What we understand so far is:
* the measurement process can be described as an entanglement of a quantum system with a large external system, followed by a dephasing of the wave function that is caused by the huge number of degrees of freedom in the external system.
* this dephasing decouples the individual terms of the wave function of the system that is being measured, thereby effectively suppressing any further quantum effects in those measured states. This is what we call a transition from a quantum state to a "classical" state.
* the measurement process itself is not a discrete event: We can perform continuous weak measurements on a system's state, which will only partially collapse the wave function (there have been many experiments done on this e.g. by Serge Haroche's group and more recently with superconducting systems as well).
* this whole process is completely reversible and can be described by the Schrödinger equation.
Now, if we want to introduce irreversibility into this picture (which is required for the Copenhagen interpretation), we need a mechanism for it to arise. To my knowledge, no one has come up with a good theory for this, as it would require to modify the Schrödinger equation in a way that subtly depends on the characteristics of the system being measured and the measurement system. This mechanism would need to contain a variable A that would account for the size of the measurement system, as we need to preserve reversibility when the measurement system is small (i.e. has a small number of degrees of freedom), while destroying it when the measurement system is macroscopic.
I'm honestly a bit surprised that no one makes this argument in favor of the many-worlds interpretation of quantum mechanics, as it's the only theory which accounts for all experimental evidence while not forcing us to invent a mechanism that "eliminates" the many realities that we don't want to accept, while in fact they arise naturally out of the theory. I think that many people just don't want to accept that the universe could work this way, even if it's the simplest and most straightforward explanation.
I think you're projecting the existence of these worlds. Certainly you could view the equations that way, or you could view the particles as fundamentally real and obeying a non-classical law of motion, as in de Broglie-Bohm, which was actually the first the interpretation to correctly account for measurement.
That's a very odd way of going about things. We can't actually observe galaxies over long enough timescales to be sure that gravity applies to them but their appearance is consistent with the existence of gravity so we don't even both to consider the possibility that there might be some separate force causing them to look that way.
I didn't. I said math doesn't always predict reality, sometimes it's just interesting math. Some maths are also physics, some maths are just maths and have no bearing on physics.
Conjecture. It seems self-evident that our reality reflects the structure of basic discrete mathematics, ie. if there are two apples, eating one leaves 1 apple. No amount of rationalization will refute this fact. The fact is, the basic structure of our world is mathematical in some way.
> The fact is, the basic structure of our world is mathematical in some way.
Yes, but that doesn't imply the inverse, that all maths are reflections of reality. Reality can be described by maths, but not all maths describe reality. Or to further simplify, physics is the subset of maths that describe reality, which necessarily implies that not all maths do.
Even if you wanted to subscribe to some form of mathematical naturalism, that still doesn't support your point that math that doesn't appear to have a natural analogue, doesn't physically exist. We thought this of many prior mathematical abstractions, like complex numbers and non-euclidean geometry, and they are both now indispendensible tools for describing reality as we know it.
> hat still doesn't support your point that math that doesn't appear to have a natural analogue,
I never made that point, and if you think I have, you've failed to understand the point actually being made.
What is the physical analog of the square root of -1? If all math is physics, then what physics does that predict? Maths are a language invented by humans, some of those language describe physics, some don't, that's not a conjecture, that's a fact.
You didn't make any points, you merely repeated the dogma that there exist maths that have no physical analogue, which I already addressed in my first post. I merely provided more context on the philosophy of mathematics so you can read up on why your position is problematic at best.
> You are effectively claiming that all maths are physics
No I didn't. I pointed out the least problematic and most accepted position on that question, which refutes your claim that your position on mathematics is obviously the only valid position.
Your question about the sqrt(-1) is perfectly exemplary of the elementary misunderstanding of what your position entails. Abstractions don't exist a vacuum. I can just as easily ask you of the physical analogue of the number 1.
It's a meaningless question. Mathematics is an abstraction describing structure, and many things share the structure of the number 1. The structure of the sqrt(-1) appears in many places, like in wave mechanics.
The fact that you conflate maths with the particular syntax we use is another elementary misunderstanding. A grammar also has a structure, and we use that to represent the structure of mathematical objects, but math is not about syntax.
Finally, on the matter of absurdity, I suggest you reread my previous post. While you amazingly seem to think it's devoid of content, I can assure you that I point to two primary philosophies of mathematics, one which disagrees and one which sort of agrees with you, but still doesn't support your claims. It's up to you if you actually want to learn what mathematical truth is really about.
> No I didn't.
Great, then you agree with me, all math isn't physics, and there's nothing more to talk about.
Here's what you don't seem to grok.. from your own original rebuttal...
> The fact is, the basic structure of our world is mathematical in some way.
I agree, I've never once disagreed with that position, you simply failed to understand the point being made and that you're continuing to try and argue it is just... boring now.
No I don't. I'm disagreeing that your position is self-evident as you've claimed, and you've still failed to recognize that.