What did Dirac mean?
Gene Partlow
rare interviews, where he said (and I have to paraphrase) that he'd
'lately begun to suspect that Einstein may have been correct all along'.
Very frustratingly, neither he nor the interviewer said anything more in
that vein, and I had to wonder what Dirac had meant by that. Since
he'd been one of the premiere architects of QM and QFT I was struck
by the possibility that Dirac was rethinking the foundations of these
fields. I do remember that he had previously urged theorists to try
reinventing the whole shebang *from scratch* as it were, I believe
on the assumption that the old trail blazers had homed in too early
on an *adequate* way of doing microphysics and possibly missed
a better and deeper way.
Does anybody out there know what he may have been referring to?
Was he coming around to some more deterministic view in the
sense of Einstein? Something else?
--Gene
Brian J Flanagan
> Some years before P.A.M.Dirac died he gave one of his extremely
> rare interviews, where he said (and I have to paraphrase) that he'd
> 'lately begun to suspect that Einstein may have been correct all along'.
[...]
> Does anybody out there know what he may have been referring to?
I don't know the answer to your question, but as I am fond of pointing
out, one often encounters statements in introductory QM texts to the
effect that Schrodinger's equation contains "in principle" all that
can be known about a physical system, whereas Schrodinger himself
disagreed. Thus, in his wonderful little book on 'Mind and Nature',
Schrodinger writes that, if you ask a physicist what is his idea of
yellow light, he will answer that it is EM waves of 590 nm wavelength.
But if you ask him, "where does the yellow come in?" he will reply,
"in my picture, not at all". So, one of the most salient aspects of
light--its color--is not mentioned in physics at all. Therefore it
would seem that QM is prima facie incomplete in the sense of EPR
because not all "elements of reality" are contained therein. Now, to
be sure, various scams have been tried to get around this little
problem. Galileo, Newton, and some among their philosophical
contemporaries shoved color and the other so-called secondary
properties into the category of the mental. The trouble here, as Mach
argued, ("Analysis of Sensations") is that colors vary with physical
parameters and so colors would seem to fit our ideas of what it means
to be physical. Others try to identify colors with wavelength, but
that won't do because, as Schrodinger and Feynman tell us (Feynman,
'Lectures'), colors behave like vectors and wavelengths, being
lengths, are scalars. Now, I have made the innocuous suggestion that
perhaps the secondary qualities just are the hidden variables of EPR,
but this notion is often viewed as highly speculative, in spite of the
wealth of evidence available which would seem to support such a
notion.
Danny Ross Lunsford
> Does anybody out there know what he may have been referring to?
> Was he coming around to some more deterministic view in the
> sense of Einstein? Something else?
Just a speculation, but having gone through a good deal of Dirac's later
work, I can say he was usually trying to fix what he perceived as the ugly
flaws in physics - in particular, the renormalization program. He was very
dissatisfied with the entire setup of QFT.
-drl
scerir
> Was he coming around to some more deterministic view in the
> sense of Einstein?
Dirac wrote 2 or 3 papers about that. I.e. he said, in Rome,
and I was there, that he did not like Born's rule and he (too)
did not think that God was playing with dice. But his
position was much more elaborated than that. I'll post some
references soon.
-s.
Ralph E. Frost
news:861332bd.02010...@posting.google.com...
Having lived through seeing the success of introducing his own new math
symbols, possibly Dirac was reflecting on the missed opportunity of not
having been more patient -- being still and waiting for a deeper, perhaps
more bold shift from one symbol base to another. Einstein, reportedly
spent his later decades looking, again, for the lost and secret passageway.
Bohr long prophesied the coming of a more suitable 'complementary
expression'.
Have you ever heard of peer reviewers lauding any papers submitted since
1905 as exceptionally fine because the author reinvented the whole shebang
*from scratch*?
I don't read many physics journals, but I am going to take a wild guess and
say the answer is "No, the whole shebang upgrade from scratch project hasn't
made it through peer review yet".
Also, do you have an opinion why subsequent physics folks don't ever take to
heart and follow their predecessors' later, more thoughtful advice? Is it
just the lure of easy [..acceptance-by-fellow-herd-members.. ..other highly
valued physicist treats.. -- Sure can't be the easy fame or money.]?
Is there perhaps a systemic difficulty?
--
Best regards,
Ralph E. Frost
http://flep.refrost.com
phn 765/563-3711
fax 425/969-0200
Rational thought is not all it's cracked up to be.
"...Love one another..." John 15:12
Gene Partlow
> Also, do you have an opinion why subsequent physics folks don't ever take to
> heart and follow their predecessors' later, more thoughtful advice? Is it
> just the lure of easy [..acceptance-by-fellow-herd-members.. ..other highly
> valued physicist treats.. -- Sure can't be the easy fame or money.]?
>
> Is there perhaps a systemic difficulty?
Well, two things occur to me...
--It seems to me that successive waves of scientists mine a good
mother lode idea as long as it holds out, and generally don't start
casting glances elsewhere until certain data &/or logical inconsis-
tencies start showing up, which they seem to do inevitably. But
until that time it must seem hard or pointless to start hacking away
from the rich ore body, ~90 degrees from everbody else, as it were.
Yet there are always a relative handful who do wander off down odd
corridors, on their own or inspired by elder advice.
--Also, I quote something from a draft of an essay sent to me years
ago by Prof. Edward Nelson, Dept. of Mathematics, Princeton U.,
intended for inclusion in v. III of Collected Works of Norbert Wiener
(ed. P. Masani, MIT Press):
"....What motivates Einstein, Schrodinger, deBroglie, Wiener, Bohm,
and a host of others to reject the orthodox intepretation of quantum
theory and to seek alternatives? I believe that this is not an isolated
phenomenon, but is the expression of a deep drive within science.
"When a science is young, its practitioners are struck by the differences
which distinguish it from older sciences treating simpler phenomena.
New forms of explanation are discovered which are quite different
conceptually from the older forms. As these achieve successes in the
new science, the strong temptation arises to elevate these new forms
of explanation into philosophical principles which establish a
fundamental cleavage between the new science and older theories.
Later a countercurrent sets in, and attempts are made to reduce the new
theory to older principles. When these attempts at reduction are
successful -- as for example in the synthesis of urea, the explanation
of the physical nature of the chemical bond, and the discovery of the
molecular structure of the gene -- science is greatly enriched. This
contrasts with the scientific aridity of antireductionist philosophical
principles such as vitalism.
"In the twentienth century a new science has emerged: quantum
physics. It is the youngest of the natural sciences. The prevailing
opinion among its practioners is that it requires radically new forms
of explanation from those of classical physics, and these new forms
of explanation have received their philosophical apotheosis in Bohr's
principle of complementarity.
"I was discussing with Professor Bargmann my belief that the prin-
ciple of complementarity is a form of vitalism, and he told me the
following story. Some years ago Delbruck gave a lecture at Princeton
with Bohr in the audience. After the lecture there was a lively dis-
cussion which soon turned to the newly discovered Crick-Watson
model. Almost everyone expressed enthusiasm. Bohr, however.
voiced disappointment at the discovery and said, 'But where is life?' "
While I'm not sure I agree with all that Nelson wrote, I think it has
some validity and is relevant to the issues we're talking about.
It should be noted that he was part of the 'hidden variables' movement
and authored Dynamical Theories of Brownian Motion.
regards,
--Gene
Gene Partlow
> Dirac wrote 2 or 3 papers about that. I.e. he said, in Rome,
> and I was there, that he did not like Born's rule and he (too)
> did not think that God was playing with dice. But his
> position was much more elaborated than that. I'll post some
> references soon.
Great...I look forward to seeing those refs. The 'not...playing with
dice...' part sounds sympathetic to Einstein's intuition of course.
I can imagine both of them hobnobbing in some quiet corner of
the afterworld, nodding their heads and trying to figure out how
to tell the rest of us back here how it REALLY is!
cheers,
--Gene
Carl Markpost
einstein thought his CC was teh biggest mistake of his life but current
research seems to favour a non-zero CC.
> Gene Partlow :
>
> > Some years before P.A.M.Dirac died he gave one of his extremely
> > rare interviews, where he said (and I have to paraphrase) that he'd
> > 'lately begun to suspect that Einstein may have been correct all along'.
> [...]
> > Does anybody out there know what he may have been referring to?
>
[Moderator's note: unnecessarily quoted text deleted by moderator -- KS]
Murray Arnow
I'm going to have to go back and read the Born-Einstein Letters--that book
where Born published his correspondences with Einstein. There is a series of
communications where Born finally understands why Einstein has trouble with
the probabilistic interpretation. It took Pauli acting as a mediator to get
Born to appreciate Einstein's criticism. I don't remember the details and
that's why I have to reread the letters. As I recall, the argument that
Einstein used was not based on intuition or aesthetics.
Danny Ross Lunsford
> could it be einstein'd cosmological constant he was referring to? Surely
> einstein thought his CC was teh biggest mistake of his life but current
> research seems to favour a non-zero CC.
I think this is probably right! One of Dirac's many amazing ideas was the
"large numbers" hypothesis, and the work on this did involve GR with the
cosmological term.
BTW the last page and 1/5th of Dirac's 69-page book on GR (a great book!) is
about the cosmological term. Otherwise he doesn't mention it. He simply
shows that it has to be small so as not to disturb the agreement of GR with
local effects (precession etc.).
My own opinion (as if anyone asked) is that this term results from
contracting a larger group.
And to clear up the point about Einstein's blunder - it wasn't the lambda
term as such that constituted the blunder. Einstein failed to investigate
the stability of his equilibrium Universe with the lambda term. It turns out
to be unstable. This by the way shows in direct terms that Einstein was
well-acquainted with what made for mathematical "rightness" and what was
invovled in committing blunders.
-drl
Ralph E. Frost
>
> > Also, do you have an opinion why subsequent physics folks don't ever
take to
> > heart and follow their predecessors' later, more thoughtful advice? Is
it
> > just the lure of easy [..acceptance-by-fellow-herd-members.. ..other
highly
> > valued physicist treats.. -- Sure can't be the easy fame or money.]?
> >
> > Is there perhaps a systemic difficulty?
>
> Well, two things occur to me...
>
> --It seems to me that successive waves of scientists mine a good
> mother lode idea as long as it holds out, and generally don't start
> casting glances elsewhere until certain data &/or logical inconsis-
> tencies start showing up, which they seem to do inevitably. But
> until that time it must seem hard or pointless to start hacking away
> from the rich ore body, ~90 degrees from everbody else, as it were.
I follw that, but my question was more aimed at the notion that it seems in
general the folks who hit with the "BIG" chessmoves, within a solar cycle or
two in their own life, they are saying, "Whoa, there fellow herd members,
you are stampeding off on the initial approximation. Be thoughtful. Broaden
the base. Generate some parallax. Seek your own thought that is worthy of
speech."
But none of the young broncos bother to listen, their eyes wide and their
nostrils flaring. Pretty soon they have built a crystalline monolith with
fractures at its base that, like the French Court, require rigid rules to
exclude all but compliant, sanctioned thought and expressions.
After reading an essay or two of Bohr on complementarity, I got the
distinction impression he was trying to say, "Hey, we know this committee
imagery on the perplexing new experimental results is not the thing we are
looking for, but we are not smart enough to actually explain what's going on
in the non-classical realms -- except through these here rigid set of rules.
BUT YOU ALL MUST REMEMBER (Bohr screamed loudly), that after a fashion
improved symbols and linguist expression will emerge that will rationalize
this stuff and allow people to understand what now, seemingly, can only be
reflected in the abstract math."
> Yet there are always a relative handful who do wander off down odd
> corridors, on their own or inspired by elder advice.
But this is not good enough. We've seen the trend and it is us. That there
is not systemic encouragement for more explorers to set off to find other
ways out of the cul-de-sac is the systemic problem.
Brian J Flanagan
> Gene Partlow wrote:
> > Yet there are always a relative handful who do wander off down odd
> > corridors, on their own or inspired by elder advice.
>
> But this is not good enough. We've seen the trend and it is us. That there
> is not systemic encouragement for more explorers to set off to find other
> ways out of the cul-de-sac is the systemic problem.
I think it's important to remember that academia serves the
essentially conservative function of passing on the best of what's
gone before--it is the living memory of the race, if you will. Now,
having said that, it is also true that academia promotes new
scholarship and scientific investigation, meanwhile also providing a
proving ground for new works and ideas. So we have an inherent
conflict between the old and the new, an essential tension between
conservation and innovation. It is instructive to remember in this
connection that Galileo started his own school when he couldn't find a
receptive audience among the universities of his time, which were then
still under the sway of Aristotle and scholasticism. Also worth
remarking is the fact that the University of Iowa, where I studied as
an undergrad, prides itself on being the first institution of its type
to award an advanced degree for a "creative" work at its Writer's
Workshop. But consider: Modern universities have been around for
hundreds of years, and yet it is only in quite recent times that
"creative" works have been rewarded with a degree. Getting back to
physics, Neils Bohr's group clearly did a lot of groundbreaking work
... only to generate a new dogma. So I'm inclined to think that we
have here a running theme in the human comedy. Then, too, the value of
creativity has often been exaggerated in our time. It was not too long
ago when certain ideologues were proclaiming that everyone is an
artist, which means no one is an artist. And then, do we really want
(say) surgeons or engineers to be creative?
[Moderator's note: Replies not specifically about physics should
go to e-mail or to another newsgroup. -MM]
scerir
> referring to? Was he coming around to some more deterministic
> view in the sense of Einstein? Something else?
> --Gene
Useful references are:
P.A.M. Dirac, The Development Of Quantum Mechanics,
Conferenza Tenuta il 14 Aprile 1972, Roma
Accademia Nazionale dei Lincei, 1974
(11 pages) [*]
P.A.M. Dirac, The Inadequacies Of Quantum Field Theory,
1984 (his last paper), in B.Kursunoglu & E.P.
Wigner (eds.) The Dirac Memorial Volume,
Cambridge U.P., 1987
[*] pag. 6
' This statistical interpretation is now universally accepted as
the best possible interpretation for quantum mechanics, even
though many people are unhappy with it. People had got used
to the determinism of the last century, where the present
determines the future completely, and they now have to get used
to a different situation in which the present only gives one information
of a statistical nature about the future.
A good many people find this unpleasant; Einstein has always
objected to it. The way he expressed it was: 'The good God does
not play with dice'. Schroedinger also did not like the statistical
interpretation and tried for many years to find an interpretation
involving determinism for his waves. But it was not successful
as a general method. I must say that I also do not like indeterminism.
I have to accept it because it is certainly the best that we can do
with our present knowledge. One can always hope that there will
be tuture developments which will lead to a drastically different
theory from the present quantum mechanics and for which
there may be a partial return of determinism. However, so long
as one keeps to the present formalism, one has to have this
indeterminism. '
Brian J Flanagan
> A good many people find this unpleasant; Einstein has always
> objected to it. The way he expressed it was: 'The good God does
> not play with dice'. Schroedinger also did not like the statistical
> interpretation and tried for many years to find an interpretation
> involving determinism for his waves.
Thank you for those references. De Broglie also objected at one time,
and his "pilot wave" picture was later elaborated upon by Bohm, who
had the rare internal fortitude to buck the Copenhagen establishment.
Holland, in his 'Quantum Theory of Motion' quotes Born, the father of
the statistical interpretation of the wave function, as saying that,
if one does not like this picture, one is always free to add more
variables, which determine the individual result. However, one very
rarely finds any of this material in the older textbooks.
ueb
> ' This statistical interpretation is now universally accepted as
> the best possible interpretation for quantum mechanics, even
> though many people are unhappy with it. People had got used
> to the determinism of the last century, where the present
> determines the future completely, and they now have to get used
> to a different situation in which the present only gives one information
> of a statistical nature about the future.
> A good many people find this unpleasant; Einstein has always
> objected to it. The way he expressed it was: 'The good God does
> not play with dice'. Schroedinger also did not like the statistical
> interpretation and tried for many years to find an interpretation
> involving determinism for his waves. But it was not successful
> as a general method. I must say that I also do not like indeterminism.
> I have to accept it because it is certainly the best that we can do
> with our present knowledge. One can always hope that there will
> be tuture developments which will lead to a drastically different
> theory from the present quantum mechanics and for which
> there may be a partial return of determinism. However, so long
> as one keeps to the present formalism, one has to have this
> indeterminism. '
Thanks for the references and the detailed quotation.
What Dirac said is really exceptionally foresightful!
There are in fact the foreseen developments, not as new
theory but based on - GTR . That is no return of determinism
but has to do with chaos. It follows from numerical simulations.
The results are independent on the interpretation of the
based equations. (These keep even fact also when the interpretation
could be wrong !)
Ulrich Bruchholz
www.markt-2000.de/patent
Murray Arnow
>where Born published his correspondences with Einstein. There is a series of
>communications where Born finally understands why Einstein has trouble with
>the probabilistic interpretation. It took Pauli acting as a mediator to get
>Born to appreciate Einstein's criticism. I don't remember the details and
>that's why I have to reread the letters. As I recall, the argument that
>Einstein used was not based on intuition or aesthetics.
>
I finally went back to the B-E Letters. This is one of the letters Pauli
sent to Born regarding Einstein's view of determinism--I think it is the
is the most informative one. It's readablity is hampered because of ascci
limitations. This is 116th letter dated 15-Apr-1954.
=== begin
Dear Born
Thanks for your letter. I am writing from here after all,
for when I get back to Zurich on April 11th I will probably
find work waiting for me and will have no time. Also, Einstein
gave me your manuscript to read; he was "not at all" annoyed
with you, but only said you were a person who will not listen.
This agrees with the impression I have formed myself insofar
as I was unable to recognise Einstein whenever you talked
about him in either your letter or your manuscript. I t seemed
to me as if you had erected some dummy Einstein for yourself,
which you then knocked down with great pomp. In particular,
Einstein does not consider the concept of `determinism' to be
as fundamental as it is frequently held to be (as he told me
emphatically many times), and he denied energetically that he
had ever put up a postulate such as (your letter, para. 3):
`the sequence of such conditions must also be objective and
real, that is, automatic, machine-like, deterministic'. In the
same way, he "disputes" that he uses as criterion for the
admissibility of a theory the question: `Is it rigorously
deterministic?'
Einstein's point of departure is `realistic' rather than
'deterministic', which means that his philosophical prejudice
is a different one. His train of thought can be reproduced
briefly thus:
1. A preliminary question: Do all mathematically possible
solutions of the Schroedinger equation, even in the case of a
macro-object, occur in nature under certain conditions ("in my
opinion this question has to be answered in the affirmative
whatever happens") or only in those special cases where the
position of the object is `exactly', `sharply' defined?
Comment: If the latter class of solutions (which we denote
(Delta_x)^2 < L0^2) is described by K0, it has the following
attributes:
i. When Phi1(x) and Phi2(x) also belong to K0, but their mean
positions
<x1> = Int(x1*|Phi|^2*dx) / Int(|Phi|^2*dx),
<x2> = Int(x2*|Phi|^2*dx) / Int(|Phi|^2*dx),
are widely separated, that is to say (<x2> - <x1>)^2 >> L0^2,
then
(A) C1*Phi1(x) + C2*Phi2(x) = Phi(x) does "not" belong to K0.
ii. If Phi1(x, t0) belongs at a certain time t0 to K0, then
Phi1(x, t) no longer belongs to K0 when |t - t0| is sufficiently
large. It therefore seems impossible to me to confine oneself "in
principle" to the solutions of the Schroedinger equation of the
special class K0, and this cannot in principle be different for
a macro-body than, let us say, for an H atom or for a single
electron. For if quantum mechanics is correct, then a macrobody
has in principle to show diffraction (interference) phenomena,
and the difficulties are only going to be "technical" because
of the small size of the wavelength.
In that case, however, one also needs the superpositions of
type (A) from solutions of class K0 which do not themselves
belong to K0. This is, for example, the case with interference
phenomena, when a particle passes through two (or more)
openings (in this case it does not matter whether they are
`spheres which are visible under the microscope' or
'electrons').
Up to this point, it seems to me, there is agreement.
2.Now to Einstein's essential question: "How are those
solutions of the Schroedinger equation which do not belong to
class KO (for example, macro-objects) to be interpreted in
physical terms"?
Here Einstein's reasoning is as follows:
A. When one `looks at' a macro-body, it has a quasisharply-
defined position, and it is not reasonable to invent a causal
mechanism according to which the `looking' fixes the position.
Comment: Instead of `looking at', I would say `illuminating
with convergent light', and instead of the further
`looking', I would say `a suitable experimental
arrangement'. Apart from that I am still in agreement,
because in this case I do not consider that the appearance
of the "definite position" or, what amounts to the same
thing, its appearance as a result of "the observation," can
be deduced by natural laws.
Einstein's reasoning continues:
B. Therefore a macro-body must "always" have a
quasisharply-defined position in the `objective
description of reality'. As those Psi-functions which do
"not" belong to class K0 cannot in principle be `thrown
away', and must also be in accordance with nature, the
"general" Psi-function can only be interpreted as an
"ensemble" description. If one wants to assert that the
description of a physical system by a Psi-function is
"complete," one has to rely on the fact that "in principle"
the natural laws only refer to the ensemble-description,
which Einstein does not believe (not only in those at
present known to us).
What I do not agree with is Einstein's reasoning B (please
note that the concept of `determinism' does not occur in
it at all!). I believe it to be "untrue" that a 'macro-
body' always has a quasisharply-defined position, as I
cannot see any fundamental difference between micro- and
macro-bodies, and as one always has to assume a portion
which is indeterminate to a considerable extent wherever
the "wave-aspect" of the physical object concerned
manifests itself. The appearance of a definite position x0
during a subsequent observation (for example, `illumination
of the place with a shaded lantern') above the opening in
the figure[*] on the previous page, and the statement
`the particle is there', is then regarded as being a
`creation' existing outside the laws of nature, even though
it cannot be influenced by the observer. The natural laws
only say something about the "statistics" of these acts of
observation.
As O. Stern said recently, one should no more rack one's
brain about the problem of whether something one cannot
know anything about exists all the same, than about the
ancient question of how many angels are able to sit on the
point of a needle. But it seems to me that Einstein's
questions are ultimately always of this kind.
Einstein would not agree with this, and he would demand
that the `complete real description of the system' even
before the observation must already contain elements which
would in some way have to correspond with the possible
differences in the results of the observations obtained by
`illumination with a shaded lantern'. I think, on the
other hand, that this postulate is inconsistent with the
freedom of the experimenter to select mutually exclusive
experimental arrangements (for instance, radiation with
long parallel light wavelengths!).
To summarise, I should like to say this: while I have no
objection to the formal calculations your manuscript
contains -- which incidentally, were not unknown to me --
it completely bypasses the problems which are of interest
to Einstein. In particular it seems to me misleading to
bring the concept of determinism into the dispute with
Einstein.
A further remark here, independently of Einstein, to
illustrate the difference between classical mechanics and
quantum mechanics when `measuring' a `path'.
A. Classical mechanics: Let us consider, for example, the
determination of the path of a planet. One should measure
the position "repeatedly" (at different moments of time
t0, t1, . . .) always with the same accuracy Delta_x0, If
one is in possession of the simple "laws" for the motion
of the body (for example, Newton's law of gravitation),
one is able to "calculate" the "path" (also position "and"
velocity at any given time) of the body with "as high" an
accuracy "as one likes" (and also to test the assumed law
again at different times). Repeated measurements of the
position with limited accuracy can therefore successfully
replace "one" measurement of the position with high
accuracy. The assumption of relatively simple laws of
force like that of Newton (and not some irregular zig-zag
motion or other on a small scale) then appears as an
idealisation which is permissible in the sense of
classical mechanics.
B. Quantum mechanics: The repetition of positional
measurements in sequence with the same accuracy Deleta_x0
is of "no use at all" in predicting subsequent positional
measurements. For every positional measurement to an
accuracy Delta_x0, at the time tn implies the inaccuracy
Delta_x_tn ~ h/(m*Delta_x0)*(t(n+1) - tn)
at a later time, "and destroys the possibility o f using
all previous positional measurements within these limits
of error"! (If I am not mistaken, Bohr discussed this
example with me many years ago.)
The main difference between the theories A and B, which is
that in B information obtained as a result of earlier
measurements can be lost after "one" measurement, has not
been expressed clearly enough in your manuscript.
With kind regards
I remain
Yours
W. Pauli
=== end