2.11 Quantum theory, historical
53
How clearly Bohr saw from the very outset the principal problem can be
attested by a quote from his 1913 report to the Danish Academy of Sciences:
Before closing, I
4.3 Space and time
95
elements of the symmetry group of the ur. Consequently position space ought
to be a homogeneous space of SU (2).
The most natural homogeneous space of SU (2) is SU (2) itself. It
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
4.2 Reconstruction of quantum theory via variable alternatives
87
subobject. Then the state space of a free particle is the direct sum of infinitely
many finite-dimensional state spaces of subobjects.
4.3 Space and time
97
wish to describe this in the tensor space of the urs. As the simplest model
(2)
we consider T , the space of symmetric tensors over the binary vector space
V (2) . We consider th
5.1 Open questions
E. alternatives.
one
expansion postulate
107
108
5 Models of particles and interaction
tensor space of the urs
p
p
p>
p
p
p
interaction
p>
p
uniquely
program
homogeneous space
T
mod
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
4.3 Space and time
103
for the special Lorentz transformations Ni4 , and in (4.38) for the special conformal transformations Ki . In Minkowski space it also holds for the space and
time translations P
4.1 Concrete quantum theory
83
also evolutionary as the reason for our form of perception.3 But precisely these
empirical facts about the spatiality of empirically known objects, as well as
about the
4.2 Reconstruction of quantum theory via variable alternatives
89
4.2.2 Ur alternatives
1. Theorem of the logical decomposition of alternatives. An n-fold
alternative can be mapped into the Cartesian
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
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
On Weizs
ackers philosophy of physics
xxxiii
Books on Weizs
ackers philosophy of physics
P. Ackermann, W. Eisenberg, H. Herwig, and K. Kannegieer (eds.)
(1989). Erfahrung des DenkensWahrnehmung des G
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
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
2.2 Classical point mechanics
!
21
fkij ,
(2.3)
xjk xik mi mj
,
2
rij
rij
(2.4)
fik =
j=i
fkij = G
with
2
rij
=
!"
k
#2
xik xjk ,
(2.5)
and a universal constant G. Their positions at a certain time t0
2.10 General theory of relativity
49
Viewed in this way, the theory is then a stronger version of Einsteins intention,
insofar as it no longer needs to postulate the equivalence principle, deriving
it
4.2 Reconstruction of quantum theory via variable alternatives
91
and which allow a distinction between types of urs. Only with this reservation is the ur hypothesis an epistemologically justified con
2.12 Quantum theory, plan of reconstruction
55
the latest closed theory oers the best hope of being reconstructed from completely general principles. We will propose postulates which do not utilize at
76
3 Probability and abstract quantum theory
that an event e
simultaneously).
j from each alternative occurs (not necessarily !
This is an element of the combined alternative which has n = n elements.
78
3 Probability and abstract quantum theory
We can denote this postulate equivalently by the more abstract term postulate of expansion. The connection between the two names is as follows. Every
alter
5
Models of particles and interaction
5.1 Open questions
5.1.1 Recapitulation
We begin with a review of the system of theories. What in addition have we
learned by reconstructing quantum theory and th
60
3 Probability and abstract quantum theory
interpretation of probability stems from the idea that experience can be
treated as a given concept and probability as a concept to be applied to experienc
4.2 Reconstruction of quantum theory via variable alternatives
85
4.1.2 Particles
Here we only remark that the existence of particles which can be described
as point masses follows according to Wigner
2.12 Quantum theory, plan of reconstruction
57
fundamental classical physics. With this topic we begin Chap. 7. Second, directly to the quantum theoretical amplification of the theory of probability,
2.11 Quantum theory, historical
51
because it is only a small part of the whole. Perhaps our present concepts are
utterly inadequate to describe the entirety of the universe; perhaps the very
concept
72
3 Probability and abstract quantum theory
evolutionary knowledge is, as human knowledge, subject to the conditions of
such knowledge, as studied in epistemology. Also, the back of the mirror we
onl
64
3 Probability and abstract quantum theory
For the mathematical theory we can adopt Kolmogorovs text literally,
changing only some notation:
Let M be a set of elements , , , . . . which we call elem
4.3 Space and time
101
The choice of this group can be justified as follows. It is the largest subgroup of Sp(4,R ) that leaves invariant the operator
s=
1
2
(n1 + n2 n3 n4 ).
(4.34)
(is itself belong