Questions & explanations
1. Compare theory-ladenness with the logical positivist view of observation.
Logical positivists believed in a neutral observation language, where observations are pure and theory-free. They thought that science could be built on such observations. Theory-ladenness rejects this, arguing that observation always depends on concepts. For example, positivists would say that 'the needle points to 5' is a neutral observation, but theory-ladenness says that even this depends on understanding what a needle and a scale are. This difference has big implications: positivists saw observation as the foundation, while theory-ladenness shows that foundation is not as solid. Realists accept theory-ladenness but still believe in objective knowledge through scientific practice.
2. What does it mean to be a realist about evolutionary theory?
A realist about evolutionary theory believes that the entities and processes it describes, like natural selection and common descent, really exist in the world. This means that species truly evolve over time through mechanisms such as mutation and selection. Realists think that evolutionary theory gives a true or approximately true picture of how life developed. They argue that evidence from fossils, DNA, and observed evolution supports this view. For example, the fact that bacteria develop resistance to antibiotics is a real instance of natural selection. So realism about evolution is the claim that the story evolution tells is not just a useful fiction but reflects actual history.
3. Compare the problem of induction with the problem of underdetermination. Which is more damaging to realism?
The problem of underdetermination says that evidence often supports multiple theories equally well, so we cannot be sure which is true. Both problems challenge realism, but they are different. Induction questions whether past evidence supports future predictions at all. Underdetermination says even with all possible evidence, there could be rival theories. Some philosophers think underdetermination is more damaging because it suggests that truth is underdetermined even in principle. Others think induction is more fundamental because without it, we cannot even use evidence to support theories. Both are serious, but realism can survive by accepting that we aim for approximate truth.
4. What does it mean to be a realist about cognitive science and AI models?
A realist about cognitive science believes that mental states like beliefs and desires are real internal states that cause behavior. Similarly, a realist about AI models thinks that the representations and processes in an AI system, like neural network layers, correspond to something real in how the system works. For example, if an AI model recognizes cats, a realist says the model truly has internal representations of cat features. This contrasts with instrumentalists who see models only as useful tools. Realists argue that cognitive models explain behavior better if we take them literally. So realism here means that the structures posited by cognitive science and AI are actual.
5. Why is the branching structure considered to be a consequence of the Schrödinger equation alone?
The branching structure follows directly from the Schrödinger equation without any extra assumptions. The equation describes how the wave function of a system and its environment evolves over time. When a measurement happens, the interaction causes the wave function to become entangled, creating a superposition of many product states. Each product state corresponds to a different outcome and a different state of the observer. Since the Schrödinger equation is linear, these components evolve independently and never interfere again, effectively splitting into branches. So branching is a natural result of quantum mechanics if you take the wave function as real and never collapse it.
6. What does the Kochen-Specker theorem say about assigning values to all quantum measurements?
The Kochen-Specker theorem shows that in quantum mechanics, you cannot assign definite values to all physical quantities at the same time in a way that is consistent. It proves that the outcome of a measurement depends on which other measurements you do together—this is called contextuality. For example, measuring the spin of a particle along one direction can give different results depending on whether you also measure along another direction. This means that quantum properties do not have pre-existing values independent of how you measure them. The theorem uses a set of directions in three-dimensional space to show a contradiction if you try to assign non-contextual values.
7. Compare realism about evolution with realism about electrons. Are they equally well-supported?
Both are supported by strong evidence, but the kind of evidence differs. Electrons are directly detectable in cloud chambers and cause observable effects like electric currents. Evolution is inferred from patterns in nature, like fossil sequences and genetic similarities. However, evolution also produces observable changes, such as in laboratory experiments with bacteria. Realists argue that both are equally real because they explain and predict phenomena successfully. Some philosophers note that we cannot see evolution happening over millions of years, but we can see its results. So while the evidence is different, both are considered well-supported by scientific realism.
8. How does a delayed-choice experiment challenge our everyday idea of time?
In everyday life, cause comes before effect: you decide to throw a ball, then it flies. In a delayed-choice experiment, the decision about how to measure a particle is made after the particle has started its path, yet the particle seems to 'know' the decision in advance. This challenges the idea that time flows only forward. However, the experiment does not actually change the past; it just shows that quantum particles do not have definite properties until measured. The timing of the decision does not matter because the particle's state is not fixed until measurement. So time is still linear, but our common sense about cause and effect is not valid at the quantum level.
9. Give an example where the conditional wave function of a particle is not the same as its usual wave function.
Consider two particles in an entangled state where the wave function is (|up>|down> + |down>|up>)/√2. The usual wave function of particle 1 alone is a mixed state, not a pure wave function. But if we know that particle 2 is at a position corresponding to spin down, then the conditional wave function of particle 1 is |up>. So the conditional wave function depends on the actual position of particle 2. Another example: in a double-slit experiment with two particles, the conditional wave function of one particle can show interference only if the other particle's position is not known. So the conditional wave function can be very different from the reduced state.
10. What does Gleason's Theorem tell us about assigning probabilities to quantum measurement outcomes?
Gleason's Theorem says that in a Hilbert space of dimension 3 or more, any way of assigning probabilities to measurement outcomes that follows the rules of probability must come from a quantum state (a density matrix). This means the Born rule is the only possible rule for quantum probabilities. The theorem shows that quantum probability is not arbitrary—it is forced by the structure of the Hilbert space. It also implies that hidden variable theories that assign definite values to all observables cannot reproduce quantum probabilities without being contextual. So Gleason's Theorem is a key result linking the mathematical framework to physical predictions.
11. Compare contextuality with Bell's theorem: what do they each show?
Bell's theorem shows that quantum mechanics is non-local: particles can instantly affect each other over a distance. Contextuality shows that quantum mechanics is also contextual: the result of a measurement depends on the whole set of measurements you choose to do. Both ideas break common-sense assumptions. Bell's theorem breaks the assumption that distant events are independent, while contextuality breaks the assumption that a particle's properties exist before measurement. They are different: non-locality is about connections between separate particles, while contextuality is about how a single particle's measurement depends on the measurement setup.
12. What happens to the guidance equation when the wave function is real (no imaginary part)?
If the wave function is purely real, its phase is constant (zero or π), so the gradient of the phase is zero. The guidance equation then gives zero velocity: the particle does not move. For example, the ground state of a particle in a box has a real wave function, so according to Bohmian mechanics, the particle is stationary. However, this seems to conflict with the uncertainty principle, which says the particle has some momentum. In Bohmian mechanics, the particle's velocity is zero, but the quantum potential still acts, and the particle's position is uncertain. This is a subtle point that shows the theory is different from standard quantum mechanics.