tag:blogger.com,1999:blog-8027844571839885250.post3965164825008759114..comments2022-03-25T07:20:12.468-04:00Comments on Matters of Substance: What is location?Gabriele Contessahttp://www.blogger.com/profile/13607158011908969169noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-8027844571839885250.post-80817833359121451022013-05-21T05:56:57.067-04:002013-05-21T05:56:57.067-04:00I worry that what people call 'location in abs...I worry that what people call 'location in abstract space' is just the use of a spatial metaphor (or analogy) to talk about the relation of any entity whatsoever to any whole whatsoever. So, 'location'—as x's relation to the yys in whatever whole of parts you can imagine—can be described, by analogy, as x's 'location' in the whole. As such the idea that 'location' is multiply realised is not surprising.Anonymoushttps://www.blogger.com/profile/13581822685471593228noreply@blogger.comtag:blogger.com,1999:blog-8027844571839885250.post-36045822618542730972013-05-13T18:03:05.255-04:002013-05-13T18:03:05.255-04:00Right, but I have a stronger intuition in the case...Right, but I have a stronger intuition in the case of position that there could be position in classical worlds. Intuitively, position is less tightly law-bound than, say, charge.<br /><br />So I am suspecting multiple-realizability about position (and maybe momentum, as its conjugate) but not, say, about charge. In worlds where classical electrodynamic laws hold, then, nothing has any charge, but there is instead charge*, which behaves like in our world charge does in the classical limit. But the classical worlds really do have position, though it is realized differently from how it is realized in our world.<br /><br />One could, I think, try to hold that both charge and position are on par. I doubt that one could come up with a very plausible functional characterization of charge, so that would require saying that both charge and position are law-bound, and in classical worlds nothing has any charge and nothing has location or shape. Moreover, what goes for space probably goes for time, so in classical worlds there would probably be no time or even change. This is counterintuitive. Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-8027844571839885250.post-76726698917398731502013-05-13T17:29:09.609-04:002013-05-13T17:29:09.609-04:00Interesting. From the perspective of quantum mecha...Interesting. From the perspective of quantum mechanics, there's nothing particularly special about "spatial location" as opposed to any other measurable property. For example, there is a momentum wavefunction representation -- and indeed, a wavefunction representation for every self-adjoint operator. So, if quantum theory justifies talk about "partial location," then it also justifies talk about "partial properties" for every measurable property of a physical system.Bryanhttps://www.blogger.com/profile/07379669532781325751noreply@blogger.comtag:blogger.com,1999:blog-8027844571839885250.post-15773771734107452522013-05-11T10:59:22.150-04:002013-05-11T10:59:22.150-04:00The standard mathematical explanation of location ...The standard mathematical explanation of location in abstract space is that it's just set membership: 7 is in R just in case 7 is a member of R.<br /><br />In any case, the "from the inside" approach in the classical won't distinguish between momentum and position, since classically both have the same mathematical structure: they have values whose space has the structure of R^3. But I want to say what makes position position, what makes it different from momentum, or charge, etc. Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-8027844571839885250.post-670700673090656842013-05-10T21:20:25.697-04:002013-05-10T21:20:25.697-04:00Hi Alexander,
That sounds good for the case of lo...Hi Alexander,<br /><br />That sounds good for the case of location in physical space, but what about location in abstract spaces?<br />Take the real one-dimensional space R with its usual topology. Here it is not even clear what the capability of any real number <em>to interact with any other real number</em> would be. I assume that an interaction between a real numbers is any operation definable over the real field. But then it is not clear that the "capability" (I use scare-quotes because I'm assuming that it is a term with modal load; and such load may be difficult to conceive of when talking about necessary beings, as numbers are assumed to be) is correlated with distance, or that such a tendency might exist.<br /><br />I have the intuition that perhaps we should not try to determine what location is "from the outside" (i.e. by its effects) but "from the inside": perhaps by abstracting them from the abstract notion of space or of structure.<br /><br />Best,carloshttps://www.blogger.com/profile/03631476894943998012noreply@blogger.comtag:blogger.com,1999:blog-8027844571839885250.post-13421050868394803942013-05-10T04:05:02.613-04:002013-05-10T04:05:02.613-04:001. It seems like location in time is at least as ...1. It seems like location in time is at least as important for causal interaction. That's consistent with your story insofar as time and space location are fungible in Minkowski space, but it seems like you'd then have to take account of the asymmetry of causation and that time is usually taken as a separate variable in the wavefunction. Neither of these necessarily undermine your point, but I'm not fully envisioning how you'd mean to include them, either.<br /><br />2. Two objects can also fail to interact because they have insufficient charge or are insufficiently massive (neutrinos, say) despite being really close. Is location special because it cuts across all modes of interaction? Is there then a place for your definition of location in a world where we have a unified theory of all forces?<br /><br />3. What does location mean in the entangled case? It seems strange to give an account of location largely in quantum terms without taking account of this central quantum phenomenon. It seems like either solution to the Bell dilemma is problematic for your story because it undercuts our intuitions about either location or causality.<br /><br />None of this is to say that I have a better theory; just questions that occurred to me as I read your post.Ryan Millerhttps://www.blogger.com/profile/05175625979264185229noreply@blogger.com