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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 one-to-one 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

• Doesn't have to be superliminal.
• A larger symmetry being imposed where we only seeing a part of the picture.

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

• What are the arrival times of random numbers?
• What are the arrival times of prime numbers?
• Are there huge numbers of sequences that would satisfy such conditions? How to reduce the number?

2022.02.08

John

Least action.

• The Lagrangian f is the action functional.
• Gradient of the action functional f is the operator expressed in the Euler differential equation. Setting the gradient equal to zero.

Entropy from the point of view of chemistry as to whether a reaction will occur spontanteously

• History of Enthalpy.
• What are you fixing (such as pressure) and what are you letting vary (like to volume of a balloon of gas).
• Look at heat and work.
• Gibbs free energy.

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 q-bits 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:

• Integral formulation of Schroedinger equation.
• Perturbation theory for scattering, etc.

Riemann-Zeta 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.

• Explain second law of thermodynamics.
• Explain the duality of waves and particles in quantum mechanics.

Reading about relativity:

• Brian Cox. Jeff Forshaw. Why Does E=mc2? And Why Should We Care? Momentum 4-vector in relativity. Only conserved momentum vector has length {$mc^2$} with extent in space and in time ({$E$}). Where the Taylor expansion is {$mc^2$}. Even when {$v=0$}.
• Einstein. Collected papers. Einstein's original derivation of {$E=mc^2$} in 1906. Hot object radiates according to black body radiation - if moving - Doppler effect - radiates more in the forward direction. Net momentum loss in the forward direction. So object must be losing momentum in that reference frame. But can't be slowing down because of its inertial reference. Inertial mass must be decreasing {$\frac{E}{c^2}$}. Universe treats energy and mass the same.

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 co-dimension. 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 content-free, quality-free. 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, ego-competition.

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

• Universal physical laws
• Statistical mechanics (and the second law)

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.

• Lionel Barnett, Adam B Barrett, Anil K. Seth. Granger causality and transfer entropy are equivalent for Gaussian variables.

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.

One-directional 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

• Research question: How to think of agency in terms of an "applied force" or an "intervening force"? What is involved? And how does that depend on slack?
• Research question: How to think of subsystems existing? In what sense are they physical or not?
• As regards transience or intransience, what difference would it make if we were just part of a simulation? And what is the difference if we are part of a simulation or if we are a product of evolution?
• As regards his arguments regarding time, wouldn't the result be that the states in the universe converge upon their critical point - which is why we are here and now - isn't it remarkable that we are living in a critical point for our entire galaxy and perhaps the universe?
• As regards his arguments regarding time, wouldn't they apply first of all to the universe as a whole - especially if the universe is an experiment - and wouldn't they imply that the universe is, by elimination, an experiment - aren't randomness and experimental deliberateness the opposite sides of information?
• Tell John about the orthogonal polynomial - coordinate system idea - that you go out to a coordinate system (with your steps) and return (with their steps).
• How does the combinatorics of orthogonal polynomials relate to loop quantum gravity and spin networks?

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 space-time.

Space-time 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

• Orthogonal projection.
• Linear and quadratic potentials are the same for classical and for quantum, for describing the "cloud".
• Nonunitary evolution can relate the Schroedinger and Louisville points of view.
• Bleeding of quantum amplitude into other modes, different quantum statistics.
• Relaxation.
• Morphism: top idea where he sees beauty. One structure relating to another structure: Galois theory.
• Importance of groups: ergodic theory, unitary, configuration space.
• Take a look at: SU(2) covering group of SO(3). As an example to think about regarding duality in imaginary root.
• What if there was only one root of -1? What would that mean if the complex functions were symmetric? What does it mean if we use notation that respects the duality of unmarked opposites or that marks one opposite with regard to the other?

Mano klausimai John:

• What is basic in math?
• What math is key to study?
• How to organize the map of mathematics?
• What is geometry?
• How he thinks about: Lie algebras, groups, tensors, classical groups, Bott periodicity, Clifford algebras
• Duality
• What makes math beautiful?

Aptarėme

• Triviality, tensors, complexes and reals
• John Baez work
• John: Unitary dynamics - self-adjoint operator {$H*=H$}. Unitary operator.

Thomas for John

• Does a physicist do something new? that nature does not already do?
• The Large Hadron Collider generates energies that are smaller than what some incoming cosmic particles produce in collisions. Ultra high energy cosmic rays {$>5×10^{19} \textrm{eV}=8 \textrm{joules}$}, roughly the kinetic energy of a 0,5 kg object moving at 20 km/h.

From conversation with John on 2021.05.31

• I think of the {$xu(t)$} as standing for a Lie algebra and {$\textrm{ln}A(t)$} is a pseudo Lie algebra.
• {$\alpha$} and {$\overline{\alpha}$} express entanglement. They model scattering. Thus scattering is entanglement. The entanglement is evident in that {$\alpha=0$} forces {$\overline{\alpha}=0$}.
• Perturbation describes everything that comes from measurement. It stimulates a transition. And yields a model how two things come together.
• Orthogonality is quadratic in nature so it makes sense if the measures arise from the complex plane and thus the Laplace transform.
• {$e^{-x2}$} is an example of a weight that is more natural in the complex plane than on the real line.
• How to get a coordinate system? Measurements leverage a reference frame and yield a reference frame. So the types of orthogonal polynomials express the types of coordinate systems for measurements. A measurement is in one causality (every effect has had a cause) and at the decision point expresses the other causality (not every cause has had its effect).
• John is pursuing the application of Koopman Von Neumann equations to quantum mechanics. Trying to understand how the classical picture of a flow of point particles can be retained in making sense of quantum mechanics and not relying on the collapse of the wave function. He was able to show how it would look in empty space but there is simply a time dilation by a factor of 2.
• John's and my approaches are practically in opposite directions but it is helpful to work alongside each other.
• Klesch-Gordon coefficients become natural as finite dimensional representations of SO(3).
• Decomposing a direct product in terms of a direct sum of finite dimensional.
• Spherical harmonics relate {$e^{in\phi}$} and {$e^{in\theta}$}.
• Thomas's question for John: What does it mean - empty space or nonempty space?
• Agency machine is what establishes or computes a center for a subsystem. A center indicates an observer and allows for the creation of a new vertex.
• Subsystem has its own center - that is what makes it a subsystem.
• Randomness is a symmetry - John's editor may be enforcing the symmetry - just as gluons enforce symmetry.
• What tames violent quantum fluctuations of the vacuum? John's question: What tames deviation from randomness - what is the editor for randomness? How does that relate to going back and forth in time?

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 non-free 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?

• For John: the belt trick may be related to the holographic principle whereby the angle for the circumference {$2\pi r$} is related to the the angle for the area {$\pi r^2$} by a factor of 2. Classical may measure area and quantum may measure angle, or vice versa.
• For John: How could we get negative energy? Consider how to get imaginary square roots. For example, if a speed is greater than the speed of light, then the relationship between time and position is multiplied by an imaginary number.
• https://iopscience.iop.org/article/10.1088/1361-6382/acad60 "Relativity of superluminal observers in 1 + 3 spacetime"
• https://www.sciencealert.com/study-shows-how-the-universe-would-look-if-you-broke-the-speed-of-light-and-its-weird "Study Shows How The Universe Would Look if You Broke The Speed of Light, And It's Weird"
• Conservation of momentum may be why momentum space is more natural than position space. We can relate that possibility to Noether's theorem. Conservation of momentum is apparently why topological invariants are discussed with regard to momentum space. Material defects are a matter of position space.
• The original spectral theorem: Look for subrepresentations such that S is a one-dimensional matrix eigenvalue. Induction argument.
• Classical (both x, p) and quantum (x).
• Evolution is indicated by learnability and also by sparse communication and natural differences between hierarchies, different orders of magnitude, allowing for a natural hierarchy of niches. Not only the laws of physics are sparse but also the states in nature are sparse.