I dream of reformulating the Classical and Quantum Electrodynamics.

**Why it is necessary?**

It is necessary for better understanding the corresponding physics and for having better equations since currently the equations are such that their solutions need modifications (this fact reflects lack of physics understanding while constructing these equations).

**Why it has not been done before?**

Many have tried, but none prevailed. And currently it is renormalizators (practitioners) who are teaching the subject, not theory developers, so they do everything to convince students to accept “bare particle” physics. In Classical Electrodynamics (CED) some teach that (the remainder after the mass renormalization) is a good radiation reaction term [1, 2] even though it leads to “false start” solutions; some, on the contrary, teach that is not applicable at “small times” and one must use instead [3], but up to now no mechanical equation was found to conserve the energy-momentum exactly and in a physical manner. We content ourselves with an approximate description. The Noether theorem did not help!

Similarly in QED – although the equation set is different from that of CED, the renormalization is still a crucial part of calculations. And in addition, soft mode contributions (absent in the first Born approximation) are obligatory for obtaining physically meaningful results. If one is obliged to sum up some of its contributions to all orders, it indicates a bad initial approximation used for the perturbation theory.

Many theory developers (founding fathers) were looking for better theory formulations. It happened to be an extremely difficult problem, mainly due to prejudices implicitly involved in theoretical constructions. Paul Dirac, a rare physicist who was not thinking of fame and money at all, never gave up. His motto – a theory must be mathematically and physically sensible [4], and for the sake of that we must search for better Hamiltonians, better formulations, better description than the current one, is my motto too.

If you have read my blogs (this one, http://fishers-in-the-snow.blogspot.fr/ , http://vladimir-anski.livejournal.com/) and articles, you may have an idea what I mean by reformulation. If you like, my program can roughly be understood as fulfilling the counter-term subtractions exactly:

and including some of this (“good”) Lagrangian terms into a new initial approximation, i.e., figuratively speaking:

Then the “interaction term” will be different too:

so that no renormalization will be needed and the soft diagram contributions will be taken into account automatically in the first Born approximation (like in [7]).

**What I need?**

In order to pursue my research, **I need funds**. I believe that we can achieve a better description if we abandon some prejudices and employ some physical reasoning instead of doing by a blind analogy. I have already outlined possible directions in my articles [5-8]. But currently I am working for a private company, fulfilling subcontract studies, and it takes all my time and efforts. This activity is far from my dream, though. I have to abandon it in order to concentrate myself on my own subject. I’ve got to break free!

Academia does not support this “reformulation approach” anymore. I can only count on private funding. If you or your friends or friends of your friends are rich people, then create a fund for supporting my research, run it and we will make it possible.

I do not need a crazy amount like a Milner prise, no! A regular salary of a theorist will suffice.

(Small donations may be sent to my PayPal account: vladimir.kalitvianski@wanadoo.fr)

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[1] Sidney Coleman, *Classical Electron Theory from a Modern Standpoint*, http://www.rand.org/content/dam/rand/pubs/research_memoranda/2006/RM2820.pdf

[2] Gilbert N. Plass, *Classical Electrodynamic Equations of Motion with Radiative Reaction*, Rev. Mod. Phys. V. **33**, 37 (1961), http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.33.37 or https://drive.google.com/file/d/0B4Db4rFq72mLcUN6bEhweTgyWkE/edit?usp=sharing

[3] V. L. Ginzburg, *Theoretical Physics and Astrophysics*, Pergamon Press (1979), http://www.amazon.com/Theoretical-Physics-Astrophysics-Monographs-Philosophy/dp/0080230679 , https://drive.google.com/file/d/0B4Db4rFq72mLWGhCTXVJLUU1WVk/edit?usp=sharing

[4] Jagdish Mehra (editor), *The Physicist’s Conception of Nature*, (1973), https://drive.google.com/file/d/0B4Db4rFq72mLWnIyM1FSOGcxaDA/edit?usp=sharing

[5] *Reformulation instead of renormalization*, http://arxiv.org/abs/0811.4416

[6] *Atom as a “Dressed” Nucleus*, http://arxiv.org/abs/0806.2635

[7] *A toy model of Renormalization and Reformulation*, http://arxiv.org/abs/1110.3702

[8] *Unknown Physics of Short Distances*, https://www.academia.edu/370847/On_Probing_Small_Distances_in_Quantum_World

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S. Weinberg wrote a paper “Living with infinities” devoted partially to the memory of Gunnar Källén. Also he outlined there his personal view on the problem of renormalization. Good for him.

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I just take his title and refer to a movie clip where some live with divergences too. I rephrase L.J. Washington’s **sober** words:

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“*It’s a condition of mental divergence: we find ourselves in the Wilsonian world, being a part of intellectual elite and subjugating infinities. But even though the renormalization ideology is totally convincing for us in every way, nevertheless it is actually a construct of our psyche. We are mentally divergent. In that we escape certain unnamed realities that plague our lives here. When we stop appealing to it, we’ll be well.*“

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(Behind L. J. Washington someone resembling P. Dirac solves a puzzle.)

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Let us take QED – the first QFT Nobel prises were given for. Its Lagrangian is the following:

It is relativistic and gauge-invariant because the bare particles are such. Parameters and are bare particle mass and charge and the term is how bare particles interact. Of course, bare particles have spin and other quantum numbers.

You may wonder how do we physicists know all that if the bare particles are non-observable (and why do they interact if they are non-interacting particles)?

Good questions. Very intelligent! The answer is – due to our physical insights. You know, insight is the ability to see the invisible, to penetrate mentally into the unknown, to figure out everything correctly from small, rare, and distorted pieces of a whole picture. Factually we, from long distances (from low-energy experiments with physical particles), penetrated to the end – to the point where bare particles live. Thus we insightful nailed the bare particle properties and their interaction laws correctly despite their hiding from us.

And yes, the bare non-interacting particles do interact and even self-interact. It is they who permanently do this hard work. At a first, naive, glance these statements are inconsistent, but no. It is a kind of duality in physics. This duality is not much advertised because the bare particles are really modest bricks.

(It’s a joke without humor.)

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“*We will be considered the generation that left behind unsolved such essential problems as the electron self-energy.*“

I think the essence is here and avoiding it created just a shaman’s practice where cheating and self-fooling are essential parts. To prove that, let me be more specific and let us consider the electron electromagnetic mass. This notion had arisen in Classical Electrodynamics (CED) well before the famous was derived [1] and it remains an unsolved problem even today (there are still publications on this subject). We must not confuse it with the electromagnetic *mass defect*, though, i.e., with a *calculable interaction energy*.

The electromagnetic mass can be thought of as a Coulomb energy of the electric field surrounding the electron when we calculate the total field energy. In other words, it is a consequence of the field concept. This part of the field energy is cut-off dependent and thus can take any value at your convenience. We all are familiar with the classical radius of electron , but if we take into account the electron magnetic moment field energy too, we will obtain another radius, closer to the Compton length . Still, in nature there is no electron of the classical or any other radius. And normally this part of the field energy is entirely discarded and what is left is an interaction energy of charges. Thus, when we calculate a *field energy*, the electromagnetic mass is just of no use.

Apart from the total field energy, the electromagnetic mass of a point-like charge enters the usual “mechanical” equation of a charge when we decide to insert the charge proper field into the charge equation of motion in the frame of a self-action ansatz. The latter is done for the sake of taking into account a weak radiation reaction force, which must provide the total energy conservation. The motivation – energy conservation – is understandable, but in a field approach with , we insert the entire filed , not just a radiation field , in the mechanical equation. We do it by (a wrong) analogy with an external force . So, before this our intervention we have a good “mechanical” equation (I use a non relativistic form)

which works almost fine (the near field, whatever it is, easily follows the charge according to Maxwell equations), and after our noble intervention it becomes

that does not work any more. The corresponding self-force term with makes it impossible for a charge to change its state of a uniform motion . This is a self-induction force, an extremely strong one. It’s an understandable “physical effect”, but first, it is not observed as infinite, and second, the self-induction force is not a radiation reaction force in any way, so our approach to describing the radiation influence via self-action is blatantly wrong. Albeit of an anticipated sign (and even when made finite and small), it does not help conserve the total energy. Microsoft Windows would say:

Instead of recognizing this error, physicists started to search a pretext to keep to the self-action idea in place. They noticed that discarding the term “helps” (we will later see how it helps), but calling it honestly “discarding” makes fun of physicists. Discarding is not a calculation. Thus, another brilliant idea was advanced – an idea of “bare” mass that “absorbs” (a “mechanism” called later a mass renormalization). Tricky is Nature, but clever are physicist. In a fresh historical paper Kerson Huang expresses the common attitude to it [2]:

“*One notices with great relief that the self‐mass can be absorbed into the physical mass in the equation of motion*“

and he writes down an equation, which experimentally follows from nowhere:

It is here where the negative bare mass is introduced in physics by physicists, introduced exclusively with the purpose to subtract the harmful electromagnetic mass. This introduction is not convincing to me. A negative mass makes the particle move to the left when the force pulls it to the right. We never observed such a silly phenomenon and we never wrote the corresponding equations. We cannot pretend that (1) describes such a wrong particle in an external field, but adding its self-induction makes the equation right, as it does Kerson Huang. It’s all the way around: in order to make the wrong equation (2) closer to the original one (1), we just **discard **the electromagnetic mass whatever value it takes. Kerson Huang should have written honestly “*One notices that the self‐mass ought to be omitted*“.

As well, those who refer to a hydrodynamics analogy, present this silly speculation about arbitrary and as a typical calculation, a calculation like in hydrodynamics where everything is separately measurable, known, and physical. In CED it is not the case. And if the electromagnetic mass is present already in our phenomenological equation (1), the method of self-action takes it into account once more which shows again that such an approach is self-inconsistent. You know, self-induction of a wire is in fact a completely calculable physical phenomenon occurring with many* interacting* charges. Similarly in plasma description we calculate* interactions* for dynamics. Interaction is a good concept, but a self-action of an elementary particle is a bad idea. It describes no internal dynamics by definition.

If a bare particle is not observable, we cannot even establish an equation for it and we cannot pretend that its equation is of the same form as the Newton equations for physical particles. They, however, say the bare mass is not observable alone – it always comes in (3) together with the electromagnetic one: . But it is not true either: equation (1) contains the physical mass and in addition, if the external force in (1) contains the omnipresent gravity force, say, for simplicity, the latter does not acquire any addendum when we add that self-induction force. In reality, we fight our own invention with help of another one – , but too many people believe in both.

This is the real truth about mass “renormalization” procedure. We ourselves introduce the self-mass in our equation and then we remove it. As nothing remains from it anywhere (the physical mass stays intact), I can safely say that there is no electromagnetic mass at all, that’s my answer to this question (again, not to confuse with the mass defect due to interaction). (By the way, renormalization does not work without fail – there are many non renormalizable theories where bad interaction terms spoil not only the original equation coefficients, but also introduce wrong “remainders”. Success of renormalization is based on lucky accidents, see my opus **here** or **here**. P. Dirac clearly called it a fluke.)

Here I naively wonder why not from the very beginning to use just the radiated field instead of the total field to take into account the “radiation reaction”? Then they might never obtain the harmful jerk term , but they do not do it. They stick to the self-action patched with the “bare mass mechanism” and they hope that *the jerk *“reminder” of self-action will correctly describe the radiation reaction. Let us see.

So, after shamefully camouflaging discarding silly , they are left with the jerk called a “radiation reaction” force:

Fortunately, it is wrong too. I say “fortunately” because it reinforces my previous statement that the self-action is a wrong idea. This remainder **cannot be used** as it gives runaway solutions. Not small radiation reaction, but a rapid self-acceleration. Microsoft Windows would say:

In other words, all terms of self-action force in (2) are wrong. Briefly, this self-action idea was tried and it failed miserably. Period.

A. Unzicker speaks of a fake and for some readers this may look as an exaggeration. If you want to see physicists cheating, here is another bright example. This cheating consists in using in their “**proof**” of energy conservation [3], as if the corresponding equation (4) had physically reasonable quasi-periodical solutions. But it doesn’t! Runaway solutions are not quasi-periodical and are not physical at all, so the proof is just a deception. (They multiply by and integrate it by parts to “show” that on average it is a radiation power.) If they insist on using quasi-periodic solutions in their proof, these solutions do not belong to Eq. (4). (A “jerky” equation like (4) does not even have any physical Lagrangian to be directly derived from!)

As a matter of fact, after cheating with the “**proof**“, this harmful jerk term is also (quietly) abandoned in favor of some small force term used in practice instead. This small term is (or alike):

Equation (5) is much better, but here again, I notice cheating once more because they represent it as a “derivation” from (4). Now cheating consists in ** replacing ** with as if we solved (4) by iterations (perturbation method). However, in the true iterative procedure we obtain a given function of time on the right-hand side rather than a term expressed via

the first perturbative term is a known external periodic (resonance!) driving force whereas the replacement term is unknown damping force (kind of a friction):

A perturbative solution to (6) (a red line in Fig. 2)

is different from a damped oscillator solution (a blue line in Fig. 2). Solution to a damped oscillator equation is non linear in , non linear in a quite certain manner. It is not a self-action, but an *interaction* with something else. This difference in equations is qualitative (conceptual) and it is quantitatively important in case of a strong radiation reaction force and/or when (I used in this example with , and ). I conclude therefore that a damped oscillator equation (7) is not a perturbative version of (6), but is another guesswork result tried and left finally in practice because of its physically more reasonable (although still approximate) behaviour. Similarly, equation (5) is not a perturbative version of (4), but another (imperceptible) equation replacement [3], [4]. Of course, there is no and may not be any proof that perturbative series for (4) converge to solutions of (5).

Hence, researchers have been trying *to derive equations* describing the radiation reaction force correctly, but they’ve failed. For practical (engineering) purposes they constructed (found by trying different functions) approximate equations like (5) that do not provide the exact energy conservation and do not follow from “principles” (no Lagrangian, no Noether theorem, etc.). Factually the field approach has been “repaired” several times with anti-field guesswork, if you like. Anyway, we may not represent it as a continuous implementation of principles because it isn’t so.

Guessing equations, of course, is not forbidden, on the contrary, but this story shows how far away we have gone from the original idea of self-action. It would not be such a harmful route if the smart mainstream guys did not raise every step of this zigzag guesswork into “the guiding principles” – relativistic and gauge invariance, ** restricting**, according to the mainstream opinion, the form of interaction to . Nowadays too few researchers see these steps as a severe lack of basic understanding of what is going on. On the contrary, the mainstream ideology consists in dealing with the same wrong self-action mechanism patched with the same discarding prescription (“renormalization”), etc., but accompanied also with anthems to these “guiding principles” and to their inventors. I do not buy it. I understand the people’s desire to look smart – they grasped principles of Nature, but they look silly to me instead.

Indeed, let us for a moment look at Eq. (5) as at an *exact* equation containing the desirable radiation reaction correctly. We see, such an equation exists (at least, we admit its existence), it does not contain any non physical stuff like and , and together with Maxwell equations it works fine. Then why not to obtain (5) directly from (1) and from another physical concept different from a wrong self-action idea patched with several forced replacements of equations? Why do we present our silly way as a right and unique? Relativistic and gauge invariance (equation properties) must be preserved, nobody argues, but making them “guiding principles” only leads to catastrophes, so (5) it is not a triumph of “principles”, but a lucky result of our difficult guesswork done against the misguiding principles. Principles do no think for us researchers. Thinking is our duty. Factually we need in (1) a small force like that in (5), but our derivation gives (2). What we then do is a lumbering justification of replacements of automatically obtained bad functions with creatively constructed better ones. Although equations like (5) work satisfactorily in some range of forces, the lack of mechanical equation with exact radiation reaction force in CED shows that we have not reached our goal and those principles have let us down.

Note, although the above is a non relativistic version of CED, the CED story is truly relativistic and gauge invariant and it serves as a model to many further theory developments. In particular, nowadays in QFT they “derive” the wrong self-action Lagrangian from a “principle of local gauge invariance” (a gauge principle for short). They find it beautiful mathematically, enjoy the equation symmetries and conservation laws that follow from this symmetry. They repeat QED where they think there is this “gauge principle”. However such gauge equations do not have physical solutions, so their conserved quantities are just a bullshit. During enjoying the beauty of gauge interaction, they omit to mention that the solutions are non physical. The gauge principle in QED does not lead to physical equations. We are forced to rebuild a gauge theory, as I outlined above. In CED the bare and electromagnetic masses appear and disappear shortly after, but in QED and QFT they are present in each perturbative order. In addition, the physical charge also acquires unnecessary and bad “corrections”, and their omnipresence makes an impression of their belonging to physics.

Next, new “principles” come into play – they come into play with the purpose to fix this shit. Those principles serve to “allow” multiple replacements of bad terms in solutions with better ones – bare stuff and renormalizations, of course. A whole “fairy science” about a “vacuum polarization” around a still “bare” charge is developed to get rid of bad perturbative corrections in this wrong gauge construction (renormalization group). It boils down to adding a counter-term Lagrangian to the gauge one :

so the interaction becomes *different* from a purely gauge one. (Often it is presented as imposing physical conditions to a (bad) theory.) Thus, bare stuff and bad corrections cancel each other and do not exits any more. That’s their fate – to disappear from physics forever, if you understand it right. And it is we who make them disappear, not physical phenomena like vacuum polarization, etc. In other words, renormalization is not a calculation, but a specific modification of calculation results.

But this fix is not sufficient either. They need to sum up soft diagrams too (to all orders) in order to obtain physically meaningful results because, alas, the electron does not correctly radiate otherwise and calculation fails! The latter fact shows eloquently that some part of “perturbation” (8) (let’s call it figuratively ) is not small and should be taken into account exactly (joined with , hence, removed from the “perturbation”):

Fig. 3. Electron scattering from an external field in the first Born approximation, as it must be.

Such taking into account exactly is in fact using another, more physical, zeroth-order approximation with Lagrangian (9). The electron charge is involved there non perturbatively, so the electron is already *coupled* with the field variables, at least, partially (I call such an approximation an “electronium” [5]). Interaction (10) is even more different from the “gauge” one. (A good qualitative and quantitative analogy to such IR-divergent series and their exact sums is the second atomic form-factor (3) and its series in powers of when and , see Fig. (3) in [5].)

You see, our former initial approximation (decoupled electron in ) is not physical. You know why? Because we admit free particles in our minds and thus in equations. We observe interacting macroscopic bodies. In the simplest case we speak of a probe body in an external force. Sometimes the external forces add up into nearly zero and they do not change noticeably the body kinetic energy. Then we say the probe body is “free”. But we observe it with help of interactions too (inclusive image obtained with photons, for example), so it is never free, as a matter of fact, and, of course, its mass is not bare. For electron it also means that its very notion as a “point particle” and its equations is an inclusive picture of something compound [5]. An electron coupled within field oscillators has a natural mechanism of “radiation reaction” and a natural inclusive picture. Such a coupling is always on and never is off, unlike the gauge term treated perturbatively. W. Pauli always argued that one should look for a formulation of QED (or a field theory in general) which would mathematically not allow the description of a charged particle without its electromagnetic field. Now, seeing to what extent and are different from (9) and (10), I can safely say that they really do not understand what to start with in their “gauge theories”. Even a physical solution of a partially coupled electron (a “hairy” electron line in Fig. 3) is not written, understood, and explained in QED, but who cares?

In electroweak unification they wanted to make the weak part of interaction to be a “gauge” too, but the gauge fields are massless. What a pity! Not only this construction needs counter-terms and soft diagram summations, now it needs a special “mechanism” to write down the mass terms in . Such a fix was found and it is known now as a Higgs mechanism. This fix to a bad gauge interaction idea is presented now as the ultimate explanation of the nature of mass: “Every ounce of mass found in the universe is made possible by the Higgs boson.” I wonder how were we doing before Higgs? With writing down phenomenological mass terms, we were in error, weren’t we? No. Then why all these complications? Because they do not know how to write down *interactions* with massive particles correctly (an old story, see (9) and (10) above). All they write is not only non physical, but also non renormalizable, so they decided to try here the gauge principle too. Fortunately or unfortunately, but some such constructions are renormalizable, thus they survived.

We remember the fiasco with the electron electromagnetic mass, and the Higgs proper mass is not really different since the Higgs boson acquires its own mass due to “self-action” too. It is not a calculation, but a fake since the Higgs boson mass is taken from experiment.

The Standard Model is also furnished with “fine tuning mechanism” because otherwise it is still a bullshit. And let me mention *fitting parameters* coming with the “Higgs mechanism”. Now the fitting properties of theory increased. Some, however, confuse it with increase of “predictive power”.

To me the Higgs is a fix, a fix somewhat similar to the bare mass term in CED compensating an obviously wrong construction, but a more complicated fix. I do not think it is an achievement. A bare mass notion is not an achievement in physics. The freedom in choosing the cutoff in a relationship (à la renorm-group) is not physics, -independence of is not a CED “universality”. I hope I am clear here. But nowadays particle physics is stuffed with artefacts of our patches and stopgaps, so it is really difficult to distinguish what is physical and what is a fairy tale (a fake).

Today they sell you the bare stuff, its self-action dictated with the gauge principle, then counter-terms, IR diagram summation, Higgs field with self-action and fine tuning, poisons and antidotes, shit with nutlets, etc. as a physical theory. They are very pushy in that. They grasped all the principles of Nature.

No, they fool themselves with “clever insights” and fairy tales instead of doing physics. They count on “guiding principles”, they are under the spell of the gauge and other principles. Sticking to them is like being possessed. This fact underlines the shaky grounds the modern QFT is based on.

We have no right to dope ourselves with self-fooling and self-flattering. The conceptual problems have not been resolved, let us recognize it.

(To be updated.)

[1] Laurie M. Brown (editor). *Renormalization From Lorentz to Landau (and beyond)*, 1993, Springer-Verlag, the talk of Max Dresden.

[2] Kerson Huang, *A Critical History of Renormalization*, http://arxiv.org/abs/1310.5533

[3] H. Lorentz, Landau-Lifshitz, R. Feynman, etc.

[4] Fritz Rohrlich, *The dynamics of a charged particle*, (2008) http://arxiv.org/abs/0804.4614

[5] Vladimir Kalitvianski, *Atom as a “Dressed” Nucleus*, Central European Journal of Physics, V. 7, N. 1, pp. 1-11 (2009), http://arxiv.org/abs/0806.2635

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I wonder whether the photon field filled the whole space then?

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Many think that renormalization belongs to relativistic quantum non linear field theories, and it is true, but it is not all the truth. The truth is that renormalization arises every time when we modify undesirably coefficients of our equations by introducing somewhat erroneous “interaction”, so we return to the old (good) values and call it renormalization. Both modifications of coefficients show our shameful errors in modeling and this can be demonstrated quite easily with help of a simple and exactly solvable equation system resembling the Classical and Quantum Electrodynamics.

Let us consider a couple of very familiar differential equations with phenomenological coefficients (two Newton equations):

One can see that the particle acceleration excites the oscillator, if the particle is in an external force. In this respect it is analogous to the electromagnetic wave radiation due to charge acceleration in Electrodynamics. When there is no external force, the “mechanical” and the “wave” equations become “decoupled”.

The oscillator equation system can be equivalently rewritten via the external force:

It shows that the external force application point, i.e., our particle, is a * part* of the oscillator, and this reveals how Nature works (remember P. Dirac’s: “One wants to understand how Nature works” in his talk “Does Renormalization Make Sense?” at a conference on perturbative QCD, AIP Conf. Proc. V. 74, pp. 129-130 (1981)).

Systems (1) and (2) look like they do not respect an “energy conservation law”: the oscillator energy can change, but the particle equation does not contain any “radiation reaction” term. Our task is to complete the mechanical equation with a small “radiation reaction” term, like in Classical Electrodynamics. It is namely here where we make an error. Indeed, let me tell you without delay that the right “radiation reaction” term for our particle is the following:

If we inject it in system (2), we will obtain a correct equation system:

Here we are, nothing else is needed for “reestablishing” the energy conservation law. System (4) can be derived from a physical Lagrangian in a regular way (see formula (22) here). We can safely give (4) to engineers and programmers to perform numerical calculations. ~~Period.~~ But it is not what we actually do in theoretical physics.

Instead, we, roughly speaking, insert (3) in (1) with help of our wrong ansatz on how “interaction” should be written. Let us see what then happens:

Although it is not visible in (5) at first glance, the oscillator equation gets spoiled – even the free oscillator frequency changes. Consistency with experiment gets broken. Why? The explanation is simple: while developing the right equation system, we have to keep the right-hand side of oscillator equation a known function of time or, more precisely, an external force, like in (2), rather than keep its “form” (1) (I call it “preserving the physical mechanism, the spirit, not the form”). Otherwise it will be expressed via *unknown* variable , which is *coupled* now to , and this modifies the coefficient at the oscillator acceleration when in the oscillator equation is replaced with the right-hand side of the mechanical equation. In other words, if we proceed from (1), then we will make an * elementary mathematical error * because we not only add the right radiation reaction term, but also modify coefficients in the oscillator equation, contrary to our goal. As a result, both equations from (5) have wrong exact solutions. If we insist on this way, it is just our mistake (blindness, stubbornness) and no “bare” particles are responsible for undesirable modifications of equation coefficients.

However, in CED and QED they advance such an “interaction Lagrangian” (self-action) that spoils both the “mechanical” and the “wave” equations because it preserves the equation “form”, not the “spirit”. In our toy model we too can explicitly spoil *both* equations and obtain:

with advancing a similar “interaction Lagrangian” for “decoupled” equations from (1):

Here in (6) – masses with “self-energy corrections”. Thus, it is the “interaction Lagrangian” (7) who is bad, not the original constants in (1), whichever smart arguments are invoked for proposing (7).

Moreover, there is **a physical Lagrangian** for the correct equation system (4). Therefore, we simply have not found it yet, so ** we** are the main responsible for modifying the equation coefficients in our passage from (1) to (6), not some “bare particle interactions”.

In CED and QFT they perform a second modification of coefficients, now in perturbative solutions of (6) to obtain perturbative solutions of (4), roughly speaking. Such a second modification is called “renormalization” and it boils down to deliberately discarding the wrong and unnecessary “corrections” to the original coefficients in (6):

In other words, renormalization is our brute-force “repair” of spoiled by us coefficients of the original physical equations, whatever these equations are – classical of quantum. Although it helps sometimes, it is not a calculation in the true sense, but a “working rule” at best. A computer cannot do numerically such solution (curve) modifications. The latter only can be done in analytical expressions by hand. Such a renormalization can be implemented as *a subtraction* of some terms from (7), namely, a subtraction of

(called counter-terms) and it underlines again the initial wrongness of (7). It only may work by chance – if the remainder (3) is guessed right in the end, as in our toy model.

P. Dirac, R. Feynman, W. Pauli, J. Schwinger, S. Tomonaga, and many others were against such a “zigzag” way of doing physics: introducing something wrong and then subtracting it (physically we add an electron self-induction force that prevents the electron form any change of its state and then we discard its contribution entirely). However nowadays this prescription is given a serious physical meaning, namely, they say that no discarding we do, but it is the original coefficients who “absorb” our wrong corrections because our original coefficients in (1) are “bare” and “running”! Of course, it is not true: nothing was bare/running in (1) and is such in (4), but this is how the blame is erroneously transfered from a bad interaction Lagrangian to good original equations and their constants. Both modifications of coefficients (self-action ansatz and renormalization) are presented as a great achievement today. It, however, does not reveal how Nature works, but **how human Nature works**. Briefly, this is nothing else but a self-fooling, let us recognize it. No grand unification is possible until we learn how to get to (4) directly from (1), without renormalization.

Most of our “theories” are non renormalizable just for this reason: stubbornly counting that renormalization will help us out, we, by analogy, propose wrong “interaction Lagrangians” that not only modify the original coefficients in equations, but also bring **wrong ** “radiation reaction” terms. Remember the famous leading to runaway exact solutions in CED and needing a further “repair” like or so.

We must stop keeping to this wrong way of doing physics and pretending that everything is alright.

**P.S.** Wilsonian framework, as any other, proceeds from an implicit idea of *uniqueness* and *correctness* of the spoiled (i.e., wrong) equations, and cutoff and renormalizations are simply and “naturally” needed there because “we do not know something” or because “our theory lacks something”. Such a “calming” viewpoint prevents us from reformulating the equations from other physical principles and “freezes” the incorrect way of doing physics in QFT. Wilsonian interpretation, as any other, is in fact a covert *recognition of incorrectness* of the theory equations (equations (6) in our case), let us state it clearly. First, one cuts off a correction under some “clever pretext”, and next, one **discards it entirely** anyway because this correction is **just entirely wrong** whatever cut-off value is, so the “clever pretext” for cutting off is put to shame.

And those who still believe in bare particles and their interactions, “discovered” by clever and insightful theorists despite bare stuff being non observable, believe in miracles. One of the miracles is the famous “absorption” of wrong corrections by wrong constants in the right theory (i.e., the constants themselves absorb corrections, without human intervention).

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The slides without comments are here and here, and with comments (but smaller in size) are here and here.

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There are so many different “expoundings” of renormalizations in the literature. I think mine is the only correct one. The others mislead and even fool you. For example, one geek considers the Archimedes effect as a mass renormalization and says that it may give a negative effective mass. What a shit! Don’t buy it! Whatever is the resulting force applied to a body , the body mass remains the same. ;-)

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