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 form of our perception, are what we do not want to pres
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
7.1 Irreversibility as problem
185
attain a precise meaning only after an accurate specification of what must be
understood under object, environment, state, quantity, change,
A sucient mathematical condition for reversibility is that there are, as
state
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 can be determined empirically.6 These positions are th
248
9 The problem of the interpretation of quantum theory
particle conforms to the laws of probability, but the probability itself is propagated in accordance with the law of causality (Jammer, p. 40). Orthodox
quantum theory followed him there.
Neverthel
2.9 Special theory of relativity
41
2.9 Special theory of relativity23
The preconceptions of the special theory of relativity comprise among others
Euclidean geometry and Newtonian mechanics. Here both may be considered
closed theories whose semantic cons
128
5 Models of particles and interaction
f 10 =
f 20 =
f
30
=
1
2
2
2
1
1
2 (u u2 + u u1 ) = 2 (u1 u2 ),
21 (u1 u2 u2 u1 ) = 12 (u21 + u22 ),
21 (u1 u1 u2 u2 ) = u1 u2 .
(5.72)
f k0 defines a skew-symmetric self-dual tensor
f ik = f ki ,
f
= if
k0
m
(5
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
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
268
9 The problem of the interpretation of quantum theory
neither is it a contradiction to admit that the same density matrix can be built
from dierent systems of basis vectors; as already for the pure state, it only
means that it expresses probabilities
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 Pi (1 = 1, 2, 3, 4), in the anti-de Sitter space for the
8
Information and evolution
8.1 The systematic place of the chapter
If one defines physics as one of several natural sciences, then this chapter does
not belong to the reconstruction of physics. Information is a reflexive concept,
pertaining to all scienc
3.3 Empirical determination of probabilities
67
atoms of the lattice of events) from any other. In this sense they are all
equally possible. Therefore one assesses them to be all equally probable, i.e.,
one predicts an equal relative frequency for their o
5.2 Representations in tensor space
113
commutation relations for field operators which admitted the most general
representation of indistinguishable particles. We have postulated the indistinguishability of the urs, hence face the same problem as Green.
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 Ganzen: Carl
Friedrich von Weizs
acker als Physiker und
98
4 Quantum theory and spacetime
time runs without periodicity from t = to t = + and thereby creates
infinitely many sheets, each of which is an anti-de Sitter space. For that
space we have
(4.26)
x20 x21 x22 x23 = |F |,
i.e., the position space is a hyp
9.2 The semantic consistency of quantum theory
263
the dual rule for the change of .13 No contradiction arises if we follow these
simple arguments. But we can now see that the name state for is misleading. is a catalog of knowledge that follows from one o
56
2 The system of theories
Time
3: Probability
8.3: Evolution
7: Thermodynamics
No classical physics
Individuality
Quantum theory of probability
9: Interpretation of
quantum theory
3.5: Abstract
quantum theory
Hilbert space
3.6: Quantum lattice
4.1: Ur-h
10
1 Introduction
reconstruct it. How is it possible that such a successful theory can be built
upon such a shaky foundation?
We formulate the self-critique and the limited self-justification of quantum
theory in Chap. 11.
Classical logic, as the mathemat
6.2 Ur-theoretic vacuum and particle states
169
state (6.18) of quantum bits for the interior. For according to Bekenstein and
Hawking the amount of information in the interior of a black hole can be
estimated which, as indicated, in its concrete form is
8.5 Evolution as growth of potential information
221
growth of entropy necessarily corresponds to a reduction of structure.5 The
present account does express the opinion that the solution of the problem is
perhaps always to be sought in the fourth answer.
9
The problem of the interpretation of quantum
theory
9.1 About the history of the interpretation
Was wei ich, wenn ich wei?
9.1.1 The task
The interpretation of physics is a philosophical task. It is a supplementary
task, such as we are confronted with i
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
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
7.3 Documents
195
verification; without them the concept of experience would have no sensible
meaning. Now the existence of documents for the past but not for the future
appears to be a physical fact for which one will look for a reason in the laws
of phy
26
2 The system of theories
the paradoxical assertion of the existence of a Nothing was one of the theoretical points of criticism. Plato uses a word (chora), which we must translate
as space, to denote the principle of a pure possibility that Aristotle c
200
7 Irreversibility and entropy
on the system could make the inference from documents more dubious, the
knowledge of special causal connections can make them more precise. But in
the end, the validity of our argument is not aected, on the average over a
xxviii
On Weizs
ackers philosophy of physics
of multiple quantization it is equally possible to derive a wave equation for
the four massless spin-1 bosons , which might perhaps be interpreted as
gravitons.28
Yet again these considerations do not lead to a
Part II
Time and information
7
Irreversibility and entropy1
7.1 Irreversibility as problem
At every instant there exists an unmistakable dierence between past and
future. A factual event A which I have experienced I will not with a clear
mind mistake for
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
only see in the mirror. But the mirror in which we see the