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In several different contexts, I've heard the claim that quantum gravity in an accelerating universe messes with our ability to define precise quantum observables.* One version of the argument goes roughly as follows; we need to perform a measurement infinitely many times to get a precise outcome. To prevent quantum fluctuations of the measurement apparatus from destroying the result before we're done averaging, we need our apparatus to be infinitely big. Therefore any measurement performed in a finite space is fundamentally indeterminate, and thus 'local observables' do not exist. Even more troublingly, we can't actually make our experimental apparatus infinitely big, since our accelerating universe has a cosmological horizon. So no measurement of any observable can give an arbitrarily precise result.

I gather that this argument or something like it has been known and worried about for decades, and is given as strong evidence that quantum mechanics is in tension with cosmology in De Sitter space. But at a philosophical level I can't see why it should imply something so profound. The inability of a finite measurement apparatus to average forever seems like a practical limitation, and not something a theorist should worry about so much.

So my questions are the following:

  1. Why should the inability of an experiment to average infinitely long imply that the observed quantity is fundamentally ill-defined? There's even a way to give operational meaning to these observables, if you'll grant me multiple copies of the universe; a theorist outside the universe can still define and compute experimentally accessible observables to arbitrary precision, and this prediction can be compared against the combined outcomes of many experiments conducted in an ensemble of identical universes.

  2. The above argument is a bit vague, and I suspect that it is an attempt to simplify a sharper, more mathematical statement. Is this so, and if so then what is the more precise statement of the issue at hand? Does it have a name, or a body of literature where can I read more? I gather it may be related to issue with defining the S matrix in cosmology, since you can't take the ingoing and outgoing states to infinity (though I'm not sure).

You can find this argument given by Nima Arkani-Hamed at the time linked within this video. And it's not like he thinks this is just some philosophical issue. He takes it as evidence that we need to understand how time emerges from something deeper, analogous to how space emerges in holography (i.e. AdS/CFT).

*Note that this argument goes way beyond the usual argument that you cannot probe distances smaller than the Planck length, since attempting to do so would create a black hole. This simpler thought experiment is taken to imply that there is no operational definition of length below the Planck length. It is a statement about the interpretation of a single measurement/observation, and unlike the above it really prevents even a theorist from saying anything of observable consequence about shorter distances.

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Why should the inability of an experiment to average infinitely long imply that the observed quantity is fundamentally ill-defined?

Experiments are carried out all the time, and the usefulness of theoretical models is gauged by how well the predictions of the model fit the experimental data and observations, and how predictive they are. If the theoretical model leads into unobservable by experiments predictions, the problem is with the mathematical model, called a theory.

I realize that extending theories that are successful at the laboratory level to cosmological observations is not an easy task, and the theories have been successful in fitting observations up to the inflationary epoch as with the Big Bang model . But it is the observations that choose the model, not the model the observations.

Experiments with ensembles of universes and other thought experiments may prove useful for the formulation of a realistic theory, one that predicts cosmological observations better than existing models. But to claim that reality follows the mathematics of a theory, without the possibility of checking with observations, but just with thought experiments, seems to me to be off track of what physics is about.

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  • $\begingroup$ What types of impossible experiments should be taken as evidence of something deep missing from the theory? Does the finite quantity of mass/energy in the universe imply a fundamental uncertainty to precision, since that limits how big we can make a measurement apparatus and how many digits of precision it can store? What if details of the experimental apparatus determine how precise different measurements can be performed; do I need to maximize precision over all possible constructions? Surely these are details that a theorist can tweak by hand without changing the content of the theory. $\endgroup$
    – user34722
    Mar 21, 2023 at 16:50
  • $\begingroup$ I would also like to also draw attention to part 2 of my question: are there sharper/more precise statements of the above issue, or how/where can I read more about it? That seems more likely to be resolved on StackExchange then such thorny philosophical issues :) $\endgroup$
    – user34722
    Mar 21, 2023 at 16:51
  • $\begingroup$ You have to wait for somebody else to answer you, as I hope I have made clear that IMO, real life experiments and observations pick up the mathematical models that fit them, not the way you are expecting : the theoretical model determines the real observations. $\endgroup$
    – anna v
    Mar 21, 2023 at 20:46
  • $\begingroup$ It's not entirely clear to me still, and it comes back to my first comment. In your view, do the limitations of finite mass in the universe impose equally fundamental limitations on measurement precision? If not, what distinguishes these two cases? $\endgroup$
    – user34722
    Mar 26, 2023 at 1:13
  • $\begingroup$ IMO this cannot be answered until and iff there is a TOE en.wikipedia.org/wiki/Theory_of_everything $\endgroup$
    – anna v
    Mar 26, 2023 at 5:23

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