Looking for Dirac quotation on quantum mechanics
Camm Maguire
describing the mystery of the phase of the wavefunction in quantum
mechanics. Alas, I cannot find it now. The gist was that the
wavefunction modulus representing probability was all well and good,
but that "there was this 'other thing' which nobody really
understands, ...." Does this ring a bell with anyone?
Thanks in advance!
--
Camm Maguire ca...@maguirefamily.org
==========================================================================
"The earth is but one country, and mankind its citizens." -- Baha'u'llah
Maybe Perhaps
Maguire" <ca...@maguirefamily.org> wrote:
> Greetings! I seem to recall reading somewhere a quotation by Dirac
> describing the mystery of the phase of the wavefunction in quantum
> mechanics. Alas, I cannot find it now. The gist was that the
> wavefunction modulus representing probability was all well and good,
> but that "there was this 'other thing' which nobody really
> understands, ...." Does this ring a bell with anyone?
>
> Thanks in advance!
According to Yang, in a conversation with Dirac shortly before he died Dirac
expressed the view that the fundamental issue raised by Quantum phenomena is
the physical meaning of imaginary values. The source reference is an
article/chapter by Yang in the book "Schrodinger: a centenary tribute" (?
approximate title) edited by Clive Kilmister published in the early 80's, I
think.
Sorry, I am too busy to dig out the exact reference.
PS I don't recognise your quotation source. Any relation to Bebop'ulluhla
Bob_for_short
>The gist was that the
> wavefunction modulus representing probability was all well and good,
> but that "there was this 'other thing' which nobody really
> understands, ...." �Does this ring a bell with anyone?
P. Dirac contributed so much in QM and QED, including magnetic
monopoles that I cannot imagine him puzzling over the wave-function
phase.
In particular he formulated a gauge-invariant QED in terms of Dirac
variables where the phase transformations helped exclude non-physical
degrees of freedom. And monompoles have such a vector potential that
directly affects the wave-function phase.
Probably it was A. Einstein's non-understanding. He was the only who
never expressed any appreciation of QM and was uneasy with
probabilities.
Juan R. González-Álvarez
> Greetings! I seem to recall reading somewhere a quotation by Dirac
> describing the mystery of the phase of the wavefunction in quantum
> mechanics. Alas, I cannot find it now. The gist was that the
> wavefunction modulus representing probability was all well and good,
> but that "there was this 'other thing' which nobody really
> understands, ...." Does this ring a bell with anyone?
>
> Thanks in advance!
The "mistery" is solved in the density matrix formalism where the pure
state is unique: rho = |Psi><Psi|.
--
http://www.canonicalscience.org/
BLOG:
http://www.canonicalscience.org/en/publicationzone/canonicalsciencetoday/canonicalsciencetoday.html
a student
> Greetings! �I seem to recall reading somewhere a quotation by Dirac
> describing the mystery of the phase of the wavefunction in quantum
> wavefunction modulus representing probability was all well and good,
> but that "there was this 'other thing' which nobody really
There is a transcript of an interview in 1963
between Dirac and Thomas Kuhn, at
http://www.aip.org/history/ohilist/4575_5.html
It includes, in part:
Kuhn:
Were you concerned about the physical meaning
of the undetermined phase?
Dirac:
I did worry about it for a bit, I believe.
Kuhn:
You again exploit that in the paper on quantized
singularities and I wondered whether this was an
older �. Do you know when you worried about that?
Dirac:
Probably from the start of the transformation theory.
The phase was always something more
unphysical than the amplitude of the oscillations
So perhaps Kuhn has some record of this
in one of his books?
Bob_for_short
> There is a transcript of an interview in 1963
>
> It includes, in part:
>
> Kuhn:
> Were you concerned about the physical meaning
> of the undetermined phase?
> Dirac:
> I did worry about it for a bit, I believe.
> Kuhn:
> You again exploit that in the paper on quantized
> singularities and I wondered whether this was an
> Dirac:
> Probably from the start of the transformation theory.
> The phase was always something more
> unphysical than the amplitude of the oscillations
I think P. Dirac meant the known difference between the phase and
group velocities because in fact there is nothing else to puzzle about
in case of a wave packet.
In case of interaction with the electromagnetic filed there is also a
gauge phase impact but it is clear anyway that it can be eliminated or
simplified to get physically transparent phase.
Igor Khavkine
wrote:
That's an interesting take on Dirac's opinion. Perhaps you can provide
a quote where his puzzlement about phase velocity vs group velocity is
expressed in his own words?
Igor
Bob_for_short
> That's an interesting take on Dirac's opinion. Perhaps you can provide
> a quote where his puzzlement about phase velocity vs group velocity is
> expressed in his own words?
No, I cannot. I expressed my own guess basing on my own observations.
Agree, a wave cannot be described with its amplitude solely. Its
frequency
(or phase) is also an important feature. It does not create any
problem in
understanding whatever form is used: Asin(kx-wt) or Aexp(ikx-iwt).
But the group and phase velocities are more complicated things because
they
are connected with the dispersion law w(k) and the information
transfer speed.
It needs much more explications, reflection and it is always non-
trivial for students.
Vladimir
Arnold Neumaier
> Greetings! I seem to recall reading somewhere a quotation by Dirac
> describing the mystery of the phase of the wavefunction in quantum
> mechanics. Alas, I cannot find it now. The gist was that the
> wavefunction modulus representing probability was all well and good,
> but that "there was this 'other thing' which nobody really
> understands, ...." Does this ring a bell with anyone?
Here are some quotes:
According to Collins, Renormalization, p.10, Dirac said in 1981:
''Interacting QED is full of nonsense.''
Alisa Bokulich quotes in
http://muse.jhu.edu/journals/perspectives_on_science/v016/16.1bokulich.html
and
http://www.mitpressjournals.org/doi/pdf/10.1162/posc.2008.16.1.103
the following:
[p.84 in: P. Dirac,
The Early Years of Relativity. In G. Holton and Y. Elkana (Eds.),
Albert Einstein: Historical and Cultural Perspectives:
The centennial symposium in Jerusalem, 14-23 March 1979. (1982)]
''It seems clear that the present quantum mechanics is not in its
final form. Some further changes will be needed, just about as
drastic as the changes made in passing from Bohr's orbit theory to
quantum mechanics. Some day a new quantum mechanics, a relativistic
one, will be discovered, in which we will not have these infinities
occurring at all. It might very well be that the new quantum
mechanics will have determinism in the way that Einstein wanted.
This determinism will be introduced only at the expense of
abandoning some other preconceptions that physicists now hold.
So under these conditions I think it is very likely, or at any
rate quite possible, that in the long run Einstein will turn out
to be correct.''
[p.49 in: P. Dirac,
The Evolution of the Physicist's Picture of Nature.
Scientific American, 208(5) (1963), 45-53.]
''I think one can make a safe guess that uncertainty relations in
their present form will not survive in the physics of the future.''
In his 1975 book 'Direction of Physics', Dirac writes on p.10:
''And I think it is quite likely that at some future time we may
get an improved quantum mechanics in which there will be a return to
determinism and which will, therefore, justify the Einstein point of
view.''
(With this he cannot have meant Bohmian mechanics, since this was
at the time no longer in the future. It clearly did not convince him as
a solution of the foundational problems of quantum mechanics.
And he continues:)
''But such a return to determinism could only be made at the expense
of giving up some other basic idea which we now assume without
question.''
In his book 'The principles of quantum mechanics' (3rd ed.,
Oxford 1947), Dirac writes:
''In the general case we cannot speak of an observable having a
value for a particular state, but we can speak of its having
an average value for the state.'' (S.47)
More quotes can perhaps be found in
PAM Dirac, in:
Duke and Owens
Perturbative Quantumelectrodynamics
New York 1981
P.A.M. Dirac,
The Inadequacies Of Quantum Field Theory, 1984,
in: The Dirac Memorial Volume,
B.Kursunoglu & E.P. Wigner (eds.)
Cambridge U.P., 1987
I don't have these sources at hand; so if someone finds a relevant
quote there, I'd be interesting to know the page and the wording.
Arnold Neumaier
Bob_for_short
wrote:
> Here are some quotes:
>
> According to Collins, Renormalization, p.10, Dirac said in 1981:
> ''Interacting QED is full of nonsense.''
Although somewhat off-topic, I agree with it. And the nonsense origins
from CED where the electron self-action is admitted. I can safely say
that nobody can explain why the classical point-like electron should
act on itself.
Borrowing the classical interaction Lagrangian jA makes the
perturbative QED senseless without renormalizations. After the
renormalizations the solution does not belong any more to the original
interaction jA.
>
> ''It seems clear that the present quantum mechanics is not in its
> final form. Some further changes will be needed, just about as
> drastic as the changes made in passing from Bohr's orbit theory to
> quantum mechanics. Some day a new quantum mechanics, a relativistic
> one, will be discovered, in which we will not have these infinities
> occurring at all.
The renormalization ideology - bare self-acting particles rectified
with counter-terms - is just like the Bohr orbit postulates: there is
more postulations than physics implemented in it, IMHO.
As the author of "electronium", I confirm that there has been
necessary a conceptual step forward in order to eliminate the physical
nonsense and mathematical difficulties.
As to "determinism", it is, of course, already present in QM as the
average variable dynamics (Ehrenfest equations).
It is a rather funny coincidence that I recently added an APPENDIX to
my "Reformulation instead of Renormalization" just about classical
electro-dynamical model of electronium with all that "determinism". In
many-body (multi-mode) systems the determinism is practically
impossible to observe - we have to and we measure some average values
anyway (as well as their dispersions, if necessary).
Vladimir.
Daryl McCullough
>Although somewhat off-topic, I agree with it. And the nonsense origins
>from CED where the electron self-action is admitted. I can safely say
>that nobody can explain why the classical point-like electron should
>act on itself.
If the electromagnetic field is an independent entity, then it is
hard (for me, anyway) to understand how an electron could *not* act
on itself. As a charged particle moves through space, it is affected
by the local electromagnetic field. There are no extra variables in
the electromagnetic field recording which charged particles produced
it.
On the other hand, Feynman had a theory that did *not* treat the electromagnetic
field as an independent entity, but instead treated all electromagnetic
interactions as particle-to-particle interactions. I think this theory more or
less worked, but required some ad hoc assumptions, such as the assumption that
there are no free photons---that every photon originates at a charged particle
and eventually is absorbed by a charged particle.
--
Daryl McCullough
Ithaca, NY
Bob_for_short
wrote:
> Camm Maguire wrote:
> ...
> I don't have these sources at hand; so if someone finds a relevant
> quote there, I'd be interesting to know the page and the wording.
I saw a 4-volume edition (four books) of P. Dirac's publications
(translated and published in Russian). There is plenty of articles
devoted to QM and QED. In particular:
Complex Variables in Quantum Mechanics // Proc. Roy. Soc, London. A.
1937. V. 160. P. 48-59.
But I think that the OP question concerns the early QM development
stage (the transformation theory) when everything was new and
different from the Classical Mechanics. Later on P. Dirac managed to
connect the physical meaning of phase with the Lagrangian that finally
resulted in the path integral formalism.
Vladimir.