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Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
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Reichenbach, H. | Fraassen Vs Reichenbach, H. | I 170
Mixture/Probability/prblty/Quantum Mechanics/QM/Fraassen: "mixture" or "mixed state" as opposed to "pure" state: is in quantum mechanics what the difference between micro-state and macro-state is in statistical mechanics. Two problems: (in connection with probability): 1) how mixtures are connected with pure states 2) the relation of pure states to each other. Mixture: is typically introduced in the context of uncertainty. I 171
Ignorance Interpretation/Statistical Mechanics: here you can say likewise that a gas is in macro-state D iff. it is in one of the micro-states which are compatible with D. Problem: VsIgnorance Interpretation, VsReichenbach. Degeneration/QM/prblty/Fraassen: there is usually more than one way to decompose a mixed state, then (1) is compatible with (2) 1/3 w = 1/3 w1 + 1/3 w’2 + 1/3 w’3. VsIgnorance Interpretation: 1) according to it we would now have to come to a probability >1! Namely 1 + 1/3. Because we would have to add up all probabilities of incompatible (disjoint) events. That cannot be: E.g. naive statistical interpretation: says,
A) that state w’ cannot be attributed to a single particle, but only to ensembles. And that the number 1/3 expresses the relative size of the sub-ensemble w1, w2, and w3. Problem: we would have to say the same thing also for w’2 and w’3. I 172
With that we end up higher than 1 with 5 x 1/3. That cannot be. They must not overlap, otherwise a particle would simultaneously be in several pure states, which is impossible. Or
B) if we may not ascribe any state to particles, we ask: which state belongs to sub-ensemble, which is the common part of the sub-ensemble w2 and w’2? Should not any part of an ensemble that is in a pure state also be in a pure state?Solution/Fraassen: weakening the ignorance interpretation: (FN 10). Then we say that the specification of state w is incomplete, that there is lost information about the nature that has been lost in the attribution of the mixed state. I 172
Metaphysics/QM/Fraassen: Thesis: usually the latter is an unintended metaphysical bonus. There is usually no physical difference. But:
VsIgnorance Interpretation: 2) There is another situation in which the mixtures are formed naturally: Interaction: according to this, there are sometimes two separate systems X and Y which are isolated, but we only have one pure state for a complex system. Then it may be inconsistent to attribute a pure state each to X and Y. (Schrödinger: call this "the new specialty of QM").Solution: certain mixed states are attributed to X and Y ("reduction of the density matrix" (FN 11). VsIgnorance Interpretation: that would make it impossible: because according to it, the attribution of a mixed state contains the assertion that the system is in reality in a pure state! According to it we can ascribe neither a pure nor a mixed state. I 183
Probability/Statements/Reichenbach/Fraassen: Solution: we should think of statements about probability in physics as related to ideal extend indefinitely long series. VsReichenbach: that contradicts his assertion that a probability statement is nothing more and nothing less than a statement about relative frequency in an actual reference class (which then also must be able to be small). Problem: how should we consider the actually finite series, as representing a random sample themselves of a non-actual infinite series? But which non-actual series? Thus a modal element is already introduced. ReichenbachVsModality/Fraassen: his approach of strict frequency is precisely an avoidance of modality. Infinite/Fraassen: let’s assume instead the pure case of an actual very long series. (To avoid modality): But how are we to interpret probability then? Reichenbach: we should focus only on the actual results (of a long series). I 184
Questions: 1) Is it consistent to say that probability is the same thing as relative frequency? I.e. they have the functions P(-) and relative frequency(-, s) the same properties? 2) Even if this is consistent, is the interpretation not too wide or too narrow? I.e. does the relative frequency introduce structures such as probability spaces that do not have the right properties, or vice versa, are some probability spaces not capable of providing a function of relative frequency (rel. Fr.) in the long run? FraassenVsReichenbach: the problem of his approach of strict frequency is that he hardly answers these questions. I 185 FraassenVsReichenbach: ...therefore we cannot say that relative frequencies are probabilities. Law of Large Numbers/Loln/Reichenbach/Fraassen: It is often said that these laws provide a connection between probability and relative frequency. They do that, but they do not allow a strict interpretation of the frequency. (FraassenVsReichenbach). |
Fr I B. van Fraassen The Scientific Image Oxford 1980 |