Thomas Nagel: Mind and Cosmos: Why the Materialist Neo-Darwinian Conception of Nature Is Almost Surely False:
But it seems to me that, as it is usually presented, the current orthodoxy about the cosmic order is the product of governing assumptions that are unsupported, and that it flies in the face of common sense…
My skepticism is… just a belief that the available scientific evidence, in spite of the consensus of scientific opinion, does not… rationally require us to subordinate the incredulity of common sense…
Everything we believe, even the most far-reaching cosmological theories, has to be based ultimately on common sense, and on what is plainly undeniable…
I have argued patiently against the prevailing form of naturalism, a reductive materialism that purports to capture life and mind through its neo-Darwinian extension…. I find this view antecedently unbelievable— a heroic triumph of ideological theory over common sense…
If you are going to reject scientific theories because they fail to match up to your "common sense"...
...it seems to me the place to start is here:
Peter Woit: Quantum Mechanics for Mathematicians http://www.math.columbia.edu/~woit/QM/fall-course.pdf
1.2 Basic axioms of quantum mechanics…
Axiom (States). The state of a quantum mechanical system is given by a vector in a complex vector space H with Hermitian inner product <·,·>…. Note two very important differences with classical mechanical states:
- The state space is always linear: a linear combination of states is also a state.
- The state space is a complex vector space: these linear combinations can and do crucially involve complex numbers, in an inescapable way. In the classical case only real numbers appear, with complex numbers used only as an inessential calculational tool….
[T]he notation introduced by Dirac for vectors in the state space H: such a vector with a label ψ is denoted:
|ψ⟩
Axiom (Observables). The observables of a quantum mechanical system are given by self-adjoint linear operators on H….
Axiom (Dynamics). There is a distinguished observable, the Hamiltonian ℋ. Time evolution of states |ψ(t)> ∈ H is given by the Schrodinger equation:
d/dt(|ψ(t)⟩) = − (i/ħ)(ℋ|ψ(t)⟩)
The Hamiltonian observable ℋ will have a physical interpretation in terms of energy, and one may also want to specify some sort of positivity property on ℋ in order to assure the existence of a stable lowest energy state. ħ is a dimensional constant, the value of which depends on what units you use…. We will see that typically classical physics comes about in the limit where
(energy scale)(time scale)/ħ
is large….
Principle (Measurements). (1) States where the value of an observable can be characterized by a well-defined number are the states that are eigenvectors for the corresponding self-adjoint operator. The value of the observable in such a state will be a real number, the eigenvalue of the operator. (2) Given an observable O and states |ψ1⟩ and |ψ2⟩ that are eigenvectors of O with eigenvalues λ1 and λ2 (i.e. O|ψ1⟩=λ1|ψ1⟩ and O|ψ2⟩=λ2|ψ2⟩), the complex linear combination state c1|ψ1⟩ + c2|ψ2⟩ may not have a well-defined value for the observable O. If one attempts to measure this observable, one will get either λ1 or λ2, with probabilities c1^2/(c1^2 + c2^2) and c2^2/(c1^2 + c2^2), respectively.
This principle is sometimes raised to the level of an axiom of the theory, but it is better to consider it as a phenomenological over-simplified description of what happens in typical experimental set-ups…
I remember when I asked about this "Principle (Measurements)" while taking Physics 143 Pass/Fail, I got three answers from my section leader:
- It produces answers that conform to experiment: shut up and calculate.
- In the Copenhagan interpretation, this principle captures the physics of the collapse of the wave packet under measurement, which is not a process we understand.
- In the many-worlds interpretation, it happens that the process of decoherence as the experimental setup interacts with the wider world of which we are a part leads to this outcome. No, we do not understand where the factors c1^2/(c1^2 + c2^2) and c2^2/(c1^2 + c2^2) come from.
If you are going to reject any branch of science on the grounds that it flies in the face of common sense, require[s] us to subordinate the incredulity of common sense, is not based ultimately on common sense, or is a heroic triumph of ideological theory over common sense--quantum mechanics is definitely the place to start…
