Doug's efforts here take us even further into a pool of obtainable
understanding of omnifferencings among classical equilibrium and
quantum~equilibrium.
We have much to do here, and it will abundantly apply directly
to Doug's year~long plus efforts in his QELR of equilibrium.
Keep in mind that all this extensive work is prerequisite for
Doug's continuing Chapter 4 of his online FEP Economic Value
Feuilleton Chautauqua textbook.
Doug - 17Aug2011.
| Text Segment |
Quoted Text Segment with Problematics |
Doug's Text Segment Commentary |
Text Segment with Quantonics
Remediation |
Relevant Equilibrium Topics |
| 1 |
"We shall now move on to discuss the
temporal evolution of quantum systems. As in classical
mechanics, the Hamiltonian
plays a fundamental role. As we have seen, in quantum mechanics
it is replaced by the Hamiltonian operator
Hop. |
Basic issues, classical
vis-à-vis
quantum
include these:
- Linguistically definite articles [e.g., 'the']
aren't permitted in real quantum language systems. Why?
Macroscopic quantum~uncertainty.
- Unitemporality [i.e., One Time Fits All, OTFA]
isn't valid in real quantum systems and languages which
describe them.
- Quantum~systems æv¤lve quintessentially via
ubiquitous scintillation of quanta. Therefore all quantum~evolution
issi quantum~uncertain (classically indeterminate). Quantonics HotMeme™ "Quantum~evolution requires its adherents to
gnostically embrace indetermination."
Quantonics
HotMeme™
- Classical Hamiltonian
logic depends upon classical commutation which is invalid in
real quantum systems. Indeed all classical 'equivalence
relations' are invalid in real quantum systems.
- Classical operator mathematics are formal-mechanical and
dialectical and thus
their classical-evolutionary 'states' are scalars.
This whole system of classical thingking
is bogus, ersatz, facile, faux, pseudo, inutile, deceit, etc.
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A classical notion of Hamiltonian Operator
may now be remediated using a CeodE 2012 graphic
image Doug created called EWing
Ensembles. See that graphic.
Here is relevant text nearby that graphic:
"Following Prigogine and Stengers' lead, Doug's graphic
is a kind of quantum Hamiltonian, but non static,
dynamically everywherings-everywhenings quantum~fractal~recursive.
See pp. 220-221 out of 349 total, Order Out of Chaos."
Recursion labels on that graphic represent
quantum~fractal~hologra[[m][ph][il]]ic~stindyanic interrelationshipings
among EWings composing ensemble qwfs. Those pluralities of comcurrent
evolutionings imply indetermination (uncertainty), noncommutation,
non identity, non equivalence, absence of any notions of 'scalar'
holds-still-isms.
They imply presence of massively heterogeneous
and coobsfective chance~choice~changings borne of perpetual quantization~scintillationings at each recursion instance.
Dialectics
cannot offer any exegeses of pure quantum~dynamicity.
State cannot explain: choice, chance, nor change.
Doug - 29Feb2012.
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| 2 |
This energy operator plays a central role:
on the one hand, its eigenvalues correspond
to the energy levels; on the other hand, as in classical
mechanics, the Hamiltonian operator determines
the temporal evolution of the system. |
Basic issues, classical vav quantum include these:
- Classical eigenvalues are scalars. Often they are distilled
to bivalency [zero or one]. Scalar and bivalent 'values' are
of n¤ Value in real quantum~systems.
- Classical notions of 'energy levels' are simply bogus in
real quantum systems since quantum~energy is flux, quantized
and absolutely changing and evolving flux which may n¤t
be classically sampled and held as ideally, Platonically stoppable
state.
- Hamiltonian 'operators' do n¤t classically-determine
anything. Quantum reality is macroscopically uncertain and in
n¤ way is or can be classically deterministic. Quantum
reality scintillates quanta which massively SOrON
ensemble~select whatings
happenings nextings [Peircean] abductively based upon evolving
energy wellings in said quantal
scintillation processings' l¤cal and n¤nl¤cal
[as described in Bell's Theorem(s); bogusly described as "hidden
variables" by retarded quantum-mechanics] comtextings. We
see instead of classical idealism and positive realism, ensembles
of evolving quantum energy wellings choosings, chancings, and
changings many to many coobsfectively at up to Planck rates of
quantum flux. There is n¤ monotime, and there is n¤
monodirection (trajectory). Doug - 12Aug2011.
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| 3 |
In quantum mechanics the role played by the
canonical equation of classical mechanics is taken
by the Schrödinger equation, which expresses the
time evolution of the function characterizing the quantum state as the result of
the application of the operator Hop on the
wave function  (there are,
of course, other formulations, which we cannot describe here). |
Basic issues, classical vav quantum include these:
- Classical canon
'laws,' 'principles,'
'dogma,'
and 'orthodoxy'
are all without [f]lux essential
Value in quantum reality.
In quantum~reality they are ESQ,
dead.
- Classical canon 'laws,' 'principles,' 'dogma,' and 'orthodoxy'
depend upon a classical presumption of 'state,'
'stoppability,' 'zero momentum,' etc., in order to be 'classically
valid.'
- "The wave function,"
appears to be saying one can specify, classically, an analytic
lisr 'wave function.'
Quantum wave functions
are n¤t classically localable, isolable, separable, reducible.
Quantum absolute change
plus holographic middle inclusion deny essentially all classical
lisr notions. Doug - 17Aug2011.
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| 4 |
The term 'wave function' has been chosen to emphasize
once again the wave particle duality
so fundamental in all of quantum physics. |
Basic issues, classical vav quantum include these:
- How many ways can we think about this? Let's use two terms
as representative of dialectical (SOM) thingking and two terms
as representative of quantum thinkqing. Dialectically
let's use quantity and objective. Quantumly let's use quality
and subjective. Then using text in a graphical way let's use
dichon(~, o) to classically show its closed-continuous wave lisr
duality as objective and quantitative (particulate). Similarly
allow Doug to use quanton(~,¤) to quantumly show its open~quantized
wave holographically EIMA complementarity as subjective and qualitative
(fluxic). In summary, then:
- dichon(~, o) represents classical wave-particle lisr duality,
and
- quanton(~,¤) represents quantum wave~wavicle complementarity.
- So Doug offers two vastly omniffering world views of classical
wave-particle duality vis-à-vis quantum wave~wavicle complementarity.
Doug - 17Aug2011.
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| 5 |
is a wave
amplitude that evolves according to a particle type of equation determined
by the Hamiltonian. |
Basic issues, classical vav quantum include these:
- Classically 'wave amplitude' is a valid metric for energy.
Quantumly only wave flux rate is a valid metric for energy.
- Classical maths only work with dichons(~, o): static
middle-exclusion is required. Classical maths have no means of
'operating' on quantons(~,¤): fluxing middle~inclusion
is mandatory.
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| 6 |
Schrödinger's equation, like the canonical equation
of classical physics, expresses a reversible
and deterministic
evolution. |
Basic issues, classical vav quantum include these:
- In general classical notions of reversibility are invalid
in quantum~reality. Bosons and gluons may offer partial
apparitions of reversibility, and that is all. Fermions and their
CH3ings
are quintessentially irreversible.
- In general classical notions of determinism are invalid in
quantum~reality. Quantum~reality is stochastic which means we
are always uncertain
to greater and lessor extents. We are limited to probable, plausible,
and likely stochastics of quantized
"guessing." In some cases our guesses, though, can
be very precise (n¤t necessarily 'accurate'). Doug - 17Aug2011.
See Doug's QELRs of chance,
change, and choice.
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| 7 |
The reversible change of
wave function corresponds to a reversible
motion along a trajectory. |
Basic issues, classical vav quantum include these:
- There are n¤ 'classical trajectories' in quantum~reality.
- There is n¤ 'classical reversibility' in quantum~reality.
- etc.
Doug - 17Aug2011.
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It may k~now~ings be obvious to readers that quantization
disables and invalidates classical notions of
- linearity,
- cause-effect,
- y=f(t) continuity,
- determination,
- trajectories,
- reversibility,
- stability (especially in any sense of social OSFA planning
and state-ic equilibrium borne on such invalid notion of social
planning),
- closure,
- monism,
- dualism,
- positivism,
- formal realism,
- dialectic, and
- so on...
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| 8 |
If the wave function at a
given instant is known, Schrödinger's equation
allows it to be calculated for any previous
or subsequent instant. |
Basic issues, classical vav quantum include these:
- Static 'event'
instances AKA 'occurrences'
may n¤t be 'determined' in quantum~reality.
- Predication of 'previous' and 'subsequent' instances is always
uncertain thus never classically determinate.
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| 9 |
From this viewpoint, the situation is strictly similar
to that in classical mechanics. This
is because the uncertainty relations of quantum mechanics do
not include time. Time remains a number, not an operator, and
only operators can appear in Heisenberg's uncertainty relations." |
Basic issues, classical vav quantum include these:
Bold green is closest to a real quantum description Prigogine
and Stengers uncloak in this paragraph. Overall though, their
words belie countless classical SOM
deceptions.
There is an abundance of learning to be had in this single
paragraph. Don't waste it!
Doug - 17Aug2011.
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