Quantum interpretations

Dmitry67

I do believe that numbers exist independently of us. Otherwise how could physical laws work before we existed?

I even completely share Max Tegmark's idea that any mathematical system defines a universe.

The Dagda

I don't know how to answer this, it's so fundamentally odd that I'm not sure what you are suggesting, that the laws of nature need to be numbered to work? Or? Anyway I think your view is Platonic old fashioned and nonsense.

Dmitry67

Lets assume that you are right and numbers are not the reality, but just a way how we think. On another planet aliens can probably live without any numbers at all, using absolutely different concepts, which do not have any intersections with our mathematics.

Then in order to prove that you are right you just need to show, that it is possible to build:
* a different mathematics/different sort of reasoning
* which is not isomorphic to our mathematics
* and which can correctly describe the universe

If you manage to do it, I will eat my hat!

The Dagda

Ask an alien you mean? You can't expect me to prove it, you asserted numbers are real, onus is on you. I tell you what though, since most of the concepts of maths developed independently and often in different ways, I'd say that all that reflects is, numbers are useful, and that sooner or later in any civilisation or tribal society it will be useful, it's rather like the wheel or the alphabet/pictogram/x or roads, they always turn up. There are some pretty bizarre counting systems out there, even on this world that don't resemble what we have remotely though, I know that much.

jambaugh

The shadow of a sphere is a circle. It don't matter that no matter how I shine the light I still get a circle to the point that the circle is not the sphere.

In particular their mathematical description cannot both be non-isomorphic to ours and describe the same class of physical phenomena except where the mathematics DOES describe non-real aspects of nature. This is the role of Occam's razor to cut away all but what is essential to the physics.

It is also curious that the non-isomorphism between CI and MWI (and Bhomian pilot waves) doesn't satisfy you that there's something non-real (or as I rather say non-actual) in one or all of the interpretations given all are consistent with observable phenomena.

Further note that the density operator formulation of quantum mechanics is superior in many ways (more general description of systems). You can dispense with "wave-functions" all together. You will note that the density operator is more easily interpreted in its proper (CI) "probabilistic description of..." role. So tell me which is the "real part" the wave function or the density operator?

Mathematical note, the role the density operator plays in QM is its use in defining functionals on operators i.e. as co-operators. So imagine your aliens formulated QM straight from an operator algebra and its dual co-operator co-algebra and never defined a Hilbert space equivalent.

Side note: the choice of pi as a fundamental constant is not convention free. 2pi would have done as ratio of circumference to radius of a circle (or ratio of surface area to central cross-sectional area of a sphere (suppose the aliens' principle sense is tactile and they feel the sphere is a more fundamental shape). Now if you want to communicate with aliens start with a binary expansion of e. (And hope they work with continuum calculus instead of an umbrial equivalent.)

The Dagda

What if they are blind and use sound to see and talk and pheromones to designate emotion and inflection of words, in that case 1 to an alien would mean nothing, the impression of more than one source of reflection of sound and it's smell would be his numerical system or something like that. In fact it bewilders me that we think just because we are so formed that anyone in the Universe might be so bizarre as to put our limited comprehension of sense to shame. They might communicate with shapes only as thoughts for all we know, in which case 2 would be meaningless, pi wouldn't though. The shape of two objects would be a number, in that sense we'd have infinite numbers without any fixed number system, with distinctions for location rather than number in the numerical system, it'd be weird. But two shapes together wouldn't mean 2 objects, it would mean 1 object with x shape. The only thing that's eternal and exists is the Universe, everything else is a matter of conception and perception and etymology. What is at least constant from our beginnings is our humanocentric insistence on things.

jambaugh

What do you mean here by "correctly"? If it isn't operationally in terms of how we observe the universe behave then what?

And if that is the criterion then clearly any component of the mathematical description which doesn't matter on this point can't be determined as correct or incorrect w.r.t. the universe, only correct or incorrect with regard to the appropriateness of its inclusion in this context of empirical science vs. philosophical speculation of the same nature as "how many angels...?"