I was telling my teenage children about the at-at theory of motion: an object moves if and only if it is in one location at one time and in another location at another time. And then my son asked me a really cool question: How does this fit with the possibility of being multiply located at one time?
The answer is it doesn’t. Imagine that Alice is bilocated between disjoint locations A and B, and does not move at either location between times t1 and t2. Nonetheless, by the at-at theory, Alice counts as moving: for at t1 she is in location A while at t2 she is in location B.
My response to my son was that this was the best argument I heard against the at-at theory. My son responded that the argument doesn’t work if multilocation is impossible. That’s true. But there is good reason to think bilocation is possible. First, the real presence of Christ in the Eucharist appears to require multilocation. Second, God is present everywhere, but never moves. Third, there is testimonial evidence to saints bilocating. Fourth, the argument only needs the logical possibility of bilocation. Fifth, time-travel would make it possible to stand beside oneself.
(The time-travel case is probably the least compelling, though, as an argument against the at-at theory. For the at-at theorist could say that the times in the definition of motion are internal times rather than external ones, and time travel only allows one to be in two places at one external time.)
I’ve been inclining to think the at-at theory is inadequate. Now I am pretty much convinced, but I am not sure what alternative to embrace.
One might just try to tweak the at-at theory. Perhaps we say that an object moves if and only if the set of its locations is different between times. But that isn’t right. Suppose Alice is bilocated between locations A and B at t1, but at t2 she ceases to bilocate, defaulting to being in location A. Then the set of locations at t1 is {A, B} while at t2 it is {A}. But Alice hasn’t moved: cessation of bilocation isn’t motion. Nor will it help to require that the sets of locations at the two times have the same cardinalities. For imagine that Alice is bilocated at locations A and B at t1, and then she ceases to be located at B, defaulting to A, and walks over to location A′ at t2. Then Alice has moved, but the sets of locations at t1 and t2 have different cardinalities. I don’t know that there is no tweak to the at-at theory that might do the job, but I haven’t found one.
14 comments:
Thought experiment:
Suppose Alice is bilocated between locations A and B at t1, but at t2 she ceases to bilocate, defaulting to being in location A. Then the set of locations at t1 is {A, B} while at t2 it is {A}. But Alice hasn’t moved: cessation of bilocation isn’t motion.
ANSWER:
Pr(A,B,T) -> OBSERVATION OF ALICE AT T(t2) -> CREATES MEASUREMENT HISTORY(A,t2->t1)
You are correct bilocation is not motion; bilocation means treating space & time as probabilities.
Now, can Alice observe herself? No.
It's just that God loves Alice so much he can't take his eyes off her...
I should point out that recent quantum experiments at Cambridge (UK) confirm that this is the correct mechanism that creates local reality:
Pr(A,B,T) -> OBSERVATION OF ALICE AT T(t2) -> CREATES MEASUREMENT HISTORY(A,t2->t1)
The Cambridge result has very interesting consequences...
I'd love to know why philosophers thought that they needed such a theory of motion in the first place. Physics has never seen the need to have such a theory of motion. It tends to assume that motion is continuous, but has no problem postulating quantum jumping as and when. If it needs to go beyond such pictures, in which there is no need to have such an analysis of "motion," then it uses mathematics alone. There must have been a good reason to introduce the at-at theory. Does that reason tell us what sort of replacement we would need?
Martin Cooke
It is because of the "wish" to remove "observation" as the creator of local-reality.
Essentially, the at-at-theory is a jargon version of Quantum Darwinism which forms the linchpin in Everett's Many-World-Interpretation of QM. And Everett's whole rationale in coming up with the theory was to remove "observation" from QM measurements. Everett was a militant atheist who hated the idea of measurement being the result of observation; so, he came up with a strictly deterministic interpretation that did not require observation to "collapse the wave-function".
The Cambridge results would appear to be the demise of Quantum Darwinism. The results were quite surprising for me. Though I have always used information-physics; not many physicists use the approach in physics.
Hi Alex,
Try this one: An object O moves if and only if there are two locations A and B such that O is in A at t1 and O is in B at t2 and O is not in A at t2 and O is not in B at t1.
Best,
Emanuel
Just another tangential thought, but of course motion is relative.
And even if it is not: suppose that an object at one location remains stationary (or stationary relative to some object) and that the location moves. Then it has not moved (or moved relative to that object). But by the at-at theory it has moved; and by Emanuel's theory too. Obviously those have to be basic locations, like points in space itself. But space might not have such parts (and is unlikely to if motion is relative).
1/ at-at theory of motion says motion is being at different places at different times. Space & time are equivalent; therefore the statement should be broken into two parts:
1a/ Motion is being at different places.
1b/ Motion is being at different times.
2/ at-at theory has to do with what is happening at nearby moments and nothing to do with what is happening during a moment.
Statement 2/ conflicts with statement 1/ because a moment should also be included with nearby moments since motion concerns different times.
My previous post concerning the theory gave it way too much credit...
The solution to paradoxes that take the form of Zeno's require consideration of the mean kinetic energy of the system.
I've never read of such approaches but it would be the appropriate approach. I may have come across a mention of energy with respect to the Thomson Lamp thingy by Grunbaum in his book when I was a kid...but that is all...
Emanuel,
Nice, but I don't think it works.
Start with this. Suppose I am bilocated, being both in the kitchen and the living room at t1. I then simultaneously walk from the living room to the kitchen and from the kitchen to the living room by t2. Then I moved even though I am in the same places at both times.
Yeah, but maybe you can say that at some time like t1.5, I will be in a place I wasn't at t1, say some place half-way between the kitchen and the living room.
OK, to counter that response see today's post. :-)
Small point. I've been corrected twice on the internet for saying Christ "bilocates" in the Eucharist, apparently this is a heresy with a name I don't remember. See St III q76 a5
Martin: I think it's not a heresy. It's just not St Thomas's view.
It looks like my son was scooped by Shieva Kleinschmidt: https://philpapers.org/rec/KLEAIA-4
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