On Saturday, December 7, 2019 at 12:22:01 AM UTC-6, Bruce wrote: > > On Wed, Nov 27, 2019 at 8:55 AM Bruce Kellett <[email protected] > <javascript:>> wrote: > >> >> Quantum mechanics itself is not counterfactually definite. Einstein was >> wrong about this. A free electron is described by a wave packet which is a >> superposition of states of definite momentum and position. There is no >> actual "position" for the electron until it interacts with a screen or some >> similar device. This is demonstrated by simple two-slit interference. There >> is no pre-existing position, unless you want to embrace Bohm's pilot wave >> theory, in which the electron does have a definite, though unknown, >> position at all times. >> > > I have come across an interesting video > > https://www.youtube.com/watch?v=5D9HkoHScdY > > in which Gerard 't Hooft, Roger Penrose, Tim Maudlin and a couple of > others talk about interpretations of quantum mechanics from their different > perspective. I found the segment by Tim Maudlin particularly interesting, > given his new book on the philosophy of quantum mechanics. His segment > starts at about the 10 minute mark. But the other contributions also have > some interest -- particularly Philip Ball towards the end (about the 20 > minute mark). > > No definite conclusions are advocated, but it is interesting to hear the > different perspectives. > > Bruce >
Not sure what this is. *Tim Maudlin - Linear Structures* https://academic.oup.com/aristoteliansupp/article-abstract/84/1/63/1780015 The standard mathematical account of the sub-metrical geometry of a space employs topology, whose foundational concept is the open set. This proves to be an unhappy choice for discrete spaces, and offers no insight into the physical origin of geometrical structure. I outline an alternative, the Theory of Linear Structures, whose foundational concept is the line. Application to Relativistic space-time reveals that the whole geometry of space-time derives from temporal structure. In this sense, instead of spatializing time, Relativity temporalizes space. https://www.sciencedirect.com/science/article/pii/S1355219815000842 : Causal set theory and the theory of linear structures (which has recently been developed by Tim Maudlin as an alternative to standard topology) share some of their main motivations. In view of that, I raise and answer the question how these two theories are related to each other and to standard topology. I show that causal set theory can be embedded into Maudlin׳s more general framework and I characterise what Maudlin׳s topological concepts boil down to when applied to discrete linear structures that correspond to causal sets. Moreover, I show that all topological aspects of causal sets that can be described in Maudlin׳s theory can also be described in the framework of standard topology. Finally, I discuss why these results are relevant for evaluating Maudlin׳s theory. The value of this theory depends crucially on whether it is true that (a) its conceptual framework is as expressive as that of standard topology when it comes to describing well-known continuous as well as discrete models of spacetime and (b) it is even more expressive or fruitful when it comes to analysing topological aspects of discrete structures that are intended as models of spacetime. On one hand, my theorems support (a). The theory is rich enough to incorporate causal set theory and its definitions of topological notions yield a plausible outcome in the case of causal sets. On the other hand, the results undermine (b). Standard topology, too, has the conceptual resources to capture those topological aspects of causal sets that are analysable within Maudlin׳s framework. This fact poses a challenge for the proponents of Maudlin׳s theory to prove it fruitful. https://pdfs.semanticscholar.org/1db1/0fc014a2182a572ad11f4253df26e6c54f0f.pdf @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/66858055-225c-44df-8bd8-9e3be2b685fc%40googlegroups.com.
