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Andrius Kulikauskas

  • m a t h 4 w i s d o m - g m a i l
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

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  • 读物 书 影片 维基百科

Introduction E9F5FC

Questions FFFFC0

Software

物理学

General concepts

  • 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?
  • How do things arise in nature?
  • Is there a sense in which rotational energy unites (complex) angular momentum and (real) velocity as with polar decomposition?
  • Understanding of effect. Physics, why does it work? How can I describe it efficiently and correctly?

Challenges

  • Derive theoretically, as a prediction, a number for the fine structure constant.
  • Maybe nature is not inanimate brute matter but a medium that is knowing of the past and future but with which the present is negotiable? Newton stated that "it is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact."
  • Is spin a measure of truth or consistency? An electron goes around itself once and gives the opposite spin - it negates itself - along a Moebius strip. Whereas a circle is consistent.
  • How to think of the vacuum?
  • In what sense is Faraday's pail a paradigmatic subsystem? In what sense is it the quantum harmonic oscillator? How to think of its minimal implementation and maximal implementation?
  • Change in energy gives change in momentum thus change in kinetic velocity or change in inertia (mass)(potential energy). What determines which?
  • In what sense is a planet to be thought of as a subsystem with a center of mass, etc.? Is there a sense in which it is a quantum, as regards to the supersystem?
  • In what sense do masses exert gravitational forces?

Study math: Tensor

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.
  • 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.

Readings

Books

Videos

Courses

People

Ideas

  • Susskind: Gravity and quantum mechanics are too close to one another to pull them apart and put them back together through quantization.
  • In childhood, I thought of time as slowing down before death so that you never actually die but you live forever. I recall this again when I think about the way that matter enters a black hole. From the outside it looks like we die, or it looks like matter disappears. But from the inside we just keep on living and the matter keeps on falling.
  • The speed of light establishes a boundary between things that are too far apart to affect each other, and likewise a black hole establishes a boundary.

Vacuum

  • For the vacuum, it is not that nothing is there. Way of figuring things out: Do nothing.

Physics

  • Faraday's pail subsystem's inside and outside express equal and opposite reactions, thus actions.
  • In physics, everything is action. Action gets divided into perspectives, as with angular momentum: p r = m v r.
  • Forces, such as gravitational forces, are ever present. Thus they do not exert them but they express the geometry of space-time. The notion of "exertion" arises from conceiving the bodies as entering a system.

Rethinking Physics

Locality does not apply within a system. Locality is relevant between systems. Within a system, as defined by its action, change of state can be spontaneous because it is a change of state of the whole system. A system is that which can be in a state.

Action (the path in between) is preserved, kept stable, despite small changes in the coordinates of the intial and end states. This is a principle of continuity.

Action (= energy X time = momentum X length) is the size of a system. It has the same units as angular momentum. Spin measures the action of a system with regard to itself. A particle coheres with itself and this coherence manifests as spin, as a recurring action whereby it equals itself.

A particle has no position and does not even exist until there is a basis. A basis establishes the location of the particle (at the origin) and also its orientation (in SU(2)). Changing bases involves calculating probabilities.

F = p/t = E/x = A/tx. Force is the impulse attributed to the system from outside of it, by which two systems cohere. Force is the relationship of one system upon another system. To get the force, we have to neutralize the growth of the action (in t or x) and then we have to show the relation across the system (from center to extreme - in the remaining variable).

Action is the coherence within a system. Force is the coherence between two systems - one upon another - thus there are equal and opposite forces. Conservation of momentum.

How does the Lagrangian U-V participate in my theory of action? How is that related to spooky action? Spooky implies a single entity, a spirit.

Notes

  • What does the dispersal of the wave packet mean spatially? Is that in one dimension or in three dimensions? It is the variance. How is the probability density affected?
  • In space time, event is a point. In quantum mechanics, have subspaces.
  • John Baez. Categorifying Fundamental Physics
  • Thinking about the expansion of the universe as a reduction of density, by which the mass of particles becomes ever less important, by which we have an increase of entropy (becoming less deliberate). And we can reverse this by starting with an increase in entropy and arriving at the expansion of the universe.
  • First Person Physics
  • Laws of physics are time-symmetric for particles traveling at the speed of light so time does not change
  • https://physics.stackexchange.com/questions/15082/how-did-feynman-derive-the-physics-of-medallion-vs-plate-wobble-rate
  • In physics, orthogonal polynomials relate what is necessary (top down) and actual (bottom up) as with string theory, questions and answers.
  • Wick's theorem - are operators of the same particles - propagator connects
  • Rules of physics plus configuration space plus location within that space.
  • Uncertainty principle - has to do with representations - representation adds a perspective - so that interferes with measuring certain things.
  • Measurement establishes a quantity with regard to boundaries - it establishes the zone within which it is - identifies with a step in the algebra - whereas analysis demarcates the boundaries.
  • Brody. Quantum Mechanics and Riemann Hypothesis.

Could momentum space be thought of as kinetic energy space? And position space as potential energy space? We have {$i\hbar\frac{\partial}{\partial t}\Psi(x,t)=[K(x,t)+V(x,t)]\Psi(x,t)$}

  • Kinetic energy is zero in your own frame.
  • Potential energy is zero in free space.
  • When kinetic and potential energy have similar form, then we have the Hermite case, quantum harmonic oscillator, where we have the reset (0,0)

Purcell. Electricity and Magnetism

Stephen Wolfram. Metamathematics Foundations & Physicalization

Multiplying by quaternion j reverses angular momentum for electron. Is spin a clock? Like a particle clock?

Hamiltonian is the sum of all the projections onto the energy eigenstates with the energies being the weights.

Action (one system - wave behavior) vs. force (two systems - particle behavior).

Shing-Tung Yau, Steve Nadis. The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions.

Energy can be defined as the "separation constant" in Schroedinger's equation. If we can separate the wave function into a time dependent function and a position dependent function, then we can segregate the two sides of the equation so that one side depends on time, the other side depends on position, and both sides are constant, and that constant is the energy.

Frequency is the internal, qualitative expression of energy and intensity is the external, quantitative expression of energy. Is this potential energy and kinetic energy?

"belt trick", aka the "Dirac scissors" or "Balinese candle dance

  • Two reflections give you a rotation. So is a reflection the square root of a rotation? And does that relate to spinors?

Dirac's plate trick Plate trick

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This page was last changed on November 15, 2024, at 01:09 AM