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R. Barrett and P. P. Delsanto
possible to formulate the theory of the universe in a finite number of statements.
This is very reminiscent of Gödel’s theorem. This says that any finite system of
axioms is not sufficient to prove every result in mathematics.”
The concept is reiterated at the conclusion of his lecture:
“Some people will be very disappointed if there is not an ultimate theory that can
be formulated as a finite number of principles. I used to belong to that camp, but
I have changed my mind. I’m now glad that our search for understanding will
never come to an end, and that we will always have the challenge of new discovery.
Without it, we would stagnate. Gödel’s theorem ensured there would always be a
job for mathematicians. I think M-theory will do the same for physicists.”
In other words, Hawking concludes, on a note of optimism for the new
generations of young physicists, that a TOE would be bad news for physicists looking for a job: much better if there is no TOE and, as a consequence,
always something new to discover.
Hawking was not the first to question the impact of Gödel’s theorem on
physics. Stanley Jaki in his book “The Relevance of Physics” [5] states that
a TOE must be a consistent non-trivial mathematical theory, and hence,
following Gödel, incomplete. Freeman Dyson maintains: the laws of physics
are a finite set of rules, and include the rules for doing mathematics, so that
Gödel’s theorem applies to them.” [6] On the other hand, many physicists find
the use of Gödel’s theorem in this context to be unconvincing, and that in an
infinite universe, there will always be some things that cannot be proved.
If Hawking’s conjecture is correct, how do we begin the search for evidence
of Gödel’s incompleteness in physics? We cannot simply seek out some area
that is at the moment poorly understood, since it is more likely that our
ignorance depends only on the fact that we have not yet discovered the right
theory. This has always been the case in the past, before any of the great
discoveries of science.
More interesting is when we are faced with a theory, such as Quantum
Mechanics (see Chap. 5), that seems to work extremely well, since it fits all
the observations or experimental data, and yields accurate predictions, but
which defies our common sense. Here the question arises: is this evidence of
some incompleteness of the theory, or is it only a consequence of the fact
that our common sense has evolved in an environment markedly different
from the realm of Quantum Mechanics? Indeed, in our everyday life we are
in contact only with macroscopic objects and phenomena, while Quantum
Mechanics helps us deal with a quite different microscopic world.
R. Barrett and P. P. Delsanto
possible to formulate the theory of the universe in a finite number of statements.
This is very reminiscent of Gödel’s theorem. This says that any finite system of
axioms is not sufficient to prove every result in mathematics.”
The concept is reiterated at the conclusion of his lecture:
“Some people will be very disappointed if there is not an ultimate theory that can
be formulated as a finite number of principles. I used to belong to that camp, but
I have changed my mind. I’m now glad that our search for understanding will
never come to an end, and that we will always have the challenge of new discovery.
Without it, we would stagnate. Gödel’s theorem ensured there would always be a
job for mathematicians. I think M-theory will do the same for physicists.”
In other words, Hawking concludes, on a note of optimism for the new
generations of young physicists, that a TOE would be bad news for physicists looking for a job: much better if there is no TOE and, as a consequence,
always something new to discover.
Hawking was not the first to question the impact of Gödel’s theorem on
physics. Stanley Jaki in his book “The Relevance of Physics” [5] states that
a TOE must be a consistent non-trivial mathematical theory, and hence,
following Gödel, incomplete. Freeman Dyson maintains: the laws of physics
are a finite set of rules, and include the rules for doing mathematics, so that
Gödel’s theorem applies to them.” [6] On the other hand, many physicists find
the use of Gödel’s theorem in this context to be unconvincing, and that in an
infinite universe, there will always be some things that cannot be proved.
If Hawking’s conjecture is correct, how do we begin the search for evidence
of Gödel’s incompleteness in physics? We cannot simply seek out some area
that is at the moment poorly understood, since it is more likely that our
ignorance depends only on the fact that we have not yet discovered the right
theory. This has always been the case in the past, before any of the great
discoveries of science.
More interesting is when we are faced with a theory, such as Quantum
Mechanics (see Chap. 5), that seems to work extremely well, since it fits all
the observations or experimental data, and yields accurate predictions, but
which defies our common sense. Here the question arises: is this evidence of
some incompleteness of the theory, or is it only a consequence of the fact
that our common sense has evolved in an environment markedly different
from the realm of Quantum Mechanics? Indeed, in our everyday life we are
in contact only with macroscopic objects and phenomena, while Quantum
Mechanics helps us deal with a quite different microscopic world.