Greetings Professor Paul Davies:
Without a clear picture of creation then perhaps your last statement is prescient.
"...one arrives at a startling eschatological conclusion: not only is the fate of the universe undecided, it is actually undecidable."
Consider a picture of creation based on common 3D physics without resorting to mathematical assumptions as a Richard Feynman study as presented in my essay- Common 3D Physics Depicts Universe Emerging From Chaos.
Regards
Charles Sven
Dear Paul. I enjoyed your essay. I thought you described the pathway of how physics and cosmology arrived at where they are today very well. I believe your summary statement: "... not only is the fate of the universe undecided, it is actually undecidable" is logical based on the current fundamental/foundational "beliefs" in science, philosophy and mathematics that went into the development of the thesis. In my essay: Clarification of Physics: A Derivation of a Complete, Computable, Predictive Model of "Our" Universe I ask and answer the question: Are the basic assumptions of physics wrong? In the essay I also question the foundations of math, computability, and philosophy. In fact I question the foundations of human understanding of "all of the order in existence". In your essay you mention "...cosmological models other than the traditional Big Bang ..." My essay presents a new meta-physical, meta-philosophy, meta- mathematical Successful Self Creation model. It is a model of the creation of all of the order in existence. Note: in the essay I focused primarily on the physical world. It says that all of the order in existence comes from one origination process - the C*s to SSCU transformation described in the appendix of my essay. This transformation converts chaos to order and overcomes entropy. That transformation provides the fundamentals (foundation) for the Successful Self Creation (SSC) processing that creates all intelligence, the complete physical world and the processing that interweaves them in every "unit" of the SSC progression. After the C*s to SSCU transformation the process proceeds by a self replication/ self organizing process analogous to the progressions in living, biological and psychological systems. In its origination and progression SSC creates Planck Actions, Quantum Mechanics, the space, time, mass, speed and direction variables/relationships of the Relativity Theories and their conversion to the forms and functioning of the original SSCU and its scale up to become the physical universe and its contents. It also creates its own mathematics, computations and philosophy. It is a new/different model that solves many of the unresolved problems/ questions of science, math and philosophy that you describe. I hope you will read and comment on my essay as it relates to your essay. John D Crowell
Dear Dr. Davies,
I enjoyed your clear and succinct essay. You state that physicists divide into two camps. One camp regards laws as convenient formalizations that humans have invented to organize observational and experimental data. The other camp regards the laws as 'fundamental.' You then continue that fundamental laws "are an idealization that cannot even in principle be tested. For example, most laws of physics make use of infinitesimal quantities and real numbers. But the set of all real numbers is an idealization: all measurements and observations yield only rational numbers."
Physical prediction of infinite resolution is indeed untestable, and this is a valid criticism. However, there is a third camp that avoids this criticism. This camp could assert that physical laws are fundamental and infinitely precise, but that physical reality itself has finite resolution.
In my essay, I suggest that infinite resolution of physical reality is based on an idealized and unrealistic assumption of absolute zero ambient temperature. I propose that physical reality is contextually defined with respect to a positive ambient temperature. On a cosmological scale, the ambient temperature of the universe is currently equal to the 2.7K cosmic microwave background temperature. Given a contextual physical reality, the expansion of the universe and decline in the cosmological ambient temperature would lead to increasing entropy as a fundamental physical property and to irreversible and intrinsically undecidable "fine-graining" of physical reality. It would lead from a nearly homogeneous, hot, and "coarse-grained" early universe to the diverse and fine-grained current state.
Absolute zero is an idealized and unrealistic assumption that can be approached, but never reached. Yet, the absence of fundamental thermal randomness is an implicit assumption of (most) interpretations of physics.
I hope you have a chance to look at my essay and comment on it.
Thank you and sincerely,
Harrison Crecraft
(1) no, Landauer's principle is only a limit on dissipative computation.
In my opinion the black-body cavity of Planck's quantum theory is actually a bridge between dissipative and non-dissipative systems. Otherwise why speak of its radiation spectrum?
That is, the energy you require to build up bits of information into a complex system only go in as the binding energy. Same energy is what you account for as the ionization energy of which the Landauer limit perhaps constitutes the threshold.
The point thus is that overall one has a standing wave or so-called black-body cavity; and which may in turn model the self-referencing state of Godel's theorem.
Or isn't it?
Great essay! I agree with your thesis of the undecidability of physics. However, I believe we are missing one crucial ingredient - quantum mechanics.
Wheeler's "It from Bit" and "mutability" is often understood, as you say, "vague deliberations" however, in his unpublished notebooks, he was looking for a connection between undecidability and quantum mechanics in a much more lucid way. Both undecidability and QM set epistemological limits on what we can know. His "higgledy-piggledy" world is built on quantum mechanics, on what he calls "elementary acts of observation."
So we have a triangle between math, philosophy, and physics. Math: Undecidability, Philosophy: Epistemological limits, Physics: Quantum mechanics.
While discussing the philosophy of physics is essential, we don't want to miss out on the physics which actually proves this point. My essay, "Undecidability as a framework for Quantum Theory and Spacetime" posted on this forum, describes Wheeler's vision on the physics side if you wish to read more. The last section agrees with your essay, so the two go together nicely.
In short: Excellent essay, I agree 100%, but don't forget about the quantum-undecidability connection!!
Hi Paul!
Great essay! I wonder if there's some space in-between these two camps of thought. For biology, it seems that objects like proteins change what they can possibly interact with depending on their sequence and how they've folded. Viruses are only able to propagate their genetic information if a "successful" genetic mutation is able to reproduce in a host. Failed mutations lead to malformed viruses, which are unable to propagate and continue in the evolutionary state space.
With examples like these, do you think some "laws" are intrinsic to the physical configuration of a system? Should these laws be thought more of a map that guides a system through a particular state space, or a causal landscape between possible states? And if so, would you think that our idea of physical laws is more a way to represent successive state transitions in a way that is compressible to a few symbols? Also if so, then how can we make predictions about some transition from any arbitrary state to another arbitrary state? I'd be curious to know what you think! I talk about these ideas in my essay as well, so I'd also be very curious to know what you think of those too!
Cheers!
Alyssa
Dear Paul,
You have raised in your extremely important essay many questions and problems that truly confirm that fundamental science is in a deep crisis of understanding.
Understanding is the event of "grasping the structure" (G. Gutner "Ontology of mathematical discourse"). "Grasp" of what structure? The original, ontological - that structure, which is the basis of knowledge and the universe, the basis of thinking and being. Umberto Eco called this super structure "absent". Is it possible to simulate it? As G. Hegel said, "The owl of Minerva begins its flight only at dusk '...
"Roughly speaking, uncomputability does for the foundations of mathematics what Gödel's incompleteness theorem does for the foundations of logic."
The "foundations of mathematics" and the "foundations of logic" have the same ontological basis (ontological structure). Morris Kline was well represented in "Mathematics: The Loss of Certainty" all the steps of a centennial epic of attempts to solve the problem of the foundations of mathematics. But this is an ontological problem and it was solved by inadequate methods. New breakthrough ontological ideas are needed. Godel's results only exacerbated the problem of the "foundations of mathematics", and read out knowledge in general.
Carlo Rovelli in his article Physics Needs Philosophy / Philosophy Needs Physics provided a list of issues that are discussed in the physical community. And the first of them is the question "What is space?". With this I completely agree. Here it is good to recall the philosophical testament of Paul Florensky: "We repeat: worldunderstanding is spaceunderstanding". "Space" is a general category for mathematics and physics. What "space" must be understood, that is, to "grasp" the structure? Ontological space. And only by "grasping" the ontological structure of space can we understand the nature of the phenomenon of time.
"What manner of entity are the laws of physics? Where do they come from? What is their ontological status? Physicists divide into two camps. One camp regards the laws as convenient formalizations that humans have invented to organize observational and experimental datai. The other camp regards the laws as 'fundamental', by which I mean they constitute the ontological ground on which physical reality rests. Of course, the laws that we know and love from today's textbooks may not be the true and final version of the laws of the universe, merely successively improving approximations thereto. However, second campers assume that the true laws really are 'out there,' and that scientists inexorably grope towards them."
This is again the problem of ontology - the nature of the "laws of Nature." Here we need an understanding of the first law ("meta-zaon") - "Logos". Here, a methodology is needed for the total unification of matter at all levels of the Universe as a whole generative process + plus a dialectic in the spirit of Cuzansky - "coincidence of opposite positions" = plus extremely sharp "Occam's razor .
"The ontological status of the laws matters little for almost all of science. Where it does have relevance is in cosmology. In the traditional big bang model, the universe springs into existence from nothing. Fifty years ago, the big bang itself was regarded as an event without a cause and therefore beyond the scope of science. The laws of physics were assumed to be imprinted on the universe from the get go, implying that the package of marvels 'universe + laws' popped into being spontaneously in a singular process, something that simply has to be accepted as a brute fact."
When we determine the ontological status of the "laws of Nature", we will have to abandon "the traditional big bang model". It is too philosophically naive and introduces maximum uncertainty into the scientific picture of the world.
"Now it is clear that infinitely precise, universal, immutable, eternal laws are an idealization that cannot even in principle be tested. For example, most laws of physics make use of infinitesimal quantities and real numbers. But the set of all real numbers is an idealization: all measurements and observations yield only rational numbers.iii If you believe the laws of physics exist in some Platonic heaven then this idealization isn't troubling. But what if this godlike status of the laws is a misconception?"
It is precisely to start understanding the "beginning" from Plato, from his understanding of matter, the methodology of its total unification: matter is that from which all forms are born. with . ontological interpretation of his "celestial triangle" (taking into account all the problems in understanding matter - "dark matter" and so on). Only in this way will we be able to see the "god-like status" of the first law - the "Logos" and the generated laws of Nature.
"And if one accepts the idea of 'loose laws,' can that be made quantitative, such as by appealing to meta-laws formulated as superpositions of laws? Does my prescription open the way to a unification, not just of physics, but of physics and mathematics?"
It is the understanding of the meta-law (Logos) that makes it possible to construct a single ontological basis of knowledge: an ontological framework, an ontological , an ontological foundation. Here I recall the philosophical covenant of John Archibald Wheeler:"Philosophy is too important to be left to the philosophers."
Today, a global brainstorming is needed to overcome the crisis of understanding. Someone from the physicists proclaimed: "It takes a lot of crazy ideas!" Let's put together a list of these ideas and try to look for the truth, which "should be drawn ..." (A. Zenkin SCIENTIFIC COUNTER-REVOLUTION IN MATHEMATICS).
Please also see my ideas .
with kind regards,
Vladimir
Dear Prof. Davies,
When I was browsing through this contest's entries and saw the name Paul Davies, I wondered if this could possibly be the well-known physicist. I decided it must be someone who just happens to have the same name. Then I clicked on your entry's title and read your bio. You ARE the famous physicist, after all.
Last year, I sent you an email for some reason (I simply can't remember what it was about). Anyway, you wished me the best. One example of my best is my entry in this contest, NON-COMPUTABILITY AND UNPREDICTABILITY ARE SO YESTERDAY: WITH COMPUTABLE AND PREDICTABLE COSMIC STRUCTURE, PLUS IMPLICATIONS FOR MATHEMATICS AND SCIENCE, new paradigm
Your "Undecidable Universe" seems to be the exact opposite of my COMPUTABLE AND PREDICTABLE COSMIC STRUCTURE. Your entry appears to be an excellent example of compatibility with the present interpretation of science's data while my entry seems to be compatible with a new paradigm ... a fresh way of understanding that data. If I may borrow from the inside-front-cover of your 1991 book "the matter myth" (cowritten with astrophysicist John Gribbin), this new paradigm can be stated as
"(Future) developments at the frontiers of science are challenging our views about ourselves and the nature of the cosmos as never before."
Nevertheless, I sincerely wish you the best. Whichever of our entries ends up closest to the science accepted in a thousand years, we both have the same purpose - to enjoy the pursuit of scientific truth.
Rodney (Bartlett)
Your essay was informed, intelligent and interesting. Of course, I am familiar with your work so I expected nothing less. Even when I disagree with your fundamental assertions you make an intelligent argument what is worth considering.
What I found most interesting is that, as I read many different essays by many different authors, each one is trying to espouse some idea or concept that is in one way or another beyond what has been established. Whereas your essay is a informed survey of the fundamental ideas, concepts and questions that surround this difficult topic.
Thus, my only complaint would be that I would like to have seen a more robust rebuttal of Platonism. Of course, that just identifies me as one of those authors...
You wrote: "By combining these deep insights, one arrives at a startling eschatological conclusion: not only is the fate of the universe undecided, it is actually undecidable."
Death to Laplace's Demon!
This is certainly a very interesting essay, however, I find myself a bit baffled by a certain recurring theme that I consider disturbing, and that is the implicit anthropocentricity of some of the ideas.
To exemplify my concern let us focus on a topic that appears prominently in the essay:
Gödel's lesson, regarding the undecidability of the truth values of certain statements within an axiomatic ( mathematical) system . What Gödel showed is that there are certain true statements that cannot be proven by following the ``axiomatic-logical path", but there is no issue at all regarding the truth of those statements. However, here the author seems to give a dramatically strong role to an aspect of the question that seems rather anthropocentric: The fact that there are meaningful statements for which no man could ever ascertain their truth value, is somehow taken as casting doubts about the statement having a truth value in itself. Furthermore, in fact, the very possibility of producing Gödel's result relies on a notion of the "truth value" of a statement ( within an axiomatic system) that is independent of the notion of proof .
This is taken further regarding computability: the fact that nor man or man-made machine ( for which a Turing Machine is an idealized characterization) can compute in a finite time ( a criteria further reduced to take into account the finiteness of the time made available by cosmology) a certain number, is somehow taken to mean that such number does not exist. Thus, existence is made strongly dependent on men (or similar thinking organisms). This is , in my view, a step back from the lessons, that are often considered as starting with N. Copernicus, having shaken our conception of being at the center of the universe, and further enhanced by Darwin's theory of evolution that shook our conviction that we were the center of creation [with newly adapted versions of the idea, in my view equally erroneous, which somehow see us, humans as the ultimate goal of evolution : i.e. to create the simple cells and take live into more and more complex forms so that the world might end up with beings like us].
Here physical laws are required to be such that their predictions are computable.
This posture seems rather problematic to me. This is even so when taken in the realm of mathematics: should we take the view that say existence proofs, say of solutions to differential equations with given initial data, are meaningless unless they are constructive? We are often content to know the solution exist and is unique, while the question of
actually finding the solution is taken as one of quite a different nature.
To adopt Landauer's view of physical laws as necessarily tied to the capacities of a computer, even the most conceivably versatile version thereof ( say a superefficient universal Turing Machine or even a quantum version of it) is to place us humans at the center once again. This time not merely at the center the universe, but at the basis of the very essence of existence. I think we can all imagine a world where there are no sentient beings, no computers, and nothing like that. In fact, our own theories of cosmology indicate that for a very long time that was precisely the state of the universe. Thus, unless one adopts a teleological posture, it seems that we must accept that the emergence of the conditions that made beings like us possible (i.e. the formation of galaxies, stars, solar systems, life and the emergence intelligence as a successful adaptation) are mere contingent facts, and that the universe could easily be conceived as having gone into a different path.
I think it is hard to dispute the notion that physical laws can limit what is, in principle, computable, but, one must recognize that the notion itself of what is computable ( say in terms of Turing Machines and the like) has a very strong anthropocentric component ( what the machines we can device can compute), and thus the posture that computability limits physics is in a sense, going back to placing ourselves at the center.
It is natural to expect that the extent of the things we might be able to know, be strongly anthropocentric, it is quite different to claim that the same applies to the world out-there itself.
I should say, however, that in certain aspects what is considered here resonates with one idea I considered in my own essay, but I think, we part ways dramatically at considerations like " ...reality is the total sum of what sentient beings can actually measure or observe (e.g. classical bits of information and rational numbers)...". Similarly, information is a notion that acquires meaning in the context where we have taken for granted the existence of sentient beings, who might store it in devices which in idealized terms they describe, using the notion of bits, but it seems hard to give a meaning to information in the absence of such beings. Placing information at the center like in Wheeler's " it from bit" catchy phrase, is again returning to an admittedly more sophisticated than older ones, but nonetheless, clearly anthropocentric world view.
As I said I am convinced there is a world out-there and there is a question of the extent to which we can, through our own very human theoretical constructions, produce accurate descriptions thereof. Here the posture seems to make the very existence of world out-there dependent on us.
Dear Prof. Davies,
Thank you for writing this essay. I wonder if you are familiar with the work "Machines, logic and quantum physics" by Deutsch, Ekert and Lupacchini, where they argue that it is the physical laws what determine what is computable. So I guess they would agree with the first part of your claim that "the laws of physics determine what can be computed, and computability determines what can be the laws", but not with the second one. I was wondering what your standpoint on that work was.
Thank you and best regards,
Gemma
Dear Prof. Davies,
I have been enjoying your books since I was a teenager (which means for a very long time)and greatly enjoyed your essay here.
It made me wonder if physicist should heed the advice of Nicolas Gisin and abandon the infinities of the reals?
https://www.nature.com/articles/s41567-019-0748-5
Best of luck in the contest!
Rick Searle
Hello Paul,
What size T-shirt do you wear? The formula that represents the Universe, the only Universe you know where all is in motion and all is motion is the equation of motion. For more info please see my 4 contest entries especially the 2008 one.
V=S/T
Thanks, all the best,
Gerry
I hope the attached image is visible.
last attempt to send image
Dear Professor Davies
It seems to me that you have accidentally made a strawman of the Reals. Your arguments against infinite precision in measurement, seem quite solid, but they have nothing to do with continuity or uncountability or any property unique to the Reals. They would seem to pertain equally to the Algebraics and (yes) even the Rationals.
You quote Chaitin "All measurements and observations yield only rational numbers." Okay..., but in the context of your paper would it perhaps be clearer to say "All measurements and observations yield only truncated rationals" or some other such wording? One cannot, of course, get an infinity of digits by measuring something, and if some theory has numbers with an infinity of digits, doesn't it exhibit the identical "infinite precision" problem?
Dear Paul,
I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.
"There is, however, a contrarian concept, deriving from the field of computation, and exemplified by Rolf Landauer's hypothesis that as idealized mathematical relationships cannot be implemented in the real universe they should not be invoked as fundamental laws; real computations always involve imprecision and uncertainty. Even on a cosmic scale the observable universe will have a finite computational capacity. John Wheeler famously championed the notion that the laws of physics are ultimately mutable and imprecise. These considerations of Landauer and Wheeler suggest a new source of unknowability in the universe deriving from limitations on computational power, and invite a reformulation of the halting problem of the theory of computation".
While the discussion lasted, I wrote an article: "Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus", due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 "Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability".
I hope that my modest results of work will provide you with information for thought.
Warm Regards, `
Paul,
Nice essay. I do like your fundamental thinking, as you may see from mine, suggesting some better fundamental laws! They do indeed lead to a more coherent 'cyclic' cosmological model.
You may have seen Wolframs recent update to Lloyd at 10^116, but more importantly I find is the Elementary Length at 10^-93, consistent with a recent SUB-matter gravity paper of mine (cited in the essay). The link to Wolfram is arxiv.org/abs/2004.08210 (most interesting from p.360), but I hope you'll read & score my essay first. As ours are close, and to avoid yet more 1's, I hope you equally like mine to allow the gentlemanly approach!
Time now runs out so I'm very glad I got to yours.
Very best regards
Peter
Dear Paul Davies,
> ... which is to say that the originating event, or process, is treated as lawlike, and not as an unexplained initial condition.
I suppose the idea of "A lawlike origin" has been traversed by researchers in many different ways, particularly in the sense, what could create those laws. Even mathematical origin has run into problems, what mathematics must be selected, and what provides physical existentialism to that. Also, mathematics is arbitrary to the extent that it depends on axiomatic system selected, and there cannot be any limit to what can be selected. So, even the discovery of mathematical relations (theorems) are contingent on the arbitrariness of axioms. A totally different viewpoint is required now; one such possibility of creation is discussed in the essay, Mother of all Existence, that shows even pure lawlessness or random exchanges between null reality and existence can create a physical universe or function like the known universe.
> In addition, the (ultimate, fundamental) laws are taken to be infinitely precise mathematical relationships.
One of the reasons that infinite precision is opted is because changes do occur upon interaction with definite results, and if interactions are non- deterministic, then how does a definite consequence arise? Moreover, entirely deterministic function with finite quantized states can only be cyclic over eternity, and continuum like infinity is indeterminate as discussed in the essay. Moreover, a deterministic universe (function) cannot come into and go out of existence, that would require an arbitrary jump, and the function cannot switch from one set of laws to another as may be required even in case of a priori Platonic existence (though I am not sure of the term Platonic). A limited indeterminism is the only path of rescue for creation, and it is possible to argue that limited indeterminism may arise when underlying reality is a continuum, but the permissible observable transitions are in quanta.
Rajiv
