In yesterday’s post, I offered an argument by my son that multilocation is incompatible with the at-at theory of motion. Today, I want to offer an argument for a stronger conclusion: multilocation shows that motion does not even supervene on the positions of objects at times. In other words, there are two possible worlds with the same positions of objects at all times, in one of which there is motion and in the other there isn’t.
The argument has two versions. The first supposes that space and time are discrete, which certainly seems to be logically possible. Imagine a world w1 where space is a two-dimensional grid, labeled with coordinates (x, y) where x and y are integers. Suppose there is only one object, a particle quadlocated at the points (0, 0), (1, 0), (0, 1) and (1, 1). These points define a square. Suppose that for all time, the particle, in all its four locations, continually moves around the square, one spatial step at a temporal step, in this pattern:
Then at every moment of time the particle is located at the same four grid points. But it is also moving all the time.
But there is a very similar world, w2, with the same grid and the same multilocated particle at the same four grid points, but where the particle doesn’t move. The positions of all the objects at all the times in w1 and w2 are the same, but w1 has motion and w2 does not.
Suppose you don’t think space and time can be discrete. Then I have another example, but it involves infinite multilocation. Imagine a world w3 where the universe contains a circular clock face plus a particle X. None of the particles making up the clock face move. But the particle X uniformly moves clockwise around the edge of the clock face, taking 12 hours to do the full circle. Suppose, further, that X is infinitely multilocated, so that it is located at every point of the edge of the clock face. In all its locations X moves around the circle. Then at every moment of time the particle is located at the same point, and yet it is moving all the time.
Now imagine a very similar world w4 with the same unmoving clock face and the same spacetime, but where the particle X is eternally still at every point on the edge of the clock face. Then w3 and w4 have the same object positions at all times, but there is motion in w3 and not in w4.
I think the at-at theorist’s best bet is just to deny that there is any difference between w1 and w2 or between w3 and w4. That’s a big bullet to bite, I think.
It would be nice if there were some way of adding causation to the at-at story to solve these problems. Maybe this observation would help: When the particle in w1 moves from (0, 0) to (1, 0), maybe this has to be because something exercises a causal power to make a particle that was at (0, 0) be at (1, 0). But there is no such exercise of a causal power in w2.
I don't think that the at-at theorist's denial is for her a big bullet to bite.
ReplyDeleteYou simply assert that in the one case the particle is moving.
According to the at-at theory of motion, it would not be moving.
My own intuition is that there is no possible justification for your assertion that it is moving. How is it moving from where it is to where it is, as opposed to already being there? If it has four distinct bits, which are re-identifiable independently of where they are, then those bits can indeed be said to be moving, but then they are not multiply located, and so even the at-at theorist can agree that there is motion. If not, then how do you do it?
Dr Pruss
ReplyDeleteYour son should be congratulated for his insight (he appears to be able to visualise, a good thing for a physicist should he pursue such a profession).
Your thought experiments are very good. Unfortunately, I cannot do the thought experiments justice (the explanation would require a paper...no, probably a book). I'll just point you in a possible approach (it does in fact lead to a theistic result if you follow the logical trajectory).
KE=kinetic energy
V=velocity
Qualitatively we know:
KE(w1) > KE(w2)
KE(w3) > KE(w4)
V(w1, w2, w3, w4) = ideal velocity value (mean velocity value); the mean value need not be specified.
The question is how can one quantify the motion or lack of motion in the worlds?
The only way to do this is to observe/measure each world using a metric, i.e probe.
Introducing a probe into each world system would "create" a perturbation in the mean velocity of each world. This would result in changes in KE of each world.
Quantitatively we would then know
V(w1,w2,w3,w4) fluctuate from their ideal values. Therefore, all worlds exhibit motion; the degree of motion would be reflected in the quantified skewness of the KE values.
I suppose you might say, Alex, that when the circularly multiply located particle of world 3 is moving in a circle, then there is angular momentum that is not there in world 4.
ReplyDeleteSuch angular momentum might be measured, in such ways as Philip mentions.
But even were it measured, the at-at theorist could quite easily deny that such a thing was really due to motion, and claim instead that it was just a weird property of this weird world 3, that it could not be due to motion because there was no motion, there was just a particle remaining in the same places.
You could reply that the measured property was just like angular momentum.
But then the at-at theorist could point to the spin of an electron.
Martin Cooke
ReplyDeleteJust wondering...are you stating that a photon illuminating an electron will have no effect on the electron?
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ReplyDeletePerhaps this picture of w4 before and at the moment of measurement will help.
ReplyDeleteBoth the particle(O) and the probe(↓) have mass.
OOOOOO Before measurement mean velocity=0
OOO↓OOO At the moment of measurement mean velocity > 0
A photon illuminating an electron has an effect, Philip, but it is not as if the electron is literally spinning, as though it was a tiny billiard ball. Not at all. And perhaps not very similarly, were it found that the effects of probing w4 were just like angular momentum changing, one could argue that it was a superficial similarity since motion was logically impossible. The thing is, such probing is hypothetical, and so its nature depends on how we have built up w4 in the first place. And when we build w4 the at-at theorist can point out that such motion is not only impossible by her lights, it is also intuitively implausible. That is clearest in w3. In w3 the particle is wholly at (0, 0) and wholly at (1, 0), so it is logically impossible for the particle at (0, 0) to move to (1, 0). It is already there. It makes no sense at all to say that the particle at (0, 0) moves to (1, 0), while the particle at (1, 0) moves away, because they are exactly the same particle, if the particle is indeed multiply located there. To think otherwise is to be confused about what multiple location means.
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ReplyDeleteNo. Such electron probing is NOT hypothetical. The sphericity of an electron has been experimentally measured (within an astronomical tolerance) using such techniques.
ReplyDeleteNothing wrong concerning the w1,w2,w3,w4 thought experiments; they are very revealing and defeat the at-at-theory.
In fact, the w4 thought experiment (with some alteration) is analogous to the Klein-Gordon & Wheeler-DeWitt interaction at the creation of the universe.
However, the analysis of the w1 and w2 case is much more informative about the true nature of motion (and it has absolutely nothing to do with discrete space... that idea is just plain nonsense).
I had to delete posts on account I was not aesthically pleased with the look...
Concerning w3 you are very mistaken. I could give you many examples... but, I'll give you just one from Quantum Field Theory... in QFT that single particle is smeared across spacetime.
ReplyDeleteThe sphericity of the wavefunction perhaps.
ReplyDeleteIn QFT the single particle is possibly in lots of places, but a measurement will find that it is actually in just one. A multiply located particle is actually in lots of places.