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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

Physics, Chemistry Discovery, Math Discovery

Collect ways of figuring thing out in physics

  • What is the role of economic questions in physics? For example, how research in solar cells becomes focused not on how to make them more effective physically but rather more inexpensive economically.

Sources

Ways of figuring things out

Independent phenomena

Survey examples for irregularities.

  • Consider double stars, whether their fluctuations in intensity are regular or ever appear scrambled. De Sitter double star experiment
  • Among the stars there are planets.
  • Cosmic rays are of different kinds.

Observe signals from batch of standard objects

Generate events and analyze the outcomes logically and statistically

  • Smash linearly polarized photons into nucleons and look for output particles that indicate hybrid or exotic mesons. GlueX

Math-physics duality

  • Theoretical physics
  • Doing calculations - each mathematical term has a physical meaning.
  • Math models closed subsystems. Closed subsystems (like gauge theories) express freedom.

Self-interference

Path splitting with discrepancy yields self-interference

Scale the detector

Proportions

Scale the detector

  • Make the detector very large, very pure, very sensitive, so that it consists of a multitude of independent detectors (chlorine atoms) specific to the problem (capturing neutrinos). Homestake experiment

Improved observation: select ideal circumstances

  • To measure the curvature of the earth, choose a long, straight trench filled with calm water. Bedford Level experiment
  • Use a high altitude balloon to measure cosmic rays above most of the atmosphere, before they are scattered. Cosmic Ray Energetics and Mass Experiment Or do the measurements at the International Space Station. (ISS-CREAM)

Compare With Doing Nothing

Given a path from point A to point A, compare its effect upon regularities (clocks, speeds, energies...) with that of doing nothing.

  • This is leaving a state and returning to it. But to leave a state, as regards motion, is necessarily to change the motion, thus to accelerate.
  • What does this mean in the propagation of a wave? It means that a wave has energy. Work is force times distance. Energy of a wave is force times wavelength? {$E=h\nu$} where {$\nu$} is frequency. {$c=\lambda\nu$} thus {$E=hc/\lambda$} This yields {$E/\lambda=hc/{\lambda}^2=F$}. Unit of {$h$} is energy times time, and unit of {$hc$} is energy times length.
  • Take maser clock on trip to outer space and back. Gravity Probe A
  • Take gyroscopes on trip to outer space and back. Measure the change in direction of spin to test the geodetic effect and the frame-dragging effect. Gravity Probe B
  • Newton's First law: In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force. (Situation when change in velocity is zero.)
  • Center is a reference frame that differs from itself by zero.
  • In relativistic problems, go to the rest frame of a particle.

Balance

Balance unknown force with known force

Increasing sensitivity by counterposition

  • A pulley with two similar counteracting masses reduces the acceleration and makes it easier to measure the change in position. Atwood machine

Cancel out extraneous effects

  • In measuring the speed of light, have it travel both backwards and forwards. Fizeau experiment

Compare travel in opposite paths

Work with deviation rather than total.

  • Olaus Roemer noticed a difference between predicted timings of Io's eclipses of Jupiter and those observed as Earth and Jupiter moved towards each other or away from each other. He used this to measure the speed of light. Rømer's determination of the speed of light
  • Netwon's Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.
  • Conservation of momentum.

Distinct forces

  • Newton's Second law: In an inertial frame of reference, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma.
  • Force is (change in velocity)X(resistance to change in velocity) (why times?)
  • Set of local forces. Force is the time derivative of momentum.
  • Kinematically complete experiment

Scaffolding

  • Astronomical ladder
  • List of orders of magnitude of changes in velocity.
  • Scaling.
  • Hierarchy problem

Tail end

Focus on the extreme of a distribution (the domain)

  • Long tail of distribution - source of slow neutrons.

Maximum/Minimum value

Detection along a spectrum to record maximums and minimums (of the range)

Probe (Lowest upper bound, greatest lower bound)

Count persistence of batch of standard objects

  • Count number of muons that penetrate atmosphere. Experimental testing of time dilation
  • Attract electrons (giving a particular energy) through mercury atoms. Franck–Hertz experiment
  • Bombard gold foil with alpha particles. Count what portion go straight through and what portion are scattered in various directions. Geiger–Marsden experiment aka Rutherford gold foil experiment.
  • Place detector 50 km from nuclear power plant, observe incoming neutrinos, whether they change in transit. Jiangmen Underground Neutrino Observatory
  • Probe as weakly as possible to disturb the system as little as possible. And probe by steadily increasing the signal strength.
  • Geiger counter sets up an electric potential near the limit where additional charge by a cosmic ray would pass it over the limit.

Synchronize

Synchronization of two clocks

  • The speed of light can be measured when the travel of a light beam away and back is synchronized with the opening of one gap and another. Fizeau–Foucault apparatus

Totally determine an isolated system

Place one system inside another system

  • Place electrostatic charge in a cavity within a conductor that is insulated from the surroundings. Faraday's ice pail experiment
  • Capture an (extraterrestrial) antideuteron in a silicon atom (in a high altitude balloon) and study the outputs (X-rays, subatomic particles) of deexcitation. General antiparticle spectrometer
  • Smash linearly polarized photons into nucleons and look for output particles that indicate hybrid or exotic mesons. GlueX
  • Trapped air, when compressed, transfers pressure. Heron's fountain

Shield a system from the background

Basis for defining entropy

Absurdity (Contradiction)

Absurdity: Difference between the familiar and unfamiliar

  • Tychonic system Tycho argued that if Copernicus's system were true, then a parallax of stars would have to be observed over six months. And if the stars were too far away for the parallax to be observed, then the stars would have to be so large that they would reach from the Sun to the Earth.
  • Schroedinger's cat being both dead and alive. Schroedinger presented this as an absurdity.

Compare theory and practice

Difference between apparent and actual. Comparison of theoretical and experimental.

  • Olaus Roemer noticed a difference between predicted timings of Io's eclipses of Jupiter and those observed as Earth and Jupiter moved towards each other or away from each other. He used this to measure the speed of light. Rømer's determination of the speed of light
  • Negation of the theory that the speed of light can add to the speed of the source. De Sitter double star experiment
  • Aberration is the apparent displacement of objects towards an observer's direction of motion. Aberration Aberration is historically significant because of its role in the development of the theories of light, electromagnetism and, ultimately, the theory of special relativity. It was first observed in the late 1600s by astronomers searching for stellar parallax in order to confirm the heliocentric model of the Solar System. However, it was not understood at the time to be a different phenomenon.[2] In 1727, James Bradley provided a classical explanation for it in terms of the finite speed of light relative to the motion of the Earth in its orbit around the Sun,[3][4] which he used to make one of the earliest measurements of the speed of light. However, Bradley's theory was incompatible with 19th century theories of light, and aberration became a major motivation for the aether drag theories of Augustin Fresnel (in 1818) and G. G. Stokes (in 1845), and for Hendrik Lorentz's aether theory of electromagnetism in 1892. The aberration of light, together with Lorentz's elaboration of Maxwell's electrodynamics, the moving magnet and conductor problem, the negative aether drift experiments, as well as the Fizeau experiment, led Albert Einstein to develop the theory of special relativity in 1905, which presents a general form of the equation for aberration in terms of such theory.
  • Parallax

Reverse engineer - vary inputs

Change in state shows dependence of subject on that state

Alter circumstances

Add inputs to a system and monitor the external reaction of the evolving system

  • Mixing additives to a hot beverage creates air bubbles, changes the speed of sound, raises the frequency when the cup is tapped Hot chocolate effect

Show independence of variation

Independence of variation - same conditions - simultaeneity - vary parameter

Sequential

Causal step: Register a change in state

  • A chlorine atom captures a neutrino to yield the radioactive isotope argon-37. Homestake experiment

Causal series

Global survey (map)

Make measurements in all directions

Substitution

Replace part of a system

  • Kite experiment An electrical circuit is adapted to include input from electrically charged storm clouds to show that it can charge a capacitor with electricity. By extension, imagining the system in the cloud, it can be inferred that lightning is electricity.

Shear

Discriminate forces or movements by nonlinearity along dimensions of coordinate systems

  • In Earth's frame, distinguish gravitational force (and mass) and Earth's rotational force around its axis (and inertial mass) Eötvös experiment

Independence of gravitational force and Earth's rotational force around its axis.

Divergence

Property based divergence

Squeeze transformation

Squeeze transformation of conserved unit (small component becomes big, big component becomes small)

  • Momentum and energy conserved - big mass with small velocity becomes small mass with big velocity Galilean cannon

Context: Nonexistence of signal

  • The nonexistence of a signal - the lack of evidence - can have a huge effect on a scientist and their society.
  • For example, the disappearance of a signal, the lack of an expected noise or image.
  • A persistent, negligible signal upon the subsystem (like starlight on the retina of a scientist) can ultimately be observed by the subsystem so that the subsystem ends up observing the supersystem.
  • Similarly, the scientist can consider the system they themselves are in, and the system beyond that.
  • False positives and false negatives from reliable, sophisticated testing equipment can have disproportionate effects or not.
  • we get what we model
  • The system models itself. Become increasinbly sensitive.
  • Unimportant signals become important.
  • The observer finds themselves in a system. Cosmology. Then the universe becomes a system.

Fizikos išsiaiškinimo būdas "red shift" reikalauja, iš vienos pusės, reiškinių pastovumo ir begalinio tikslumo, o iš kitos pusės, visų reiškinių (jų visumos) dėsningo iškreipimo. Tai primena "auto-associative" derinius smegenyse, kas svarbu išplečiant "domain". Tai bene astronomų kopėčių esmė.

Nonequivalence of coinciding properties confirmed or disconfirmed by small order discrepancy in known system

  • Possible nonequivalence of gravitational mass and inertial mass that could be observed in gravitational self-energy of the Earth and Moon with regard to the Sun. Nordtvedt effect

Improved observation: strengthen the signal

  • Telescope. Galileo: phases of Venus, Jupiter's four largest moons, sun spots.

Unsorted

Difficult and complicated

Instruments

Diffusion measurement

Keep complications from disrupting the simplicity.

  • In physics, probing establishes a sequence of least noticeable differences. Probing lets us approach critical cases (like the maximum and minimum) and explore what happens in gaps of our knowledge, especially at the edges of the gaps. Synchronization then allows us to establish certain boundaries. Those boundaries let us distinguish a subsytem. The levels of scale likewise are important, qualitatively, in distinguishing the subsystem.
  • Calculation - math-physics daulity - every term in an algebraic expression has a physically meaningful interpretation.
  • Combinatorics is the physics within mathematics, as with thinking about "units".
  • Lane's video. 47:30. (Topological insulators) Way of figuring things out: Think up and try to make happen, as with the exotic topological insulators. This is unusual for physics as usually it is the other way around, you notice something unexpected and generate a theory for it.
  • In the house of knowledge for physics, it is a formal science but perhaps once removed, so that there are about 24 (or 21? or 19?) parameters that need to be set empirically.
  • Periodic behavior collapses itself, resets itself. It is self-entangled.
  • Periodic behavior comes from synchronization, also self-synchronization.
  • 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.
  • 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.
  • The algebra wing of the house of knowledge for physics is about the qualititative aspects of measurement, especially what we consider physically intuitive. Thus the levels of scale are physically intuitive in that they are additive, that one affect can be much more relevant than another, and they are simply added.
  • Math studies closed systems. Measurement takes place within a closed subsystem. Thus measurement occurs within time - the system must be opened before the measurement and after the measurement.
  • In a closed system time is symmetric.
  • An observer is in the supersystem and so time is asymmetric.
  • The supersystem causes the subsystem.
  • Quantization comes from establishment of subsystem?
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This page was last changed on January 31, 2024, at 07:34 PM