Is Quantum Mechanics Non-Local or Can Local Models Explain the Universe?

[Dmitry67]

since there is no explanation why most of those would be only mathematical constructs and only one of them with real conscious human beings.

No, no!
ALL these branches DO contain conscious human beings!
You should not ask 'why I am in that particular branch' or 'why may can is dead, not alive'
You exists in multiple copies in all branches, you do not randomly 'fall' into one branch!

 

[jambaugh]

I think I found why our views are so different.

3
Take the Classical mechanics. let's take F=ma. Do you see any 'we', 'our knowledge about'? For that reason Hilbert wanted to find the axiomatisation of physics.

No! Hilbert's program was to axiomatize all of mathematics with proven mutually consistent sets of axioms. But Godel blew that out of the water with his incompleteness proof.

But take F=ma. What is an acceleration? Define (interpret) it for me. Tell me how to measure the acceleration of an object without using observers with clocks and measuring rods. This isn't a trivial question considering Einstein's equivalence principle. There's all kinds of "we" implicit in the semantics of F=ma. What's more you can define force via F=ma in terms of the acceleration of a test particle. It isn't any longer an axiom, it is a definition. More generally you define F=dP/dt and the F=ma is simply the P=mV definition.

1
No, the fundamental of science is a THEORY. An experiment is just a tool to prove or disapprove it. Without theories, the science would be just a heap of recepies... like alchemistry... This is what science about: the underlying formulas!

No the fundamental root of science is the way we decide if your theory is better than my theory. It is the epistemology! Without experiments science would be just a heap of theologies. You invoke alchemy but you fail to note that it was not the empiricism in alchemy it was the underlying "theory" based on a mystic world view which kept it from being a science. When one sticks to the epistemological root then the theories branching from it are well grounded and not subject to floating off into la la land.

Let me ask some questions again

What do you think about the max Tegmark program 'physics from scratch'
We define TOE is a pure mathematical form, TOE(f)=0. So there are only equations, no words. Then we derive everything from there. We ask 'what a complicated system would percieve?" building frog's view from the equations?

You keep invoking Termark but a quick glance at his website shows me he acknowledges:"...

Termark: "Every time I've written ten mainstream papers, I allow myself to indulge in writing one wacky one, like my Scientific American article about parallel universes."

I don't think Mr. Termark takes this as seriously as you do.

I'll have to study his "mathematical universe" stuff in some detail to answer your question but I'll make two comments "off the cuff"...

Firstly he starts with the question of which mathematical model is isomorphic to "the universe" and so his axiom is that the universe is equivalent to some mathematical model. It isn't a conclusion it is an assumption. As to the validity of that assumption, his ERH...

It is exactly the problem of holding onto an absolute objective reality while accepting QM which, to avoid the fact that these two are incompatible in their essence, one must re-interpret QM. It is again exactly analogous to holding onto absolute simultaneity while accepting the predictions of SR which requires one to invoke a preferred frame along with the unobservable aether which defines it.

I think he'd be well facilitated by updating his ERH to an EAH (External Actuality Hypothesis).

Or do you believe that there are some 'physical' axioms which can not be expressed in forms of equations?

Any statement S can be reformulated in equation form... I don't get your point here. But I think the phrase "physical axioms" is an oxymoron. There are physical interpretations of mathematical constructs. Then axioms about these constructs will map to physical assumptions. But the form of the axiom is dependent on our choice of interpretation. I think you're seeing this in this discussion.

Note that mathematics is an inherently "we" based system. Mathematics says nothing until "we" choose a particular set of axioms, choose a particular set of "interesting" definitions, and then apply deductive logic. Consider how Godel mapped axiomatic systems to numbers...Here is the list of all axiomatic systems: 1,2,3,... Which is the one for the universe?

The richness of the mathematics is not in the axioms. It is in the definitions and how they relate to what we do with the math...what we do with the math!

Push any subject far enough and you will find a mirror.

The role of mathematics in physics it to assure that our logic is consistent and to see where assertions have operational meaning. When two axiomatic systems when interpreted in terms of physical models yield identical empirical predictions we then recognize that the difference in the axioms is not a difference in the physics but rather a choice of viewpoint, a choice of convention (like c = exactly 299,792,458 m/s).

We could btw formulate GR as a theory of variable speed of light with the metric interpreted as the covariant permittivity tensor. We would then have a "fixed geometry" and variable vacuum dynamics. The equivalence principle is an equivalence (two way mapping) not a one way street. I cringe when people say "gravity is just geometry"... it isn't any more than "geometry is just gravity".

Do you agree that MWI is the best to be expressed in the TOE(f)=0 form?

No. I can't as I don't know what you mean by TOE(f)=0. You'll have to parse it down to the operational meaning of what observable predictions it makes and procedures it describes and I suspect you'll find that when this is done the predictions will be independent of any assumptions about other worlds.

Do you agree that MWI (when we pay a contre-intuitive price of accepting parralel realities) saves not only determinism, but also realism?

Whether or not "parallel realities" is intuitive or counter-intuitive is immaterial. Intuition is just our hidden assumptions and integrated knowledge bubbling up from our subconscious. What concerns me is what "parallel realities" means physically. Can you smell them? Can you traverse them? Can you in other words falsify your assumption of them?
(Again refer to our earlier discussion in the other thread.)

As far as saving determinism, QM dynamics is deterministic (In CI as in any other interpretation)
in that any observation may be assured (in principle) by prior preparation of the system an arbitrary period of time earlier.

The fact that the wave-functions in-deterministically collapse is only your problem when you confuse them with the physical system. Again you are objecting to CI by assuming a non-CI interpretation of the wave-functions.

As for reality ("what is") I don't think it needs saving, rather I think it needs updating to actuality (what happens).

 

[jambaugh]

A note to other posters/readers. I know I get long winded so let me know if you are weary of my sermons. I'll move this one into a private message domain.

 

[Dmitry67]

jambaugh,
regarding Hilbert you mix 2 things:
Hilbert's program http://en.wikipedia.org/wiki/Hilbert's_program
and Hilbert's problems http://en.wikipedia.org/wiki/Hilbert's_problems
Check 6th problem pls.

Regarding other questions, do you plan to read Max Tegmark's article?
If so I would rather wait until we are on the same page...

 

[Hurkyl]

No! Hilbert's program was to axiomatize all of mathematics with proven mutually consistent sets of axioms. But Godel blew that out of the water with his incompleteness proof.

To axiomatize physics was the 6th out of Hilbert's famous list of 23 problems. And the intent, I assume, was merely to put the mathematical aspects of physics on a rigorous footing -- e.g. to have a fully rigorous formal theory of 'particles', 'forces', and whatnot, so that the physical content of classical mechanics is nothing more than making the assertion "reality is a model of this formal theory".

As far as saving determinism, QM dynamics is deterministic (In CI as in any other interpretation)
in that any observation may be assured (in principle) by prior preparation of the system an arbitrary period of time earlier.

Now come on; that statement is blatantly false! "Identical preparation yields identical results" is simply not true in the basic formulation of QM; to get that, you either have to add hidden variables (e.g. Bohm) or drop the assumption of definiteness (e.g. MWI).

 

[Hurkyl]

P.S. can you falsify definiteness? More specifically, can you propose an experiment that proves that outcomes really are definite, rather than simply being indefinite in a coherent way? If not, then you really are being rather hypocritical when you reject 'parallel realities'.

 

[jambaugh]

To axiomatize physics was the 6th out of Hilbert's famous list of 23 problems. And the intent, I assume, was merely to put the mathematical aspects of physics on a rigorous footing -- e.g. to have a fully rigorous formal theory of 'particles', 'forces', and whatnot, so that the physical content of classical mechanics is nothing more than making the assertion "reality is a model of this formal theory".

I beg everone's pardon on my ignorance of the 23rd problem.

Now come on; that statement is blatantly false! "Identical preparation yields identical results" is simply not true in the basic formulation of QM; to get that, you either have to add hidden variables (e.g. Bohm) or drop the assumption of definiteness (e.g. MWI).

Be careful here. I didn't say sequence of measurements but rather a single measurement. Sequences of incompatible measurements (non-commuting) do not occur with 100% probability but that is a function of the measurement process and their incompatibility.

If I am going to measure the polarization of a photon in the vertical direction, say after traveling a given distance through a tank of sugar water then I can assure that the measured value will occur given the dynamics linking that measurement to a corresponding initial mode of preparation (polarization along some rotated plane).

| \langle \psi | U | \psi'\rangle|^2 = 1

[edit: Clarification I choose the initial mode so as to assure the final measurement.]

(This of course subject to the same attenuation and thermal noise we see in classical evolution in non-idealized systems.)

What is more if I create a correlated pair the dynamics preserves the correlation, how is this not deterministic? Any measurement of one will correlate with the corresponding (compatible) measurement of the other. The dynamics did not introduce any inherent (non-unit) probabilities into the outcomes.

The indeterminacy occurs only at the point of measurement. Measurement is a fundamentally entropic process. You are amplifying a signal. A measuring device must by its nature interact with an entropy dump.

 

[Hurkyl]

What is more if I create a correlated pair the dynamics preserves the correlation, how is this not deterministic?

Because with any other initial mode of preparation, you don't get an assured outcome.

Be careful here. I didn't say sequence of measurements but rather a single measurement. Sequences of incompatible measurements (non-commuting) do not occur with 100% probability but that is a function of the measurement process and their incompatibility.

I wasn't talking about repeated measurements in one experiment, I was talking about repeated experiments: e.g. do 1000 experiments with identical experimental setups.

For example, if you have a device that creates photons guaranteed to be spin-up about the x-axis, and you point it at a device that measures spin about the z-axis; you have 1000 identical experiments, but the results will be split 50%-50%.

Okay, I suppose you could try postulating an interpretation of QM that included a theory of measurement where the randomness is due to unknown variables in the measuring device... (But note that this is no longer relevant to your thesis, because we're no longer talking simply about QM)

But things still don't work out. Now consider using a device that produces entangled photon pairs, one of which is pointed at our measuring device, and the other is isolated from interaction during the experiment. Suppose we can also prepare the measuring device so that all of its hidden variables are in identical states for each experiment. It turns out the results are still split 50%-50%, despite the fact that both the source and the measuring device has identical preparation.


Maybe we could tweak our theory of measurement... but the point is it's already too late. To even get this far required us to create a theory of measurement and reinterpret the probability axiom, further changes just take us even further away from the basic formulation of QM. Maybe we'll succeed and build a determinstic interpretation of QM, but this is a failure as an attempt to argue that the basic formulation of QM is deterministic.


CI is even more cut and dry. It says that wavefunction collapse happens, without any further explanation; nondeterminism is right there its very definition! (And note that if you take some weird variant of CI where the wavefunction is not a complete description of physical state even in principle, then what you have a hidden variable theory, with the extra information hidden therein being nonobservable)

 

[jambaugh]

Because with any other initial mode of preparation, you don't get an assured outcome.

All parallel measurements of the two systems correlate. No information loss will have occurred by virtue of the dynamic evolution between entangled preparation and subsequent measurement.

You don't get and assured outcome because you are inherently not preparing individual modes for the individual particles. Measuring the pair halves singly is not compatible with the mode of preparation here by the definition of entanglement. You can in principle recombine the pair and there is an equivalent measurement compatible with the entangled mode which will be assured.

I wasn't talking about repeated measurements in one experiment, I was talking about repeated experiments: e.g. do 1000 experiments with identical experimental setups.

For example, if you have a device that creates photons guaranteed to be spin-up about the x-axis, and you point it at a device that measures spin about the z-axis; you have 1000 identical experiments, but the results will be split 50%-50%.

You are talking about the equivalent...preparation and measurement are the same thing...the best way to prepare is to measure until you get the value you want and let that one be "the system". But go further with your example. Create a vertical photon and try to observe a horizontal one. You get 0% probability. This is no different from what happens with a "classical photon". This isn't the indeterminacy of the dynamic evolution.

Again of course the measurement process for incompatible measurements or equivalently incompatible mode of preparation and subsequent measurement is not deterministic in this sense. You can't assure arbitrary pairs of classical measurements!

Parse what I said originally more carefully. You choose what you are going to measure and what value you want it to have and I can throw you a system which will have the measured value you chose. The dynamic evolution, the part of quantum physics which is talking about what's happening "out there" and thus where we need to be to talk about determinism, is deterministic.

Okay, I suppose you could try postulating an interpretation of QM that included a theory of measurement where the randomness is due to unknown variables in the measuring device... (But note that this is no longer relevant to your thesis, because we're no longer talking simply about QM)

No the assumption of QM is that the measurement process yields indeterminate outcomes. It isn't an interpretation. Quantum mechanics also has deterministic dynamics (my thesis). I point out the details of the measurement process so you can see that it is no different from the classical indeterminacy you find in say the classical description of a thermal gas and that this indeterminacy is not distinct from classical indeterminacy in this sense. It is just that by virtue of measuring variables at the quantum level you cannot even in principle remove this indeterminacy. Whereas in classical physics you can. Quantum theory is not classical theory with noise in the measuring devices.

But things still don't work out. Now consider using a device that produces entangled photon pairs, one of which is pointed at our measuring device, and the other is isolated from interaction during the experiment. Suppose we can also prepare the measuring device so that all of its hidden variables are in identical states for each experiment. It turns out the results are still split 50%-50%, despite the fact that both the source and the measuring device has identical preparation.

As you see I am no longer in your counter hypothesis. But if you want to use a quantum description of the measuring device in a "Wigner's friend" type extension then again you'll find that the measuring device (with its entropy dump) must be described with density operators and you'll see quantum decoherence (with CI) of the description of the device+system and the quantum probabilities become classical ones. The probabilistic description doesn't imply fundamental indeterminacy any more than the probabilistic description of a coin flip implies fundamental classical indeterminacy.

...CI is even more cut and try. It says that wavefunction collapse happens;

And CI also says the wave function is our description and not the system! Understand CI before you quote it please!

You update your bet in blackjack once you see the dealers hole card (when the rules allow as when you double down). You update your expectation of winning the hand. This doesn't reshuffle the cards it is not the cards which updates but your knowledge.

nondeterminism is right there its very definition!

Not in the dynamics! In the measurement process. Again read my post before you raise what you think are objections.

 

[colorSpace]

No, no!
ALL these branches DO contain conscious human beings!

I know. It was an argument for that in MWI there *are* parallel universes. I was saying that to see MWI as not having parallel worlds wouldn't make sense. Call them branches, or worlds, it is the same: In MWI there are trillions multiple versions of each human being, each experiencing something different.

You should not ask 'why I am in that particular branch' or 'why may can is dead, not alive'
You exists in multiple copies in all branches, you do not randomly 'fall' into one branch!

Sure, that is how I understand MWI. Still, you cannot predict the results of quantum measurements in any other way, other than statistically, in the sense that if you make multiple experiments, and compare the results (in any specific branch) with your prediction. And also, still, your prediction is based on complex number arithmetic, not on showing a physical process of how elements of reality move (or modify themselves) into a new configuration. You can make statistical predictions for the probability of a certain outcome (or, to put it diffrently, for the percentage of worlds where one thing will happen versus the percentage of worlds where another thing will happen), but the process leading there is a mathematical calculation, not the description of a physical process.

 

[colorSpace]

ColorSpace, regarding the physical explanations

There are some constants (like water density at 0C) which can be derived from c,h,and other parameters of the Standard Model.
However, the fundamental constants like G, h,c can not be calculated this way

The same for the laws. Some things, like viscosity, have someunderlying mechanisms, so you can give a physical explanation of a phenomena. However, fundamental physical laws do not have any futrher explanations and do not have any sub-components... just formulas

Are you sure we will *never* be able to calculate these constants? But that is another question.

The point here is that nobody assumes that constants have a physical existence. They only describe the relationship between physical events, but they are not physical themselves. They are mathematical. You can't put them in a plastic bag. :)

Similarly, a description of water waves which may cancel each other out, or not, as a description of the surface of the water, allows you to make predictions of what is going to happen, but still the description doesn't describe something that could possibly exist physically. A surface can't exist by itself. It needs something that it is the surface of, and even then it itself still doesn't exist in a physical sense.

In the same way, I don't see how the wavefunction could possibly directly describe something that exists physically. It might be the limit of our knowledge (I hope not), but it doesn't make quantum physics "real". Newton's physics and Einstein's physics describe a (more or less) possible physical world, but MWI doesn't. It is mathematical, not physical.

 

[Dmitry67]

who promised that physical variables are real, not complex?
colorSpace, then now it is your turn.

Please define, what is a difference between "mathematical" and "physical".

Say I provide a description of some process. What requirements must be satisfied so you don't say "no, it is just a formula, I need an underlying physical mechanism " ?

 

[jambaugh]

jambaugh,
regarding Hilbert you mix 2 things...

Right. Sorry 'bout that.

Regarding other questions, do you plan to read Max Tegmark's article?
If so I would rather wait until we are on the same page...

Which of his articles are you most particular about. I've skimmed a couple and as I see it he, like you, keep assuming the conclusion that wave-functions are real. This automatically negates CI by assumption so he/you naturally must invoke a distinct interpretation. I feel sorry for his students at MIT if he's being this monolithic in his understanding of QM.

Example: In the caption for Figure 2 of his Nature article...

"According to quantum theory, a card perfectly balanced on its edge will fall down in what is known as a "superposition" - the card really is in two places at once."

You see he automatically is negating CI which asserts that the superposition occurs in the description not in the card. Just as Schrodinger was trying to show with his cat. I understand his position and itself consistency (along with EMWI). I understand this viewpoint fully and reject it. He and you need to understand CI fully before rejecting it.

In the card example. If we choose a classical probabilistic description of the two card positions then we get a classical "superposition" of outcomes (probability density function with two spikes). We don't call it a superposition because probability densities don't add like vectors. But the probability density function still "collapses" when we actually look at the classical cards and update our knowledge.

Also in that article he states: "Everett's theory is falsifiable by future lab experiments: no matter how large a system they probe, it says, they will not observe the wave function collapse."

A blatant denial of CI. Again we don't observe wave functions (except in that we look at them on paper) so of course we don't observe their collapse (except when we collapse them on paper) This "logic" is similar to the old joke:
{ "I'm banging two rocks together to keep away the dragons!" But there aren't any dragons! "See its working!" }

His prediction that we'll never see wave-function collapse is like the the assertion that we will never see dragons do the hula dance. Clearly that's falsifiable! (sarcastic tone of voice)

Skimming some of the other articles on his website I don't see any sign that he even understands CI and what wave-function collapse means in CI. I'm not strongly inclined to read further at this stage... I've classes to teach and a presentation to prepare.

Tegmark wants a "mathematical" (ontological) description of the universe. He's a cosmologist so I understand the desire, especially given the current geometric model of classical GR. But in so assuming he automatically denies CI. Fine for him but you can't argue from your conclusion. Any "arguments" he makes as to why MWI is superior to CI are circular.

His dismissal of CI as metaphysical solipsism is a category error. Denial of reality (as can be described in terms of objective states) is not denial of external "actuality" but of the format one is choosing to describe it. CI may be characterized as ontological solipsism if you like but this doesn't preclude knowledge about external nature. Only knowledge of its "objective state". But really CI goes slightly further in that it even denies ignorance about the world's "objective state". CI asserts that "objective state" is meaningless at the quantum level. This assertion is not a physical statement it is a semantic one. In science "meaning" implicitly has an "operational" qualifier.

 

[Dmitry67]

BTW just one another reason forloving MWI:

quote from another thread:

As I said, you end up with unreconcilable contradictions otherwise. The primary problem is that it would mean that an extremely accurate gravitational measurement would allow you to get around the uncertainty principle. So at the very least it must be possible for General Relativity to be such that it can be represented as a superposition of states, so as to accord with the superpositions of states we see in quantum mechanics.

To attempt to illustrate this, imagine that I have a quantum particle (say, a hydrogen atom), prepared in the following state:

|psi> = |0> + |1>

...where |0> is the ground state of the hydrogen atom, and |1> is the first excited state. A hydrogen atom prepared in this superposition of states has no definite energy, and therefore no definite mass.

So what is its gravitational field?

Even we don't know how QM can be joined with gravity, MWI does not have any problems answering the questions like the one above even right now.

 

[Dmitry67]

jambaugh,
I don't have any hope to makeyou believe in MWI. We aregoing in circles.

But I am curious what do you think about the "Tegmark wants a "mathematical" (ontological) description of the universe" - forget for the moment about CI vs MWI and level 3 universes.

MWI is only a small part of his article, and not a main point he wanted to make.

 

[Hurkyl]

Parse what I said originally more carefully. You choose what you are going to measure and what value you want it to have and I can throw you a system which will have the measured value you chose.

That is what it looked like you said -- but it's such an obvious error, I didn't think you could possibly mean it. Determinism means that initial conditions uniquely determine the outcome always, not just in a few cherry-picked circumstances.

 

[The Dagda]

who promised that physical variables are real, not complex?
colorSpace, then now it is your turn.

Please define, what is a difference between "mathematical" and "physical".

Say I provide a description of some process. What requirements must be satisfied so you don't say "no, it is just a formula, I need an underlying physical mechanism " ?

The difference between 6 and 6 oranges. Numbers are abstractions, they are only "real" when applied to something that exists independently of our conceptions, something physically exists if it would still be there if the human race blinked out of existence, well except all the human based stuff obviously. I am of a feeling that although this would provide the Universe with a net loss of physical matter, on the whole it would be considered by most if not humans as a net gain, as we were only taking up real estate anyway.

 

[Dmitry67]

The difference between 6 and 6 oranges. Numbers are abstractions, they are only "real" when applied to something that exists independently of our conceptions, something physically exists if it would still be there if the human race blinked out of existence, well except all the human based stuff obviously.

both Numbers and physical reality satisfy your criteria of "existing independently of our conceptions".

No matter how you want it, you can neither wipe out quasars from the sky nor make number 9 a prime one.

So that part of you definition is not useful.

Another part of your definition is recursive (check BOLD) - it says that "real" - is something that "physically" exist. But I asked what is "physical" in the very beginning!

So sorry, but I don't see any useful definitions...

 

[The Dagda]

both Numbers and physical reality satisfy your criteria of "existing independently of our conceptions".

No matter how you want it, you can neither wipe out quasars from the sky nor make number 9 a prime one.

So that part of you definitio is not useful.

Another part of your definition is recursive (check BOLD) - it says that "real" - is something that "physically" exist. But I asked what is "physical" in the very beginning!

So sorry, but I don't see any useful definitions...

No numbers are a made up concept, they don't exist without a mind to conceive them unless you are some weird post modernist. Like infinities, they may - and in all sensible talk - don't actually physically exist.

Wipe us out and our concept of numbers goes with it, unless some aliens find our probes or are listening in on our transmissions. Don't you think the idea, an old fashioned one I might add, that numbers actually physically exist belongs in Plato's time? If not on another thread?

"real" is in inverted commas because I'm using it beyond its definition, or not as it's meant exactly. The difference is a semantic one between pure and applied maths of interest only to philosophers with too much spare time, which for most philosophers of the age is practically all of them.

 

[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 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.

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]

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!

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]

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 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]

...
* and which can correctly describe the universe

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...?"