Outer Limits of Reason (68 page)

11
. Goethe (1749–1832) said it poetically: “Let us seek to fathom those things that are fathomable and reserve those things which are unfathomable for reverence in quietude.”

12
. Feynman 1963, vol. 3, 1-1.

13
. In the language of 
section 3.3
, before the measurement, there is no epistemic vagueness, rather there is ontological vagueness.

14
. Quoted in Pais 1979, 907.

15
. Heisenberg 2007, 129.

16
. In an uncanny way, the quantum physicists of the last century anticipated current sensibilities. They were very careful with living creatures and only performed a thought experiment on Schrödinger's cat. Thus quantum physics advanced, and no lives were lost.

17
. This is actually slightly different from the original EPR experiment. In that experiment they measured position and momentum. I am discussing David Bohm's version of the experiment in which spin is the phenomenon examined.

18
. Newton's formula that characterizes the force between two objects (which we met in the last section) also has a feeling of nonlocality to it. The force is strong when the two objects are close to each other. The larger the distance between two objects, the weaker the force. Nevertheless, as large as the distance is, there is still a force. In real life what this says is that even though a grain of sand is very small, and the moon is very far away, by moving a grain of sand on Earth you are affecting the gravitational force between the Earth and the moon. This change is extremely minuscule but it still exists. However, there are two major differences between gravity and entanglement. For one, gravity works at the speed of light. That is, it takes time for any changes on Earth to affect the moon. In contrast, entanglement is instantaneous. A second major difference is that the gravitational force fades as the two objects get further apart. In contrast, the entanglement phenomenon remains as powerful and as instantaneous, regardless of whether the two objects are five feet apart or five million light-years apart. This makes entanglement much stranger than gravity.

19
. Einstein expressed his discomfort with measurements affecting distant objects in a letter to Max Born. He started by describing some characteristics of physics: “It is further characteristic of these physical objects that they are thought of as arranged in a space-time continuum. An essential aspect of this arrangement of things in physics is that they lay claim, at a certain time, to an existence independent of one another, provided these objects ‘are situated in different parts of space.' Unless one makes this kind of assumption about the independence of the existence (the ‘being-thus') of objects which are far apart from one another in space—which stems in the first place from everyday thinking—physical thinking in the familiar sense would not be possible. It is also hard to see any way of formulating and testing the laws of physics unless one makes a clear distinction of this kind. . . . The following idea characterizes the relative independence of objects (A and B) far apart in space: external influence on A has no direct influence on B; this is known as the ‘principle of contiguity.' . . . If this axiom were to be completely abolished, the idea of the existence of (quasi-) enclosed systems, and thereby the postulation of laws which can be empirically checked in the accepted sense, would become impossible” (Born 1971, 170–171).

20
. We have already seen this with the double-slit experiment and more emphatically with the Kochen-Specker experiment. Although the Kochen-Specker result is cleaner and does not require two particles to prove that superposition is a fact, Bell's theorem was published three years earlier than the Kochen-Specker theorem. Furthermore, Bell's results were shown to be true experimentally, which had a huge impact on the physics world. In contrast, the Kochen-Specker theorem has been largely ignored by experimentalists until recently.

21
. The inequality that I am describing is not actually Bell's original formulation. Rather, I am describing a variation of Bell's theorem that is due to Bernard d'Espagnat. The results of this formulation are the same as those of Bell's original.

22
. This is one of the most detailed theorems I am going to discuss in this book. More than one reading is required for a complete understanding. Press on!

23
. “Spukhafte Fernwirkung.”

24
. I am really simplifying the actual experiment here. The real experiment has to do with turning the diagonal filter on and off and is done with entangled particles. For simplicity's sake, I am describing the spirit of the experiment.

25
. People have free will if their actions are not predetermined by what happened in the past. In other words, they act for no other reason than that this is what they want. (Whatever
they
means. As I stressed in 
chapter 1
, human beings are full of conflicting ideas and desires. Which is the real person—the one who wants the cake or the one who wants to lose weight?) This is not a simple idea. After all, if I help an old lady cross the street because my mother used to tell me that I should do that, am I performing a freewill action or am I governed by previous programming by my mother? What if my mother had not told me to take such actions? Another question: If someone puts a gun to my head and tells me to perform a bad deed, and I do perform the deed, am I exercising free will or is the criminal forcing me to do it? After all, I do not need to perform the deed. At what point does a freewill act become an act of randomness? None of these questions have easy answers.

26
. In 2006, John H. Conway and Simon B. Kochen published what they called the “Free Will Theorem.” This theorem is based on an experiment that is a combination of the EPR and Kochen-Specker experiments. Whereas the Kochen-Specker experiment concerns one particle, the Conway-Kochen result depends on two spin-1 particles that are entangled. Two different observers are making measurements on the two particles. They claim that if a human being has free will, then so do the particles. There is some controversy as to whether this result was actually proved. Regardless, I believe I have duplicated their result from the delayed-choice quantum erasure experiment.

27
. It is not clear how an experimenter's free will is impeded by the fact that a photon has knowledge of what freewill choice the experimenter will make. Even if the experimenter had knowledge of future choices, does that imply a lack of free will to choose? Free will is about control of actions, not about knowledge of actions.

28
. There is one possibility that I did not mention. Maybe particles do have free will and the experimenter's decision on whether to pull away the diagonal polarization filter is somehow determined by the particle's decision to go into a superposition or not. That is, the particle controls the human observer. This, of course, is ludicrous. Nevertheless, an important experiment by Benjamin Libet (1916–2007) is worth mentioning. He found that certain regions at the back of the brain were excited seconds before people became aware of making certain decisions. In other words, there is a place in the brain that is controlling us and telling us what to want and what to do. For more, see part III of the excellent Nørretranders 1998. Recently neurologists have taken Libet's experiments much further.

29
. This is similar to a game of bingo in which the winner of a round jumps up and screams that it is a miracle that she won. To all the other players who did not win, this is clearly not a miracle. However, to the “external” viewer—who knows that
someone
will win the game and scream out that this is a miracle—this is expected and very deterministic.

30
. In mathematical language, one only has to deal with unitary operators and not with Hermitian operators.

31
. Birkhoff and von Neumann (1936).

32
. Deutsch 1997, 4–6.

33
. From the end of the second part of Hume's
Dialogues Concerning Natural Religion
(Hume 1988, 19).

34
. Bohr 1935, 702.

35
. Exactly how far can we go with this process? One might argue that we cannot measure anything smaller than an atom and that should be the ideal measuring unit. In other words, count how many atoms are passed from the top of Norway to the bottom. This will make the coast of Norway a very large but finite number. If we were to go beyond an atom, we could get into a situation similar to that of the Mandelbrot set discussed in 
section 7.1
. The boundary of that mathematical object does not have an atomic level where we must stop measuring. Rather, it has infinite complexity. It can be proved that the border of the Mandelbrot set is infinitely long but the area it surrounds is finite. What about Norway?

36
. Galileo 1953, 186–187.

37
. Galileo used this fact in his defense of Copernicus's view that the sun—not the Earth—is the center of the universe (heliocentric). People who believed that the Earth was the center of the universe (geocentric) argued that the Earth is not moving because we do not feel it moving. When we throw a ball up in the air, it lands in our hand, not where the Earth was. This seems counter to the idea that the Earth is moving. Galileo defended Copernicus by pointing out that we cannot feel movement if the movement is not accelerating.

38
. The passenger is looking out the window and knows that he is moving toward the front of the train. He might reason that he is moving toward the front light and that is why he sees it first. But he is also aware of Einstein's postulate that the speed of light is measured as constant regardless of whether he is moving toward it or away from it.

39
. Obviously one would lose weight simply from the exertion of climbing Mount Everest.

Chapter 8

1
. Weinberg 1994, 259.

2
. We must wonder what would happen if we did find a pink swan. We might say that it is not, in fact, a swan. After all, all swans are white, so this pink bird must be a different species. To what extent is being white part of the definition of being a swan? If it is in the definition, then without any observations we can safely say “all swans are—by definition—white.” This is all theoretical and not real. A quick Internet search confirms that there are, indeed, black swans and white ravens.

3
. Wheeler and Zurek 1984, 195.

4
. Hume 1955, 51.

5
. In symbols: ∀x(Raven(x)→Black(x)).

6
. This is simply the contrapositive: ∀
x
(
NotBlack
(
x
) →
NotRaven
(
x
)).

7
. The idea can be found about a hundred years before the birth of William of Occam in Maimonides's
Guide for the Perplexed.
While discussing the different possible motions of the sun, he writes: “He will, besides, endeavour to find such an hypothesis which would require the least complicated motion and the least number of spheres: he will therefore prefer an hypothesis which would explain all the phenomena of the stars by means of three spheres to an hypothesis which would require four spheres” (Maimonides 1881, part 2, chap. 11, 1904). There are also similar statements in Aristotle.

8
. We saw this idea in our discussion of quantum mechanics in 
section 7.2
. We will see it again when dealing with the anthropic principle in 
section 8.3
.

9
. Dirac 1963, 47.

10
. Criticizing such a view, Einstein is quoted as saying, “If you are out to describe the truth, leave elegance to the tailor.” (Something similar was said earlier by Ludwig Boltzmann.)

11
. Steven Weinberg brings down two examples of seemingly beautiful theories that did not live up to expectations. One is an early version of Watson and Crick's theory of DNA, and another is an early theory of Kepler's describing the distance of the planets from the sun. Both of these theories would really be beautiful if they worked. But, alas, they are false.

12
. Weinberg 1994, 162–164.

13
. Russell 2009, 67. This quote is taken slightly out of context. Russell was criticizing Eddington's type of metaphysics, where unity and wholeness play a role.

14
. For an interesting history of the ever-increasing importance of mathematics in physics, see Burtt 1932.

15
. I go much deeper into the nontrivial relationship of mathematics and physics in the next section.

16
. With apologies to the related biological theory developed by Niles Eldredge and Stephen Jay Gould.

17
. Kuhn 1987.

18
. One must be careful when writing about Kuhn. His book was hijacked by many different philosophers, who took some of his ideas to the extreme. Kuhn spent much time trying to clarify his views and protesting against some of the ideas that seem to be consequences of his writings. Over time, he also modified and transformed his ideas. I will not go into the details of who said what at what time, or what was really meant. Rather, I am going to pose questions about the limitations of reason based on some of the ideas initiated by Kuhn.

19
. In the literature, the example of finding the source of the Nile is attributed to Steven Weinberg in Weinberg 1994. In fact, he illustrates this point with the example of finding the North Pole (pp. 231–232). He illustrates another point with the example of finding the source of the Nile (p. 61).

20
. Kant 1949, section 57, p. 122. George Bernard Shaw famously toasted Albert Einstein by saying, “Science is always wrong. It never solves a problem without creating ten more.”

21
. When exactly is “very soon”? It has been more than a decade and a half since John Horgan (1996) published his famous book predicting an imminent end to science. However, I do not know anyone who thinks this prediction has come true. Is science closer to ending now than in 1996? Making a prediction that science will end “soon” without providing a time table is not a falsifiable prediction.
Soon
is simply not a word that can be pinned down. How can we tell if the prediction is wrong?