Open letter to professor John.A.Wheeler
Dear Dr.Wheeler
35 years ago You are together with Charles W.Misner and Kip S.Thorne published wonderful book "Gravitation",which call "Bible" of
relativity theory. Lot of peoples remember next quotation from this book:
"Behind it all is surely an idea so simple, so beautiful, that when we grasp it - in a decade, a century, or a millennium - we
will all say to each other, how could it have been otherwise? How could we have been so stupid."
But first of all i want reminding to You other quotation belong to Richard Feynman from his Nobel lecture:
"I was inspired by the remarks in these books; not by the parts in which everything was proved and demonstrated carefully and calculated,
because I couldn't understand those very well. At the young age what I could understand were the remarks about the fact that this doesn't
make any sense, and the last sentence of the book of Dirac I can still remember, "It seems that some essentially new physical ideas are here
needed." So, I had this as a challenge and an inspiration. I also had a personal feeling, that since they didn't get a satisfactory answer to the
problem I wanted to solve, I don't have to pay a lot of attention to what they did do."
When i was young(now i am 68 years old)such kind of remarks, i meet in the вook P.Fraenkel, Yehoshua Bar-Hillel, FOUNDATIONS
OF SET THEORY, North-Holland, 1958) following :
"The bridging of the chasm between the domains of the discrete and the continuous,or between arithmetic and geometry, is one of the most
important - may, the most important - problem of the foundations of mathematics....Of course, the character of reasoning has changed, but,as
always, the difficulties are due to the chasm between the discrete and the continuous - that permanent stumbling block which also plays an
extremly important role in mathematics, philosophy,and even physics."
This remark get me inquizitive.When i was get older i am starting to ask peoples next question:
"This is present day problem or not?" to comparision of 1958 and get next answers:
From Frank Wilczek Nobel Laureat for Physics,2004
Hi,
I don't know how to rate it in importance, since I don't see any specific suggestion of a paradox or anomaly in Nature related to it, but it does
bother me that the real number continuum, which is so fundamental to our present formulation of physics, is so complicated and apparently
artificial when considered as a logical construction.
All best wishes,
Frank Wilczek,
From G. 't Hooft Nobel Laureat for Physics,1999
I don't perceive this as a chasm - or a stumbling block. Surely symmetry
is playing a central role in physics, both discrete and continuous.
Indeed, both kinds of symmetries are bewing used as tools to
construct theories; gauge fields are fields whose equations can only
be understood in their relation to local, continuous symmetries.
In quantum mechanics, particle theory, condensed matter theory,
superconductivity, symmetries are at the centre of our formalisms.
I wouldn't call such an essential aspect of our theories a
stumbling block.
Cordially,
G. 't Hooft,
From Yuri Manin Laureat of Cantor Medal
Briefly, I think that:
1) Foundations of math. have nothing to do with this "chasm"
2) On the one hand, it is being bridged permanently
in all good math works.
3) On the other hand, it can never be deleted completely,
partly because it is one of the most important
sources of creative tension.
Yu. Manin.
As we see i did'nt get clear cut answer.Then my attention was concentreted to notions of discret and continue symmetries .Then i put forward
following questions:
WE HAVE 2 DIFFERENT KINDS OF SYMMETRY: DISCRETE AND CONTINOUS.
BASIC DIFFERENCE BETWEEN THEM
DISCRETE SYMMETRY IS STATIC SYMMETRY(REFLECTIONS,PARITY,ETC). NOT DEMANDING MOTION,CHANGE IN TIME
CONTINOUS SYMMETRY IS DYNAMIC, DEMANDING MOTION(ROTATIONS,TRANSLATIONS,SHIFTS,ETC) CHANGE IN TIME.
THE MOTION SUPPOSED TO BE DIFFERENT VELOCITY (FROM SMALL TO RELATIVISTIC)
WHEN WE GOING TO RELATIVISTIC VELOCITY OBJEKT GET DIFFERENT LORENTCIAN DEFORMATION AND CONTINOUS
SYMMETRY LOST ITS SENSE.WE GET SOME KIND SELF-REJECTION OF CONTINOUS SYMMETRY.
DOES DISCRETE SYMMETRY ONLY REAL SYMMETRY?
I get next answers:
From Vitali Efimov Professor at the Washington State University
The space and time remain uniform in relativistic case. This is why we have the same three great conservation laws -- conservation of linear
and angular momentum and conservation of energy -- as we do in nonrelativistic case. We even acquire a deeper understanding of these
laws because the uniformity of space and uniformity of time -- which are separate symmetries in the nonrelativistic case -- are now combined
into the uniformity of four-dimensional space-time.
Vitaly
From: G.Hooft 't Nobel Laureat for Physics,1999
Dear Sir,
It is true that one can distinguish discrete and continuous
symmetries, but what you say about continuous symmetries does
not make much sense to me.
You talk about deformations like Lorentz contractions due to
relativity, but, relativity itself is nothing but a continuous
symmetry: that of the Lorentz transformations. All one has
symmetry: that of the Lorentz transformations. All one has
to do is ensure that a symmetry in question (say isospin
symmetry, gauge symmetry or supersymmetry) is compatible
with Lorentz symmetry, then there is no problem.
Cordially,
G. 't Hooft
From Julian Barbour Author of book The End of Time
I do not know the answer to your questions. However, I do believe
continuous symmetries are fundamental except perhaps the Lorentz boosts.
Best wishes, Julian Barbour.
All these answer also not satisfy me.Then i meet book W..Heisenberg (Physics and
Beyond, Harper and Row, New York (1974), where talking about some Christmascard send by Pauli to Heisenberg about some
incomplete idea.
Text was very enigmatic:
"Division and reduction of symmetry, this then is the kernel of the
brute! The former is an ancient attribute of the devil."
i send letter to Professor Hans Primas, a explorer legacy of Pauli for more detail and get letter
From Hans Primas Professor for Theoretical Chemistry at ETH; Zuerich, Switzerland
Dear Yuri Danoyan,
The original German quotation is:
"Zweiteilung und Symmetrievemindeung, das ist des Pudels Kern. Zweiteilung ist ein sehr altes Attribut des Teufels. (Das Wort Zweifel soll
urspünglichch Zweiteilung bedeutet haben)."
It is in a letter by Pauli to Heisenberg, who quote it (without given the date of the letter) in:
W. Heisenberg, Wolfgang Paulis philosophische Auffassungen, Die Naturwissenschaften, vol. 46 (1959), pp.661-663.
It is again quoted in W. Heisenberg, Der Teil und das Ganze , Piper Verlag , Muenchen (1969), p.317. In the English translation of this book
(Physics and Beyond, Harper and Row, New York (1974), p.234) it is translated as:
"Division and reduction of symmetry, this then is the kernel of the
brute! The former is an ancient attribute of the devil."
It is notoriously difficult to translate Pauli's striking and succinct German in another language. Here Pauli refers to Goethe's Faust, part 1,
second scene "Faust's study":
"Das war also des Pudels Kern ... "
In German, this phrase has become proverbial, known to everyone (even if to people who do not know the Faustian context), essentially in the
sense "that is the crux of the matter".
The phrase you quote "WHERE ACTUALLY THE DOG LIES EXACTLY BURIED !" seems to me not to be a literal translation of a remark by
Pauli, but a translation of the German saying: "da liegt der Hund begraben". This saying is probably more then 400 years old, and the
authoritative "Deutsches Woerterbuch" by Grimm leave the question of the origin of this saying open. Probably "Hund" does not refer to "dog",
but to the Middle High German "hunte" (meaning "centum", "hundred coins"), or more generally "booty" or "treasure". Nevertheless, the
present-day meaning is clear to every German-speaking child. It means roughly: "that is the crux of the matter".
I hope that these explanations are a bit helpful. Wit my best regards
Hans Primas
Then i starting to ask people next question:
"What Pauli mean?"
From Peter Woitt Lecturer in Mathematics
Columbia University
Dear Yuri,
Dear Yuri,
I'm afraid I'm not
a reincarnation of Pauli, and really have not idea what he meant by the
quotation. To understand its significance I assume you would have to know what
he and Heisenberg were talking about. Also Pauli was often very ironic, so you
need to take that into account.
Best wishes,
Peter
From:G. Hooft 't Nobel Laureat for Physics,1999
Pauli cannot have meant to say that continuous symmetry should not be
examined. We should examine everything. What he meant may have been
that in Nature one sees the tendency of symmetries to be reduced or even
disappear. This could be caused by explicit forces or effects which simply
aren't symmetric, such as the weak interaction causing transitions
among particles that otherwise would be forbidden, but in more interesting
cases it could be that, although all forces are symmetric, it is the
asymmetric solutions of the equations that often dominate. Famous example
is the Donkey of Buridan: it was given two identical haystacks, some
distance apart. Since they were identical, the donkey could not choose,
so it died of starvation. Of course, real donkeys will immediately choose
one of the two and start eating, but whatever solution it takes, the
solution will break the perfect symmetry between the two haystacks.
Pauli probably meant that Nature is full of such Donkeys, choosing
one haystack, no matter which, and breaking symmetries that way.
This holds both for discrete and for continuous symmetries, so I
don't think Pauli wanted to make any distinction there.
G. 't H
From Yuri Manin Professor of Mathematics
In many cultures, small integers are associated
with various sacral/metaphysical ideas
(cf "trinity" in Christianity).
"Two" in indoeuropean languages is associated
with "doubt", the roots of "doute" (fr.),
"Zweifel" (germ.), "doubt", more general underlying
idea being that of "breaking of integrity".
Remarkably, the blessed state of "nirvana"
in Sanskrit has the etimology "nir-dva-n-dva",
"there is no doubling", "everything is One".
Goethe calls Mephisto (I remember only Russian
version) "Duh otrican'ya i somnen'ya".
Perhaps, "Teufel" = "devil" also directly refer
to this root: one should consult an etymological
dictionary.
Pauli surely refers to these connotations.
They were commonplace in the German culture
of the first half of XX century.
From Lev Okun Lev Okun, a prominent physicist
Dear Yuri,
Zweiteilung= division in two parts
Symmetrieverminderung(you deleted r) is reduction of symmetry.
Pudel's Kern= central point (idiom)
Zweifel =doubt.
I believe , Pauli wanted to stress the central point of symmetry breaking
in physics and its connection with doubt and with devil.
best regards,
Lev
Lev
All these interpretations not satisfy me and i invent idea of Metasymmetry: symmetry between discret and continue symmetry.
Now to Methasymmetry. If we try to represent discrete symmetry and continuous symmetry with minimal means by using at least two symbols,
what should we do? We can use signs 0 and 1 or + and -. Then the minimal discrete symmetry may be represented as 10 or 01 and minimal
continuous symmetry as 00 or 11.In this case, to represent continuous symmetry we used some APPROXIMATION without which our
reasoning would be impossible. Now, going back to symmetry between the discrete and the continuous we may use representation of one
version as 10 & 11. Because there is no long vertical on the keyboard I used the symbol of & in the English keyboard.
What can be said about Methasymmetry now? A general conclusion is as follows: the ratio of the total number of zeros (unities) to that
of unities (zeros) makes up certain invariant ratio of 3:1 or 1: 3. This is the numerical measure of Methasymmetry.
I call this effect BROKEN METHASYMMETRY (+++1-) or (---1+)
In Nature we often come across the ratio 3:1, or 1:3, the sequence being of no importance:
1. Space is 3-dimensional and Time is 1–dimensional.
2. Only 3 elementary particles are stable with a half-integer spin (proton, electron, neutrino) and 1 is stable with an integer spin (proton),
3. 3 of 4 fundamental interactions (strong, electromagnetic, weak) are relatively closed by their intensity magnitude but are greatly different
from gravitational Again the 3:1 ratio.
4. In the Standard Theory of weak electric interaction bosons (W+, W-, Z) have a mass but a proton does not. Again we have the 3:1 ratio.
5. Beta decay where 1 neutron converts into a proton, an electron and a neutrino. Again the 3:1 ratio.
6. Mmin u-quark/Mel+ 1.5Mev/0.51 Mev = 3:1 ratio.
3:1 may be the fundamental symmetry of the Universe?
THE BINARY REPRESENTATION OF THE 3:1 RATIO IS 11:1.
JUST ONE SYMBOL USED!
Finnaly my own interpretation of Pauli’s enygmatic phrase:
Exepting the Time from presentation. Then continuous symmetry transformations are full eliminated(because need time) .Also "reversal of
time" eliminiteted from discrete symmetries. In the end, finally left only C and P, our "old friends" discreteness (anti-symmetry) and pseudocontinuity
(symmetry). Their symmetry leads to Methasymmetry (the ratio 3:1 that we have seen above). We have had Time go out through
the window and it has come back through the door.
Very crazy idea!
Dear Dr Wheeler !
My be this idea "so simple, so beautiful, that when we grasp it - in a decade, a century, or a millennium - we will all say to
each other, how could it have been otherwise? "I hope to get some answer.
Sincerely
Yuri Danoyan,,Riverton,Utah
P.S.1 Excuse my poor English, because i am emigrant from Armenia
2. I published this idea in russian magazine "Khimiya i zizn" ,1988,#5,p.82
