In Pursuit of the Unknown (63 page)

http://en.wikipedia.org/wiki/Vacuum_energy

7
Penrose's work is reported in: Paul Davies.
The Mind of God
, Simon & Schuster, New York 1992.

8
Joel Smoller and Blake Temple. A one parameter family of expanding wave solutions of the Einstein equations that induces an anomalous acceleration into the standard model of cosmology.
http://arxiv.org/abs/0901.1639

9
R.S. MacKay and C.P. Rourke. A new paradigm for the universe, preprint, University of Warwick 2011. For more details see the papers listed on
http://msp.warwick.ac.uk/~cpr/paradigm/

1
The Copenhagen interpretation is usually said to have emerged from discussions between Niels Bohr, Werner Heisenberg, Max Born, and others, in the mid-1920s. It acquired the name because Bohr was Danish, but none of the physicists involved used the term at the time. Don Howard has suggested that the name, and the viewpoint that it encapsulates, first appeared in the 1950s, probably through Heisenberg. See: D. Howard. ‘Who Invented the “Copenhagen Interpretation”? A Study in Mythology',
Philosophy of Science
71
(2004) 669–682.

2
Our cat Harlequin can often be observed in a superposition of the states ‘asleep' and ‘snoring', but that probably doesn't count.

3
Two science fiction novels about this are Philip K. Dick's
The Man in the High Castle
and Norman Spinrad's
The Iron Dream.
Thriller writer Len Deighton's
SS
-
GB
is also set in a counterfactual Nazi-ruled England.

1
Suppose I roll a dice [see Note 1 of Chapter 7] and assign symbols
a, b, c
like this:

a
The dice rolls 1, 2, or 3

b
The dice rolls 4 or 5

c
The dice rolls 6

Symbol
a
occurs with probability
, symbol
b
has probability
, and symbol
c
has probability
. Then my formula, whatever it is, will assign an information content
H
(
,
,
).

However, I could think of this experiment in a different way. First I decide whether the dice rolls something less than or equal to 3, or greater. Call these possibilities
q
and
r
, so that

q
The dice rolls 1, 2, or 3

r
The dice rolls 4, 5, or 6

Now
q
has probability
and
r
has probability
. Each conveys information
H
(
,
). Case
q
is my original
a
, and case
r
is my original
b
and
c
. I can split case
r
into
b
and
c
, and their probabilities are
and
given that r has happened.
If we now consider only this case, the information conveyed by whichever of
b
and
c
turns up is
H
(
,
). Shannon now insists that the original information should be related to the information in these subcases like this: