[Marxism] Re: godel etc (was ...)

Les Schaffer schaffer at optonline.net
Thu Mar 17 00:03:49 MST 2005


Scott Palmer wrote:

> (( So we can say that Godel et al, do for Enlighment mathematics and 
> logic what Marx et al did to philosophy? ))
>
> Gödel's work was important but not as generally applicable as one 
> might think.


in fact, neither is Heisenberg's uncertainty principle (HUP). it's a 
principle with a lot of historical value, indicative of a certain deep 
sea change in the structure of physical arguments. nonetheless in modern 
quantum physics it does not lie at the core of a set of principles which 
__generate__ the subject, instead it follows as a kind of constraint on 
the measurements of (conjugate) pairs of observable properties from 
simpler first principles: states, superposition of states, and relation 
of states with observables.

be THAT as it may, HUP, seen as a limitation in principle, in practice 
has spurred much effort to at least " get in the face" of this limit. 
and remember this limitation is not open-ended, HUP actually states that 
the product of the uncertainties must be greater than OR EQUAL TO a 
certain very small number.

i remembered after reading Carlos' email yesterday that i had actually 
written a post for the list last August that i had facetiously entitled 
"Heisenberg's certainty principle". i saved it because it needed work, 
and then never worked on it. so here it is, warts and all:


Subject: Heisenberg's certainty principle
Date: 8/31/2004 3:29 PM


To the marxism list (and blind-copied friends) {1}:

This summer-like afternoon i find myself reading a fascinating article 
in this week's online version of Nature -- for the physics hip, it is 
entitled "De Broglie wavelength of a non-local four photon state" and 
authored by the fabulous Anton Zeilinger and his quantum optics crew in 
Vienna {5}. Pondering this paper absent-mindedly while listening to a 
wood thrush singing in a nearby glen, it suddenly occured to me that the 
time is fast approaching for an efficient turning-on-its-head of 
Heisenberg's uncertainty principle [as Marx did to Hegel, so we do unto 
others]. As we've discussed during the last week, quantum uncertainty 
and other ideas from quantum mechanics (QM) have been rather 
metaphysically abused in the last 80 years {2}. Hence the breezy 
Subject: line of this email. In fact, one wonders whether 30 years ago 
for example, during the Peter Drucker management "revolution", I might 
have subtitled the message: "and the efficient management of uncertainty".

I intend to look historically at the uncertainty principle in later 
posts. For now, one piece of background for the lay reader. In 1926 
Werner Heisenberg created the new quantum mechanics by first creating a 
new quantum kinematics -- that is, a new quantum description of motion. 
Shortly thereafter, young Werner (then in his early 20's) and his father 
professor Niels Bohr in Copenhagen endeavoured to produce an 
interpretation of the new theory. In the first few papers on this topic 
Heisenberg used the thought-experiment of "seeing" an electron by 
illuminating it with light (photons) and viewing the electron-reflected 
light with an optical microscope. His aim was to provide a warm 
comfortable feeling for physicists who might be offended with his new 
mechanics' statement that the position AND momentum of our resident 
electron could not be simultaneously determined with absolute exactness. 
Instead, there would be some fuzz in the determination (to be sharp, the 
fuzz would be in measurements of a suite of identically prepared 
electrons). The amount of this fuzz to be proportional to a relatively 
new constant of nature, named after its originator Max Planck { }.

The original uncertainty analysis depended in part on the fact that 
viewing a reflection of the illuminating photon in the optical 
microscope was itself classically limited due to the wave nature of 
light. The classical optics principle -- around for many years at the 
time of Herr Heisenberg -- goes by the name of the "diffraction limit". 
In classical optics, it is not possible to resolve features in a 
microscope smaller than the wavelength of light used to illuminate the 
specimen being viewed { }. In Werner's case, we were playing mind games 
to "view" an electron, and the diffraction limit was causing us some 
difficulty in determining precisely the electron's position (it's 
kinematical properties).

In response to the Copenhagen interpretation of QM by Heisenberg and 
Bohr, Einstein and colleagues Podolsky and Rosen (known as EPR) offered 
up another thought experiment involving a specially prepared pair of 
photons with opposite pointing "spins" (actually, the photons were David 
Bohm's idea, but for now, whatever). As they traveled apart from each 
other at the speed of light, EPR pointed out that a determination of the 
spin of one photon would automatically and instantly nail down the spin 
of the other, even if they were light years apart. This seemed like a 
no-no from the perspective of relativisitic causality. EPR was used by 
physicists who disliked the new quantum mechanics and its 
interpretation, and the subsequent conflict and contradictions have 
since lead to several new and important insights in quantum physics. 
These two-photon preparations came to be known as quantum two-particle 
entanglements { }.

Fast-forward to today. Zeilinger's crew -- the Vienna group has been at 
the forefront of EPR-type experiments and insights -- have prepared a 
quadruple of entangled photons and subsequently created a diffraction 
pattern with them. As per the predictions of now-standard quantum 
mechanics, the diffraction pattern was a sub-multiple of the wavelength 
of this light, one-quarter to be precise, thus __beating__ the classical 
diffraction limit {3}.

So put this in your metaphysical pipe and smoke it: utilizing ideas 
originally intended to discredit QM (EPR's entangled photons), QM 
physicists have now succeeded in breaking a classical optical limit 
originally utilized by Heisenberg in his uncertainty analysis, thereby 
imaging a diffraction grating to a better precision ("certainty") than 
hitherto attained. It is perhaps time then to stand Heisenberg on his 
head, and proclaim quantum mechanics to be a certain science, whereby 
the uncertainties of life (we're smoking now, aren't we???) are 
effectively limited to within an absolutely small amount (Planck's 
constant). Further -- and following Feynman {4} -- this small 
uncertainty is not only neccessary for the consistency of the theory, 
but creates the conditions whereby we can even break the "uncertainty 
limits" of classical physics.

Exhale ......

I don't mean to imply that QM doesnt have any kind of odd behavior, or 
that its standard interpretation can't be substantially revised, or that 
QM cannot be overthrown in the future. But the time for wallowing in a 
metaphysical realm of absolute uncertainty supposedly substantiated by 
quantum mechanics is now over.

Les Schaffer



Notes:
-------

{1.} I'd appreciate feedback from non science people [as well as the odd 
physicist here] on the readabilty of this post, as i would like to 
refine it for presentation to non-physics audiences. For example, does 
the post need to explain diffraction? Are there other physics terms that 
are unclear? Do i need to explain how more precisely how uncertainty can 
be turned on its head, or does the example experiment of Zeilinger make 
it clear that quantum uncertainty does not preclude making more precise 
measurements than even classical physics allows, etc.

{2.} Links to previous posts:

{3.} The Hubble Space Telescope is placed above the earth's atmosphere 
so that it can view distant galaxies at the diffraction limit of 
starlight's wavelength without atmospheric disruption such as "twinkling".

{4.} David Bohm has written extensively on how these entanglements paint 
(can be interpreted as) a picture of wholeness / holism in our universe, 
a topic for another time.

{5.} As an interesting side-note, various Soviet physicists have 
described Planck's constant as the modern way to give an absolute 
meaning to the term "small".

{6.} For physicists: Dirk Bouwmeester writes in Nature regarding 
Zeilinger's paper:

    Entangled photons conspire to create interference patterns that
    would normally be associated with a wavelength much smaller than
    that of the individual photons — beating the diffraction limit.

    If a double slit is illuminated with a laser beam of wavelength
    lambda, the familiar rippling pattern of interference fringes
    arises, even if the attenuation of the laser is so strong that only
    single photons pass through the double slit at any given instant. To
    emphasize this quantum feature, Paul Dirac wrote [1] that "Each
    photon interferes only with itself. Interference between two
    different photons never occurs." Dirac would probably have been more
    cautious had he read this issue of Nature. Starting on page 158,
    Mitchell et al. [2] and Walther et al. [3] report their
    demonstrations of interference patterns produced by specific
    entangled states of three and four photons.

I like the good natured jab at Dirac, as it shows that interpretations 
at one time and place advance the cause, later on, they can get in the 
way. Dirac's comment on single photons is reproduced in a large fraction 
of quantum mechanics and field theory texts.

{7.} Feynman is very good on quantum uncertainty. I've posted some 
scanned in remarks from his Lectures on Physics to:

http://folks.astrian.net/godzilla/feynman-qm-uncertainty.html

{8.} Abstract of paper:

Nature 429, 158 - 161 (13 May 2004); doi:10.1038/nature02552

De Broglie wavelength of a non-local four-photon state

PHILIP WALTHER [1], JIAN-WEI PAN [1,*], MARKUS ASPELMEYER [1], RUPERT 
URSIN [1], SARA GASPARONI[1] & ANTON ZEILINGER [1,2]

1 Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, 
1090 Wien, Austria
2 Institut für Quantenoptik und Quanteninformation, Österreichische 
Akademie der Wissenschaften, Boltzmanngasse 3, 1090 Wien, Austria
* Present address: Physikalisches Institut, Universität Heidelberg, 
D-69120 Heidelberg, Germany

Superposition is one of the most distinctive features of quantum theory 
and has been demonstrated in numerous single-particle interference 
experiments [1-4]. Quantum entanglement [5], the coherent superposition 
of states in multi-particle systems, yields more complex phenomena [6, 
7]. One important type of multi-particle experiment uses path-entangled 
number states, which exhibit pure higher-order interference and the 
potential for applications in metrology and imaging [8]; these include 
quantum interferometry and spectroscopy with phase sensitivity at the 
Heisenberg limit [9-12], or quantum lithography beyond the classical 
diffraction limit [13]. It has been generally understood [14] that in 
optical implementations of such schemes, lower-order interference 
effects always decrease the overall performance at higher particle 
numbers. Such experiments have therefore been limited to two photons 
[15-18]. Here we overcome this limitation, demonstrating a four-photon 
interferometer based on linear optics. We observe interference fringes 
with a periodicity of one-quarter of the single-photon wavelength, 
confirming the presence of a four-particle mode-entangled state. We 
anticipate that this scheme should be extendable to arbitrary photon 
numbers, holding promise for realizable applications with 
entanglement-enhanced performance.






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