Physics and its a pre-Gödelian mindset by Olaf Dreyer

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

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

Hi Olaf,

Your idea of emergence is at the center of the physics is very beautiful...which is including consciousness and incompleteness... Very good...

Here in my essay energy to mass conversion is proposed................ yours is very nice essay best wishes .... I highly appreciate hope your essay and hope for reciprocity ....You may please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

Some of the Main foundational points of Dynamic Universe Model :

-No Isotropy

-No Homogeneity

-No Space-time continuum

-Non-uniform density of matter, universe is lumpy

-No singularities

-No collisions between bodies

-No blackholes

-No warm holes

-No Bigbang

-No repulsion between distant Galaxies

-Non-empty Universe

-No imaginary or negative time axis

-No imaginary X, Y, Z axes

-No differential and Integral Equations mathematically

-No General Relativity and Model does not reduce to GR on any condition

-No Creation of matter like Bigbang or steady-state models

-No many mini Bigbangs

-No Missing Mass / Dark matter

-No Dark energy

-No Bigbang generated CMB detected

-No Multi-verses

Here:

-Accelerating Expanding universe with 33% Blue shifted Galaxies

-Newton's Gravitation law works everywhere in the same way

-All bodies dynamically moving

-All bodies move in dynamic Equilibrium

-Closed universe model no light or bodies will go away from universe

-Single Universe no baby universes

-Time is linear as observed on earth, moving forward only

-Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

-UGF (Universal Gravitational Force) calculated on every point-mass

-Tensors (Linear) used for giving UNIQUE solutions for each time step

-Uses everyday physics as achievable by engineering

-21000 linear equations are used in an Excel sheet

-Computerized calculations uses 16 decimal digit accuracy

-Data mining and data warehousing techniques are used for data extraction from large amounts of data.

- Many predictions of Dynamic Universe Model came true....Have a look at

http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.html

I request you to please have a look at my essay also, and give some of your esteemed criticism for your information........

Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.

In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from "http://vaksdynamicuniversemodel.blogspot.in/ "

I request you to please post your reply in my essay also, so that I can get an intimation that you replied

Best

=snp

I was intending to respond with a longer discussion. I will have to postpone that until later. I will say that I think an aspect of the quantum measurement problem as an undecidable proposition is related to an aspect of quantum gravitation. If you read my essay you find I propose a duality between the unitarity and equivalence principles of quantum mechanics and general relativity. This in a quantum context leads to a sort of paradox of the same nature as the quantum measurement issue.

I will return to this in the near future. It got late today and I will probably write a better discussion tomorrow.

Cheers LC

Dear Olaf Dreyer

Just letting you know that I am making a start on reading of your essay, and hope that you might also take a glance over mine please? I look forward to the sharing of thoughtful opinion. Congratulations on your essay rating as it stands, and best of luck for the contest conclusion.

My essay is titled

"Darwinian Universal Fundamental Origin". It stands as a novel test for whether a natural organisational principle can serve a rationale, for emergence of complex systems of physics and cosmology. I will be interested to have my effort judged on both the basis of prospect and of novelty.

Thank you & kind regards

Steven Andresen

Dear Olaf,

I have enjoyed reading your concise and to the point essay. Just wondering whether I got it right that you use 'emergence' not in the naturalistic (bottom up), but rather in the sense of 'spontaneous idea' implying human agency.

Heinrich

To continue onwards with what I started, I thought I would break this out some with regards to quantum gravitation.

With the measurement issue a quantum system with some set of states, usually rather small in number or with a few number of degrees of freedom, by a classical-like system. By the use of "like" it is a reference to the fact this system is really in fact quantum mechanical. In the sense that Zurek outlines there is a form of quantum decoherence that induces superposition or entanglement phase of the system to enter into a large reservoir of states. Hartle then illustrates how decoherence leads to a form of macrostates that are decoherent sets of states. These are subjectively assigned groups of states, similar to the idea of macrostates in phase space in statistical mechanics. We then see in this physics the split between objective physics, which might be seen as the dynamical evolution of quantum states, and subjective physics that occurs with the phenomenological report observers make.

I do not think it is unreasonable to see this as a case of quantum states encoding information about quantum states. In order to fully understand this process it requires some understanding of how the reservoir of quantum states define the final needle states, which requires a measurement system of the measuring system, which then of course gets into this recursion. The many world interpretation has this feature in it of a product structure of increasingly entangled states. This ψ-ontological interpretation has its mirror in ψ-epistemic interpretations, such as in GRW objective collapse models. Further, quantum interpretations tends to be incomplete and contradict each other. I see this as a possible feature of a Gödelian nature of quantum physics.

When it comes to quantum gravity there is a similar gap. Currently the firewall is a major obstruction to the unital description of quantized gravity. Hawking bet that information, here information as the number of quantum bits, qubits or qu-Nits for N >= 2, is not conserved. The conservation of information appears to be a reasonable requirement of physics, which was the stance of Susskind. Susskind won a bet with Hawking, but then Almheiri, Marolf, Polchinski, and Sully demonstrated something interesting. A failure of accounting for entanglements of states meant that either unitarity of quantum mechanics or the equivalence principle of general relativity fails. In my essay I illustrate how these two principles are complementary and not compatible in a classical sense.

The vacuum is filled with virtual pairs of fields. With a black hole the gravity field causes one of these pairs to fall into the black hole and the other to escape. This means the quantum particle or photon that escapes as Hawking radiation is entangled with the pair that falls into the black hole, and so this means Hawking radiation is entangled with the black hole. So at first blush there seems to be no problem. However, if we think of a thermal cavity heated to high temperature photons that escape are entangled with quantum states of atoms composing the cavity. Once the entanglement entropy reaches a maximum at half the energy released the subsequent photons released are entangled with prior photons released. This would hold with black holes as well, but because of the virtual pair nature of this radiation it means Hawking radiation previously emitted in a bipartite entanglement are now entangled not just with the black hole, but with more recently emitted radiation as well. This means a bipartite entanglement is transformed into a tripartite entanglement. Such transformations are not permitted by quantum unitary evolution. This is called quantum monogamy requirement, and what this suggests is unitarity fails. To prevent the failure of quantum mechanics some proposed a firewall that violates the equivalency principle. This is called a firewall.

The firewall occurs when half the possible radiation is emitted, which is also the Page time. This also corresponds to the failure of a quantum error correction code. Error correction codes involve some deep mathematics; it is connected with the RT formula and I illustrate in my essay the connection with Mirzakhani's mathematics on the geodesics in hyperbolic spaces. Error correction is also tied with the packing of spheres or how oranges stack at the grocery store, the Kepler problem. This gets into the guts of what my paper is about. However focusing in an error correction corrects the mixing of information. Think of a library, in particular an elementary school library with little kids, and the patrons scramble up the order of books. The distance a books ends up from its right position is the Hamming distance. As the library gets mixed up an algorithm can manage this disordering. However, at about half mixing up things break down. The librarian has to virtually start over.

In the end it may be that the equivalence principle and the unitary principle are complementary and in a quantum setting are not observable in a simultaneous observation. This is similar to the Heisenberg uncertainty principle with position and momentum. Back to the Gödelian issue, this means the universe presents itself in entirely different ways depending on the type of measurement performed. This is also a sort of form of "collapse" if thought of in a ψ-epistemic sense, which would agree with Hawking and Penrose. A ψ-ontological perspective would be more in line with Susskind. These perspectives are I think ultimately a form of G and NOT-G for G a true but undecidable Gödelian proposition.

Cheers LC

I just boosted your voting score a bit. I realized that I had not voted for your paper yet.

Cheers LC

Horrors, the message above I copied from MSW looks terrible. Here it is again

Thanks for your remarks on my paper. I can say that a part of this was motivated by Maryam Mirzakhani's death. She died of breast cancer last July, and the news for various reason made me angry. I had read one of her paper's back in 2014 when she won the Fields medal, and at the time I thought this had something maybe to do with physics. Last spring I studied the Ryu-Takayanagi (RT) formula and for some reason the day I heard of Maryam's death the insight on how her work connects with this hit me.

There is this problem with how gravitation and quantum mechanics merge or function in a single system. It is often said we understand nothing of quantum gravity, and this is not quite so. Even with the based canonical quantization of gravity from the 1970s in a weak limit is computable and tells you something. This theoretical understanding is very limited and big open questions remain. Of course since then far more progress has been made. The AdS/CFT correspondence, the Raamsdonk equivalence between entanglement and spacetime and the RT formula are some of the more recent developments. These indicate how spacetime physics has a correspondence or maybe equivalency with quantum mechanics or quantum Yang-Mills fields. However, an obstruction exists that appears very stubborn.

The vacuum is filled with virtual pairs of fields. With a black hole the gravity field causes one of these pairs to fall into the black hole and the other to escape. This means the quantum particle or photon that escapes as Hawking radiation is entangled with the pair that falls into the black hole, and so this means Hawking radiation is entangled with the black hole. So at first blush there seems to be no problem. However, if we think of a thermal cavity heated to high temperature photons that escape are entangled with quantum states of atoms composing the cavity. Once the entanglement entropy reaches a maximum at half the energy released the subsequent photons released are entangled with prior photons released. This would hold with black holes as well, but because of the virtual pair nature of this radiation it means Hawking radiation previously emitted in a bipartite entanglement are now entangled not just with the black hole, but with more recently emitted radiation as well. This means a bipartite entanglement is transformed into a tripartite entanglement. Such transformations are not permitted by quantum unitary evolution. This is called quantum monogamy requirement, and what this suggests is unitarity fails. To prevent the failure of quantum mechanics some proposed a firewall that violates the equivalency principle. This is called a firewall.

The firewall occurs when half the possible radiation is emitted, which is also the Page time. This also corresponds to the failure of a quantum error correction code. Error correction codes involve some deep mathematics; it is connected with the RT formula and I illustrate in my essay the connection with Mirzakhani's mathematics on the geodesics in hyperbolic spaces. Error correction is also tied with the packing of spheres or how oranges stack at the grocery store, the Kepler problem. This gets into the guts of what my paper is about. However focusing in an error correction corrects the mixing of information. Think of a library, in particular an elementary school library with little kids, and the patrons scramble up the order of books. The distance a books ends up from its right position is the Hamming distance. As the library gets mixed up an algorithm can manage this disordering. However, at about half mixing up things break down. The librarian has to virtually start over.

The solution with Susskind and others is to say spacetime variables and quantum states are equivalent. I do not disagree completely, but I think this is a complementarity instead of an equivalency. It means with either spacetime or quantum states you can account for the system, but at the expense of abandoning a description of the system by the other. You can't describe quantum gravity completely by both in the same measurement description. So this is a sort of Heisenberg uncertainty, if you will.

Cheers LC