Essay Abstract
This essay raises questions concerning whether nature is infinite or finite, and how infinity is related to the physical importance of Gödel's 1st and 2nd incompleteness theorems, Church's theorem (also proved by Alan Turing in 1937), and the currently accepted formulation of quantum field theory.
Author Bio
David Brown has an M.A. in mathematics from Princeton University and was for a number of years a computer programmer.
Errors in original essay: In the last paragraph of the essay, I misquoted David Lindley: "Reluctantly, Einstein conceded the technical correctness of the system Bohr and Einstein laid out" needs to be replaced by "Reluctantly, Einstein conceded the technical correctness of the system Bohr and Heisenberg laid out". In the section "WHAT IS DECIDABLE? WHAT IS COMPUTABLE? WHAT IS PREDICTABLE?" there is a typo in my quote from Francis Crick, "two area" should be "two areas".
Another error: In the section "STRING THEORY AND UNCERTAINTY", I misquoted Einstein -- replace "algebraic theory theory" by "algebraic theory".
Is string theory essential for understanding uncertainty? I say yes. Is is possible that string theory is "not even wrong" as alleged by Woit? I say no. I say that string theory is the mathematical way to geometrize Feynman diagrams so as to derive gravitons and general relativity theory. However, Motl thinks Woti is 100% wrong about string theory, but I think that Woit is about 80% wrong on string theory and about 20% correct on string theory. I agree with Motl that Green, Schwarz, and Witten are in the same ballpark as Tomonaga, Schwinger, and Feynman -- however, Motl believes in string theory with the infinite nature hypothesis and I believe in string theory with the finite nature hypothesis.
As indicated in my essay,(as of January 2020) Nobel laureate Steven Weinberg and most string theorists believe that string theory with the infinite nature hypothesis implies that Milgrom's MOND is wrong and that dark-matter-compensation-constant = 0. Google "dark matter compensation constant". My guess is that string theory with the finite nature hypothesis implies dark-matter-compensation-constant has the value (3.9±.5) * 10^-5 and MOND is empirically valid. See Professor Giuseppe Pipino's 2019 article "Evidences for Varying Speed of Light with Time". Is the fundamental basis of nature an Einstein-Riofrio duality principle? In terms of general relativity theory, it seems to me that Riofrio, Sanejouand, and Pipino are wrong unless the boundary of the multiverse is steadily losing gravitational energy into the interior of the multiverse -- my guess is that string theory with the finite nature hypothesis requires 3 modifications to Einstein's field equations (after quantum averaging). It seems plausible that string theory with the infinite nature hypothesis implies supersymmetry, while string theory with the finite nature implies no supersymmetry. Google "fredkin-wolfram information".
Is Milgrom's MOND relevant to questions of undecidability and non-computability? I suggest that MOND is empirically valid and relevant to every aspect of human philosophy. However, MOND (as of the beginning of 2020 C.E.) lacks a relativistic extension (with thorough validation).
In section "9. Relativistic theories" of "MOND--a pedagogical review", Milgrom wrote, "We still want a relativistic extension of MOND. Such a theory is needed for conceptual completion of the MOND idea. But, it is doubly needed because we already have observed relativistic phenomena that show mass discrepancies, and we must ascertain that there too the culprit is not dark matter but modified dynamics."
Milgrom, Mordehai. "MOND--a pedagogical review." arXiv preprint astro-ph/0112069 (2001).
My speculative theory concerning string theory with the finite nature hypothesis depends upon 7 foundational components: (1) string theory, (2) MOND, (3) atomic time versus astronomical time according to Fernández-Rañada & Tiemblo-Ramos, (4) the Koide formula, (5) Lestone's heuristic theory, (6) the ideas of Riofrio, Sanejouand, and Pipino, & (7) the speculative ideas of Fredkin and Wolfram. I am confident about string theory and MOND, but not so confident about the other 5 components. Is it possible that there are MOND-chameleon particles that have variable effective mass depending upon nearby gravitational acceleration? What is relativistic MOND? What is the ultimate meaning of the empirical successes of MOND?
How might uncertainty be related to the inflaton field and string theory? According to Guth, Kaiser, and Nomura, "... the final stage of inflation could plausibly have begun by tunneling from some other metastable state."
Guth, Alan H., David I. Kaiser, and Yasunori Nomura. "Inflationary paradigm after Planck 2013." Physics Letters B 733 (2014): 112-119.
"Inflationary paradigm after Planck 2013", by Guth, Kaiser & Nomura, arXiv preprint
I say that Milgrom is the Kepler of contemporary cosmology -- on the basis of overwhelming empirical evidence. In terms of string theory, it seems to me that there are 2 basic possibilities for explaining MOND: (1) String theory with the finite nature hypothesis implies that Einstein's equivalence principle is slightly wrong, there is an uncertainty principle for graviton spin, and the Riofrio-Sanejouand cosmological model defines the inflaton field. (2) String theory with the infinite nature hypothesis implies that Einstein's equivalence principle is 100% correct (after quantum averaging), gravitons are spin-2 bosons without a graviton uncertainty principle, and gravitons have one or more D-brane charges that somehow allow MOND to be empirically valid (in the non-relativistic approximation).
It seems that quantum field theory has a problem at the Planck scale involving calculations with Feynman diagrams -- my guess is that string theory is the only plausible way to deal with the problem.
According to Stetz, "The finite energy portion of divergent electron-positron pair production diagrams ... should contribute to the mass-energy density of the universe."
"A Very Short Introduction to Quantum Field Theory" by A. W. Stetz, 21 November 2007 (See page 6 of pdf.)
How might D-branes be related to uncertainty? Do D-branes occur in nature?
How might uncertainty be related to the inflaton field and string theory? According to Guth, Kaiser, and Nomura, "... the final stage of inflation could plausibly have begun by tunneling from some other metastable state."
Guth, Alan H., David I. Kaiser, and Yasunori Nomura. "Inflationary paradigm after Planck 2013." Physics Letters B 733 (2014): 112-119.
"Inflationary paradigm after Planck 2013", by Guth, Kaiser & Nomura, arXiv preprint
I say that Milgrom is the Kepler of contemporary cosmology -- on the basis of overwhelming empirical evidence. In terms of string theory, it seems to me that there are 2 basic possibilities for explaining MOND: (1) String theory with the finite nature hypothesis implies that Einstein's equivalence principle is slightly wrong, there is an uncertainty principle for graviton spin, and the Riofrio-Sanejouand cosmological model defines the inflaton field. (2) String theory with the infinite nature hypothesis implies that Einstein's equivalence principle is 100% correct (after quantum averaging), gravitons are spin-2 bosons without a graviton uncertainty principle, and gravitons have one or more D-brane charges that somehow allow MOND to be empirically valid (in the non-relativistic approximation).
It seems that quantum field theory has a problem at the Planck scale involving calculations with Feynman diagrams -- my guess is that string theory is the only plausible way to deal with the problem.
According to Stetz, "The finite energy portion of divergent electron-positron pair production diagrams ... should contribute to the mass-energy density of the universe."
"A Very Short Introduction to Quantum Field Theory" by A. W. Stetz, 21 November 2007 (See page 6 of pdf.)
According to Silverstein, "D-branes play a major role in theoretical black hole physics ...."
My guess is that D-branes occur in nature if and only if nature is infinite.
Does the fundamental nature of undecidability, uncomputability, and unpredictability depend upon string theory? Why is string theory likely to be correct? According to Michio Kaku, "The number 24 appearing in Ramanujan's function is also the origin of the miraculous cancellations occurring in string theory ... each of the 24 modes in the Ramanujan function corresponds to a physical vibration of a string. Whenever the string executes its complex motions in space-time by splitting and recombining, a large number of highly sophisticated mathematical identities must be satisfied. These are precisely the mathematical identities discovered by Ramanujan. ... The string vibrates in ten dimensions because it requires ... generalized Ramanujan functions in order to remain self-consistent."
Let the symbol " 
" denote mathematical embedding. Classical field theory quantum field theory (QFT). My guess is that there are 4 fundamental possibilities for physical law: (1) QFT string theory with the infinite nature hypothesis and without further generalization. (2) QFT string theory with the infinite nature hypothesis and with further generalization. (3) QFT string theory with the finite nature hypothesis and without further generalization. (4) string theory with the finite nature hypothesis and with further generalization. Is it possible to rule out any of the 4 preceding possibilities? Can supersymmetry be empirically refuted? Each superpartner might have such a long wavelength that it is undetectable.
In terms of quantum gravity, does the Heisenberg uncertainty principle need to be replaced by an uncertainty principle involving the string constant alpha-prime? See page 29 of the following.
"Reflections on the fate of spacetime" by Edward Witten, Physics Today, April 1996
According to Callender and Huggett, "In recent years it has sometimes been difficult to distinguish between articles in quantum gravity journals and articles in philosophy journals."
Do D-branes occur in nature? How might uncertainty be related to the inflaton field and string theory? According to Guth, Kaiser, and Nomura, "... the final stage of inflation could plausibly have begun by tunneling from some other metastable state."
Guth, Alan H., David I. Kaiser, and Yasunori Nomura. "Inflationary paradigm after Planck 2013." Physics Letters B 733 (2014): 112-119.
"Inflationary paradigm after Planck 2013", by Guth, Kaiser & Nomura, arXiv preprint
I say that Milgrom is the Kepler of contemporary cosmology -- on the basis of overwhelming empirical evidence. In terms of string theory, it seems to me that there are 2 basic possibilities for explaining MOND: (1) String theory with the finite nature hypothesis implies that Einstein's equivalence principle is slightly wrong, there is an uncertainty principle for graviton spin, and the Riofrio-Sanejouand cosmological model defines the inflaton field. (2) String theory with the infinite nature hypothesis implies that Einstein's equivalence principle is 100% correct (after quantum averaging), gravitons are spin-2 bosons without a graviton uncertainty principle, and gravitons have one or more D-brane charges that somehow allow MOND to be empirically valid (in the non-relativistic approximation).
It seems that quantum field theory has a problem at the Planck scale involving calculations with Feynman diagrams -- my guess is that string theory is the only plausible way to deal with the problem.
According to Stetz, "The finite energy portion of divergent electron-positron pair production diagrams ... should contribute to the mass-energy density of the universe."
"A Very Short Introduction to Quantum Field Theory" by A. W. Stetz, 21 November 2007 (See page 6 of pdf.)
According to Silverstein, "D-branes play a major role in theoretical black hole physics ...."
My guess is that D-branes occur in nature if and only if nature is infinite.
It seems that quantum field theory has a problem at the Planck scale involving calculations with Feynman diagrams -- my guess is that string theory is the only plausible way to deal with the problem.
According to Stetz, "The finite energy portion of divergent electron-positron pair production diagrams ... should contribute to the mass-energy density of the universe."
"A Very Short Introduction to Quantum Field Theory" by A. W. Stetz, 21 November 2007 (See page 6 of pdf.)
To what extent does uncertainty play a fundamental role in physics and philosophy? According to Callender and Huggett, "In recent years it has sometimes been difficult to distinguish between articles in quantum gravity journals and articles in philosophy journals."
Do D-branes occur in nature? How might uncertainty be related to the inflaton field and string theory? According to Guth, Kaiser, and Nomura, "... the final stage of inflation could plausibly have begun by tunneling from some other metastable state."
Guth, Alan H., David I. Kaiser, and Yasunori Nomura. "Inflationary paradigm after Planck 2013." Physics Letters B 733 (2014): 112-119.
"Inflationary paradigm after Planck 2013", by Guth, Kaiser & Nomura, arXiv preprint
I say that Milgrom is the Kepler of contemporary cosmology -- on the basis of overwhelming empirical evidence. In terms of string theory, it seems to me that there are 2 basic possibilities for explaining MOND: (1) String theory with the finite nature hypothesis implies that Einstein's equivalence principle is slightly wrong, there is an uncertainty principle for graviton spin, and the Riofrio-Sanejouand cosmological model defines the inflaton field. (2) String theory with the infinite nature hypothesis implies that Einstein's equivalence principle is 100% correct (after quantum averaging), gravitons are spin-2 bosons without a graviton uncertainty principle, and gravitons have one or more D-brane charges that somehow allow MOND to be empirically valid (in the non-relativistic approximation).
According to Silverstein, "D-branes play a major role in theoretical black hole physics ...."
My guess is that D-branes occur in nature if and only if nature is infinite.
Is there an Einstein-Riofrio duality principle that is related to uncertainty and string theory? Is string theory empirically valid? I suggest that string theory is empirically valid -- beyond a reasonable doubt. String theory with the infinite nature hypothesis implies dark-matter-compensation-constant = 0 and supersymmetry is part of nature.
"Why string theory implies supersymmetry" by Motl, 24 June 2010
I have suggested that string theory with the finite nature hypothesis implies dark-matter-compensation-constant = (3.9±.5) * 10^-5 and supersymmetry does not occur in nature. If string theory with the finite nature hypothesis works, then how might a model of string theory with the finite nature hypothesis be embedded into a model of string theory with the infinite nature hypothesis? Assume that gravitons have one or more D-brane charges. Make the same assumption for gravitinos and inflatons. The 3 previous assumptions might allow string theorists to make adjustments to the cosmological constant, the gravitational field, and the inflaton field (in order to approximately model MOND and the Riofrio-Sanejouand model). According to Polchinski, if "j is a world-sheet weight (1,0) current" then "String states carry the world-sheet charge associated with the current j ..."
"Dirichlet-Branes and Ramond-Ramond Charges" by Joseph Polchinski, 1995, arXiv, page 1
How uncertain is the empirical validity of MOND? Admittedly, my speculations about string theory might be wrong. However it seems to me that Milgrom's MOND is (non-relativistically) empirically valid -- beyond a reasonable doubt. Kroupa is a skeptical scientist and he has thoroughly investigated possible MOND failures -- so far, Kroupa has not found any clear MOND counter-evidence. According to Milgrom, "MOND is a paradigm that contends to account for the mass discrepancies in the Universe without invoking 'dark' components, such as 'dark matter' and 'dark energy'. It does so by supplanting Newtonian dynamics and General Relativity, departing from them at very low accelerations."
"MOND vs. dark matter in light of historic parallels" by Mordehai Milgrom, 2019, arXiv
Does the empirical validity of MOND necessarily entail a modification of Einstein's General Relativity? My guess is that MOND is actually compatible with string theory (as currently understood by the majority of string theorists) provided that D-brane charges are assigned to gravitons and gravitinos in various MOND-compatible ways (there is considerable wiggle-room because MOND is not 100% precisely defined).
Dear David Brown
In your essay you showed your high erudition and you can deservedly be called a professor. You know so much about modern physics that I envy you. However, to answer your question: "WHERE DO WE COME FROM? WHAT ARE WE? WHERE ARE ", one needs to look at modern physics through the prism of the identity of space and matter of Descartes and, separating physical space from geometric, and to understand forever that space moves as it is matter. I invite you to discuss some aspects
The neo-Cartesian generalization of modern physics, which I set out in my essay: "The transformation of uncertainty into certainty. The relationship of the Lorentz factor with the probability density of states. And more from a new Cartesian generalization of modern physics. by Dizhechko Boris Semyonovich »
"In new Cartesian physics any movement is seen as the result of rotors of space." To me the idea seems somewhat similar to loop quantum gravity.
"Atoms of Space and Time" by Lee Smolin, 2004
Let us imagine that the Heisenberg uncertainty principle can be explained by some type of Semyonovich certainty. In that case, I think there might be a theory of double-loop quantum gravity in which each loop (in the Smolin theory) has a Semyonovich rotor-display forming a double loop structure which can introduce certainty into the Smolin theory of loop quantum gravity.
Can Heisenberg's uncertainty principle be explained by a principle of multiverse causality? Are my speculations concerning the foundations of physics correct? Perhaps not. My guess is that string theory is empirically valid, either in the form of string theory with the infinite nature hypothesis or in the form of string theory with the finite nature hypothesis.
According to Crick, "A single isolated bit of evidence, however striking, is always open to doubt. It is the accumulation of several different lines of evidence that is compelling."
"What Mad Pursuit" by Francis Crick, p. 37
My guess is that string theory with the infinite nature hypothesis is empirically valid if and only if dark-matter-compensation-constant = 0 if and only dark matter has an explanation in terms of ordinary (non-MONDian) dark matter particles and MONDian dark matter particles if and only if our universe is expanding if and only gravitons are spin-2 bosons. My guess is that string theory with the finite nature hypothesis is empirically valid if and only dark-matter-compensation-constant = (3.9±.5) * 10^-5 if and only if MOND is derivable from Wolfram's (4 or 5) simple rules if and only if the Riofrio-Sanejouand cosmological model is empirically valid (and gives the correct definition of the inflaton field) if and only if gravitons are not quite spin-2 bosons (thus allowing some gravitons to escape from the boundary of the multiverse into the the interior of the multiverse). Is it possible that MOND is a mistake based upon data dredging? I say no.
McGaugh, Stacy S. "The baryonic Tully-Fisher relation of gas-rich galaxies as a test of ΛCDM and MOND." The Astronomical Journal 143, no. 2 (2012): 40.
Ghari, Amir, Hosein Haghi, and Akram Hasani Zonoozi. "The radial acceleration relation and dark baryons in MOND." Monthly Notices of the Royal Astronomical Society 487, no. 2 (2019): 2148-2165.
Can we certain about supersymmetry (SUSY)?
According to John Ellis, "We are never going to know that SUSY is not there. ... I and my grandchildren will have passed on, humans could still be exploring physics way below the Planck scale, and string theorists could still be cool with that."
In the interview, Ellis mentions neither MOND nor Milgrom. Here is my opinion:
According to Witten, "... the orbit of a string in spacetime is two-dimensional (over the reals) and should be regarded as a complex Riemann surface. Physics without strings is roughly analogous to mathematics without complex numbers."
I say that Witten's statement is correct -- strings are the geometric completions of quantum probability amplitudes. How do we know that string theory is empirically valid? String theory with the finite nature hypothesis implies Milgrom's MOND, and there is no other mathematically plausible way to justify MOND. What good is SUSY? You need SUSY to do the "Einstein" part of the Einstein-Riofrio duality principle. Google "riofrio sanejouand". Use SUSY to embed the finite model of string theory into various infinite models of string theory -- this allows the expanding universe in which the observers are not shrinking to be (approximately) mathematically mapped into the non-expanding universe in which the observers are shrinking.
How is uncertainty related to Bell's theorem and string theory?
Consider Bell's theorem:
I have conjectured that string theory with the infinite nature hypothesis implies that Bell's theorem is empirically valid, but string theory with the finite nature hypothesis implies that Bell's theorem is empirically irrefutable but based on false assumptions about empirical reality. (This is part of what I call the "Einstein-Riofrio duality principle".) How might the preceding conjecture be given a precise meaning?
Szabó described a spin-correlation experiment suggested by Aharonov and Bohm in 1957. The experiment is similar to the experiment suggested by Einstein, Podolsky, and Rosen in 1935. On page 4 of Szabó's article there is the statement:
"Assumption 4 The choices between the measurement setups in the left and right wings are entirely autonomous, that is, they are independent of each other and of the assumed elements of reality that determine the measurement outcomes.
Otherwise the following conspiracy is possible: something in the world predetermines which measurement will be performed and what will be the outcome. We assume however that there is no such a conspiracy in our world."
My theory concerning string theory with the finite nature hypothesis depends upon what one might call "a conspiracy of Fredkin-Wolfram information controlling measurement". My speculative theory concerning string theory with the finite nature hypothesis depends upon (at least) 7 foundational components: (1) string theory, (2) MOND, (3) atomic time versus astronomical time according to Fernández-Rañada & Tiemblo-Ramos, (4) the Koide formula, (5) Lestone's heuristic theory, (6) the ideas of Riofrio, Sanejouand, and Pipino, & (7) the speculative ideas of Fredkin and Wolfram. Are all 7 of the foundational components correct? Perhaps not. My speculations also derive in part from several dozen physicists who have suggested that Bell's theorem is wrong. What might be the strategic plan for developing string theory with the finite nature hypothesis? (Step 1) Write down 4 or 5 simple rules that correctly and completely describe Wolfram's cosmological automation. (Step 2) Using the 4 or 5 simple rules, derive empirically satisfactory approximations to quantum field theory and general relativity theory, together with new empirical predictions. (Step 3) Verify the new empirical predictions by valid empirical tests.
Hello David,
I have downloaded your paper, and enjoyed reading your conversation with yourself. Some of your talking points make a lot of sense. There is some tension between naturalness in ST, and what we observe astrophysically. I think Vafa and Steinhardt (with Obied and Agrawal) are on to something, where we should be looking for cosmological clues to how the landscape collapses into real-world possibilities. My thought is that most of the stable vacua are in the pre-decoupling phase of cosmology, and that the universe we reside in appears headed for a cold dark end, so it can't be exactly stable. There is gross time-asymmetry on the cosmological scale that conventional interpretations of ST cannot reckon with. Perhaps you could respond to that.
Best,
Jonathan