User:MichaelCPrice/draft

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Draft page. For draft work and formula library.

1 Dispute resolution
2 Complementarity critique
3 History and Development
4 Templates
5 Users
6 Aether critiques
7 Matrices
8 An illustrative example
9 Useful References
10 References

[edit] Dispute resolution

Wikipedia:Resolving disputes Wikipedia:Requests for arbitration Wikipedia:Ignore all rules Wikipedia:Policies and guidelines Wikipedia:How to create policy Wikipedia:Stable versions Wikipedia:Criteria for speedy deletion Wikipedia:Administrators' noticeboard/3RR

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[edit] Complementarity critique

Niels Bohr stated "a complementary way of description is offered precisely by the quantum-mechanical formalism"^[1]

In this view, since the photons in the experiment obey the precise mathematical laws of quantum mechanics (the formalism), they can be described by Bohr's principle of complementarity. Cf:

"I think Bohr would have had no problem whatsoever with this experiment within his interpretation. Nor would any other interpretation of quantum mechanics. It is simply another manifestation of the admittedly strange, but utterly comprehensible (it can be calculated with exquisite precision), nature of quantum mechanics."^[2]
"There is absolutely nothing mysterious about Afshar's experiment. [....] And of course, the conventional quantum mechanics is compatible with the principle of complementarity."^[3]
"It was claimed that this experiment could be interpreted as a demonstration of a violation of the principle of complementarity in quantum mechanics. Instead, it is shown here that it can be understood in terms of classical wave optics and the standard interpretation of quantum mechanics."^[4]

Shahriar S. Afshar, "Sharp complementary wave and particle behaviours in the same welcher weg experiment", (2003) IRIMS www.irims.org/quant-ph/030503/; Proc. SPIE 5866 (2005) 229-244; AIP Cof. Proc. 810, (2006) 294-299. (Crossed beam experiment).

John G. Cramer, "A Farewell to Copenhagen?" (2005), Analog Science Fiction and Fact. (A non-technical discussion in a popular forum)

Marcus Chown, "Afshar's Quantum Bombshell", "Quantum rebel" (July 24, 2004) New Scientist magazine; "A great leap forward", [9] (October 6, 2004) The Independent.
Ira Flatow, "Einstein, Bohr and the Nature of Light", [10], (July 30, 2004) Science Friday radio prgram, NPR.

^
^ Unruh W (2004). "Shahriar Afshar - Quantum Rebel?".
^ Motl L (2004). "Violation of complementarity?".
^ Steuernagel O (2005). "Afshar's experiment does not show a violation of complementarity". ArXiv:quant-ph/0512123.

[edit] History and Development

Orthomolecular megavitamin therapies, such as "megadose" usage of tocopherols^[5] and ascorbates^[6], date back to the 1930s.

The term "orthomolecular" was first used by Linus Pauling in 1968, to express the "idea of the right molecules in the right amounts"^[7] and subsequently defined "orthomolecular medicine" as "the treatment of disease by the provision of the optimum molecular environment, especially the optimum concentrations of substances normally present in the human body." or as "the preservation of good health and the treatment of disease by varying the concentrations in the human body of substances that are normally present in the body and are required for health." ^[8]

Since 1968 the orthomolecular field has developed further through the works of mainstream and non-mainstream researchers. Despite thus it still is often closely associated by the public with Pauling's advocacy of multi-gram doses of vitamin C for optimal health.

An example of a recent mainstream researcher is nutrition researcher Bruce Ames although he does not use the term itself. However his research deals with nutrition and specific genetic disease conditions (as indeed did Pauling's original article which defined the term "orthomolecular"^[7]). Ames' research includes investigating the effects of large doses of, for example, the nutrients alpha-lipoic acid (a coenzyme precursor) and the carnitine (an amino acid complex) on restoring metabolic health, and in particular mitochondrial function, in animal models^[9] ^[10] ^[11] Ames has also investigated the role of high dose B-vitamin therapy in alleviating in approximately 50 defective co-enzyme binding affinities, of which one, at least, every human suffers from ^[12] (example of one genetic disease condition: Over 40% of the population is hetro- or homo-zygous with the thermolabile variant of 5,10-methylenetetrahydrofolate reductase ^[13] and as a result requires extra riboflavin ^[14] ^[12]).

Ames has, based on his research, developed a supplement for human use^[15].

[edit] Templates

this list of tags ^{[not in citation given]} ^{[original research?]} ^{[attribution needed]} Template:Betterfact

[edit] Users

User talk:Autarch User talk:Avraham User talk:Bryan Vare User talk:Byrgenwulf User talk:Cadwgan Gedrych User talk:Canon User talk:CDiPoce User talk:Enoent User talk:Galizur User talk:GregorB User talk:Kevin Langdon User talk:May-Tzu User talk:Mingano User talk:Mstewarthm User talk:Promking User talk:Sbharris User talk:Sijo Ripa User talk:Sol.delune User talk:SOUTH User talk:Tim Smith User talk:Tox User talk:Tstrobaugh User talk:Wjhonson User talk:Zorro24

[edit] Aether critiques

Mainstream critics point out that Einstein's special theory of relativity is an extension of the principles of Galilean relativity or invariance from classical mechanics to include Maxwell's equations and thereby optics.

In the mainstream view, therefore, any attempt to formulate a new aether theory by recourse to Galilean relativity, is doomed since Galilean invariance is already incorporated into special relativity under the name Lorentz invariance; any putative aether is considered to be devoid of mechanical properties, unobservable and hence superfluous.^[16] It is held that any non-superfluous aether theory would yield predictions that are incompatible with Lorentz invariance and thereby Maxwell's equations; however the latter is empirically very well attested.

Consequently the concept of a "Galilean" aether or space has not been used in the Theory of Relativity, Quantum mechanics, or other modern theories of physics.

[edit] Matrices

$\begin{matrix} |\mbox{electron, apparatus}_{before} \rang = |e^{-} \mbox{: x-spin} \rightarrow \rangle \otimes |\mbox{m: no bubbles} \rangle \\ \ = (|e^{-} \mbox{: z-spin} \uparrow \rangle + |e^{-}\mbox{: z-spin} \downarrow \rangle)\frac{1}{\sqrt{2}} \otimes |\mbox{m: no bubbles} \rangle \end{matrix}$ $\begin{matrix} = |e^{-}\mbox{: z-spin} \uparrow \rangle \otimes |\mbox{m: no bubbles} \rangle\frac{1}{\sqrt{2}} + |e^{-}\mbox{: z-spin} \downarrow \rangle \otimes |\mbox{m: no bubbles} \rangle \frac{1}{\sqrt{2}} \end{matrix}$

$\begin{matrix} |\mbox{electron, apparatus}_{after} \rang = \\ & |e^{-}\mbox{: z-spin} \uparrow \rangle \otimes |\mbox{m: bubbles along upper path} \rangle \frac{1}{\sqrt{2}} \\ +& |e^{-}\mbox{: z-spin} \downarrow \rangle \otimes |\mbox{m: bubbles along lower path} \rangle \frac{1}{\sqrt{2}} \end{matrix}$

$\begin{matrix} |\mbox{electron, apparatus}_{after} \rang = & \ \\ |e^{-}\mbox{: z-spin} \uparrow \rangle \otimes |\mbox{m: bubbles along upper path} \rangle\frac{1}{\sqrt{2}} \ \end{matrix}$ $\begin{matrix} + |e^{-}\mbox{: z-spin} \downarrow \rangle \otimes |\mbox{m: bubbles along lower path} \rangle \frac{1}{\sqrt{2}} \end{matrix}$

[edit] An illustrative example

MWI describes measurements as a formation of an entangled state which is a perfectly linear process (in terms of quantum superpositions) without any collapse of the wave function. For illustration, consider a Stern-Gerlach experiment and an electron or a silver atom passing this apparatus with a spin polarization in the left-right or x direction and thus a superposition of a spin up and a spin down state in up-down or z-direction. As a measuring apparatus, take a bubble or tracking chamber (a nonabsorbing particle detector). And finally let a cat observe the bubble tracks that form in the bubble chamber. The electron passes the apparatus and reach the same site in the end on either way so that, except for the up-down z-spin polarization, the state of the electron is finally the same regardless of the path taken (see The Feynman Lectures on Physics for a detailed discussion of such a setup). Before the measurement, the state of the electron and measuring apparatus is:

The state is factorizable into a tensor factor for the electron and another factor for the measurement apparatus. After the spin measurement (bubble formation), the state is:

The state is no longer factorizable -- regardless of the vector basis chosen the state has to be expressed as the sum of a number of terms (in this example, at least two). The state of the above experiment is decomposed into a sum of two correlated or so-called entangled states ("worlds") both of which will have their individivual history without any further interaction or quantum interference between the two due to the physical linearity of quantum mechanics (the superposition principle): All processes in nature are linear and correspond to linear operators acting on each superposition component individually without any notice of the other components being present.

This would also be true for two non-entangled superposed states, but the latter can be detected by interference which is not possible for different entangled states (without reversing the entanglement first): Different entangled states cannot interfere; interactions with other systems will only result in a further entanglement of them as well. In the example above, the state of a Schrödinger cat watching the scene will be factorizable in the beginning (before watching)

$\|electron, apparatus_{after}, cat_{before}\rangle = ($	$\frac{1}{\sqrt{2}} ($	$\|e^{-} \mbox{: z-spin} \uparrow \rangle \otimes \|\mbox{m: upper bubbels} \rangle \ +$
	$\|e^{-} \mbox{: z-spin} \downarrow \rangle \otimes \|\mbox{m: lower bubbles} \rangle) \otimes \|\mbox{cat: ignorant of the bubbles} \rangle$

but not in the end (after watching)

$\|electron, apparatus_{after}, cat_{after}\rangle = \frac{1}{\sqrt{2}} ($	$\|e^{-} \mbox{: z-spin} \uparrow \rangle \otimes \|\mbox{m: upper bubbels} \rangle \otimes \|\mbox{cat: sees upper bubbles} \rangle \ +$
	$\|e^{-} \mbox{: z-spin} \downarrow \rangle \otimes \|\mbox{m: lower bubbles} \rangle \otimes \|\mbox{cat: sees lower bubbles} \rangle)$

This example also shows that it's not the whole world that is split up into "many worlds", but only the part of the world that is entangled with the considered quantum event. This splitting tends to extend by interactions and can be visualised by a zipper or a DNA molecule which are in a similar way not completely opened instantaneously but opens gradually, element by element.

Imaginative readers will even see the zipper structure and the extending splitting in the formula:

$\|\psi_2' \rangle = ($	$\alpha \ \|e^{-} \mbox{:}e_1 \rangle \otimes \|\mbox{m:}m_1 \rangle \otimes \|\mbox{c:}c_1 \rangle \otimes \|\mbox{a:}a_1 \rangle \ + \quad \Longrightarrow$
	$\beta \ \|e^{-} \mbox{:}e_2 \rangle \otimes \,\|\mbox{m:}m_2 \rangle \,\otimes \,\|\mbox{c:}c_2 \rangle\, \otimes \|\mbox{a:}a_2 \rangle \ )\ \otimes \|\mbox{b:}b_0 \rangle \otimes \|\mbox{d:}d_0 \rangle \otimes \|\mbox{f:}f_0 \rangle \otimes \|\mbox{g:}g_0 \rangle \otimes \|\mbox{h:}h_0 \rangle$

If a system state is entangled with many other degrees of freedom (such as those in amplifiers, photographs, heat, sound, computer memory circuits, neurons, paper documents) in an experiment, this amounts to a thermodynamically irreversible process which is constituted of many small individually reversible processes at the atomic or subatomic level as is generally the case for thermodynamic irreversibility in classical or quantum statistical mechanics. Thus there is -- for thermodynamic reasons -- no way for an observer to completely reverse the entanglement and thus observe the other worlds by doing interference experiments on them. On the other hand, for small systems with few degrees of freedom this is feasible, as long as the investigated aspect of the system remains unentangled with the rest of the world.

The MWI thus solves the measurement problem of quantum mechanics by reducing measurements to cascades of entanglements.

The formation of an entangled state is a linear operation in terms of quantum superpositions. Consider for example the vector basis $|e^{-}\mbox{: a}\rangle \otimes |\mbox{m: c}\rangle, |e^{-}\mbox{: a}\rangle \otimes |\mbox{m: d}\rangle, |e^{-}\mbox{: b}\rangle \otimes |\mbox{m: c}\rangle, |e^{-}\mbox{: b}\rangle \otimes |\mbox{m: d}\rangle$

and the non-entangled initial state $|\psi_1\rangle = |e^{-}\mbox{: a}\rangle \otimes |\mbox{m: c}\rangle$

The linear (and unitary and thus reversible) operation (in terms of quantum superpositions) corresponding to the matrix

$\begin{bmatrix} 0 & 0 & 1 & 0 \\ 1/\sqrt{2} & 1/\sqrt{2} & 0 & 0 \\ -1/\sqrt{2} & 1/\sqrt{2} & 0 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$

(in the above vector basis) will result in the entangled state $|\psi_2\rangle = \frac{1}{\sqrt{2}} (|e^{-}\mbox{: a}\rangle \otimes |\mbox{m: d}\rangle - |e^{-}\mbox{: b}\rangle \otimes |\mbox{m: c}\rangle)$

[edit] Useful References

[edit] References

^
^ Unruh W (2004). "Shahriar Afshar - Quantum Rebel?".
^ Motl L (2004). "Violation of complementarity?".
^ Steuernagel O (2005). "Afshar's experiment does not show a violation of complementarity". ArXiv:quant-ph/0512123.
^ New/Old Findings on Unique Vitamin E
^ AscorbateWeb: Timeline from 1935 to 1939
^ ^a ^b Orthomolecular psychiatry. Varying the concentrations of substances normally present in the human body may control mental disease,Science 1968 Apr 19;160(825):265-71.(PMID 5641253) [1]
^ Definition of Orthomolecular medicine at www.orthomed.org Accessed June 2006 and What is Orthomolecular Medicine?, Linus Pauling Inst.
^ Age-associated mitochondrial oxidative decay: improvement of carnitine acetyltransferase substrate-binding affinity and activity in brain by feeding old rats acetyl-L- carnitine and/or R-alpha -lipoic acid. Liu J, Killilea DW, Ames BN in Proc Natl Acad Sci U S A 2002 Feb 19;99(4):1876-81 (PMID 11854488)
^ Memory loss in old rats is associated with brain mitochondrial decay and RNA/DNA oxidation: partial reversal by feeding acetyl-L-carnitine and/or R-alpha -lipoic acid. Liu J, Head E, Gharib AM, Yuan W, Ingersoll RT, Hagen TM, Cotman CW, Ames BN in Proc Natl Acad Sci U S A. 2002 Feb 19;99(4):2356-61. (PMID 11854529)
^ Feeding acetyl-L-carnitine and lipoic acid to old rats significantly improves metabolic function while decreasing oxidative stress. Hagen TM, Liu J, Lykkesfeldt J, Wehr CM, Ingersoll RT, Vinarsky V, Bartholomew JC, Ames BN in Proc Natl Acad Sci U S A. 2002 Feb 19;99(4):1870-5. (PMID 11854487)
^ ^a ^b High-dose vitamin therapy stimulates variant enzymes with decreased coenzyme binding affinity (increased K(m)): relevance to genetic disease and polymorphisms. Ames BN, Elson-Schwab I, Silver EA in Am J Clin Nutr 2002 Apr;75(4):616-58 (PMID 11916749) Abstract:As many as one-third of mutations in a gene result in the corresponding enzyme having an increased Michaelis constant, or K(m), (decreased binding affinity) for a coenzyme, resulting in a lower rate of reaction. About 50 human genetic dis-eases due to defective enzymes can be remedied or ameliorated by the administration of high doses of the vitamin component of the corresponding coenzyme, which at least partially restores enzymatic activity. Several single-nucleotide polymorphisms, in which the variant amino acid reduces coenzyme binding and thus enzymatic activity, are likely to be remediable by raising cellular concentrations of the cofactor through high-dose vitamin therapy. Some examples include the alanine-to-valine substitution at codon 222 (Ala222-->Val) [DNA: C-to-T substitution at nucleo-tide 677 (677C-->T)] in methylenetetrahydrofolate reductase (NADPH) and the cofactor FAD (in relation to cardiovascular disease, migraines, and rages), the Pro187-->Ser (DNA: 609C-->T) mutation in NAD(P):quinone oxidoreductase 1 [NAD(P)H dehy-drogenase (quinone)] and FAD (in relation to cancer), the Ala44-->Gly (DNA: 131C-->G) mutation in glucose-6-phosphate 1-dehydrogenase and NADP (in relation to favism and hemolytic anemia), and the Glu487-->Lys mutation (present in one-half of Asians) in aldehyde dehydrogenase (NAD + ) and NAD (in relation to alcohol intolerance, Alzheimer disease, and cancer).
^ (PMID: 15681105)
^ Riboflavin as a determinant of plasma total homocysteine: effect modification by the methylenetetrahydrofolate reductase C677T polymorphism. Hustad S, Ueland PM, Vollset SE, Zhang Y, Bjorke-Monsen AL, Schneede J in Clin Chem 2000 Aug;46(8 Pt 1):1065-71 PMID: 10926884 The riboflavin-tHcy relationship was modified by genotype (P = 0.004) and was essentially confined to subjects with the C677T transition of the MTHFR gene [homo- and hetero-zygous]. CONCLUSIONS: Plasma riboflavin is an independent determinant of plasma tHcy.
^ Zey.com
^ Einstein said: "We may assume the existence of an aether,; only we must give up ascribing a definite state of motion to it, i.e. we must by abstraction take from it the last mechanical characteristic which Lorentz had still left it." Albert Einstein, "Äther und Relativitätstheorie", Rede gehalten am 5. Mai 1920 an der Reichs-Universität zu Leiden, Springer, Berlin 1920.
^ Hugh Everett, The Theory of the Universal Wavefunction (1956), Appendix I. "Monotone decrease of information for stochastic processes" pp 128-129 in The Many-Worlds Interpretation of Quantum Mechanics, Princeton Series in Physics, Princeton University Press (1973), ISBN 069108131X, pp 3-140
^ "Whether you can observe a thing or not depends on the theory which you use. It is the theory which decides what can be observed." Albert Einstein to Werner Heisenberg, objecting to placing observables at the heart of the new quantum mechanics, during Heisenberg's 1926 lecture at Berlin; related by Heisenberg in 1968, quoted by Abdus Salam, Unification of Fundamental Forces, Cambridge University Press (1990) ISBN 0521371406, pp 98-101
^ Wojciech H. Zurek, Decoherence and the transition from quantum to classical, Physics Today, 44, pp 36-44 (1991)
^ Wojciech H. Zurek, Decoherence and the transition from quantum to classical, Physics Today, 44, pp 36-44 (1991); and an updated version from 2003:[2]
^ Wojciech H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Reviews of Modern Physics 2003, 75, 715 or [3]
^ Wojciech H. Zurek, Pointer Basis of Quantum Apparatus: Into what Mixture does the Wave Packet Collapse?, Physical Review D, 24, pp. 1516-1525 (1981)
^ Wojciech H. Zurek, Environment-Induced Superselection Rules, Physical Review D, 26, pp.1862-1880, (1982)
^ Wojciech H. Zurek, Decoherence, Einselection, and the Existential Interpretation (The Rough Guide), Philosophical Transactions of the Royal Society of London A, 356, pp 1793-1820, (1998)
^ "There is absolutely nothing mysterious about Afshar's experiment." "And of course, the conventional quantum mechanics is compatible with the principle of complementarity." Lubos Motl at [4]
^ "Bohr would have had no problem whatsoever with this experiment within his interpretation. Nor would any other interpretation of quantum mechanics. It is simply another manifestation of the admittedly strange, but utterly comprehensible (it can be calculated with exquisite precision), nature of quantum mechanics." Bill Unruh at [5]
^ "It was claimed that this experiment could be interpreted as a demonstration of a violation of the principle of complementarity in quantum mechanics. Instead, it is shown here that it can be understood in terms of classical wave optics and the standard interpretation of quantum mechanics." Ole Steuernagel at [6]
^ "Bohr would have had no more problem accounting for the Afshar result than he would in accounting for the aforementioned pre- and post-selection spin experiment, in which the particle's preparation state is confirmed by a nondestructive measurement prior to post-selection." Ruth Kastner at [7][8]

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Category: Wikipedia articles needing factual verification

$\|electron, apparatus_{after}, cat_{before}\rangle = ($	$\frac{1}{\sqrt{2}} ($	$\|e^{-} \mbox{: z-spin} \uparrow \rangle \otimes \|\mbox{m: upper bubbels} \rangle \ +$
	$\|e^{-} \mbox{: z-spin} \downarrow \rangle \otimes \|\mbox{m: lower bubbles} \rangle) \otimes \|\mbox{cat: ignorant of the bubbles} \rangle$