Embed Size (px)
Citation preview
Chapter XIX
PLANCK'S QUANTUM:
THE NEXT 100 YEARS
§ X I X - l . Introduct ion .
What remains? where is it all going? and who can tell? Kleppner [1] has recently enumerated some of the many historic failed a t tempts to project the future of physics. The lesson to be learned is that such projections are impossible - even over very short time intervals. Kleppner too was trying to foresee the possibilities of the next fifty years and simply concluded with unbridled optimism tha t physics would continue its proliferating successes. His reasoning is tha t physics is an experimental science in which there are "ever more perfect eyes within a cosmos in which there is always more to be seen." Physics creates these more perfect eyes in new and more powerful experimental methods which will continue to drive our subject with ever more discoveries.
We share Kleppner's enthusiasm and optimism for physics in general; and also his wariness of predicting the future. The task we set ourselves is perhaps no more possible, but it is much more constrained. We restrict our speculations to the realm of quantum mechanics for its own sake, which we will try - for simplicity
- to limit to the non-relativistic regime. Certainly the impact of the relativistic - even the extreme relativistic Planck scale - may well intrude and may even determine everything in a top-down flip-flop.
Is formal quantum mechanics per se - in the form left to us by the original creators Heisenberg, Born, Jordan, Dirac, Schrodinger, Bohr, Feynman, • • • - as far as it goes? Is there something deeper which underlies the original canonical s tructure inferred from the classical Action Principle? The answer is surely 'Yes!' and the progression through quantum field theory and the Standard Model to some form of string theory in an extended space-time is well underway. There no doubt will be surprises - both triumphs and disasters - for our contemporary
526
100
Yea
rs o
f Pl
anck
's Q
uant
um D
ownl
oade
d fr
om w
ww
.wor
ldsc
ient
ific
.com
by N
AN
YA
NG
TE
CH
NO
LO
GIC
AL
UN
IVE
RSI
TY
on
11/0
5/14
. For
per
sona
l use
onl
y.
Chapter XIX. The Next 100 Years 527
ideas. An ongoing and persistent failure to find any explicit spectrum of Higgs or super-symmetric particles would be a political and financial disaster for the field of high-energy experimental physics but no doubt there would be a new Higgs with a new way of breaking symmetries not apparent to us now. In a sense, failure could be more fruitful than success - forcing physicists to think of more subtle and abstract ideas not so simply related to the structures employed in the traditional Standard Model. The ultimate boundary condition on any such construction is - thanks to Linde's proliferation of universes - no longer the mother of all correspondence principles. The top-down theory need no longer produce uniquely the world we see, but must only include it as a possibility. This seems to be the case for present string-theories, where there is no clear preference for one among many groundstates.
What could be the conceivable impact on the structure and results of non-relativistic quantum mechanics of the full realization of the fondest dreams of the advocates of string-theory? It is tempting to say none at all but such negativism precludes thought, so lets try a little harder. Wilson's renormalization group analysis shows how ostensibly fundamental theories (e.g., quantum electrodynamics) are in fact 'effective' phenomenological theories valid as low energy approximations in the Gell-Mann-Low running coupling analysis of more fundamental theories, which are similarly defined at a succession of higher energy regimes. The Feynman Path Integral formulation is the ideal way to 'integrate out ' degrees of freedom as the energy is decreased through various thresholds and the more massive fields are 'frozen out ' in a sequence of phase transitions. The sole impact of the degrees of freedom of each frozen out higher energy regime appears in the parameters of the lower energy theory (e.g., mass spectrum, running coupling strengths of induced interactions). The present situation is that there appears to be a small number of viable candidate theories at the Planck scale, but no way to choose one among many (billions?) of possible low energy limit theories. The criteria for a successful string theory (T.O.E. - Theory of Everything) include its ability to satisfy the correspondence principle requirement of producing the Glashow-Salam-Weinberg standard model. Presumably the success of the standard model at the scale of ~ 1 Tev or ~ 1 0 - 4 fm insulates all of non-relativistic quantum mechanics and
100
Yea
rs o
f Pl
anck
's Q
uant
um D
ownl
oade
d fr
om w
ww
.wor
ldsc
ient
ific
.com
by N
AN
YA
NG
TE
CH
NO
LO
GIC
AL
UN
IVE
RSI
TY
on
11/0
5/14
. For
per
sona
l use
onl
y.
528 100 Years of Planck's Quantum
related phenomena from details of higher energy models. We are still left groping for any phenomenological or theoretical impact of the eventual T.O.E. especially on non-relativistic quantum mechanics but actually including even applications of relativistic quantum field theory in the laboratory domain.
One idea - suggested by the top-down derivation of the non-relativistic quantum mechanical world from the Planck T.O.E. - is the possibility to derive the interpretation of the theory also in a top-down way. In this way, the meaning or interpretation of quantum mechanics would be contained within the primary theory at each stage of the renormalization group analysis. Information from the higher regime (massive particle spectrum, interactions) is manifested in the succeeding lower regime in a 'jet experiment' where the massive particles appear as annihilation jets of the approximately massless particles of the lower energy regimes. This suggests tha t the fundamental measurement process is a jet experiment with the consequent loss of resolution and coherence at the lower level. The quantum coherence of the jet structure cannot get past a digital—►analog conversion (in the optic nerve of the observer, if not sooner) so the ultimate thought processes involve neither the digital nor the quantum nature of the input information. The decoherence of the measurement event resides in an infra-red catastrophe in the jet event constituting the fundamental detection.
In summary: it seems inescapable that the top-down T.O.E. will have no impact on the results of quantum theory. We are as passionate as anyone about the pursuit of such knowledge and we are fully cognizant of the fact tha t no one can anticipate the unknown. None the less, our assessment of the situation is tha t this difficult goal must be pursued only for its own intrinsic interest. Looking back to Vilenkin's quantum theory of the origin of the universe as a tunneling event from nothing, we find the T.O.E. epoch hidden behind the potential barrier at a = 0 + preceding the slow roll-over of Guth 's inflation, and all at times much smaller than the Planck time. Linde's chaotic inflation makes our connection to the T.O.E. vastly more remote, since it requires only that the T.O.E. contain our realization of physics as one random chance in an incredible lottery.
§ X I X - 2 . Interpretat ion of Q u a n t u m Mechanics .
We find the present interpretation schemes - even with recent contributions -
100
Yea
rs o
f Pl
anck
's Q
uant
um D
ownl
oade
d fr
om w
ww
.wor
ldsc
ient
ific
.com
by N
AN
YA
NG
TE
CH
NO
LO
GIC
AL
UN
IVE
RSI
TY
on
11/0
5/14
. For
per
sona
l use
onl
y.
Chapter XIX. The Next 100 Years 529
to be lacking in any kind of beauty or elegance or imagination, and in that sense to fail Dirac's criterion for Truth. We look forward to a top-down interpretation of quantum mechanics as the ultimate limiting 'Quantum Information Theory' imposed by the quantum of action h. In this way, we would abandon the crutch by which the wave function is thought of as a quantum precursor to a physical field attached to a quantum system like the Coulomb potential is attached to a classical charge. Quantum mechanics would be more truly associated with our 'right to think' and with the limit imposed on valid logic by the existence of the quantum; and only secondarily with the physical realization of any logical thought progression. Quantum theory would be more about thought and less about matter . Not thoughts of a mundane sort about life, death, hunger, love, beauty, etc., which would be recognized as grossly macroscopic analog processes. But thoughts at the most elemental level - than which nothing can be simpler - which we presume to be governed by the most primitive digital (i.e., quantum) information theory contained in or containing quantum mechanics. Such an idea may be wrong, or vacuously tautological, or even already existing (like the proverbial pony buried in the dung-heap) but we find it a more significant role for quantum mechanics to be the fundamental limiting theory of how we must think, given the quantum.
Finally the ideal quantum information content is degraded by our very thought processes. In this view - admittedly not so different from all the others because, after all, they do 'work' - the information acquisition involves an unavoidably imperfect digital to analog conversion (in the optic nerve, in our example) prior to the analysis by the macro-molecular - classical, analog and non-quantum -thought processes. A possible merit of this interpretation would be to reduce every observation to a jet experiment - like a photo-multiplier cascade - in our own eyeballs. Whether or not this can be formalized in any way preferable to the existing interpretations, or whether it is worthwhile or even true, remains to be decided. The goal of making the wave function the unique optimal quantum information theoretic device governing the observer's possible thought processes, rather than into a left-over relic of 19"1 century classical field theory is as close to a top-down interpretation of quantum mechanics as we have been able to imagine so far.
100
Yea
rs o
f Pl
anck
's Q
uant
um D
ownl
oade
d fr
om w
ww
.wor
ldsc
ient
ific
.com
by N
AN
YA
NG
TE
CH
NO
LO
GIC
AL
UN
IVE
RSI
TY
on
11/0
5/14
. For
per
sona
l use
onl
y.
530 100 Years of Planck's Quantum
§ XIX-3. Unresolved Problems.
There are a number of very long-lived puzzles in the class of applications of quantum mechanics which have resisted a generation of concerted effort toward their full resolution. There is no indication that these unresolved problems are fundamental matters of principle in the basic quantum theory, nor that these are problems which will occupy the main stage for more than another one or two decades; but each is a major goal of widespread interest in its own right. Among these goals, we would include a fundamental understanding of: 1) Color confinement in quark-gluon chromodynamics. This is perhaps not a problem of non-relativistic quantum mechanics. And indeed there is no shortage of suggestive models to mimic the result. But there is still no fundamental insight to connect this essential requirement of the quark model of hadron structure in any rigorous formal way to the universally accepted (?) underlying fundamental (?) gauge theory of quantum chromodynamics. 2) The spin structure of the nucleon. This problem is presumably not as fundamental as that of confinement but it is a bothersome experimental result that has stood without full understanding for a generation. Experiments indicate that some 50% or more of the nucleon's spin ft/2 actually resides in the gluons rather in the quarks. Whatever the precise experimental result turns out to be, there is certainly a serious inability to apply quantum mechanics to understand the detailed structure of the hadronic particles even in a qualitative way. 3) High temperature superconductivity. The impasse here has been comparable in difficulty and longevity with that in low temperature superconductivity. That problem was resolved eventually by the Bardeen-Cooper-Schrieffer theory based on the mechanism of an energy-gap due to the formation of Cooper pairs. The energy-gap dynamics of the mechanism is rather universal and might be applicable to high energy superconductivity and to confinement, or to explain any robust quantum state.
All these problems and many more are surely not any failure of quantum mechanics per se. They are more likely the subtle results of phase transitions in which the degrees of freedom are most effectively described in some collective form, witness the Cooper pairs resulting from density correlations induced by
100
Yea
rs o
f Pl
anck
's Q
uant
um D
ownl
oade
d fr
om w
ww
.wor
ldsc
ient
ific
.com
by N
AN
YA
NG
TE
CH
NO
LO
GIC
AL
UN
IVE
RSI
TY
on
11/0
5/14
. For
per
sona
l use
onl
y.
Chapter XIX. The Next 100 Years 531
lattice vibrations.
These problems of application are all conjectured to be resolvable on the time scale of one or at most two decades. None could conceivably require fundamental changes in the structure of the underlying theory of quantum mechanics, but they all have resisted sustained efforts of great ingenuity, intuition and imagination. Their resolution is eagerly anticipated.
One common feature in a//such problems - from the proton spin deficit through the BCS-theory of superconductivity to the fractional quantum Hall effect - is the lack of an intuitive explanation based on a model coordinate space wave function tha t is comprehensible to anyone except a physicist expert in the specialty. Talented students and other physicists are reduced to believing but not really understanding.
In their recent popular discussion Doubt and Certainty, Rothman and Sudar-shan [2] play the devil's advocate in a refreshing and stimulating review of the endless controversies and debates inherent in the ongoing understanding of quantum theory per se. They make clear that each new generation must debate these problems anew, and in the process incrementally increase our collective understanding. This debate is the sine qua non for any revolutionary progress. But convergence is slow and - as in any civil war - closure on many emotional issues is never achieved. Dissatisfaction still exists on such problems as:
1) the origin of the direction of time in quantum mechanics. We would hold with Veneziano [3] that the origin of the direction of time is in the expansion of our universe, and must be imposed on quantum mechanics through the density matrix and measurement process by the 'collapse of the wavefunction'.
2) the interface between quantum mechanics and statistical mechanics involving the classical Boltzmann factor e~ElkT is regarded as ad hoc. 3) even the recent decoherence interpretation of quantum mechanics generates stubborn dissatisfaction, typified on one extreme by adherents of Bohmian trajectories and on the other by proponents of the Everett many universes interpretation. We view these (and others) as metaphysical constructs designed to have no consequences, and therefore not worthy of further attention but they show no signs of going away.
100
Yea
rs o
f Pl
anck
's Q
uant
um D
ownl
oade
d fr
om w
ww
.wor
ldsc
ient
ific
.com
by N
AN
YA
NG
TE
CH
NO
LO
GIC
AL
UN
IVE
RSI
TY
on
11/0
5/14
. For
per
sona
l use
onl
y.
532 100 Years of Planck's Quantum
The above questions relate to inanimate systems. What about the role of quantum mechanics in the life sciences? The density functional description - developed for atomic-, molecular-, surface-, and solid-state effects - shows great promise [4] for fundamental model building of life mechanisms like cell transport which are on the cusp of quantum processes. There is the suggestion of new applications of quantum mechanics to understand in a more fundamental way the heuristic mechanisms constructed already in chemistry, biology, neural sciences, medicine, and even psychology. All - it seems to us - are reactive responses to 'explain' classical intuitive results obtained in traditional ways, rather than any pro-active creative strategy leading the way to new mechanisms. This is a near infinite realm of application of quantum model building but we foresee no reverse impact on quantum mechanics per se, but also no intrinsically quantum dependence of life processes on h itself, beyond the current understanding of quantum chemistry.
There still remains the possibility that the logic of quantum mechanics might have a parallel in thought processes. This would seem to be limited to the result of a coherence of reinforcing thought patterns analogous to the coherence of classical diffraction patterns in the scattering of sound or water waves, or of holography, and not of any intrinsic dependence on Planck's quantum per se.
§ XIX-4. Quantum Sociology.
In this section we confess in advance what will soon become obvious to anyone who reads on: we succumb to the inevitable pessimism of the old predicting a future they have failed to create and will not be here to witness. We focus in particular on the role of non-relativistic quantum mechanics in the education and intellectual life of - say - 2050 or 2100. What are the prospects? We assume that non-relativistic quantum mechanics is already a mature science encapsulated from any essential impact of anticipated developments such as an eventual Theory of Everything including super-symmetry, super-strings, space-time compactification, and so on; or further refinements of interpretation.
Quantum mechanics will live on with Newton's mechanics and Maxwell's equations as indispensable foundation subjects of engineering, technology and science. However it will no longer be a subject of primary interest to research physicists and most of those who teach it and use it will be concerned - as now, actually -
100
Yea
rs o
f Pl
anck
's Q
uant
um D
ownl
oade
d fr
om w
ww
.wor
ldsc
ient
ific
.com
by N
AN
YA
NG
TE
CH
NO
LO
GIC
AL
UN
IVE
RSI
TY
on
11/0
5/14
. For
per
sona
l use
onl
y.
Chapter XIX. The Next 100 Years 533
with acquiring a heuristic and intuitive understanding good enough f.a.p.p. (Bell's mantra: for all practical purposes). Quantum mechanics differs from these classical subjects, though, in being the perpetual target of critics unwilling to accept the abstractions of the subject. One fears for the erosions and degradations of the subject by unrefuted critics and philosophers and by unprincipled (literally) revisionists, free to run amok without dispute from anyone qualified by the singular experience of first-hand fundamental scientific contributions in the subject.
The educational system is inevitably forced to teach less and less about more and more until everyone knows something about everything but never enough to really understand anything beyond the level of rote response. We don' t condemn! we sympathize. In the face of this pressure, generation after generation of text books and courses are forced to pander more and more. The material will be elided to the level good enough f.a.p.p.
On the brighter side, computerized multi-color perspective graphics of quantum systems evolving in time and space as full-fledged faithful solutions of Schrodinger's equation will (have) become wide-spread and powerful as an instruction aid and interest grabber. Translating this wonderful tool into a deep understanding for the self-selected few interested in the underlying quantum theory will remain a tremendous challenge. Again on the bright side, the computerization of even the algebra promises (as now, in a variety of symbolic manipulation programs) to relieve the theoreticians of overwhelming tedium and leave time, energy, and enthusiasm for more global thinking. The price paid is the intimacy of our involvement with the subject, attenuated as it must be by the 'black-box' of the computer manipulations.
With a world population of 10-15-20-billion people, surely there will be a small elite - bigger in actual numbers than now - capable of pursuing quantum mechanics to the same level of understanding that is presently obtained by the current small but (more than?) sufficient elite. So what is the problem? Maybe none. There is the story of the mayor of Calcutta welcoming an international symposium of physicists visiting his city and pointing out that there were 1000 beggars in the streets of Calcutta as smart as they. Will it be 10,000? 100,000? in 2050. So what is the problem?
One can't help but feel disheartened by the projected absence of any cumula-
100
Yea
rs o
f Pl
anck
's Q
uant
um D
ownl
oade
d fr
om w
ww
.wor
ldsc
ient
ific
.com
by N
AN
YA
NG
TE
CH
NO
LO
GIC
AL
UN
IVE
RSI
TY
on
11/0
5/14
. For
per
sona
l use
onl
y.
534 100 Years of Planck's Quantum
tive or even progressive impact on the collective human psyche of all the marvelous acquired knowledge and understanding of the first one hundred years of quantum mechanics. We must acknowledge a collective failure to interest people at large and especially educators and humanists in even the rudiments of our subject -physics as a whole - let alone in the more abstract and abstruse topic of quantum mechanics. Perhaps interest is not the exact word. People are interested but the physics community has generally failed to make its ideas attractive, palatable and digestible without removing its intellectual content [5]. Can anything be done? Hundreds of popularizations in book and video form have been put forth, but the key people - the K—>12 teachers - have not been reached. Great efforts have been made in this direction - witness the Feynman Lectures on physics. But the Feyn-man Lectures - as even Feynman acknowledged - ended up preaching to the choir (i.e., the faculty) and not the congregation (in this case, of eager and gifted Caltech undergraduates), to say nothing of the unconverted. The conclusion has become ever more clear - tha t the primary act of creation of knowledge must be followed by an unending devotion to the process of - put bluntly - salesmanship. During the cold war era, when physics and physics funding were intimately connected to military power, there was no such need. But already - in spite of the intimate link between physics and the technology of the internet, which is the primary engine driving the economic boom at the turn of the 21s (-century - physics as it exists is being declared sufficient f.a.p.p. At present, there is not enough respect and prestige given within the physics profession to the difficult, challenging, and most essential task of bringing an understanding of quantum mechanics to a wide audience including educators and children, and college undergraduates of all interests. Computer graphics, videos and lectures can be only part of the effort. The process has to involve interaction, visualization, verbalization, discussion, debate. An incredible commitment by all scientifically knowledgeable people will be required for this vast and ever increasing task [6]. This is the only conceivable way to teach enough quantum mechanics to enough people to insure the continuing viability of our subject, even enough for all practical purposes.
Wha t about the future generations' Heisenbergs and Diracs? Schwarzes and Wittens? As now, we imagine the identification, education and nurturing of genius
100
Yea
rs o
f Pl
anck
's Q
uant
um D
ownl
oade
d fr
om w
ww
.wor
ldsc
ient
ific
.com
by N
AN
YA
NG
TE
CH
NO
LO
GIC
AL
UN
IVE
RSI
TY
on
11/0
5/14
. For
per
sona
l use
onl
y.
Chapter XIX. The Next 100 Years 535
will continue to be a haphazard inefficient enterprise, as wasteful in the economically advanced countries as in the less privileged, but for complementary reasons: people on both sides of the economic divide are driven by the completely natural materialistic instinct to struggle from survival to security and equally franticly from security to luxury. Combined with a further limiting motivation to be somehow 'useful' (e.g., cure death), and the inevitable truth that 'a fat dog won't hunt ' , we are left with barriers to young people ever even aspiring to the ultimate heights of our quantum profession.
The problem at the research university level is a lack of will rather than any lack of resources. It can be - and in rare instances, even is - addressed in simple terms with the most informal of structures. Our best suggestion involves discussion groups of perhaps five or six people including able, interested and self-selected students of all levels - first year through graduate student - and junior and senior faculty. A brown-bag lunch or afternoon tea is a friendly environment, or a journal-club. It is not necessary or even desirable to have a fixed agenda and any lecture format is surely fatal. Simply talk, question, argue, explain, explore. The simplest questions can lead to the most profound concepts - which must then be related back to fundamental concepts accessible to everyone. It is no mean feat to avoid dogmatism and formalistic gibberish. The goal is to get an open discussion with lots of "I don't understand • • •", "I don't know • • •", "That can't be right because • • •", "But what about • • •", "Why • • •", "How
In our experience the over-riding threats to the success of this enterprise are two: the students are worried about a grade because they have standard class demands; and the faculty too is basically worried about a grade. They have to work on publishable research to enhance their status with peers and supervisors in the university, research group and funding agencies. For both, sitting around and talking is viewed with deep suspicion. Unarguably it is not efficient, but we argue that it is desirable and maybe even necessary in the higher goals of education and development, in learning by apprenticeship, and perhaps most important of all, in giving young people at every stage a voice in the process. If we are ever to recreate the environment in which Bohr and Born nurtured the prodigious development of Heisenberg, Jordan, and many others, there has to be more direct and informal
100
Yea
rs o
f Pl
anck
's Q
uant
um D
ownl
oade
d fr
om w
ww
.wor
ldsc
ient
ific
.com
by N
AN
YA
NG
TE
CH
NO
LO
GIC
AL
UN
IVE
RSI
TY
on
11/0
5/14
. For
per
sona
l use
onl
y.
536 100 Years of Planck's Quantum
communication across all levels of the hierarchy and at every stage of the process. We need a new revolution in the presentation of our subject with an empha
sis on economy, essential ideas, and direct and rapid progress to modern topics. We need a bridge between intuition and theory that is possible only for a select few authors. We must reduce the technicalities of the formalisms to reveal clearly their essential content; clearly illustrated with a few key examples. We need Feyn-man brilliance and charisma, but made accessible where - for whatever reason -Feynman was not. Perhaps Feynman with a readers guide, or a translation with illustrations. Nothing will be lost in the transition because our present approach is confounding practically everyone anyway, with its barrier of dull and repetitive problems; of narrow details as the foundation of great ideas. The reality perceived by the students is narrow details instead of great ideas.
Pedagogical reform - informed by active research participation - is absolutely essential to the continued life of our subject. There is also the question: from whom should we learn? If the answer is - as we believe - the creators of knowledge, then most of the creators need a lot of help to make their work widely understood. If magicians never explain their tricks, surely the creative magicians of our subject are not very revealing of their innermost creative impulses. We are confronted with the accomplished fact, with the mountaineer at the top of the peak and little indication of how to get there.
§ XIX-5. Concluding Remarks.
To quote a popular philosopher "It ain't over 'til its over." So when will the story of Planck's quantum be over?
Certainly the great progress was made in a few giant strides, although at first with great temerity and hesitation: witness the five year lapse between Planck's discovery of h and Einstein's light quantum, then eight years before Bohr's atom, and eight more before de Broglie. Then the deluge of Heisenberg, Born, Jordan, Dirac, Schrodinger, and Bohr, all within three years or so. One might argue that the sole new idea since that time has been the Dirac-Feynman Path Integral formulation of quantum mechanics which had a time lag of more than fifteen years.
The actual applications of quantum theory have come thick and fast, but none have required any fundamental change either in the theory or in the Copenhagen
100
Yea
rs o
f Pl
anck
's Q
uant
um D
ownl
oade
d fr
om w
ww
.wor
ldsc
ient
ific
.com
by N
AN
YA
NG
TE
CH
NO
LO
GIC
AL
UN
IVE
RSI
TY
on
11/0
5/14
. For
per
sona
l use
onl
y.
Chapter XIX. The Next 100 Years 537
interpretation. In our view, we disdain all subsequent revisionist equivocation and fine tuning as purposely inconsequential and therefore metaphysical.
In all the above assessment we have accepted that non-relativistic quantum mechanics is the fundamental component of relativistic theories of everything which are inferred by a bottom-up deduction of a more fundamental structure. So far, a t tempts to proceed in a top-down way from a formulation of super-strings in a higher-dimensional space-time have not been uniquely constrained by any correspondence principle restriction to the world we see. Chaotic inflation provides a reason why this should be the case. This is the ultimate 'children's crusade' in physics, and an ever increasing army has been struggling across their own plains of Anatolia for more than twenty years, encouraged by occasional sightings of the Holy Sepulcher. But we - old, fat, listless, indolent and content friars that we are, sitting at home preaching our gentle gospel - wish them well in their pursuit of the greater glory of Tha t which inspires us all.
When (if?) the T.O.E. crusade conquers Jerusalem, what then? We can look forward to mountains of coffee-table books and educational videos; all with multicolored computer generated graphics of Planck size membranes spontaneously dividing and recombining and evolving and changing color and topology; looking for all the world like the amoeba we could never see through our eighth grade microscopes (which is why we became physicists in the first place), but were instructed to believe in by those who could. In spite of the fact that they defied any deeper understanding and were connected to the world we could see in ways unexplained if not inexplicable. Now the amoeba have become strings; we are firmly and in deepest tones instructed that this at last is all there is; and that it explains everything in ways that we could understand if only • • • we were smart enough, energetic enough, determined enough, patient enough, content to study our scriptures faithfully enough • • •. And if only we would take on faith that What? Tha t
the world consists of nine, ten, eleven dimensional amoeba? We don' t argue tha t this is not a necessary end-game for theoretical physics; all we are saying is tha t it is not yet a pretty sight.
Let us return to the fundamental questions that might yet remain in non-relativistic quantum mechanics. We have referred to quantum mechanics in a
100
Yea
rs o
f Pl
anck
's Q
uant
um D
ownl
oade
d fr
om w
ww
.wor
ldsc
ient
ific
.com
by N
AN
YA
NG
TE
CH
NO
LO
GIC
AL
UN
IVE
RSI
TY
on
11/0
5/14
. For
per
sona
l use
onl
y.
538 100 Years of Planck's Quantum
heuristic way as an information theoretic device. Planck was forced to invent h in order to ascribe a countable number of possible configurations to the ideal gas, and thereby a probability and finally an entropy. The great result was tha t the Action integral must be quantized, and from this follows everything.
We leave you here while we try to understand Entropy as Action, to more deeply understand "Why ft?" We are not the first to ask this question and it may already have an answer in the quantum generalization from classical Shannon information theory based on Boltzmann entropy, to quantum information theory based on von Neumann's quantum entropy [7] using the density matrix in place of the classical probability, and the concept of quantum bits of information with positive and negative handles. We might get lost, but it will be on our own plains of Anatolia.
T h e End. Footnotes and References:
1) D. Kleppner, Physics Today 51(11), 11 (1998); see also Critical Problems in Phystcs (Princeton, Princeton, NJ, 1997) V.L. Fitch, D.R. Marlow, M.A.E. Dementi, Eds., for the proceedings of a 1996 Princeton conference with similar goals. 2) T. Rothman and E.C.G. Sudarshan, Doubt and Certainty (Helix Books, PERSEUS, Reading MA, 1998). 3) G. Veneziano, see Ref. (7) in our ChXVI. 4) J. Bernholc, Physics Today 52(9), 30 (1999). The promise has become a reality described briefly here in Computational Materials Science: The era of Applied Quantum Mechanics. - "The properties of new and artificially structured materials can be predicted and explained entirely by computations, using atomic numbers as the only input." 5) E.F. Redish and R.N. Steinberg, Physics Today 52(1), 24 (1999), for current thinking on physics teaching. 6) H.J. Frisch, Physics Today 52(10), 71 (1999), for a personal account of one physicist's missionary experience. 7) N.J. Cerf and C. Adami, Phys. Rev. Lett. 79, 5194 (1999).
100
Yea
rs o
f Pl
anck
's Q
uant
um D
ownl
oade
d fr
om w
ww
.wor
ldsc
ient
ific
.com
by N
AN
YA
NG
TE
CH
NO
LO
GIC
AL
UN
IVE
RSI
TY
on
11/0
5/14
. For
per
sona
l use
onl
y.
