4.3 Space and time
93
4.3 Space and time
Du siehst, mein Sohn, zum Raum wird hier die Zeit.
Wagner, Parsifal, 1. Akt5
4.3.1 Realistic hypothesis
If in the context of abstract quantum theory, especially from the ur hypothesis, there should arise a universa
4
Quantum theory and spacetime
4.1 Concrete quantum theory
In the previous chapter we indicated a path to the reconstruction of abstract
quantum theory, i.e., the quantum theory of arbitrary alternatives and objects,
and arbitrary forces. Now our goal is
6
1 Introduction
equilibrium of a continuum, explains the stability and identity of the atoms
of an element, and oers a universal framework for physics.
The physics of the past century also began to fuse the other two foundations of classical mechanics, s
1.2 Outline
3
nature. Colloquial speech for newer theories is mostly the language available
from older theories. Certain fundamental statements are declared to be laws
of nature. The mathematical form of the laws of nature developed historically.
We disti
2.4 Chemistry
31
of the Lorentz transformation based on simple group theoretic postulates.
Nowadays one derives variational principles and dierential equations as far
as possible from invariance postulates. The question then becomes how best
to justify th
The Structure of Physics
by
Carl Friedrich von Weizscker
edited, revised and enlarged by
Thomas Grnitz
University of Frankfurt, Germany
and
Holger Lyre
University of Bonn, Germany
A C.I.P. Catalogue record for this book is available from the Library of Co
Preface (1985)
xvii
the same ideas about the relationship between quantum theory and spacetime
continuum. Periodic contact for discussions followed. Several times, P. Roman
was our guest in Starnberg for months, and he made the first and continuing
contri
16
2 The system of theories
2.2 Classical point mechanics1
2.2.1 First analysis of the meaning of the basic equations
2
mi
d xik
= fik
dt2
(i = 1 . . . n, k = 1, 2, 3)
(2.1)
If, without any further explanation, one asks a physicist nowadays for the
meanin
3.6 Reconstruction via probabilities and the lattice of propositions
77
pair of states a and b the value p(a, b) independent of the state of the environment. This means at the same time that the states of an object admit
an internal description, consistin
xiv
Preface (1985)
in theory; by Sommerfeld, de Broglie, and Schr
odinger; by Born and Jordan;
and by a great many more experimentalists.
For me, the mention of these three names also carries the personal significance of admiring and aectionate remembranc
2.8 The relativity problem
37
same time of a Euclidean space (per physical semantics). The physical theory
created this way would therefore be semantically inconsistent.
Any physicist knows how to resolve this apparent problem. The new theory
is supposed
96
4 Quantum theory and spacetime
physics; that is why in all recent times one was interested in suppressing its
paradoxical character. In Sect. 2.9 we argued in some detail to what extent
the special theory of relativity depends on the law of inertia.
Ou
68
3 Probability and abstract quantum theory
and always
p1 + p2 = 1.
(3.4)
Now one picks one of the urns, without knowing which, and proceeds to draw
and immediately return a single ball, n times in succession. If the outcome
was n1 white and n2 black bal
188
7 Irreversibility and entropy
the k-th move; the number of black balls in B is also nk , and the number of
black balls in A and white ones in B is N nk .
Our model in fact assumes the elementary laws b) to be statistical (equal
probability for each ba
46
2 The system of theories
principle. Einsteins 1916 model of the universe satisfied this principle. But
in the present understanding Einsteins view on this issue did not prevail; we
return to it in subsection c.
The second approach would be that in term
132
5 Models of particles and interaction
the photon, electron, neutron etc., nowadays leptons, quarks, photons, gluons,
etc. Beyond the particles just mentioned one naturally looks for even smaller
particles.
It is, however, by no means obvious that ther
120
5 Models of particles and interaction
j
bound state
(neutrino)
symmetric many
ur free state
m
and afterwards they disperse. For the single ur Castell specifies the Minkowski
wave function as
! "
yk k + y4 i
1
= 2
(5.54)
(yk (y4 i)2 )2 2
with fixed com
5.3 Quasiparticles in rigid coordinate spaces
117
Step 3: the functions (ur with denumerable many basis states which
are described by all possible number functions N (nr ) (N (nr)=0.) for every
function nr (r = 1 . . . R).
Etc.
For R = 2 and R = 4, the fi
xxiv
On Weizs
ackers philosophy of physics
derivation of special relativity from the quantum theory of binary alternatives.
In the ur theoretic path of the reconstruction, detailed in the present Chap. 4,
a slightly dierent strategy is employed, but with
138
5 Models of particles and interaction
with large p. The sharpness of the rest mases ought then to manifest itself as
the distinction of certain values of p. Only if such values are distinguished can
one hope to actually find field equations for distin
62
3 Probability and abstract quantum theory
using a preconceived concept of probability. These two concepts, experience
and probability, are not in a relationship of hierarchical subordination.
In practice every application of the theory of errors implie
22
2 The system of theories
no longer considered. The mass points making up a body are considered to be
held together by forces acting at a distance between them. The concept of the
force is necessarily correlated with the concept of the point mass. Histo
On Weizs
ackers philosophy of physics
xxvii
There uA denotes an ur spinor, dotted indices represent complex-conjugate
components. Weizsacker is now interested in a procedure he calls multiple
quantization. By quantization one usually means taking two step
28
2 The system of theories
into xk ). The appearance of hyperbolic rotations of space and time in the
special theory of relativity changed nothing here; it gave rise, however, to the
popular saying that time is nothing but a fourth spatial coordinate.
Th
Editors Preface
Carl Friedrich von Weizs
acker is certainly one of the most distinguished German physicists and philosophers of the 20th centuryequally renowned for his
early contributions to nuclear physics and his life-long research on the foundations o
34
2 The system of theories
definition of chemistryits two major laws span the entirety of physics. In
hindsight, the feat of abstraction lay primarily in the renunciation of deriving
of these laws from specific models. As we know now, the atomism the fou
114
5 Models of particles and interaction
Empirically, only particles with Bose or Fermi statistics have been found
thus far. For urs, however, we certainly cannot restrict attention to Bose or
Fermi statistics. For Fermi statistics the world would actual
4.3 Space and time
99
Here the bar denotes complex conjugation and the are the Pauli matrices
with 0 = 1. The k satisfy the relation
k k = (k 0 )2 (k)2 = 0
(4.29)
with k = (k 1 , k 2 , k 3 ). SU(2) rotates the vector k, two elements of opposite
sign produ
2
The system of theories
2.1 Preliminary
The title The Unity of Physics expresses the conjecture that it might be
feasible to summarize all of physics, as far as fundamental laws are concerned,
in one single theory. We have divided the outline of such a r