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, especiall
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 alternati
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 f
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
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 postu
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 r
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
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 ex
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 state
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 pers
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 res
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
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 s
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 l
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
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
p
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
! "
y
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
functi
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
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 c
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 pr
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 necessari
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
quantiza
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 t
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
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 fr
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
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) ro
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