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I am currently reading though Peskin and Schroeder and have recently encountered the UV cutoff. Basically, when we encounter an infinity in QFT which is caused by integration over momentum or energy, we can disregard this by limiting our integral as we know our formula is not exact and it is absurd to think that it should work at arbitrary energy.

This got me thinking about singularities. Basically knowing that GR is a not quantum theory and that surely at such high energy density and small volumes as found in black holes, QM effects will become very important, why is it that we are fine saying everything collapses into a singularity rather then saying we don't know and that the formula is invalid at such ranges?

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marked as duplicate by John Rennie black-holes Apr 18 '18 at 4:48

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    $\begingroup$ It's not that we're "fine" with it, it's just that we don't currently have anything better to say that has any evidence behind it. $\endgroup$ – probably_someone Apr 18 '18 at 3:06
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    $\begingroup$ What makes you think that we don't say "we don't know"? As one data point, the Wikipedia page for "effective field theory" says: "General relativity itself is expected to be the low energy effective field theory of a full theory of quantum gravity, such as string theory."(en.wikipedia.org/wiki/…) $\endgroup$ – Rococo Apr 18 '18 at 3:11
  • $\begingroup$ Well none of the literature that I have read (Most UG / pop-sci stuff) has ever made it seem like these are not a fact. $\endgroup$ – WilliamDaFoe Apr 18 '18 at 3:17
  • $\begingroup$ @WilliamDaFoe Can you give a specific example of a text that has explicitly claimed this? Also, it's worth noting that in the general types of literature you cited, oversimplifications like this one are necessary, because of three things: 1) the existence of singularities is not actually forbidden by anything we know of, despite the fact that they make you uncomfortable, so it's not strictly false; 2) they make for great pop-science reading, because the concept is really interesting; and 3) Western readers really like certainty in their scientific theories. $\endgroup$ – probably_someone Apr 18 '18 at 4:01
  • $\begingroup$ I think it is because the popularizers of general relativity are platonists at heart. Their point of view of physics is that "mathematics molds reality" rather than "mathematics models observations and measurements". It is the humanity tendency to place a creator at the beginning of everything, emerging in sophisticated mathematical constructs. $\endgroup$ – anna v Apr 18 '18 at 4:03
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Singularities are usually (however, I cannot think of an exception right now) artifacts of the mathematical models with which we describe the physical world. As such, physicists are not overly bothered by them, because we know chances are that these singularities may eventually be replaced by some structure once we've increased our understanding.

Sometimes these singularities are a nuisance, because they make our calculations difficult, as in quantum field theory for higher order Feynman diagrams. However, we have a good understanding where they come from and how to deal with them, using renormalization group theory.

The usuefulness of our mathematical models are associated with those regions where there are no singularites. In fact, the region where there is a singularity is usually not scientific, in the sense that we cannot make scientific observations there. For instance, in the case of a black hole, our ability to test predictions is restricted to the region outside the event horizon. As a result, any statements that we make about the region inside the black hole where the singularity is located are strictly speaking non-scientific.

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