Is Renormalization Ruining Physics? A Deep Dive
It relies on parameterizing the divergent term using a cut-off, add imaginary counterterms, and take the limit to 'remove' the divergence. Firstly, it is nothing short of the butchery of mathematics, the very language physics is written in.
Your equation originally was never a limit, adding these ghost terms and taking the limit completely destroys your own equation and theoretical model. Is it the same equation as it was before ? Mathematically, no, we should not have even had divergent equations in the first place !
For the sake of it, however, let us assume this butchery to somehow be correct. This then yields some very amazing and remarkable results, 12 decimal points precise, or more. Modern physicists make rounds lauding renormalization for its results. But, should we not take this precision as a wake up call to realize that we are just some divergent terms away from an actually mathematically rigorous model which does not need renormalization in the first place ?
It is not even as if these models are completely invincible, they break down foolishly in many scenarios, take for example the Cosmological Constant Problem.
Back in the 19th century, physicists were introducing ghost planets to explain away [covergent,finite] discrepancies in Mercury's orbit rather than question Newtonian Gravity. Would we have been able to formulate Einstein's GR with differential geometry by the 1920s had we stuck to the ghosts planets ? Yet here we are introducing counterterms to explain away literal infinities.
What we need are new, mathematically rigorous theories that at the very least don't end up breaking down to give infinities [LQC,TQFTs,Skyrme]. We need to explore non linear, non local, topological theories with perhaps stochastic dynamics of solitons, and not be afraid to delve into even deeper mathematics like Einstein did introducing differential geometry and tensors back in the 1910s.
[This critique is purely from a mathematically rigorous standpoint]
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