Epistemology
Introduction E9F5FC Questions FFFFC0 Software 
See: Physics John Harland's Research Program My notes from talking with John Harland 2023.11.22 Tension between spacetime model (spatial adjacency) and Hamiltonians (adjacency between states). Dirac operator is the analogue of the Laplacian to get an index. Nash embedding theorem. Collapsing ... into nonexistence. 2022.07.25 Entanglement and the second law. Culling too much information, going backward in time. There are timelines that survive. Separation of levels. Otherwise, a noise wall. Mutation. Discrete. Constants of physics. Symplectic transformations under time have a onetoone correspondence with Lagrangian dynamics. Critical action  maximum or minimum  not just "least" Real time evolution takes place in the brain. Entangled space  action at a distance. Strange coincidences. 2022.06.06 How would Jacob Robinson view the current politics of Israel? From quantum to classical is "spatial lift". From classical to quantum is "projection". John is looking for evolutionary intuition
Idea: Consider Feynman diagrams as their sizes grow. Renormalization techniques can cancel away infinite subsequences of diagrams (where level i may get cancelled by level i+1 and so on). There are diagrams that are "gold nuggets" that will remain and there are diagrams that are parts of subsequences that are just flows that get cancelled away, they are the underlying medium. But they can belong to multiple flows and so there can be ambiguities. And we may or may not be aware of which ones are "virtual" and will cancel away and which ones are "real" and will survive. 2022.05.23 Hierarchy of rationales for dynamical systems. Šachmatų ėjimų logika  tikslingas vertinimas. 2022.03.01 Riemman hypothesis
2022.02.08 John Least action.
Entropy from the point of view of chemistry as to whether a reaction will occur spontanteously
2022.01.31 John: What's a really good example of how a Lie group plays out in physics? Andrius: Look at SU(2) and then SU(3). And look at gauge theory. 2022.01.10 Next week will focus on tensors (Selcuk Bayin's book) and the theory of relativity (Einstein's book). John alerted me to Shor's algorithm, a quantum computing algorithm for integer factorization. The purely unitary (reversible) part of the computation is followed by the irreversible final steps where you read the qbits and destroy the information. See the revised version of Shor's original article. John also suggested that I think about how the Higgs boson relates to my global quantum. 2021.12.13 John is interested, in Griffiths:
RiemannZeta conjecture and the distribution of primes. The prime number theorem. 2021.12.10 Fear and control in physics. "New ideas are scary". Subsystem thinking as a form of control. 2021.11.22 Interaction between the future and the past. Modification of dynamical system.
Reading about relativity:
Future  as a mechanical clock  is a flawed idea. Isolated systems (like Jupiter) seem to have mechanical time. Not all initial states are accessible to us. High codimension. How does a bunch become two bunches? A learnable universe. Andrius: Experiment as a contract between universe and a scientist. Universe as a responsive media. Physics is about small models. Matter is made of molecules. Andrius: What is mathematics? John: Mathematics is a modeling language for nature. A gift. (Andrius: "Gift" suggests a religious feeling.) Goedel: mathematical truth not reachable by logical steps. Undecidable. Shaky foundations  Axiom of Choice. Math  questions are easily asked, and sometimes answered (that can be hard). Math is successful. Andrius: Math is contentfree, qualityfree. In that sense math is about quantity, thus about measurement. Remove all things and you are left with God. Andrius: Academic caste system: Math  theologians. Physics  priests, scribes. Chemistry  wizards. Biology  saints. Philosophy  personalities offering private languages. Community, tyranny, egocompetition. Summerhill school Education. Equity movement. Lowering standards? What math is relevant? 2021.10.25 In physics, we're setting up with too many degrees of freedom, as if we had God's point of view. John's intuition is that we should be circumscribing the space of possibilities in an empirical setting as a low dimensional manifold within the total space of possibilities. I think of that as relating the imaginable and the unimaginable. There are two kinds of spontaneous change
Here spontaneous change may take place over time. Laws of physics may arise as spontaneous change from the point of view of statistical mechanics. I think of physical laws as being symmetric in time and acting instantaneously, whereas I think of statistical change as taking place over time, not instantaneously, but mediated. I think of statistical mechanics as introducing the ambiguity of the equality of the many. That is the only difference. So the directionality of time should come from that ambiguity. 2021.10.11 Interested in: agency machine, quantum coin tosses. There is something wrong with mechanical time and with space. He has two notions of time: narrative (cumulative) and mechanical. In his study of classical and quantum mechanics, in one the time is twice the other, and in one we are measuring phase whereas in the other we are measuring group velocity. 1) His formulation of quantum mechanics (and classical mechanics?) has a particle be defined everywhere. 2) Every piece of order had to have an evolutionary process determine it. He is looking for the larger context. My question: What is local? I think of particles as local contradictions. I told him about the weak force as a background for mutation, and the notion of introns and sex as allowing for multistep evolution. 2021.09.06 Dynamical system  upper triangular matrix. Natural breaking down of subsystems. Only cyclic groups have these representations. Solvable groups  block upper triangular matrices. Which group element's responsible. Learning is knowing the basis. (Order out of chaos!) Natural subsystems breaks down. Quantum affects classical but not the other way around. Onedirectional causation. Observations  measurement ensemble. Integrate against an infinite family of linear functionals to get results of experiment. Like a bump function. This yields position without momentum, reproducing quantum, and then position with momentum, yielding classical. Andrius: It also should yield the Pearson family of distributions. Duality. Don't look directly at wave functions. Look at (observer's global) average/integral against linear functional ensemble (local subsystem)  this involves two coordinate systems. 2021.08.15 Questions for John
2021.08.07 My take: John believes in human intuition about physics. So why not study human intuition? And understand what exactly it is. And accordingly develop hypothesis and design experiment. Help understand the mystery of delayed choice. Delayed choice experiments. Quantum state is nonlocal in space. Quantum particles are nonlocal. Then there is something more than spacetime. Spacetime give confinement. That causes problems. Deeper issue: Second law of thermodynamics. Nonreversible. Free will in the context of physics. Is there a way of parametrizing what we can or can't do? Dynamical systems can be chaotic but seem to be computable. Describe the arrow of time. Define some sort of expression of free will. What states are accessible by means of free will and what states are not. Perhaps not Goedelian. Undecidable forces microscopic ... ? Human physics intuition. Free will machine. Coin flip... Suppose you can communicate with the past. Can have global hidden variables. Can't send a signal faster. What if you could send a signal faster than the speed of light. Consistent histories by Robert Griffiths. Unitary evolution is always consistent. What if our histories were modified. Extradynamical. Dynamical is current state plus the laws of physics. Alternate. Free space. Continuum of states between local and global. They obey the same laws of physics. Agency machine. Suppose you can send information back in time. Based on delayed choice experiments. Given a quantum coin. If you check and get a T then push a button and thus go back in time and interfere with the experiment. So should end up with 20 H in a row, etc. Piggyback on a well known experiment. Modified Turing machine. Inverse of information looks pseudorandom. Andrius: Measurement has observer carve up space so that possibly nothing happens. Thus there must be an outer system. Subsystem is an internal view. Undoing of possibilities. Hierarchy of systems. Hierarchy of wave function collapse. From before
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From conversation with John on 2021.05.31
Why is that rare today? What would it mean over a long true scale? Microscopic scale  maximum entriopy. Churning of microscopic scale. Edited away. Could artificially create it. Every point on a tragedy is equivalent in a unitary environment. Measurement is a set of linear functionals. Scattering theory is real. Solve for free space. How stable the Dirac potential is to perturbation? Bound Dirac states. Hydrogen atom. The book "Advanced Quantum Mechanics" by Sakurai discusses the Dirac equation. Unitary representation in quantum and classical. Quantum {$e^{iht}$} from Hamiltonian. Hamiltonian flow. Classical analogue: Von Neuman  Koopman equation. Ergodic theory. Unitary flow. What is the relationship between the unitary flows in free space  simple V=0 and in nonfree space V is not 0 ? And relate them to first order in time. Hermite polynomial  creation and annihilation operator. Rodrigues. Quantum is just a representation. Position and momentum commute  classical, do not commute  quantum. Why do we only see the mathematical possible in quantum and classical? Classical is extension of group representation for quantum. Quantum is compression of group representation for classical. Why don't we observe macroscopic superpositions? Our mathematical models are too broad. If dynamical system has upper triangular representation, you can consider dynamics of smaller subspace. Everything lower the main diagonal: when you take powers upper part is affected by lower part but not vice versa. Causality. We can live in a small niche and not worry about effects from wider sources. Logic in quantum mechanics. Evolutionary pressure for that representation to be expressed in the actual physical world  everything else got selected away (involution  "salt is good"). What would be that evolutionary pressure? When events travel faster than the speed of light you can edit your past  your history disappears. Explain: delayed choice experiments. Wipe out nonconsistent time lines. Andrius How does a term in x map out on the mother function? Automata halts. Differentiation returns 0 which is read externally by the observer. Two pyramids in sync  removing x and differentiation  they commute. Time is local. There must be a periodic behavior that is within a certain radius as given by the speed of light. Can there be a clock without oscillatory behavior? Is a living cell a clock?
