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A. Neumaier said: ↑Removing the cutoff (in the lattice case taking the continuum limit) is essential to get the correct Poincare symmetry. The approximate theories are only construction tools, not the real thing. Ilja said: ↑if Poincare symmetry would be the real thing, one would be able to construct models without infinities which have full Poincare symmetry, and one would not need such non-Poincare-symmetric "construction tools". A. Neumaier said: ↑Your argument is very misinformed.

It istypicalin mathematics that nice objects are first constructed in a messy way.

The real numbers have very nice properties but to construct them one needs artifacts that make the numbers appear to be complicated sets (Dedekind cuts, euqivalence classes of Cauchy sequences, etc.).

The exponential function has many nice properties, but to construct it one needs limits of simpler functions that do not have this property. Ilja said: ↑But I was talking about physics. Your example is also not very impressive. Essentially, it is an example of a simplification reached by going to some infinite limit. So that a mathematical simplification can be reached by going to limits. But what about reality? A. Neumaier said: ↑Another reason why Poincare symmetry is the real thing is that it gives rise (via Noether's theorem) to the conservation laws on which all basic physics relies. Drop symmetries - and you have nothing left to guide your theory building. Ilja said: ↑Hm. Maybe you are an opponent of GR, given that you cannot get conservation laws via Noether, but have only some pseudotensors, which do not even allow a physical interpretation in agreement with the spacetime interpretation, which allows only tensors to have a physical meaning?

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# A Is Poincare symmetry the real thing?

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