= 27d567bc2d48d9f40e9ccc20ea370b15)
RolfAndreassen comments on Shock Level 5: Big Worlds and Modal Realism - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (140)
I am not certain what you mean by 'continuum-many'; it sounds as though it could be either 'infinite' or 'the large number you get from a lot of combinatorics'. However, I must point out that quantum theory has the interesting property of being quantized. (Sounds almost like a lolcat slogan. "Kwantum fyziks... iz kwantised.") A particle in a bound state does not have infinitely many degrees of freedom, and since our local spacetime is apparently closed (if only just) every particle is in a bound state, it's just not obvious.
It refers to cardinality. You know Cantor showed that, while natural numbers and rationals can be put into one-to-one correspondence, there is no way to put the reals into one-to-one correspondence with the naturals, because there are 'too many' real numbers? Well, "continuum-many" means "the same cardinality as the real numbers".
Still, Douglas Knight makes a fair point - it is somewhat misleading to talk about continuum-many copies if each one has zero probability. In truth, I guess the concept of a 'number of copies' is too simple to capture what's going on.
As for particles being in bound states and having finitely many degrees of freedom: I'd be surprised if it altered the 'bigger picture' whereby all possible rearrangements of the matter in your body (or in the solar system as a whole, say) get some (possibly minuscule) amplitude assigned to them. (Of course, ideally it would be someone who actually knows some physics saying this rather than me.)
Ok, fair enough. In that case I must merely disagree that there exist this many possible arrangements of matter; it seems to me that the arrangements are actually countably infinite.
That's true, but the question is whether that number has the cardinality of the reals or the integers. I think it's the integers, due to the quantisation phenomenon in bound states; everything is in a bound state at some level. After my last post it occurred to me that the quantised states might be so close together that they'd be effectively indistinguishable; however, there would still be a finite number of distinguishable states. Two states are not meaningfully different if a quantum number changes by less than the corresponding uncertainty, so in effect the wave-function is quantised even in a continuously-varying number. Once you quantise it's all just combinatorics and integers.