“Truth alone will endure, all the rest will be swept away before the tide of time. I must continue to bear testimony to truth even if I am forsaken by all. Mine may today be a voice in the wilderness, but it will be heard when all other voices are silenced, if it is the voice of Truth.”
(Mahatma Gandhi, Basic Education (1951), p. 89.)
The Gauge Connection 
Buon anno
Anno nuovo, vita nuova !
Joseph
Thanks! Auguri e felice anno nuovo! (Happy new year!).
Dear Marco,
I do not find the renormalization ideology convincing. I see there wrong conclusions based on wrong assumptions. I wrote a simple illustrative article and I would like to learn your opinion about it. Please read it and tell me whether my reasoning is correct and convincing.
Regards,
Vladimir.
Dear Vladimir,
I think that it is an example of braveness to challenge a technique that works so well and proved to be fertile for the results it yielded. Generally, I would cite the power of renormalization group in this case that, thanks to the formulation due to Kenneth Wilson, gave us a deep understanding of phase transitions that we will have otherwise missed. Besides, in the history of science, there is nothing that agrees so well with experiments than Standard Model that largely uses renormalization techniques. Through them one is able to get all those cross sections and rates that presently people at CERN is proving to agree so perfectly well with experimental data.
By my side, working just with a classical field theory as I have widely discussed in this blog, I showed how interaction produces finite effects on mass and this is a fact being those exact solutions. So, renormalization is a really sound idea and to understand the reasons of its success we need a higher order theory with respect to the Standard Model. This is what people is currently looking for.
I think that to convince people that your criticisms are sound you will need well more than a couple of Newton equations. Otherwise it appears just like a matter of principle most in the same way the late Dirac did.
Cheers,
Marco
Dear Marco,
Thank you for your answer.
I do not deny the usefulness of renormalization. It is the only our tool in making practical calculations until we find a better formulation of theory. My toy model is exactly renormalizable and it shows that renormalization may work. As well, my toy model is exactly soluble, so its precision is absolute. What I wanted to demonstrate is that our current interpretation of renormalization is erroneous. There are no bare particles, but our errors in coupling equations. Dirac did not find an exactly renormalizable system to substantiate his concerns, and I found such a system. It can be easily promoted to QM, for example, by substituting its Lagrangian in the path integral. Simplifying it to a classical system, I just wanted to strip from renormalization those “relativistic, quantum, and non linear” clothes that hide the essence – our mathematical and physical errors in coupling equations. It is we who spoils the equation coefficients (passage from (1) to (5)), and it is we who restores the old, physical values by hand, and there are no vacuum polarization and other “bare particle interaction effects” who do renormalizations for us.
Regards,
Vladimir.
Dear Vladimir,
I think you have not a clear idea of what renormalization is. The problem is that an interacting quantum field theory has products of distribution valued operators that must be properly defined. Renormalization gives a prescription for this and it works excellently well. As a physicist I should say that there is a proper mathematical procedure that extends distribution theory as devised by Laurent Schwartz to manage such products. These mathematical operations are inescapable unless a theory is trivial.
In your case, you have to take a simple quantum field theory like that of a massless scalar field and show that you are able to produce identical results as renormalization techniques do. Then, put your computations on a paper and send them to some refereed journal. In this way you can get a hope to be heard.
Cheers,
Marco