A reader suggests the Statistical Interpretation of quantum mechanics, aka the Ensemble interpretation, is superior to others.

My main complaint is that this claims to be a "minimalist interpretation". It is not. Sometimes the many-worlds also claims to be minimalist. It is not either. The most minimal of the of the mainstream interpretations is the Instrumentalist interpretation.

The statistical interpretation essentially says that only probabilities are observable, and only in large systems. But quantum mechanics is commonly used to make predictions about small systems, such as a the energy levels of a 2-particle hydrogen atom. Turning this into a statistical observation about an ensemble of hydrogen atom is to add a lot of extraneous junk. A minimalist interpretation has to say something about one atom.

I prefer the positivist interpretation, as being truly minimalist.

Probability is a mathematical layer with multiple interpretations, and any quantum mechanics interpretation that requires probability is not minimalist.

Part of the confusion is that people think that probability is essential to quantum mechanics, via the Born rule. Probability is important to quantum mechanics in the same way that it is important to other scientific theories, but not essential.

"Quantum Reprogramming: Ensembles and Single Systems: A two tier approach to Quantum Mechanics" c. 1995 by Evert Jan Post

ReplyDelete"In quantum mechanics, physics somehow is involved in situations halfway

between science and religion. The many useful applications of the

Schroedinger equation indicate that the belief works. In fact, it works so

often and so weIl that the sheer statistical evidence of applicability is taken

as proof and substantiation of the stated beliefs. Whenever we run into an

exception we are inclined to suspect first an error in the implementation of

our beliefs and not the belief itself. We have not yet reached the courage

of our convictions to test our quantum mechanical beliefs beyond the point

where we keep overwhelming ourselves with the brute force of statistics.

In the following, two examples will be examined which give direct and

near-incontrovertible evidence of the inapplicability of the Schroedinger

equation to highly ordered systems. The experimental evidence for one of

these examples has, quite surprisingly, been around for almost three

decades. The argument goes back to the discovery of flux quantization and

it is based on the experimentally confirmed absence of a residual zero-point

flux in superconducting rings.

The second example is of more recent vintage and relates to the

quantum Hall effect."

...

"This state of affairs, in turn, places in question the

applicability of the Schroedinger process to physical situations that are

distinguished by a high degree of cooperative behavior."

"Electromagnetic Noise and Quantum Optical Measurements" by Haus

"We have taken the point of view that quantum theory is a statistical theory that predicts only the outcome of an ensemble of measurements. The outcome of a single measurement is described only probabilistically."

...

"Finally, it is the authors view, shared by many physicsts, that quantum theory is *fundamentally* a probabilistic theory that is complete in the sense defined by John Bell"

From the Evert Jan Post book:

ReplyDelete"If no thing else, the reprogramming shows that properly chosen ensemble

specifications bring the Popper proposition into a revealing quantitative

relationship with the Schroedinger equation. While this fact still does not

establish beyond a shadow of a doubt that the Schroedinger equation is an

ensemble tool, it does make the ensemble option a good deal more probable

than the single-system option. As a remaining restraint preventing an allout

support of the ensemble option, one should consider that even these

explicit quantitative relations between ensemble statistics and Schroedinger

results still fall short of aiding in a complete derivation of the Schroedinger

equation from first principles.

In fact, considering the lacunar nature of the derivational origin of the

Schroedinger equation, there should be real doubt whether this equation

will ever be derivable from first principles. After all those years of investigation

and contemplation, it is more likely that Herman Weyl's words are

to be taken more literally than ever intended: the Schroedinger equation's

relation to Hilbert space was (and still is) "afavor offortune."

With all reservations in place, it is thus concluded that the Schroedinger

equation comes conceivably closest to describing dilute ensembles of

identical single systems in quantum states that are randomized in phase and

orientation. The word "conceivably" here conveys that there is no proof by

derivation to completely substantiate this statement. All of this indicates

that there is no known context for which the Schroedinger equation can be

given a status of absolute physical exactness. The many statements to the

contrary in the quantum mechanical textbook literature, therefore, are to

be regarded as the products of wishful thinking.

Overwhelmed by the equation's unparalleled success, earlier theorizing

had always tacitly assumed an absolute and exact status for quantum mechanics'

major tool of inquiry. Physical imagery kept drifting around on

this magic cloud, which had brought so much "fortune" beyond what

physics had deserved on the basis of "merit." Hence, when the Copenhagen

interpretation became available as an intellectual vehicle for consolidating

this equation's position of "fortune," the Copenhagen view automatically,

yet unjustifiably, assumed the same aura of near-perfect truth that had already

been identified with the Schroedinger equation and spectral theory.

Now, in retrospect, physics should have had some real doubts that such a

lofty assignation, even for the Schroedinger equation, might not be on

altogether solid grounds.

In the course of this reprogramming, evidence has been compiled which

amply supports the Popper-ensemble proposition in conjunction with a required

phase-and-orientation randomness of its constituent elements. It is

the best that can be done for the Schroedinger equation, which, incidentally,

is a lot better than what the textbook literature has done for the mutual

relation of the Schroedinger equation and the single system. The textbook

method simply postulates an interrelation between single-system and

Schroedinger equation, and then, depending on Copenhagen-related convictions,

this premise is made "plausible" with mystifying statistical considerations,

which, until this day have not found their "universe of discourse. "

From Evert Jan Post:

ReplyDelete"That, in a nutshell, is how Hilbert space and its spectral properties became

the realm of reality for the Twentieth Century physicist, almost to the

exclusion of spacetime itself. Fortunately, the representation theory of

groups retained a last powerfullink between spacetime and Hilbert's configuration

space of quantum states. The group theoretical method was a

last concession to a phenomenology of microphysical symmetry.

Somehow, and again ironically, symmetry had been permitted to penetrate

the fog of uncertainty shrouding microphysical structure. Weyl and

Wigner had shown the way.

The emergence of macroscopic quantum effects, however, brought us

back from the abstract multi-dimensional Hilbert spaces into a reality of

more intuitive spacetime model-making. Over and above symmetry, the

mathematical machinery instrumental for implementing greater balance

between formal and intuitive procedures in physics must be expected to

call, more than be fo re , on the topology-oriented studies initiated in

mathematics by Poincare, Brouwer, Hopf, de Rham, and Hodge.

A recognition of this new impending reality has been very difficult for

physics. For more than half a century, it has preached the gospel of a

quantum mechanics, in which Hilbert space became almost a sole storage

place of fundamental physical truth. Those involved in the study of quantum

mechanical fundamentals have been brushing up Hilbert space formalisms,

using group theoretical methods for finding out more about the

spacetime structure of the objects gene rating the Hilbert space superstructures.

There is, at this time, no real acceptance of a need to complement

this procedure with intuitive conjecture by following in both directions the

threads of logic interconnecting suspected cause and perceived effect.

attitude is understandable in an interpretational atmosphere, which, as a result

of its own premises, had been forced to restriet the rules of causality in

the microdomain.

While the use and function of Hilbert space, as it now stands, is not to

be underestimated, its primary role is instrumental for ensembles, not for

single systems! The Hilbert integral equation as definer of eigenvalue situations

has an ensemble connotation, because it defines the wave function

W in any point in terms of W everywhere else through the process of

integration in the physical domain (chapter XVII;8).

The Hilbert integral equation as Schroedinger equivalent has an

inherent "smeared-out plurality" wh ich seems out-of-context for a single

system. The period integral assessment, by contrast, does not have this

reflexive interconnectedness of its spatial parts, which is so characteristic

of the Schroedinger plurality. The period integral's domain of integration

can be shrunk unto the single (microphysical) object of observation. It is

capable of exploring topological structure, where Schroedinger's process is

confined to essential physical features of the ensemble constituents only.

This inability of making an adequate ensemble versus single-system

distinction led quantum mechanics into the dead-end street of formal abstraction.

This escape in abstraction became misleadingly acceptable.

Getting out of this dead-end situation, the man-made fog of "uncertainty"

needs to be lifted so that horizons become visible again. After that, a view

of the single-system domain comes into focus, thus opening up a potential

for the more intuitively oriented methods of topological modelling in

actual spacetime, not Hilbert space! There is presently, at best, a general

but vague awareness of the nature of these deficiencies in contemporary

quantum mechanics. The existing situation of a long standing status quo

reveals physics' reluctance in coming to grips with the cited predicament.

The confusion continues:

ReplyDeletehttp://physics.stackexchange.com/questions/41373/is-the-statistical-interpretation-of-quantum-mechanics-dead

and then there is this guy:

http://arxiv.org/abs/1112.2446

There are some sensible answers there, including one by Motl.

DeleteI hate the name "statistical interpretation". It just causes confusion.

ReplyDeleteThe best book on quantum mechanics, Anthony Sudbery's "Quantum mechanics and the particles of nature: An outline for mathematicians" c. 1985 has nine different interpretations listed:

1. The Minimal interpretation

2. The Literal interpretation

3. The Objective interpretation

4. The Epistemic ('subjective') interpretation

5. The Ensemble interpretation

6. The Relative-state and Many-worlds interpretation

7. The Quantum-logical interpretation

8. The Hidden-variable interpretation

9. The Stochastic interpretation

According to Sudbery, Bohr's interpretation is strongly expressed by the Minimal interpretation. He sure gives Bohr a good tongue lashing too:

"Moreover, it cannot be true that the sole purpose of a scientific theory is to predict the results of experiments. Why on earth would anyone want to predict the results of experiments? Most of them have no practical use; and even if they had, practical usefulness has nothing to do with scientific inquiry. Predicting the results of experiments is not the purpose of a theory, it is a test to see if the theory is true. The purpose of a theory is to understand the physical world"

Sudbery is of the opinion that "No one interpretation is generally accepted" including the Copenhagen which he believes has been applied to at least four different interpretations listed above.

I am not familiar with that book. I agree that no one interpretation is generally accepted, that most probably accept Copenhagen but many people mean different things by that, and that Bohr's interpretation is minimalist.

ReplyDeleteThe longer quote describes the quest for scientific "realism". It sounds great until you start drawing untestable conclusions.

"...is to add a lot of extraneous junk."

ReplyDeleteThats the whole purpose of String Theory, that is for its insiders (masquerading as award winning (bogus Milner prize) "scientists") to add complexity so that the only court recognized experts are the string practitioners (tiny few) themselves.

What the thieves are doing with String Theory is fencing in science so that String Theory is considered both more fundamental than Level 1 Quantum Mechanics (see here String theory proponent Ron Maimon hierarchy in this link: http://physics.stackexchange.com/questions/22618/are-quantum-mechanics-calculations-useful-for-engineering/22620#22620) and yet provides all the tools for the bottom layer where all the engineering applications take place).

So take for example a definition of the applicability of Quantum Mechanics from "The Odd Quantum" by Sam Treiman:

"The quantum mechanical

rules, the concrete equations, are de finite and well

established. In principle one can compute the structure of oil

molecules and work out the way these molecules interact

among themselves in bulk oil and thence go on to the viscosity

of oil. But a completely detailed calculation that traverses

the whole route from the individual molecule and its ingredients

all the way up to the astronomical number (about 10E24) of

molecules present in even a small drop of oil is utterly unthinkable.

The single molecule is already complicated enough. Thus,

approximations and aggregate treatments have to be adopted

along the way, relying on various rich and active fields of scienti

c inquiry; for example, the fi eld of statistical mechanics. A

pumper who wants highly accurate predictions of flow rate is

well advised to adopt the empirical value of viscosity. But that

same pumper may also share with others a curiosity about why

things are the way they are. Moreover, there is the possibility

of learning enough at the microscopic level to design molecular

additives that can alter the viscosity in wanted directions."

Imagine, trillions of dollars of "molecular additives", coatings, etc that do not work as advertised and are deliberate fabrications (fraud). Thats the purpose of string theory.. passing off bogus science and engineering in the small as legitimate to reap obscene profits. And non observable because I bet they imbed their all subsuming "Grand Theory of Everything" into a hocus pocus "quantum" (remember String theory is more fundamental than quantum mechanics) processor run by Google. If you say "string theory is garbage" but its so big that you cannot understand it all then you lose.

Of course this is tin foil hat stuff. Roger takes an optimistic outlook in his book that science will continue to progress. I say it definitely won't in the era of internetworked communications. The singularity is an increasing wealth concentration due to ignorance of science, not an uplifting of standard of living.

Ensemble interpretation conjured up by Popper and supported by Einstein. Gee, I hope this isn't another case of physicists supporting it because of Einstein idolizing? But, as they said with "Nobody ever got fired buying IBM"...I guess the same applies here...after all, guess who is the most popular scientist of all time at the Nobel prize website?

ReplyDeleteUh oh, I found some more plagiarizers in: "E.C.G. Stueckelberg, An Unconventional Figure of Twentieth Century Physics" c.2009 by by Editors Lacki, Ruegg, Wanders

ReplyDelete"While developing his grand “field theory of matter” of the late 1930s, Stueckelberg

forged some of the basic tools that permitted contemporary and later successes

of quantum field theory."

.....

"Whether or not this isolation is judged unfair, it prevented Stueckelberg

from inflecting the course of theoretical physics as much as his genuine creativity

could have done. His unitary field theory of 1936–39 nonetheless

anticipated several features of modern grand-unified theories, and contained

Yukawa’s theory as a particular case. The tools he developed in this earlier

period permitted his and his collaborators’ post-war progress on renormalized

quantum electrodynamics, including important results on regularization,

causal Green functions, and S-matrix theory. Had these results been

expressed in a form as seductive as Feynman’s, Schwinger, and Tomonaga’s,

and Freeman Dyson’s contemporary writings, Stueckelberg would be more

often recognized as a central figure of this extraordinary episode of the history

of physics."

...

"Now,

we do not think that the value of Feynman’s fabulous contribution to physics

is in any way diminished by the historical fact that Stueckelberg had already

come up with the classical and quantum interpretation of an antiparticle as a

particle going backwards in time. With hindsight, one can only lament that

Stueckelberg’s papers, published during the war in French in a journal of neutral

Switzerland, did not receive the attention they should have merited."

....

"In

general, Stueckelberg’s style, language and choice of journals did not favour

the propagation of his ideas. He was quite isolated and his work progressed

in parallel with those of celebrities like R. P. Feynman, J. Schwinger and S.

Tomonaga. These circumstances explain why Stueckelberg’s contributions

are so little known and may seem marginal. It is, in fact, unquestionable that

some of his findings have a deep and lasting importance, such as his showing

that collision processes cannot be understood if their causal time evolution is

ignored."

PHYSICS: Its not what you know but its who you know and how its presented

Physicist Tony Rothman said terrible things about all of Physics in the 2011 May-June issue of American Scientist in the article "The Man Behind the Curtain: Physics is not always the seamless subject it pretends to be"

ReplyDelete"Nevertheless, as a physicist travels along his (in this case) career, the hairline cracks in the edifice become more apparent, as does the dirt swept under the rug, the fudges and the wholesale swindles, with the disconcerting result that the totality occasionally appears more like Bruegels Tower of Babel as dreamt by a modern slumlord, a ramshackle structure of compartmentalized models soldered together into a skewed heap of explanations as the whole jury-rigged monstrosity tumbles skyward"

...

"One doesn't have to go so far in quantum theory to be confused. The concept of electron "spin" is basic to any quantum mechanics course, but what exactly is spinning is never made clear. Wolfgang Pauli, one of the concept's originators, initially rejected the idea because if the electron was to have a finite radius, as indicated by certain experiments, then the surface would be spinning faster than the speed of light. On the other hand, if one regards the electron as a point particle, as we often do, then it is truly challenging to conceive of a spinning top whose radius is zero, not to mention the aggravation of infinite forces"

Then he attacks the 2-slit experiment:

"....Rather than describing how the light interacts with the slits, thus explaining why it behaves as it does, we merely demand that the light wave meet certain conditions at the slit edge and forget about the actual forces involved. The results agree well with observation, but the most widely used of such methods not only avoids the guts of the problem but is mathematically inconsistent"

He goes on and on...attacking Lagrangian mechanics, ....etc

"The great swindle of of introductory physics is that every problem has an exact solution. Not only that, students are expected to find it.