Bell's Argument

The Bohr-Einstein Debate

 

Reductio Ad Absurdum Arguments

 

The Double-Slit Experiment

 

Bell's Argument (Experimental Metaphysics)

Preliminary Example: Identical twins are separated in two rooms and each is asked two out of four questions:

A: Do you like apples?

M: Do you like milk?

P: Do you like pears?

Y: Do you like yogurt?

Suppose that 1,000 pairs of twins are tested in the following way: The left twin is asked questions A and Y, and the right twin is asked questions M and P.

Fact 1: Twins always give the same answers to the fruit questions.

Fact 2: Twins give the same answers to the dairy questions.

Question: If 250 out of 1,000 twins answer 'yes' to A and 'yes' to M, how many twins answer 'yes' to P and 'yes' to Y?

Answer: 250.

Reasoning: (yes, yes) answers are given to Y and P if and only if (yes, yes) answers are given to A and M.

"Bell" Example: Same as before, except that there 4,000 pairs of twins, and each twin is asked only one question. There are four possible question combinations that could be asked: (A, P), (Y, M), (A, P) and (Y, P). So, the 4,000 pairs are randomly divided into four groups with 1,000 in each group, and each group is given a different pair of questions. They have no prior information about what questions will be asked, and they are asked the questions simultaneously in different rooms separated a large distance from each other.

Group 1: Left twin is asked A and right twin is asked P.

Group 2: Left twin is asked Y and right twin is asked M.

Results 1 and 2: These results accord with facts 1 and 2 above—in each group, about of the twin pairs answer 'yes' to both questions and about answer 'no' to both questions. No twins give different answers.

Explanation: The principle of common cause says that to suppose that the correlation between the answers is too improbable to have arisen by chance. So, we need to explain it by introducing a common cause. There is, we suppose, two genetic factors. One that determines a like for fruit, and a second that determines a like for dairy products. Call these genes F and D respectively. Our explanation says that twins have the same genes. This explains our results.

Group 3: Left twin is asked A and right twin is asked M.

Result 3: About respond (yes, yes), answer (yes, no), answer (no, yes) and answer (no, no). The explanation for this is that there is a random distribution of these genes in the population.

Group 4: Left twin is asked Y and right twin is asked P.

Prediction: About will answer (yes, yes).

Result 4: The prediction is false. No twins answer (yes, yes) when Y and P are asked.

Argument: The prediction is made by a valid argument from the common cause explanation. If the conclusion of a valid argument is false, then at least one premise is false. The only premise that could be wrong is the common cause explanation.

Therefore the common cause explanation is wrong.

Ways Out

The Philosophical Lessons

  1. Reichenbach's Principle of Common Cause (PCC) is not universal. Quantum physics provides a different way of predicting non-accidental correlations, thereby removing the "cosmic coincidence."
  2. Quantum physics does not conform to everyday intuitions and expectations. While quantum physics makes the observed correlations probable, it does not use familiar concepts like 'trajectory' to explain them.
  3. Whewell is right and Mill is wrong. Scientists may believe that the concept of a particle trajectory is contained in or determined by the "trajectories" in observed in bubble-chamber photographs, but this is not correct. That concept is an element added by the mind of a scientists, and in this example, it is rejected by the theory itself.
  4. Scientists are often unaware of applying their everyday expectations in science. This is important, because as Kuhn points out, these expectations "obscure our vision", and this allows for unconscious biases to affect the judgment of scientists. Maybe scientists' judgments are inundated by cultural, racial, or gender biases?
  5. What we judge to be a good explanation is biased by our prior expectations. Therefore explanation should not be imposed uncritically as a universal standard for science.
  6. Are we never justified in postulating an objective reality behind the appearances? (Witness Kuhn's slippery slope to idealism). Antirealists, like van Fraassen, think that the postulation of a reality behind the phenomenon is never justified. His view is that the prediction of observable phenomenon is the fundamental goal of science. We turn to this issue next.