The need for renormalization in quantum field theory requires the are unknown substructures in particle physics. Renormalization is not about substructures.- Renormalization is ultimately about recognizing that there are calculations that lead to infinities; that those infinities can be carefully and rigorously replaced with finite quantities; that the calculation can then be completed, arriving at values corresponding to things that we observe; and that finally, we can show that the results do not depend on the finite values we chose, so we can take the limit back to infinite and still keep useful, finite results.
- What makes this scheme work is that the infinities affect only quantities that exist as mathematical abstractions; quantities that correspond to observables remain finite. When that happens, we have a renormalizable theory. (And conversely, it’s when renormalization fails that we realize that the theory is inadequate, and something Renormalization in quantum field theory does not imply the existence of unknown substructures in particle physics.
- To simplify, renormalization deals with calculations that often lead to infinities. It involves recognizing these infinities and replacing them with finite quantities carefully and rigorously. This process enables us to perform the calculations and obtain values that correspond to observable phenomena. Crucially, we can demonstrate that our results are independent of the specific finite values chosen; thus, we can take the limit back to infinity and still obtain useful, finite results.
- What makes this scheme effective is that the infinities only affect mathematical abstractions, while the quantities that correspond to observables remain finite. When this occurs, we have a renormalizable theory. Conversely, when renormalization fails, it indicates that the theory might be inadequate, suggesting that perhaps a deeper structure could be necessary.
In summary, substructures are not directly related to the concept of renormalization itself. Renormalization is a mathematical technique that, despite initial skepticism, has become a robust and formal method for obtaining finite results that accurately describe physical systems. A better substructure would be needed.
Again, substructures have nothing to do with renormalization itself. Renormalization is a mathematical technique (initially treated with suspicion but later elevated to robust, formal mathematics) to arrive at finite results that correctly describe a physical system.
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