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How to Learn and Understand Limitations of General Scientific Theories and Quantum Theory
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Study how science innovations grow in stages, and so that's how quantum theory of material and light were described beginning in approximately 1899:that was then formulated at the beginning of the 20th century as a result of experiments that were done in various areas of classical physics in which the classical laws of mechanics described by Issac Newton were not able to explain by the previously appropriate mathematical equations of physics/physical science.

Read examples including the failure of Newton's Laws to mathematically measure or deal with the phenomenon ofblack body radiation(that failing motivated looking for new theories), since black bodies do not emit or reflect light.The existence of black holes in the universe is a theory now supported both theoretically and by observations of distant, astronomical phenomena that seem to indicate that a black hole may "swallow" stars, planetary systems and grow until it may collapse a galaxy, disappearing into the hole. Mathematics may model (describe/show) how to theoretically calculate physical properties of remote/distant stellar bodies (of or pertaining to the stars, or consisting of stars)in the universe such as the temperature of the surface of the stars and their atomic contents. Such information is usually obtained by interpreting the detected light spectrum (diffracted colors) emitted by the specific star and analyzing wavelengths for distance and temperature  and status of a star in stages of stellar existence, such as quasar, supernova, red giant, white dwarf, collapsing to neutron star, such as pulsar, and finally to become a black hole.

Realize that some phenomena related to bending of light (deflected by gravitational fields) around celestial bodies had not given satisfactory results in mathematical equations depicting them, including light around black bodies.Light energy had always previously been assumed to travel through space in straight lines. Discoveries and related measurements were not available (since no one had made observations) when the classical physics, including Newtonian, had been written to describe laws of physics by "philosophy". This issue was not resolved until the 20th century, using quantum (new) mechanical concepts ofquantifying the energy of light" in the form of discrete (quantifiable) photons.
Photons  subatomic light particles, with no electrical charge, but having momentum and carrying electromagnetic forceas the quantum [the 'amount of/how much'] measurable force of electromagnetic radiation. They are explained by specific equations (including Schroedinger's, Einstein's and Planck's) shown below in a basic form. Also, various experiments in physics at the atomic level led to similar problems when theblack body radiationwas discovered and described. These were also settled by using similar concepts of quantifying energy and other physical observable phenomena, such as the momentum of an atomic particle, which were totally unknown in Newton's times. 
Learn why the application of the concepts of quantization, the quanta of physical observables, seemed to work well with solving the mathematical problems that arose due to failures of Newton's laws to describe, model and satisfactorily allow for newly discovered phenomena.The quantum theory was further explained by the development of theSchroedinger equation(see the image) which relies on the assumption of "waves as particles" in the duality of matter in nature:
 Ψ is the wave function andithe imaginary unit. The "Hbar" is the reduced Planck constant. The "hhat" is the Hamiltonian operator. Thed/dtlowercase "delta/delta t" indicates calculus differentiation fort(time).
 His equation in its various forms is very fundamental for the development of many areas of physics and chemistry. Schrödinger equation of motion can be examined and read about including Wikipedia: Schrödinger equation.

Evaluate the Schroedinger equation mathematically to depict types of wave forms.This explains the namewave function, and gives rise to "waveparticle duality". The wave function is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves, typically for space and time. And, its values are complex numbers. The laws of quantum mechanics (the Schrödinger equation) describe how the wave function evolves over time. The wave function behaves qualitatively like other waves, like water waves or waves on a string.

Learn about history and definitions:

Planck's constanth physical constant of the sizes ofquantainquantum mechanics. It is named after Max Planck, who received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". He was one of the founders ofquantum theory, who described it in 1899.

Planck's constant was first described as proportionality constant between the energy(E)of a photon and the frequency of its associated electromagnetic wave(ν) nu. The relation between energy and frequency is called thePlanck relationor thePlanck–Einstein equation:
E = hν
E =hc/λ  constant certain numeric value for exampleπ (pi) is a well known constant

Planck's constant was first described as proportionality constant between the energy(E)of a photon and the frequency of its associated electromagnetic wave(ν) nu. The relation between energy and frequency is called thePlanck relationor thePlanck–Einstein equation:
 Hilbert's space uses methods of vectoralgebra and of calculus from twodimensional Euclidean plane and beyond the threedimensional space to theoretical spaces with any finite or arguably infinite number ofdimensions. A Hilbert space is "abstract vector space" with the structure of aninner productthat allows length and angle to be measured. Furthermore, Hilbert spaces are required to be complete, a property that stipulates the existence of enough limits (parameters) in the space to allow the techniques of calculus to be used in a region.

Planck's constanth physical constant of the sizes ofquantainquantum mechanics. It is named after Max Planck, who received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". He was one of the founders ofquantum theory, who described it in 1899.

Study the operative theory in mathematics which should be extensive to see whether this theory can continue to be valid in all circumstances (or may be valid only for certain limitations and parameters that might be specified).Also, this theory should be examined against any possible defect in its mathematical applications and physical structures. Theories that depict natural/physical phenomena arenotto be taken for granted and search must always be continued for alternative, better more complete theories.

Realize that finding any discovery that may lead to weakening of the scientific credibility of a physics equation, as occurred with the theory of relativity, can havecatastrophic(change) effects on describing such science:This is true, being applicable in general science and on all other fields of sciences that rely in their scientific development on the formulations of these fundamental equations when they are not all directly observable and so they are theoretically based (derived by describing them mathematically).

Be very cautious when building and formulating new theories in science because of pitfalls and defects in your theory can jeopardize its scientific credibility and could eventually lead to its invalidation (for example:inconsistency).

Apply similar discussion to other theories in physics and other testable sciences.This should also include for example Newton's theory of motion of massive bodies which have already showed failure of accuracy, as on the atomic scale, involving knowledge that was not yet uncovered in Newton's era. The gravitational law area in the classical theory of motion needs to be studied further and to provide more adequate theory for its physical explanation as a unique phenomenon that is characteristic of every star and particle in the universe. The failure to formulate a theory of quantum gravity should give an alert signal as to whether these theories are precisely correct or not (as new data is recorded and analyzed).
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 A good scientific theory must withstand all scientific challenges that can face it.
 Weaknesses of the quantum theory of matter and light can be summarized as follows:
 Quantization of physical observables as contrasted with the continuous nature of these observables in classical mechanics is an assumption that works well as mathematical models, but is an exotic idea on the physical nondirect, observable aspect of particles and remote matter. Also, the uncertainty principle (meaning probability, i.e.: scoring high or not) is an exotic assumption (abstraction) that does not have an analogous phenomenon in "very concrete", classical mechanics. This principle is anexperimental factthat may be verified, and that has mathematical formulas to model.
 Vector space that supports the functions and bases of this theory is calledHilbert space. This space is a subject of investigation as to the properties of the wave functions and quantum, mechanical operators that are used extensively in this area of theoretical mechanics.
 Many factors play roles in the success of this theory of mechanics. Failure of any of these factors to give satisfactory results that commensurate with the logic behind its use can jeopardize the whole theory and lead to its invalidity. Caution here is a key factor not to be confident about any theory of the physical sciences. This is so because most of these theories were built to commensurate with experimental data only, rather than mathematical abstractions. The fact that the theory works well in predicting experimental results does not guarantee the correctness of the theory.
Warnings
 Failure of this principle to work at one occasion can lead to failure of the wholeness of quantum theory of matter. In addition the probabilistic nature of the wave function that is associated with the quantum system is also an issue of controversy but works well mathematically and their results give good predictions about the behavior of the quantized system.
 The complex nature of the wave function has no physical meaning and one must deal with its squared value in order to receive results of physical significance. Again its credibility is maintained by the satisfactory mathematical results they provide with the experimental results.
 Quantum theory of matter is an exotic (unusual) theory in its physical and mathematical structures including the theory of relativity. An example of a concept worthy of probing this theory is the zero point energy concept of physical quantities such as the harmonic oscillator ground state energy. Here the fact that quantum physical systems have nonzero ground state energies are contraindicated in the basic laws of nature which say that "every physical system in the universe tends toward maximum thermodynamic stability as manifested by its presence at a settled state of minimum energy" (i.e.: equilibrium).
 Ground state energy in the quantum theory of matter is a thoughtprovoking subject that might lead to new expressions of an entirety of the whole (complete, sustainable) theory. Also, the use of operators in this theory to depict abstracted, implied physical observables is an exotic idea (abstraction of theoretical, physical behaviors) and application of mathematical concepts to describe the natural world in physics of verified processes by more direct means.
Video: Introduction to limits  Limits  Differential Calculus  Khan Academy
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Date: 07.12.2018, 06:27 / Views: 95474