Jacobs argues that none of the standard arguments for the Planck length as immediately physically significant (dimensional analysis, black hole argument, generalised microscope, effective field theory regime due to non-renormalisabielity) is straightforwardly conclusive. The assumption Casper identifies for the EFT scenario argument (which he nevertheless takes most impressive) should sound rather harmless for physicists: namely that the same units in the quantum action are used (hbar) for gravity as for matter — an assumption dubbed by him `action-universality’. As Jacobs spells out here: \begin{quote}
The assessment of Action-Universality itself would require an account
of the nature of fundamental constants. For example, one could think of hbar
as like c, which is a fundamental feature of the spacetime arena in which
physical fields evolve. We would therefore expect any relativistic theory to
feature the same constant. (Even this is not so clear, as bimetric theories
of gravity feature multiple metrics and hence multiple local upper bounds
on two-way speeds. The possibility of such theories is one reason to reject
Action-Universality.) But one could equally think of hbar as more like G,
which is the coupling constant of a particular force. Different forces have
different coupling constants. If hbaris like this, then it is conceivable that
gravity has a different constant of action than other forces, in which case
Action-Universality is false. For as far as I am aware, there is no extant
account of the metaphysical nature of a constant such as hbar that could help
us decide this question. (p. 18)
\end{quote}
The first option here seems just the standard way of thinking. The other possibility seems to be a physical possibility of the character of a logical possibility: given that the whole idea of quantisation is suggested and backed by analogy, it is just very plausible to take this to be the case about hbar too (or at the very least one would want to prima facie pursue such a theoretical ansatz as opposed to any other one, all other things being equal).
It is illuminating how Jacobs spells out what kind of boundary the Planck length could possibly be: as an upper boundary (quantum gravity becomes only relevant at this or smaller scales); as an exact boundary (quantum gravity becomes more or less relevant at this scale, not much more below or above); or as a lower boundary (quantum gravity becomes relevant at latest at this scale). While he basically assigns many arguments to be just after the lower boundary (clearly the dimensional analysis case has not enough information to say anything), he does not discuss too explicitly how to assess what he takes to be the most convincing case — that from being an effective field theory: but he does mention that the corrections on the EFT view come in at or below the Planck length; so it is a upper boundary case.
I take here to lie a sort of conundrum then: is there something about the need of quantum gravity we do not see then on this supposed best case for taking the physical relevance of the Planck length seriously? This is in so far confusing as that everything would seem model-able on the EFT view. (But maybe this is just a hint then that gravity is not an effective field theory after all. So the argument is after all not that good.)\footnote{Maybe consider Schneider here?}
What is also a bit strange: Jacobs (rightly) points out the epistemic nature of the Planck-lenght arguments from black holes, and generalised Heisenberg microscope — but does not mention this for his preferred renormalisabielity option. Naively, one might that is just renormalisabielity (and so predictivity!) at stake here which is epistemic. But then note: the Planck scale is not the scale when the EFT breaks down — it is the scale when the EFT corrections come in.
ACTION POINTS: (1) IS GR REALLY AN EFFECTIVE FIELD THEORY (SEE ALSO SCHNEIDER). (2) WHAT DO WE IN OUR BOOK SAY ABOUT ALL OF THIS?
The assessment of Action-Universality itself would require an account
of the nature of fundamental constants. For example, one could think of hbar
as like c, which is a fundamental feature of the spacetime arena in which
physical fields evolve. We would therefore expect any relativistic theory to
feature the same constant. (Even this is not so clear, as bimetric theories
of gravity feature multiple metrics and hence multiple local upper bounds
on two-way speeds. The possibility of such theories is one reason to reject
Action-Universality.) But one could equally think of hbar as more like G,
which is the coupling constant of a particular force. Different forces have
different coupling constants. If hbaris like this, then it is conceivable that
gravity has a different constant of action than other forces, in which case
Action-Universality is false. For as far as I am aware, there is no extant
account of the metaphysical nature of a constant such as hbar that could help
us decide this question. (p. 18)
\end{quote}
The first option here seems just the standard way of thinking. The other possibility seems to be a physical possibility of the character of a logical possibility: given that the whole idea of quantisation is suggested and backed by analogy, it is just very plausible to take this to be the case about hbar too (or at the very least one would want to prima facie pursue such a theoretical ansatz as opposed to any other one, all other things being equal).
It is illuminating how Jacobs spells out what kind of boundary the Planck length could possibly be: as an upper boundary (quantum gravity becomes only relevant at this or smaller scales); as an exact boundary (quantum gravity becomes more or less relevant at this scale, not much more below or above); or as a lower boundary (quantum gravity becomes relevant at latest at this scale). While he basically assigns many arguments to be just after the lower boundary (clearly the dimensional analysis case has not enough information to say anything), he does not discuss too explicitly how to assess what he takes to be the most convincing case — that from being an effective field theory: but he does mention that the corrections on the EFT view come in at or below the Planck length; so it is a upper boundary case.
I take here to lie a sort of conundrum then: is there something about the need of quantum gravity we do not see then on this supposed best case for taking the physical relevance of the Planck length seriously? This is in so far confusing as that everything would seem model-able on the EFT view. (But maybe this is just a hint then that gravity is not an effective field theory after all. So the argument is after all not that good.)\footnote{Maybe consider Schneider here?}
What is also a bit strange: Jacobs (rightly) points out the epistemic nature of the Planck-lenght arguments from black holes, and generalised Heisenberg microscope — but does not mention this for his preferred renormalisabielity option. Naively, one might that is just renormalisabielity (and so predictivity!) at stake here which is epistemic. But then note: the Planck scale is not the scale when the EFT breaks down — it is the scale when the EFT corrections come in.
ACTION POINTS: (1) IS GR REALLY AN EFFECTIVE FIELD THEORY (SEE ALSO SCHNEIDER). (2) WHAT DO WE IN OUR BOOK SAY ABOUT ALL OF THIS?