2 }\)

\(| (B-A) \times (C-A) | = \left| \begin{pmatrix} \frac{11}{8} \\ \frac{3 \sqrt{15}}{8} \end{pmatrix} \times \begin{pmatrix} 4 \\ 0 \end{pmatrix} \right| = \left| \frac{11}{8} \times 0 - \frac{3 \sqrt{15}}{8} \times 4 \right| = \frac{3 \sqrt{15}}{2} \\ | (C-B) \times (A-B) | = \left| \begin{pmatrix} \frac{21}{8} \\ -\frac{3 \sqrt{15}}{8} \end{pmatrix} \times \begin{pmatrix} -\frac{11}{8} \\ -\frac{3 \sqrt{15}}{8} \end{pmatrix} \right| = \left| - \frac{21}{8} \times \frac{3 \sqrt{15}}{8} - \frac{3 \sqrt{15}}{8} \times \frac{11}{8} \right| = \frac{3 \sqrt{15}}{2} \\ | (A'-C') \times (B'-C') | = \left| \begin{pmatrix} \frac{11}{4} \\ -\frac{3 \sqrt{15}}{4} \end{pmatrix} \times \begin{pmatrix} \frac{3}{4} \\ -\frac{3 \sqrt{15}}{4} \end{pmatrix} \right| = \left| - \frac{11}{4} \times \frac{3 \sqrt{15}}{4} + \frac{3 \sqrt{15}}{4} \times \frac{3}{4} \right| = \frac{3 \sqrt{15}}{2} \)
and so on.

So do not confuse the map (use of Cartesian coordinates) with the territory (description within a realm of geometry). If the geometry is being faithfully applied the choice of origin is irrelevant.

 

Notice there is no duality in anything you have written. Each and every expression lacks the physical ambiguity of relativity, or simply ambiguity in general. This is a good thing within the construct which is math, and I do not mean to imply that it is otherwise.

A VECTOR DOT OR 'scalar' product has a magnitude that is the product of the magnitude of each multiplied by cosine of the projected angle (a right angle) between two vectors.

If one or both vectors involve a term that is the speed of light, there's already a BIG PROBLEM with any vector math which would compute a resultant vector.

ANY velocity vector is dimensionless when expressed in terms of light travel time per unit of time. Dimensional analysis like this hints at what is physical reality and what is contrived. The meaning is clear enough to me. If it isn't to you, perhaps your assumptions require a reexamination. It's one of the unities the OP talks about

Your math only makes sense within the confines of a certain mindset which I was taught the same as you. But I accepted its limitations a very long time ago. It seems that you have not.

I know the math. I don't worship it or the minds which created it in what they consider to be an image of the mind of G-d.

Ordinarily I post little in philosophy and tend to disparage what little it claims to have a handle on, because philosophy never bothered defining the nature of truth, a prerequisite IMO to any substantive philosophical discussion. Mathematics seems to share this disposition with bad philosophy. It's the reason its strongest appeal is in the direction of the ultra-orthodox members of the discipline, whom I consider to be the worst among OCD afflicted hypocrites.

Moreover, most people would not recognize pseudo-math if they saw it. I do, and there seems to be a great deal of it applied to physics that really doesn't belong and has no business being there. Its scope has been steadily creeping into the field for the last 40 years. I saw its beginnings, and should count myself fortunate to see it crash.

 

You mentioned in another thread that rest mass was a Lorentz invariant quantity. It definitely is, under the definition of an invariant used in a Lagrangian.

But that is a reflection of the rejection of mass as something that may physically increase kinematically with increasing relativistic speeds for the bound energy that is matter, and moreover I know for certain that you understand this mechanism in some considerable detail.

Most of the Einstein detractors of the last century were also deniers of Lorentz contraction of lengths, time dilation and the twin paradox. A spare few even doubted the relativistic Doppler shifts, or tried to use them to show that the twin paradox never "REALLY" happens. And I never had any expectation that any of those stupid people would give it up when the Higgs boson, the boson that is the origin of time itself, was discovered to provide support to relativity in its original inception. And I was not disappointed. If anything, their ranks have swollen. Some of the ba$+@rds took advantage of the intervening 40 year lull in experimental physics to study and become ordained in math.

Like the global warming deniers, they are well funded. Someone should follow the money. No doubt such educational and academic sabotage is funded largely by something like the sale of placebo medications or illicit narcotics in place of real medicine by quackpot doctors, and the sale of books on the subject to weak minded folk with similar and/or symbiotic social agendas.

When the appeal of the character of Sheldon Cooper's schtick and smarmy physics and especially math charms finally wears off and we remember that Einstein navigated the waters of a new era of physics alone and with the certitude of clear thinking beholding to no special interests, perhaps then we can reboot the ideas about physics that really matter. It may take another 1000 years at this rate.

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Yes, I reject the concept of relativistic mass \(M=\gamma m_0\) because it doesn't explain inertia and doesn't preserve Newton's F=ma as simply F=Ma. It also doesn't usefully explain the coupling between the electron and the Higgs boson which is governed by the invariant mass. It also doesn't allow you to classify the zoo of particles, because that too is done in terms of invariant mass. In general relativity, \(\gamma m_0\) is not the source of gravity as the source is a tensor, not scalar, quantity.

It's not necessary in doing physics, and while it has its applications in teaching physics, it doesn't have the same value in every coordinate system so it doesn't behave like other scalars.

Indeed, the relation between force and acceleration in the reference frame where the particle is moving is complex, best given as a matrix, not a scalar, relationship between F and a.
Einstein originally derived the longitudinal mass as \(M_{\parallel} = \gamma^3 m_0\) and \(\color{red} {M_{\perp} = \gamma^2 m_0}\) but to do so he mixed reference frames. Without mixing reference frames, \(M_{\parallel} = \gamma^3 m_0\) and \(M_{\perp} = \gamma m_0\) are what you need to preserve \(F=\mathbf{M}a\) which means M is now a matrix.

If we must change F=ma, then I prefer to factor it as \(F = m_0 \mathbf{X} a\) where X is a matrix containing the directional dependence and m as the invariant rest mass. Then only X changes upon a change of coordinates.

\( \mathbf{X} = \begin{pmatrix} \gamma + \gamma^3 \frac{v_x^2}{c^2} & \gamma^3 \frac{v_x v_y}{c^2} & \gamma^3 \frac{v_x v_z}{c^2} \\ \gamma^3 \frac{v_x v_y}{c^2} & \gamma + \gamma^3 \frac{v_y^2}{c^2} & \gamma^3 \frac{v_y v_z}{c^2} \\ \gamma^3 \frac{v_x v_z}{c^2} & \gamma^3 \frac{v_y v_z}{c^2} & \gamma + \gamma^3 \frac{v_z^2}{c^2} \end{pmatrix}\)

http://www.mathpages.com/home/kmath674/kmath674.htm
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html#addendum

 

My objection to the whole thread:

If something is "real" then it doesn't go away when you change "trivial" things about how you describe things that are "real" -- at most, details about how you describe something change as you change how you describe things -- this is "covariance." The simplest form of "covariance" is that the change is no change at all, this is "invariance." Thus if there are "real" things described by your physical theory you need some to be covariant or even invariant.

Invariants are "nicer" than covariant quantities because they remain unchanged under the "trivial" things changing. So the "trivial" changes form a monoid or group (if every change is undoable which corresponds well with the everyday notion of a trivial change). This leads into the topic of symmetry which is a "nice" thing for a physical theory because it leads to simple tests that would invalidate the theory which can be run at higher precision. A perfect symmetry means there are no seams to give evidence of something more fundamental -- so symmetries in physical theories encapsulate ignorance about unevidenced metaphysics and future physics while leaving us free to explore the physics we do have evidence for.

Within special relativity, inertial coordinate systems based on choices for a standard of rest, choices for the cardinal directions and a choice of event as the origin of the coordinates are all trivial in the same sense that choice of inertial Cartesian or inertial spherical coordinates is trivial. What remains despite the trivial choices is a hyperbolic geometry of space and time. Just as Poincaré transforms allow us to convert back-and-forth between covariant descriptions of space-time in Cartesian coordinate, more general transforms allow us to convert between spherical and Cartesian. General relativity allows general coordinate transforms where anything that is smooth is permitted at least locally because it is the underlying geometry which matters.

 

Makes perfect sense, as always, rpenner. "Longitudinal mass or inertia" is certainly one way to think of it. An energy Doppler shift that couples to the rotational propagation of energy through the Higgs field is another. But only the latter interpretation explains why time dilation also happens, exactly the way it does applying the principle of equivalence to acceleration due to gravitation. Time dilation is not "longitudinal". It happens in all directions at once, just as the perfect rotation of bound energy I have described. And your math is coming up very short on this conceptualization.

Mass expressed as a vector or a tensor is not going to get you any deeper understanding of inertia and its relationship to time dilation, nor will "space curvature" make any real sense in a universe limited to its essential elements of energy exchange events and time.

The beam energy that is dumped every 10 hours at the LHC into multi-ton graphite graphite blocks is as real it gets. Yet if instead of dumping the energy, you pushed it in a different direction, it would be as easy to accelerate the proton pancakes in ANY DIRECTION OTHER THAN THE ONE IT WAS ACCELERATED IN as it was to start pushing it from rest at the beginning of the run cycle. There are as many other directions to push it in as there are other frames of reference in which the rest mass is the same energy as when it started moving, and that would be an infinite number.

"Real" energy is always dependent on the state of motion of the observer. It isn't less 'real' because it is different from the rest mass. AND there is no limit to the number of frames of reference that are "at rest", and in which you can do physics exactly the same as any other, courtesy of the invariant that is the speed of light. As far as I am aware, this is still a unique property of that particular invariant, and that much has not changed in over 100 years.

And there is exactly no way you can understand gravitation at all without this essential dichotomy. It REQUIRES, and has always required at least two observers. If it did not, that would be an unbalanced force, and even Newton did not allow such things, commemorated in his third law and in the way the Standard Model boson force exchanges INCLUDING the Higgs mechanism work, which amounts to the same physics.

Finally, doing more math than is strictly necessary and sufficient to explain what you are modeling is a waste of both effort and brain power. That's exactly what happens when it turns out that the model you are basing the math on just reeks of extraneous elements that are not necessary to understanding anything. If you really love the math, you already know how many of those kinds of models have been discarded over the millennia.

 

I agree which is why I factored out the velocity dependent terms as a matrix and left mass as an invariant scalar.

 

Quick question off topic for rpenner.

I found this guy, John A. Macken:

http://onlyspacetime.com

Who evidently had a long and successful career in Laser physics, who in 2001 became convinced of the veracity of the idea that a photon trapped between mirrors (as in a Laser cavity) would possess inertia, and wrote a book that is highly speculative about what this may mean. So he picked up on the idea a very long time before I did (or at least, before I wrote anywhere about it). His book seems to be a quite technical through treatment of where he thinks it takes him, which is basically a universe that is relativistic. I agree with that completely, but I don't yet follow everything he wrote.

But he seems dead set against the idea of the Higgs having ANYTHING at all to do with what it is supposed to do, that is to say, he seems to think that the Higgs mechanism is NOT responsible for imparting inertia to electrons. One noteworthy decay mode of Higgs is into two electrons and an electron antineutrino. Guess he must have missed the writeup for that event, commemorated in the art of my associate's artist friend, Susan Loy.

Do you know this guy (John A. Macken)? He was evidently active on his website in 2013, and I have tried contacting him and joining another science discussion board he frequents, where there seem to be a number of VERY interesting comments and papers along the same line of inquiry that interests me.

Thanks in advance.

 

Because I understood invariance, right away I knew that could not be true.

You mean four leptons, specifically: \(H \to e^{-} e^{+} \mu^{-} \mu^{+}\), double pair production. The actual mechanism is \(H \to Z^0 Z^0\) (which is tricky since this doesn't quite check out based on rest masses and is written as \(H \to Z Z^{*}\)) and \(Z^0 \to e^{-} e^{+}\) and/or \(Z^0 \to \mu^{-} \mu^{+}\) and/or \(Z^0 \to q \bar{q}\) and/or \(Z^0 \to \nu \bar{\nu}\). This last is nearly invisible and the other involves messy QCD so the distinguishing and visible form of \(H\to 2H^0\) is \(H\to 4 \ell\) where 4 leptons appear to arise from a single unresolvably small volume with balanced charges and flavors.

The diphoton decay \(H \to 2 \gamma\) is naively harder to imagine since you can't read it off the Lagrangian in one step. So it's a sensitive test of the standard model and the Higgs boson mass.

http://www.literarycalligraphy.com/philosophy/fourleptons.html
http://biologos.org/blogs/archive/what-is-the-higgs-boson
http://www.atlas.ch/news/2012/latest-results-from-higgs-search.html
http://cds.cern.ch/record/1459500
http://arxiv.org/abs/1207.0319
https://en.wikipedia.org/wiki/Electroweak_interaction#After_electroweak_symmetry_breaking
http://profmattstrassler.com/articl...del-higgs/decays-of-the-standard-model-higgs/
http://arxiv.org/abs/hep-ph/0504137

 

Z0-> e-e+ Is this describing pair production or decay?

 

Yes. So we have A SINGLE PARTICLE, which can decay into a pair of gluons with an anti-top intermediary, and yet another decay event yielding a pair of electrons and a pair of muons. Just those two events span the range of strong to electroweak to EM.

It looks like an understanding of this particle would be pretty basic to understanding the totality of atomic structure to me. How ever could we get by for 30 YEARS without understanding or acknowledging its existence? All of QCD was developed without reference to it. So it was also with electroweak unification with EM. How could this have been accomplished with so big and fundamental a piece of the puzzle missing entirely? Quarks don't even exist without Higgs.

I AM DULY IMPRESSED, and this is not sarcasm. What I have trouble understanding is how some people insist, this doesn't change their ideas about anything and everything.

It can't possibly be that no one is interested in completing the puzzle. Higgs and its various decay modalities evidently are pieces defining the BORDERS of this puzzle. Or in mathematical parlance, the BOUNDARY CONDITIONS. That's important enough to give a second or third thought to, isn't it? I'll bet there are more than just a few previously undreamt of gauge symmetries associated with those.

A border piece would be the one that binds the entire puzzle together. I don't think this is overworking the metaphor.

 

Both. Is the fusing of sperm and egg the end for the sperm or the beginning for the zygote?

Because electroweak symmetry breaking, the Higgs mechanism and therefore the Higgs particle has been around since 1961 and has part of the Standard Model for the last 40+ years.

Misleading to the point of being wrong. The Higgs couples to every standard model field that has rest mass, because the Higgs field gives rise to fundamental particle mass and the coupling is measured to be proportional to mass as expected. So the Higgs can decay into a colorless, chargeless, flavorless, spinless pair of any massive particle and its antiparticle. If the particle (and therefore antiparticle) is electromagnetically charged, it can annihilate with its partner to form a spinless pair of photons. If it has QCD charge, then a spinless pair of gluons.

Atomic structure is almost entirely modeled correctly in semiclassical (i.e. low energy) quantum mechanics. In multi-electron atoms there are relativistic corrections, but not too much pair-production. Likewise nuclear structure happens at an energy scale too low for muons to matter much. So the Higgs particle is only found in high energy particle physics.

I guess the "we" you refer to is not a relevant group to the progress of science.

Electroweak symmetry breaking is irrelevant to tree-level QCD, but electroweak symmetry breaking was formulated first and QCD was formulated at about the same time that electroweak symmetry breaking got important experimental support.

Electroweak theory was Weak force unification with Electromagnetism.

Not missing since 1961.

Quarks don't have rest mass without Higgs, but one may assume quarks have some rest mass irrespective of theoretical origin and have a fine (low energy) model of QCD interactions.

 

Both.

 

Nice working the metaphor!

 

Yes and no.

Giving inertial mass to electrons and quarks is not exactly something I would describe as a "high energy" interaction, if that's really how the Higgs mechanism works. It is as mundane and low energy as interactions between photons and electrons. Granted, photons generally do not make things fall nor time dilate around bound and unbound energy. Higgs doesn't either, at least, not exactly. Bound energy imparts or couples some considerable amount of spin back to the Higgs field. The more bound energy in a region there is, the more energy gets coupled to the field. This is not even something you can do a test for in the LHC. Don't bother to pretend that the math is there to support this mechanism yet. I understand that there isn't.

And quantum gravity is another area of technology that completely ignored Higgs role in interactions between bound energy and the vacuum. Don't pretend that it was taken into account. I know that it wasn't. The principle of equivalence stands as firm as blood on vanilla ice cream to everyone else. I don't care if you call it "classical". To me, "classical" is just any physics that uses greek letters for variables, superscripts or subscripts. In other words, ALL of it.

But I do see your point. An awful lot of Higgs mechanism going on (a star or a planet) eventually gets to be a fairly high energy event in the aggregate. By increments.

Granted, it finally took higher energies and more sensitive / versatile instruments like the LHC for us to discern Higgs. Or just perhaps, like Hawking, no one was betting on ever finding it.