4 Gödel, Hawking and the Foundations of Physics
73
In the previous chapters we have learned that both our senses and our
reason can be very deceitful, and that our deeply-held intuitions of concepts
such as truth and reality may be dubious, or even fallacious.
Hence, if there exists indeed some incompleteness in the sense of Gödel,
where should we turn to look for it? In 2015, three mathematicians and
computer scientists, applying an admittedly simplified model, found that the
problem of determining whether there is an energy gap between the lowest
energy levels in a material is “undecidable” [7]. We shall explore what we
mean by energy levels in Chap. 8. However, for our purposes here, suffice
it to say that this issue is of major importance in the understanding of the
physics of superconductors. When we say that the question is undecidable,
we mean that it is impossible to find an answer, no matter how hard we try.
This is a direct consequence of Gödel’s theorem.
So, is there any chance that Gödel’s theorem might account for some of
the great puzzles of modern physics, that we are presently compelled to sweep
under the carpet, such as the inconsistency between Quantum Mechanics and
Relativity? We have now reached the point where we can proceed no further
towards the answers to these questions without a deeper understanding of
modern physics, and the limits to knowledge that it has revealed.
In Part 2 of this book, we make a brief visit to the various coalfaces of
current physics research, where thousands of dedicated workers are chipping
away in search of the occasional diamond. However, it is not our goal to
take part in this venture ourselves here, since we have insufficient time and
resources available for that purpose. Instead, our role will be to guide the
interested spectator.
To enjoy the beauty of a Beethoven sonata, one does not require a degree
in the theory of music, even if such a qualification may add a deeper
insight to our appreciation. Nor are all the audience members, on their
feet at Stratford-on-Avon after a stirring performance of Hamlet, graduates
from a Stanislavsky school of acting. Similarly, it should be possible for
non-specialists to obtain an appreciation of the important problems being
addressed by physicists today, and have a spot of fun for themselves along
the way. This is what we shall attempt in Part 2. In Part 3 we shall return
to tackle once more the questions raised above, taking advantage of what we
will learn in Part 2.
73
In the previous chapters we have learned that both our senses and our
reason can be very deceitful, and that our deeply-held intuitions of concepts
such as truth and reality may be dubious, or even fallacious.
Hence, if there exists indeed some incompleteness in the sense of Gödel,
where should we turn to look for it? In 2015, three mathematicians and
computer scientists, applying an admittedly simplified model, found that the
problem of determining whether there is an energy gap between the lowest
energy levels in a material is “undecidable” [7]. We shall explore what we
mean by energy levels in Chap. 8. However, for our purposes here, suffice
it to say that this issue is of major importance in the understanding of the
physics of superconductors. When we say that the question is undecidable,
we mean that it is impossible to find an answer, no matter how hard we try.
This is a direct consequence of Gödel’s theorem.
So, is there any chance that Gödel’s theorem might account for some of
the great puzzles of modern physics, that we are presently compelled to sweep
under the carpet, such as the inconsistency between Quantum Mechanics and
Relativity? We have now reached the point where we can proceed no further
towards the answers to these questions without a deeper understanding of
modern physics, and the limits to knowledge that it has revealed.
In Part 2 of this book, we make a brief visit to the various coalfaces of
current physics research, where thousands of dedicated workers are chipping
away in search of the occasional diamond. However, it is not our goal to
take part in this venture ourselves here, since we have insufficient time and
resources available for that purpose. Instead, our role will be to guide the
interested spectator.
To enjoy the beauty of a Beethoven sonata, one does not require a degree
in the theory of music, even if such a qualification may add a deeper
insight to our appreciation. Nor are all the audience members, on their
feet at Stratford-on-Avon after a stirring performance of Hamlet, graduates
from a Stanislavsky school of acting. Similarly, it should be possible for
non-specialists to obtain an appreciation of the important problems being
addressed by physicists today, and have a spot of fun for themselves along
the way. This is what we shall attempt in Part 2. In Part 3 we shall return
to tackle once more the questions raised above, taking advantage of what we
will learn in Part 2.