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Physics-measurability is not the relevant criteria of property rights. The purpose of property rights is to allow for peaceful dispute resolution so we need to know, or be able to assess, who the rightful user is of each rivalrous good.
I think that Graf uses some examples to flesh out the reason he thinks physics-measurability is relevant:
1. brain wallet theft Imagine a scenario where I create a brain wallet with insufficient entropy (I just really wanted to use a quote from my favorite book...) and someone steal the bitcoin I send to this wallet. On the one hand, it is theft. They were my bitcoin and someone took them. On the other hand I didn't secure them very well. In the case of a house or real estate, if I don't put a fence up around my property and someone comes to try to live in on it, I mostly have the right to tell them to leave, because I own the property even if I don't protect it with a fence (I'm probably getting a bit of this wrong, not being a lawyer). So what is the difference between bitcoin secured with low entropy and a lot without a fence?
I have changed Graf's example a bit, and I believe he does a better job of setting it up (except it takes him 3 or 4 chapters of groundwork). But I think I'm close to the spirit of it.
From a legal standpoint, I’m not aware of any arguments that require particular levels of security. All that matters is whether you obtained the property legitimately (homesteading or voluntary transfer).
We know how homesteading works (mining), so that shouldn’t matter. If you check in on a low entropy wallet and find money there, you know those weren’t intended for you. Is that more like finding loose cash on the street (abandoned) or seeing loose cash in someone’s unlocked car (not abandoned)?
An interesting case could be where multiple people independently use the same seed phrase and are not aware that they are not the intended recipient of a transfer.
Ah, but mostly the way Bitcoin works is that if you screw up when you send coins somewhere (either to a low entropy address or the wrong address) there ain't much you can do to get 'em back.
I think Graf is saying that for Bitcoin the distinction between cash abandoned on the street and cash left in an unlocked car is non-existent -- and that there are many such cases -- which leads him to say that there's something different about ownership when it comes to bitcoin. Maybe even it isn't possible.
Difficulty of recovery doesn’t matter in principle.
The issue is that the only evidence of ownership is knowing the seed phrase but multiple people can know it and you can’t make anyone stop knowing it.
Ok, so I’m realizing that homesteading of wallets is where the conceptual thorns are. I’ll need to read the arguments more thoroughly for myself.
I don't have the background in this kind of theory to make a cohesive argument (nor do I really think it's useful), but I believe the point of the paper is that even though bitcoins have the qualities of rivalrous goods, the fact that they lack "physics-measurability" creates so many qualifications and limitations to how ownership works in the case of bitcoin that we might as well say ownership doesn't matter.
I've replied to Conza with this post, so hopefully either Conza or Graf will be kind enough to write something up here and explain the concepts more authoritatively.