Physics and its a pre-Gödelian mindset by Olaf Dreyer

Dar Olaf,

I bare bruises for suggesting that physics has some Turing machine/Godel type of incompleteness. I suppose the idea seems to be percolating out into the world.

I think the quantum classical dichotomy is a case of this. The measurement of a quantum system couples that system with a reservoir of states. The quantum system then becomes entangled with this reservoir of states as superpositions and entanglements in that system are reduced. This all sounds unsurprising, as this is just decoherence. However, in the case of an emergent classical state, say the needle of an instrument or a general classical configuration, we lack the quantum mechanical tools necessary to understand this. Quantum mechanics is basis independent and we are demanding that it somehow produce a prediction for a fixed classical basis. I see this as a possible instance of Godel incompleteness with self-referential qubits.

Cheers LC

Hi, Olaf, thanks for your reply! Yes, we took the topic of the contest along the same lines, that's good, it means there must be something there! I think I fully agree with all what you say, my comment about the language thing is just a matter of what to stress.

> Note, though, that you need to know about solids to make this statement. What is a solid? All you have is a (long) list of positions and momenta. Finding the solids is the hardest part.

Precisely! In your example the obstacle is the definition of a solid in terms of microscopic variables. Being a definition, I referred to the problem as a matter of language. The theory is written in the language of position and momenta, but the statement is stated in the macroscopic language of large objects. There is an incompatibility between the two languages, and that is why the microscopic theory cannot assess the truth value of the macroscopic statement. Gödel's theorem, however, is not a matter of language. The unprovability of some statements is present even for statements that are written in exactly the same language as the one of the theory. In a way, Gödel identified an even more serious problem, because his unprovability is still there in the absence of translation problems.

But never mind this, it does not challenge your main emergence conclusion. Because in addition to Gödel's unprovability, we also have to deal with the scale/language/emergence un-assessability you discuss.

Best!

inés.

Dear Olaf,

Nice Essay, connected with the fundamental question of physics: "Does the fundamental theory of nature exist?" You argue, making an intriguing parallelism with Gödelian incompleteness, that the answer should be "no". Despite I agree with your statement that "To exclusively look for the fundamental theory of nature is as narrow a search as the search for the formal axiomatic system that underlies mathematics", I must add that this does not automatically imply that such a fundamental theory of nature does not exist. Einstein's position on this issue was of substantial uncertainty. We all recall his quest for a unified field theory in the latest years of his life. On the other hand, he aslo claimed that it should not exist a fundamental theory of nature but only subsequent theories which explain nature with always increasing approximation levels. I am substantially incerte in the same way.

Finally, I completely agree with your point that emergence is not a weakness of physics (despite I have various dubts on energent gravity), but it could be a useful tool instead.

In any case, I find your Essay to be entertaining and intriguing. Thus, it deserves my high score.

As I know that you are an expert on black hole quasi-normal modes (despite I am astonished that you are now working as consultant in finance), maybe you could be interested in my Essay, where I discuss about them (and also on the unified field theory) ... with Albert Einstein!

Good luck in the Contest.

Cheers, Ch.

Dear Olaf,

once more an essay with Gödel's results involved. And I like it. But I also have some suspicions.

If I take your analogy serious, I conclude that you have proven consciousness to be an emergent phenomenon. Since consciousness is needed to at all be aware of something like 'emergence' and consciousness in your framework is an emergent property of reality, it follows that consciousness has proven to itself to be an emergent property.

But now 'emergence' is 'provable' and not anymore a true, but unprovable statement.

So, once more, what is 'provable' seems to depend heavily on what one puts into the equation in the first place as an axiom. Since your axiom is 'emergence', your output will be 'emergence'.

I really don't know how such logical figures should or can say anything true and reliable about *physical* reality and the underlying origins (if there are some) of for example consciousness.

For me, it seems to only say that we don't know how consciousness comes about from dumb matter, because we cannot prove this to be factually the case. But this does not mean that consciousness must be 'emergent', in the sense that a clump of matter awakes to some awareness.

I think what you did is simply state that the concept of emergence cannot be proven to be evidently valid for 'things' like consciousness, quantum behaviour, gravity and cosmology.

Isn't there a big danger that we label things we cannot formalize in the traditional Newtonian manner as 'emergent' - and by the very premise that consciousness should itself be 'emergent' it then seems that the very concept of 'emergence' naturally emerges not only in the fact that consciousness exists, but then also 'necessarily' in the fact that this consciousness can facilitate at all the idea of 'emergence'?

The big question for me is whether or not the concept of emergence is merely an - unprovable - idea, or rather a physical necessity.

Another question for me is what or who adds new 'axioms' that can built the upwards ladder of emergence? Surely, all we can observe in physical reality should be consistent with other facts. Therefore the hierarchy of axiomatic systems should be more or less well-ordered. But is there an *end* to this hierarchy - and if yes, why and where does it stop and if no, what does the latter then mean at all for physics?

Dear Olaf,

thank you for sharing this nice essay, that I enjoyed very much reading.

Although from a very different perspective,you will find similar position in my essay. For instance, the failure of some naive fundamental research programs, like the one of a complete axiomatization of physics.

All good wishes,

Flavio

Hi Olaf,

thanks so much for your reply. Emergence is not a bad idea, i think, albeit i have the impression that it freely levitates between the assumption of nature being fully formalizable and nature being only formalizable to a certain degree due to in-principle reasons (due to some fundamentals we yet don't know for sure).

I would be eager to read your next essay!

Good luck,

Stefan Weckbach

Oh, i have an essay too in the contest. I would be happy if you would like to read and comment on it Olaf. Maybe what i describe is not so far apart from your concept of emergence?

dear Olaf,

I am glad that I read your essay because in my mind you were always about collapse.. and all from reading a lot about your past research, which was like beating a skeleton of a horse. I was surprised to hear you talking along the lines of my thinking. which I write

"Now suppose I ask you to tell me what will happen to some "object", but I don't tell you anything about it (how fundamental can you get) !! like what mass it has or what it will do if another thing is present. Ok, I'll give it a try. First I will say I will "invent a coordinate and since I don't know where it exists I will restrict it to be in some range and eventually make that range variable. This lonely thing would have a meaningless existence. i.e. it needs a partner. If we add another one next to it with similar setup and at some distance that can also be varied. Now, we can calculate all relative information just like our original idea in the essay.

Kaboom! both situations reached the same conclusion with generalization leading to all (at least important parts up to now) of physics QM, QFT, Gravity like shown. In one instance we acted like GOD and decided to design a dynamic universe, in the other we are ignorant humans but figured out how things should work, and both match and are the FUNDAMENTAL building block. "

I hope you can glance at my essay and tell me if it makes any sense. Thanks

https://fqxi.org/community/forum/topic/3127

Let me add one clarification.

As a matter of fact you don't need the coordinate, you can derive it by the NUMBERS that you have started with originally. And of course the numbers themselves are unimportant, only their relative values.Hence the pun on Pythagoreans declaration ALL is number.

Olaf fabulous essay. I have rated it very highly.

What if we could draw actual axioms for example "the definition of the imaginary unit" as a drawing element on a geometry, then we could instantly see how that relates to "complex numbers" which don't use the actual definitional imaginary unit. That is, the definition of i is very different from the "i" used in the complex numbers z=a+ib since the definitional i is alone as a "drawing element" while all the z's use only a constricted "i" enveloped with the "real numbers" a and b. In this scenario we could see if the definitional i causes the "emergence" of the "complex numbers".

I took the completely opposite route to you -- I devised a "new maths" that avoids Godel's work by looking at totalities. It basically is "a physics of complex numbers", we show that complex numbers "parts" (the real part and the imaginary parts) are due to momogamy the pure qm property of how the system and it sub-systems interact. If you some time then see my essay What is fundamental is the area of the imaginary unit" for more details. Please read the FAQ attachment on the first post.

Olaf,

Very good essay. One of the few I'd have really liked to see longer, though you argued the case well and not to concisely. Nicely written and I also agreed with just about all. I do like to 'look at old problems in new ways'.

Perhap's you could comment on an interesting proposition, not so much from this year but my 2015 'Red/Green Sock Trick' essay. I suggest a common underlying structure simply following the rules of brackets in arithmetic, which is also as modal / 'quantum' logic. Infinitely many functions within functions or spaces within spaces in motion can exist but only have direct relationships with the next one up. They carry on down with Godel (who I agree is dismissed along with agony aunt Marilyn Savant who I'm sure you're familiar with!).

Accompanying that is the Law of The Reducing Middle' No problematic binary 'excluded middle' but a Bayesian distribution of possibilities. Then perhaps read this years essay to evaluate it's power!

Great job on yours, right on topic and lovely style. Top Marks.

Very best.

Peter