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Okay, thanks. But I don't know what magical reality fluid is, so I don't really understand you.
Before I answer, I'd like to know how much you do understand, so I can answer at an appropriate level. Is this a 'I don't know what's going on here' question, or is it a statement that you understand the system well enough that the basics no longer are convincingly basic?
The former, mostly. I've read the sequences on this point and done a little side reading on my own, but I don't understand the math and I have no real education in quantum physics. In other words, I would really appreciate an explanation, but I will also entirely understand if this is more work than you're prepared to put in.
To condense to a near-absurd degree:
QM indicates that if you take any old state of the universe, you can split it up any way you feel like. Take any state, and you can split it up as a sum of 2 or more other states (A = B + C + D+ E, say). If you then 'run' each of the parts separately (i.e. calculate what the future state would be, yielding B', C', D', E') and then combine the results by adding, it's the same as if you ran the original (A' = B' + C' + D' + E').
This is because QM is a linear theory. You can add and subtract and rescale entire states and those operations pass right through into the outcomes.
This doesn't mean that you won't get any surprises if you make predictions based on just B, C, D, and E individually, then add those together. In general, with arbitrary B, C, D, and E, combining them can yield things that just don't happen when you'd expect that they would based on the parts individually (and other things that happen more than you'd expect, to compensate).
Decoherence tells you how and when you can pick these B, C, D, and E so that you in fact won't get any such surprises. That this is possible is how we can perceive a classical world made of the quantum world.
One tiny and in no way sufficient part of the technique of decoherence to require that B, C, D and E are all perpendicular to each other. What does that do? You can apply the Pythagorean theorem. When working with vectors In general, with A being the hypotenuse and B, C, D, and E the perpendicular vector components, we get AA = BB + CC + DD + EE (try doing this with three vectors near the corner of a room. Have a point suspended in air. Drop a line to the floor. Construct a right triangle from that point to one of the walls. You'll get AA = WW + ZZ, then split W into X and Y, for AA = XX + YY + ZZ)
Anyway, what the Pythagorean theorem says is that if you take a vector and split it up into perpendicular components, one thing that stays the same is the sum of the squared magnitudes.
And it turns out that if you do the math, the mathematical structure that works like probability in QM-with-decoherence is proportional to this squared magnitude. This is the basis of calling this square magnitude 'reality fluid'. It seems to be the measure of how much something actually happens - how real it is.
Thanks, that's really quite helpful. I take it then that the problem with Homunq's objection is that all the subsequent 'worlds' would have the same total reality fluid as the one in which he made the distinction, and so the 'splitting' wouldn't have any real effect on the total utility: $5 less for one person with reality R is the same disutility as $5 less for a [large number of] people with reality R/[large number]?
But maybe that's not right. At the end, you talked about 'how much reality fluid something has' as being a matter of how much something happens. This makes sense as a way of talking about events, but what about substances? I gather that substances like people don't see much play in the math of QM (and have no role in physics at all really), but in this case the questions seems relevant.
Your first paragraph is correct.
As for the second, well, substances are kind of made of colossal numbers of events in a convenient pattern such that it's useful to talk about the pattern. Like, I'm not falling through my chair over and over and over again, and I anticipate this continuing to be the case... that and a bunch of other things lead me to think of the chair as substantial.
Right, but I'm not something that happens. The continuation of me into the next second might be something that happens, and so we might say that this continuation have more or less reality fluid, but I don't know that the same can be said of me simpliciter. You might think that I am in fact something that happens, a series or pattern of events, but I think this a claim that would at least need some working out: one implication of this claim is that it takes time (in the way a motion takes time) to be me. But this is off the QM (maybe off the scientific) path, and I should say I very much appreciate your time thus far. I can't take it personally if you don't want to join me in some armchair speculation.
Your thoughts are things that happen. Whatever's doing those is you. I don't see the problem.
But it seems problematic to say that I am my thoughts. I seem to persist in time despite changes in what I think, for example. Afew days ago, I thought worlds were 'generated' on the MWI view. I now no longer think that. I'm different as a result, but I'm not a different person. I wasn't destroyed, or remade. (I don't mean this to be a point specifically about human personal identity, this should apply to animals and plants and maybe blocks of wood too).
To reiterate my concern in the grandparent, if my thoughts are a process that takes time (as they seem to be), and I am my thoughts, then it takes time to be me. Being me would then be something interruptible, so that I could only get half way to being me. This is at least odd.
I don't mean to suggest that this is a knock down argument or anything, it' not. It's little more than an armchair objection on the basis of natural language. But it's the sort of thing for which this theory should have an answer. We might just discover that the temporal persistance or identity of macroscopic objects is a physically incoherent idea (like identity based on having a certain set of atoms). But if we do discover something radical like that, we should have something to say to ward off the idea that we've just misunderstood the question or changed the topic. Again, thanks for your indulgence.
You are a 4-dimensional region of spacetime. What you normally call 'you' is a mutually-spacelike-separated cut of this 4-dimensional region, but the whole reason for calling this slice special is because of causal chains that have extent in time. For instance, your hand is considered yours because your brain can tell it what to do*. That causal chain takes time to roll out.
What's this "me" thing? Your thoughts are most likely reducible to an arrangement of neurons, their connections and electric potentials and chemical processes (ion channels opening and closing, Calcium and other ions going in and out of dendrites, electric potential rising and falling, electric impulses traveling back and forth, proteins and other substances being created, deposited and removed, etc.) Some of these processes are completely deterministic, others are chaotic, yet others are quantum-random (for example, ion channel opening and closing is due to quantum-mechanical tunneling effects). In that sense, your thoughts do take time, as it takes time for chemical and electrical effects to run their course. But what do you mean by "it takes time to be me"?
Good explanation. But you're assuming a theory in which "reality fluid" is conserved. To me, that seems obviously wrong (and thus even more obviously unproven). I mean, if that were true, my experiences would be getting rapidly and exponentially less real as time progresses and I decohere with more and more parts of the wave function.
I acknowledge that it is difficult to make probability work right in MWI. I have an intuitive understanding which feels as if it works to me, that does not conserve "reality fluid"; but I'm not so unwise as to imagine that a solid intuition is worth a hill of beans in these domains. But again, your theory where "reality fluid" is equal to squared amplitude seems to me probably provably wrong, and definitely not proven right. And it was not the assumption I was working under.
Well, yes, I'm assuming that QM is correct. That's kind of the point: we're talking about predictions of QM.
No... why do you think that you would be able to feel it? It seems to me rather like the argument that the Earth can't be moving since we don't feel a strong wind.
An important part of QM being a linear theory is that it is 100% independent of overall amplitude. Scale everything up or down by an arbitrary (finite nonzero) factor and all the bits on the inside work exactly the same.
So, whether something likely happens or something unlikely happens, the only difference between those two outcomes is a matter of scale and whatever it was that happened differently.
QM has no "reality fluid". The whole point of calling it "reality fluid" is to remind yourself that it's standing in for some assumptions about measure theory which are fuzzy and unproven.
My own (equally fuzzy and unproven) notion about measure theory is that anything which has nonzero amplitude, exists. Yes, you can then ask why probabilistic predictions seem to work, while my measure theory would seem to suggest that everything should be 50/50 ("maybe it happens, maybe it doesn't; that's 50/50"). But I believe that there is some form of entropy in the wave function, and that probable outcomes are high-entropy outcomes. No, I obviously don't have the math on this worked out; but neither do you on the "reality fluid".
I could easily be wrong. So could you. Probably, we both are. Measure theory is not a solved problem.
QM may not have 'reality fluid', but the thing we're tongue-in-cheek calling 'reality fluid' is conserved under QM!