Physics discovery, Chemistry, John Harland, Schroedinger equation

**Collect and develop ideas about physics.**

- Collect and organize the ways of figuring things out in physics.
- Can the bending of light be considered a Δx and Δt?
- At or near the horizon of a black hole, does the matter, light (and information) that falls in simply wrap itself around as in the case of a liquid with great viscosity, so that it could be rewound and reconstituted? Is the black hole just a great layering of information?
- Are black holes simply eddies of matter that get layered in space time? And what is the reverse process? Is it experienced from the inside as a Big Bang?
- Does Heisenberg's uncertainty principle allow for momentary forces? appearing out of nowhere?
- Energy = Work = Force x distance. What does it mean to apply a force? How can that make sense in a deterministic universe? What is the role of slack?
- Is there a sense in which rotational energy unites (complex) angular momentum and (real) velocity as with polar decomposition?
- How do coincidences in phase state happen?
- Understand the difference between grace and justice in entropy.
- How do things arise in nature?
- Define measurement.
- What is the simplest example of measurement in nature?
- There is conservation of energy but potential energy is infinite. So we're dealing with sums of infinity. Is this related to renormalization?
- In what sense do fermions need to be measured so that they occupy different locations in phase-space? And in what sense do bosons get measured?
- How is phase space (and space-time) related to the principle of least action?
- Is a light wave like a complex variable, an infinite corkscrew?
- Challenge: Why does the Yang-Mills theory work?
- In what sense do or can higher frequency waves carry more information? Can a wave store information related to its future decomposotion into a cascade of particles? What is the role of amplitude and what does it mean as a collection of photons?

Exercises

- Apskaičiuoti įvairių jėgų visuminius poveikius visatoje.
- Visatos rimties masė yra...
- Kaip apskaičiuoti dviejų fotonų trauką vienas kitai? Fotonus galime sulyginti su atitinkamos masės dalelytėmis. Masė gali būti labai didelė.
- Jeigu du fotonai pasigamina ir keliauja skirtingomis kryptimis, kaip reiškiasi jų trauka vienas kitai? Ir kaip gali iš viso išlėkti? Juk pradžioje juos siejanti jėga neriboto didumo?
- Why are there neutrinos of different generations - for establishing entanglement? triggering collapse of wave function?

Study math: Tensor

Ways of figuring things out

- Each way of figuring things out is a double-edged sword. It can be applied in both directions, to test an experimental object or to test the entire system. In this way it may relate to Hopf algebras as bialgebras, uniting algebras and coalgebras. In my philosophical ways of figuring things out, there were likewise two versions of each of the 24 ways, depending on how they were applied.

Systems: Classical and Quantum

System

- Momentum can be attributed to an individual particle (as its change) but it can also be attributed to the entire system (as its change). And also, changing the momentum of a particular particle can change when (and whether) we will come to a particular state of the system. In particular, the particles are interconnected and so that makes for a complicated relation between the time evolution of each particle (in terms of its position) and the time evolution of the system. This can be compared to a computer program which may change the order of its instructions.

Cause.

- Sun and earth are entangled from the beginning. Gravity is not a "cause" - there is no causal gap. "Cause" supposes a subsystem and entropy, a causal gap.

The Universe

- Visatoje pirmiausia kūrėsi bosonai (sąveikos sandai), o iš jų susikūrė fermionai (dalelytės) - tai būsimos visatos. Būsimos visatos plečiasi juodų skylių pagrindu.
- Dalelytė, tai baigtinė potencinė energija (rimties masė = rimties energija). Dalelytei taip pat galima priskirti neribotą dydį energijos. O jėgos laukas, tai nebaigtinė potencinės energijos galimybė.
- Jei mes pasitraukiame (savo protu) iš pasaulio, lieka fizika, "pasaulis".
- Dievas pradeda nuo nieko, o mes atsirandame jau duotame pasaulyje.
- Dievas išeina už savęs. Jisai yra tyrinėtojas. Jo tyrimas tampa vis tikslesnis. Tad didėja erdvė (gaubianti viską) ir tuo pačiu smulkėja. Tokiu būdu viskas tampa vis tikslesniu. Dievas išeina už savęs į save, tiek už visko (be santvarkos), tiek dalelytėse (santvarkoje). Jis yra dvasiniame pasaulyje. Mes esame žemiškame pasaulyje, tuščioje erdvėje, tarpe tarp jo dalelytėse ir danguje. Mūsų pasaulis yra nuotrupos Dievo išėjimo už savęs, tai jo rūbas. Mūsų pasaulis yra baigtinis, tačiau didėjantis. Jo pasaulis yra ribinis.
- Perhaps dark matter is made up of anti-matter and perhaps anti-matter relates to an anti-light that is related to light in the way that complex numbers are related by quaternions.

Open and closed system

- Three-cycle is a closed system. X-Y-H is an open system.

- Think in terms of "common" and "uncommon" states. Uncommon states tend to common states simply because they are more frequent. But nature has forces (like gravity) that tend to create uncommon states. So we need to distinguish between the different forces at play and how they relate to what is common and uncommon.
- Tyrimai reikalauja trijų rūšių entropijos. Tyrinėtojas sustato tyrimą. Paskui tyrinėtojas aptveria tyrimą - jisai išlieka objektyvus, jisai pasitraukia, kaip kad Dievas. Toliau tyrinėtojas stebi išdavas.
- Tyrimo išdavos turi galioti paskirame tyrime; bet kokiame tolygiame tyrime; ir taip pat nesant jokio tyrimo.
- Tyrinėtojas būtinai įsiterpia į savo tyrimą, paskui pasitraukia. Tad yra įmanoma ir tikėtina, jog ateis laikas kai visos eigos apsivers ir reiškiniai išeis už tyrimo ribų, paveiks tyrinėtojai ir jį aplenks.
- Entropija susijusi su laikinu tyrinėtojo apsiribojimu (nešališkumas) ir vėlesniu (bei ankstyvesniu) jo įtraukimu.

Symmetry breaking

- Collect examples of symmetry breaking.
- Relate symmetry breaking to the naming of the two roots of i.

Classical and Quantum

- Classical mechanics states are based on sets and c-bits (coins). Quantum mechanic states are based on vector spaces (thus ordered lists) and qubits.
- N.Mukunda: {$QM=e^{iCM}$} relation between quantum mechanics and classical mechanics. But how is this exponential related to the other exponential relating Lie groups and Lie algebras?

Heisenberg's uncertainty principle

- Heisenberg's uncertainty principle deals with units of angular momentum, ΔxΔp, ΔEΔt. Special relativity deals with units of velocity: x/t, E/p. This suggest a polar decomposition into (complex) angular momentum and (real) velocity. Note that special relativity deals with straight lines or geodesics, whereas quantum mechanics deals with rotating a detector. Thus the observed moves straight but the observer moves around.
- ΔxΔp is a box of slack described by symplectic geometry.
- Heisenberg's uncertainty principle describes the slack in a vacuum - is this related to the slack in gravitational waves? which is the relocation of slack in space-time? How much slack there is in the vacuum depends on time, so also space (and Planck's constant)?
- Heisenberg's uncertainty principle deals with measurement discrepancies, whereas relativity deals with measured values.
- Einstein relates absolute measurements of X and T, or E and P. Heisenberg relates discrepancies of ΔX and ΔP, ΔT and ΔE. Interesting coupling.
- Quantum world can't have gravity - gravity (and mass?) only exist upon collapse of the wave function.

Planck's constant

- Vasil Penchev iš Bulgarijos - Planck's constant yra atomic unit for connecting rotation between real and imaginary axes (perhaps as in my chains for Lie algebra root systems).
- Susskind: Turning the detector upside down shifts the answer from up to down. So this expresses a global symmetry. Qubit has a sense of directionality. Orientation is being distinguished. Some qubits have a sense of spatial orientation.

Possibilities

- Gamtoje yra galimybės. Iš jų atsirenka viena galimybė tiktai esant matavimui. Žmoniškasis mąstymas tai yra toksai atsirinkimas. O dieviškasis mąstymas vyksta atvirkščiai. Kaip atsiranda matavimas gamtoje? Matavimas reikalauja nepriklausomo taško.

Particles

- The infinite possibilities that emanate with Feynmann diagrams are like an independent thinker's myriad relationships with themselves including through others, as in the science of prayer.
- The Standard Model has three families which differ in mass, thus in the time that they may participate in a violation of conservation of energy. The three families may function as three levels of parsers, (as in the algebra of copyright), thus three levels of language.

Anti-particles

- Perhaps the expanding universe differentiated, segregate itself into regions of positive matter and negative matter. Pehaps dark matter and dark energy are from portions of the universe that consists of negative matter.

Light

- A photon is a complex variable that is twirling circular left or right, thus has spin up or down (clockwise or counterclockwise), which is its polarization.
- The energy of the photon is given by how fast it is turning, its angular velocity. The faster it turns, the higher its frequency, the shorter its wavelength. The critical point is when it is not turning at all, so that it has zero energy. This shows the duality of light, the disconnected nature of its spin clockwise or counterclockwise.

Time

- A moving point is a line, a moving line is a plane, a moving plane is a volume... Time is the addition of a scalar (from a field), thus the addition of choice. Time relates affine and projective space. Compare time with space. A moving "center" is a point: the center is what moves, thus what has time.
- Moving backwards and forwards in time - is a (wasteful) duality. Why is it dual?

Space-time

- The four dimensions of space-time relate to the four choice-frameworks. And perhaps time is the internal choice. And consider six pairs among the four.

Gravity

- In time, fermions (particles with mass) grow more specified in terms of their location with respect to each other. This equals a shrinking of space. And perhaps this shrinking of space is balanced by the expansion of the universe (and what does that expansion mean?)
- Visatos traukos - kad ir labai, labai silpnos - kadangi visata turi centrą - turėtų užtekti sukurti lauko nelygybę, nesimetriškumą - ir tokiu būdu įtakoti kvantinius reiškinius. Tai gali būti traukos paskirtis.

Relativity

- In the twin paradox, how do we know which twin was accelerated? What expresses force?

Reversibility of time

- Symmetric space Isometry in the reversing the direction of geodesics (reversing the path of time) is equivalent to the vanishing of the covariant derivative of the curvature tensor (so that the space is flat). Whether or not time is reversible is thus related to the flatness of the manifold.
- The reversibility of time relates to the symmetry of choices in coordinate systems (Dn). The nonreversibility of time relates to the asymmetry of choices in simplexes (An).

Field

- A field is relationship between all of space and all of time.

Least action

- Path of least action (the basis for physics, namely, for Feynman diagrams) is violated by measurements, where we can wait and nothing happens.
- Is many-worlds theory the flip-side of least-action ?

Energy

- Energy is the amount of freedom available to do something independently different. The freedom comes from the slack in Heisenberg's uncertainty principle ΔEΔt. That principle manifests in the arisal of independent entities, independent subsystems, for example, the appearance of a pair of a particle and anti-particle.

Perspectives - dimensions

- Požiūris išreiškiamas lauku (field). Nes tai leidžia keisti proporciją, santykį, didinti ir mažinti. Nes galima išversti, galima didinti ir mažinti, taip pat didėjimas ir mažėjimas vyksta dvejopai - dauginant ir sudedant. O skirtingus požiūrius derina vektorių laukas.
- Koordinatės: Bazę parinkus vektorių ir matricas galim išrašyti atvaizdu, reprezentacija. Be bazės negalime juos suvokti konkrečiai, tik abstrakčiai. Tačiau tada jie nėra sukonkretinti, jie laisvai mąstomi.
- Specialajame reliatyvume priskiriame dalelytei (ar kūnui) koordinačių sistemos centrą. Tačiau tai negalime padaryti kvantų fizikoje kadangi yra pozicijos ir judesio kiekio paklaidos. Tada tenka naudoti kitą (tyrimo) koordinačių sistemą kuri laikoma iš esmės pastovi.
- Fotonos ar kita dalelytė keliaujanti šviesos greičiu neturi jokio požiūrio - nėra kaip priimti jos požiūrį - ji nebendrauja su aplinka - tiktai kelionės pradžioje ir pabaigoje. Jeigu jinai atsimuša į kažką tai nauja išsispinduliuoja, tai naujas fotonas.
- Įsijautimas - galime įsijausti tik į tai kas gali tarnauti koordinačių sistemos centru.
- Step out, atsitokėjimas - tai yra išorinė koordinačių sistema kuria matuojame kitus reiškinius, jie gali būti netikslūs, kvantiniai, išteplioti.

Measurement

- Measurement is the notion of definition but rooted in the perspective of the participant of the system who is trying to reconstruct the definition, redicscover it. Rediscovery is the ways of figuring things out. Definition is established in the equation of life, God's dance. Measurement is the basis of geometry, which is central in math. Measurement is the determination of the relation of one to one's circumstances, one's self.
- When we measure spin - we impose the spin axis we are expecting - but that is an imposition of expectations related to the "waiting" that I am modeling. Also, how is that waiting related to emotional life and expectations? Comparing measurements yields "information" and it may be information which is limited by the speed of time.
- Measurement (crucial in physics) can be defined in terms of covectors, as being dual to vectors. Covectors can be thought to point in the same direction as vectors - they are complements of each other with regard to the inner product. This duality is thus fundamental to the concept of measurement.
- The vector and the covector divide a scalar field into its local variation (given by the vector) and its global scaling (given by the covector) which together give the value of the scalar. Thus vector and covector define the duality of local and global extremes which come together as the scalar field.
- Idea: You can measure something super exactly but then you don't know what you've measured. And that may be why all electrons are the same electron, indistinguishable.

Coordinates

- Entanglement - particle and anti-particle are in the same place and time - and they have the same clock and coordinates
- John Baez about observables (see Nr.15) and the paper A topos for algebraic quantum theory about C* algebras within a topos and outside of it.

Discreteness and continuity

- Quantum mechanics: energy is not continuous but discrete. Noncontinuity suggests jolts - what is needed for causality. Particle and wave descriptions are necessary to relate continuity and discreteness for causality.
- The Schroedinger equation has continuity. Discreteness enters in with the act of measurement, with the collapse of the wave function, with the breaking of symmetry between observer and observed.

Deviations

- If calculus (and analysis) is based on the ability to have minor deviations, then the ability to have such deviations is fundamental. And the insistence on that ability, the preservation of that freedom, is the basis for all quantum effects.

Slack

- Quaternions introduce and support increasing slack (implicit slack (complex numbers) between two explicit slacks (complex numbers) as organized by the foursome). Real numbers express decreasing slack. Complex numbers do not express slack but rather maintain the duality of increasing and decreasing slack.

Notes

Levy signal

Brownian motion in time -

Zeno's effect and anti-Zeno's effect

(small deviations) Ito-Stratanovich (big deviations)

Systems biology. Ralph Philips. Physical biology of the cell.

Cell boundaries make for an isolated system.

Rydberg atoms

Shannon networks

x's are what is, and t is what we can borrow (energy) from, in the metric: {$\sum {x_i}^2 - t^2$}

- Ženklų savybės: pirmos trys yra fermionų, kitos trys yra bosonų.
- Palyginti trinarį gyvenimą su kvarkų trejybe (trys kvarkai neišardomai susieti).

**Readings**

- Thomas Gajdosik course notes
- The Road to Reality
- Quantum Electrodynamics.
- Standard model (mathematical formulation)
- Quantum field theory
*How is Quantum Field Theory Possible?*- The Algebra of Grand Unified Theories Baez, Huerta
- The Meaning of Einstein's Equation Baez, Bunn.

Books

- Energy, the Subtle Concept: The discovery of Feynman's blocks from Leibniz to Einstein Jennifer Cooper-Smith

**People**

- Audrius Alkauskas, Electronic Structure Theory Laboratory, Savanorių ave. 231, LT-02300 Vilnius
- Vidas Regelskis (archiv), Vidas Regelskis (Surrey)

Notes

- Electrons are particles when we look at them and waves when we don't.
- Quantum mechanics superposition of states may be based on borrowing of energy. When the energy debt is too high, as when it gets entangled with an observer, then the debt has to be paid. Otherwise, the debt can be restructured in complicated ways.
- Lagrangian L=T-V expresses slack (or anti-slack), makes the conversion between potential and kinetic energy as smooth as possible. Hamiltonian H=T+V expresses the totality, the love. In this sense, they are dual, as per the sevensome - the Lagrangian expresses the internal slack, and the Hamiltonian expresses the wholeness of the external frame.
- Potential energy is bounded from below.
- Kinetic energy is always positive, absolutely. Its relation to momentum is absolute, unconditional. Whereas potential is defined relatively and its relation to position is variable.
- The wave equation is defined on phase space but in such a way that it is understood in terms of a superposition of waves for position, yielding a "blob" - a wave packet, and an analogous superposition of waves for momentum, and the two are related by the Fourier transform, by the Heisenberg uncertainty principle.
- Physics abstracts from the personality of other researchers. Have a common ground, communicate not on any consensus, but based on what we find, as independent witnesses.
- From dream: Space is made up of all possible curves. Physics is about the geodesics, the curves with no slack. They really are all one curve that goes through every curve and every single point.
- Understanding of effect. Physics, why does it work? How can I describe it efficiently and correctly?
- How many parameters do I need to describe the system? (Like an object.) Minimize constraints. It becomes complicated. Multipole is abstracting the levels of relevance. Ordering them inside the dimensions I am working with. What is the important quantity? Measures quality. How transformation leaves the object invariant. Distinguish between continuous parameters that we measure against and these quantity that we want to study. We use dimensions as a language to relate the inner structure and the outer framework. To measure momentum we need to measure two different quantities.
- Weak nuclear force changes quark types. Strong nuclear force changes quark positions. Electromagnetic force distinguishes between quark properties - charge.
- Exchange particles - gauge bosons.
- Wave function Smolin says is ensemble, I say bosonic sharing of space and time
- What is the relationship between spin (and alignment to a particular axis or coordinate system) and the alignment of magnets?
- Which state is which amongst "one" and "another" is maintained until it is unnecessary - this is quantum entanglement.
- Massless particles acquire mass through symmetry breaking:

- Geometric unity I tend to agree with Roger Penrose that spin has been one of the great mysteries in quantum mechanics. As best as I can recall, he said it was one of two primary mysteries in a talk at NYU back in the late 1990’s. ... understand spin and I think we'll understand entanglement a lot better.
- The various expansions of the universe may be caused by shifts in perspective as with the Yoneda lemma or the binomial theorem.

Parsiųstas iš http://www.ms.lt/sodas/Book/Physics

Puslapis paskutinį kartą pakeistas 2020 gegužės 02 d., 11:37