Not sure how you mathematically define complexity in this case, but MWI certainly does not reduce the effort required to make a testable prediction. You still have to write down and solve the Schroediger equation, then apply the Born rule, MWI or no MWI. Alternatively you can numerically compute the path integral, but that is a monumental undertaking even in simple cases.
Check out Eliezer’s article on Occam’s Razor, which explains what complexity means in mathematical terms. It has nothing to do with the amount of effort required for humans to solve the problem.
Thanks, but it seems to me that either the Minimum Message Length formalism or the Solomonoff induction basically measure how short a computer program required to solve the Schroedinger equation analytically or numerically can possibly be, so no advantage for MWI there. Application of the Born rule has a fixed (and negligible) complexity in that sense, by the way. I have a feeling that I am missing something, but I can’t quite see what.
Basically, collapse postulates are a lot more complicated—because they require you to figure out a reason why the wavefunction suddenly goes to zero at a point, when there’s no reason even to suspect that it does.
Your first statement seems like an appeal to authority, so I won’t even bother asking you to justify it.
As for the Eliezer’s point, it seems misguided to me, as I originally said. I do not need to worry about any of these imaginary violations, because I don’t postulate collapse as a testable mechanism of quantum measurement, only as a mathematical tool wholly described by the Born rule.
The rule, unfortunately, is a black box in any interpretation, despite many claims to the contrary. Adding MWI on top of it without testable consequences increases complexity without providing any benefits except emotional.
Once there is a viable model of the Born rule (one that predicts more than the “shut up and calculate” approach does), the issue would have to definitely be revisited, until then the MWI is a fake explanation.
Your first statement seems like an appeal to authority, so I won’t even bother asking you to justify it.
Not an argument at all, actually—just a clarification. I wasn’t sure if you were using Schrodinger’s equation as a synonym for the many worlds interpretation or not.
I’m not sure what the difference would be between postulating collapse and just using it mathematically. As you point out, you can use the Born rules to determine whatever you need to know regardless of your view on many worlds.
Adding MWI on top of it without testable consequences increases complexity without providing any benefits except emotional.
This is our point of disagreement. The links in my last comments point to a few of the reasons many worlds is strictly simpler than collapse. We aren’t adding MWI on; we’re refusing to add on an explanation of why all but one of those worlds is annihilated. We agree, I think, that the simpler explanation is the one we should use, at least until a complete theory of physics is proposed.
I guess it is indeed our point of disagreement. The orthodox approach does not add an explanation to a construct it never used to begin with. It’s the MWI proponents who misinterpret it and then state that their approach is “simpler”, whereas it just piles a bunch of untestable mumbo-jumbo on exactly the same mathematical model. But it looks like we reached an impasse, so best leave it off, I suppose, contrary to any kind of rational approach.
The difference is not in the prediction of what we see. MWI and Collapse postulates come out tied on that.
It’s what they say goes on ‘behind the curtain’. Collapse postulates say that there’s nothing behind the curtain. WMI says that the dynamics are much simpler and more like the rest of physics if there are things behind the curtain.
The problem with that is that MWI and Copenhagen do NOT have the same exact complexity. Copenhagen adds a mechanism of exceedingly high complexity. ‘Applying the Born Rule’ adds nothing to MWI as in that case it’s just an approximation—the universe doesn’t care. But with Copenhagen, it’s REAL, and it’s gotta be implemented somehow, in a way that violates all those core elements of physics that Eliezer listed so neatly.
Moreover, we should be used to the notion of stuff existing behind the curtain—stuff we can never ever see. We’ll never see photons that have been radiated away from us. Objects have insides, and there’s no theoretically viable way of doing elemental analysis on any given cubic meter of the Earth’s core, let alone cubic millimeter. Same goes for the sun, but more so. And all the other stars in the universe, even more so.
The notion that there are yet more things we can’t ever ever measure really shouldn’t be foreign.
Not sure how you mathematically define complexity in this case, but MWI certainly does not reduce the effort required to make a testable prediction. You still have to write down and solve the Schroediger equation, then apply the Born rule, MWI or no MWI. Alternatively you can numerically compute the path integral, but that is a monumental undertaking even in simple cases.
Check out Eliezer’s article on Occam’s Razor, which explains what complexity means in mathematical terms. It has nothing to do with the amount of effort required for humans to solve the problem.
Thanks, but it seems to me that either the Minimum Message Length formalism or the Solomonoff induction basically measure how short a computer program required to solve the Schroedinger equation analytically or numerically can possibly be, so no advantage for MWI there. Application of the Born rule has a fixed (and negligible) complexity in that sense, by the way. I have a feeling that I am missing something, but I can’t quite see what.
If you buy Schrodinger’s equation, you get Many Worlds. Even opponents of Many Worlds agree on that.
The advantage to Many Worlds comes from the improbability of the collapse postulate, which, as Eliezer puts it, would (if true) be
Basically, collapse postulates are a lot more complicated—because they require you to figure out a reason why the wavefunction suddenly goes to zero at a point, when there’s no reason even to suspect that it does.
Your first statement seems like an appeal to authority, so I won’t even bother asking you to justify it.
As for the Eliezer’s point, it seems misguided to me, as I originally said. I do not need to worry about any of these imaginary violations, because I don’t postulate collapse as a testable mechanism of quantum measurement, only as a mathematical tool wholly described by the Born rule.
The rule, unfortunately, is a black box in any interpretation, despite many claims to the contrary. Adding MWI on top of it without testable consequences increases complexity without providing any benefits except emotional.
Once there is a viable model of the Born rule (one that predicts more than the “shut up and calculate” approach does), the issue would have to definitely be revisited, until then the MWI is a fake explanation.
Not an argument at all, actually—just a clarification. I wasn’t sure if you were using Schrodinger’s equation as a synonym for the many worlds interpretation or not.
I’m not sure what the difference would be between postulating collapse and just using it mathematically. As you point out, you can use the Born rules to determine whatever you need to know regardless of your view on many worlds.
This is our point of disagreement. The links in my last comments point to a few of the reasons many worlds is strictly simpler than collapse. We aren’t adding MWI on; we’re refusing to add on an explanation of why all but one of those worlds is annihilated. We agree, I think, that the simpler explanation is the one we should use, at least until a complete theory of physics is proposed.
I guess it is indeed our point of disagreement. The orthodox approach does not add an explanation to a construct it never used to begin with. It’s the MWI proponents who misinterpret it and then state that their approach is “simpler”, whereas it just piles a bunch of untestable mumbo-jumbo on exactly the same mathematical model. But it looks like we reached an impasse, so best leave it off, I suppose, contrary to any kind of rational approach.
The difference is not in the prediction of what we see. MWI and Collapse postulates come out tied on that.
It’s what they say goes on ‘behind the curtain’. Collapse postulates say that there’s nothing behind the curtain. WMI says that the dynamics are much simpler and more like the rest of physics if there are things behind the curtain.
Which is simpler?
No point arguing about unquantifiable notions, so here I attempt to quanitfy “simpler”.
The problem with that is that MWI and Copenhagen do NOT have the same exact complexity. Copenhagen adds a mechanism of exceedingly high complexity. ‘Applying the Born Rule’ adds nothing to MWI as in that case it’s just an approximation—the universe doesn’t care. But with Copenhagen, it’s REAL, and it’s gotta be implemented somehow, in a way that violates all those core elements of physics that Eliezer listed so neatly.
Moreover, we should be used to the notion of stuff existing behind the curtain—stuff we can never ever see. We’ll never see photons that have been radiated away from us. Objects have insides, and there’s no theoretically viable way of doing elemental analysis on any given cubic meter of the Earth’s core, let alone cubic millimeter. Same goes for the sun, but more so. And all the other stars in the universe, even more so.
The notion that there are yet more things we can’t ever ever measure really shouldn’t be foreign.
Never say never! A near miss of the photon sphere of a black hole can send it back.
Your point still stands.