Outer Limits of Reason (41 page)

There are a multitude of advantages to believing in a multiverse. For one thing, there is no more measurement problem. There is no collapse from a superposition to one particular position; rather, there is a collapse of a superposition to every position. Furthermore, although when doing an experiment you cannot determine which outcome a superposition will collapse to within the universe you are in, if you look at the entire multiverse, determinism is restored. The physical law says that the superposition will collapse to every position in some universe. This is a deterministic law.
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Locality is also restored in the many-worlds interpretation. When Ann makes a measurement on her particle the universe splits into two universes: one where she measures spin up and one where she measures spin down. In each of those two universes, Bob's particle also has the correct spin. So one measurement does not affect the other particle; rather, an entire new universe is created. The mathematics of a multiverse is much simpler
³⁰
and hence satisfies Occam's razor, which tells us to choose the view that is simpler. The multiverse also has other advantages that we will meet when we discuss the anthropic principle in section 8.3. The many-worlds interpretation is not held by the majority of physicists. In fact, it is severely derided by most. Nevertheless, there are several major physicists, like Max Tegmark and David Deutsch, who are firm advocates of this view.

The disadvantages of the multiverse are obvious. Where are these other universes? What is the mechanism by which a universe splits? This is the ultimate in nonlocality: one universe here and one universe a great distance away simply because a little measurement was performed. The idea that there are so many universes is simply staggering. How can one posit the existence of something for which there is no physical evidence?

Hidden Variables

The hidden-variable school of thought can be traced to Louis de Broglie (1892–1987) and David Bohm (1917–1992). These two leaders were unhappy about the nondeterminism in quantum mechanics. Perhaps there are some hidden variables that explain which position a superposition collapses to. They worked on some sophisticated mathematics to actually come up with formulas for deterministic laws on how quantum mechanics works. However, the hidden-variable theory, which arose before Bell's theorem, was mostly ignored by the majority of physicists because the equations they supplied took into account features that were far away from the action. That is, their hidden variables were nonlocal. This was totally unpalatable for physicists before Bell's theorem was formulated. They felt that all of physics must be local and only take into account what is near. It was only after Bell's theorem was stated that people realized that quantum mechanics is nonlocal regardless of whether there are hidden variables.

Even if it all works out, hidden variables do not help naive realism. In other words, that simple idea that an object has a certain property before we measure it and then we discover the property after we measure it, has to be discarded. Even hidden variables will not help us get naive realism back. Nor do they help us with nonlocality. The quantum world is inherently nonlocal.

One of the major advantages of the hidden-variable program is that its laws are deterministic. For the past three millennia a major goal of science has been to give deterministic rules for all phenomena: “If this happens, then that will happen.” Why should we believe that after success in other areas of science, there is a domain of physics where determinism fails? Why should the subatomic world be different from the rest of the universe? The hidden-variable researchers have restored this important feature to our physical world.

There are, however, disadvantages to hidden variables that have kept most physicists away. For example, the equations and the mechanism of the hidden variables (pilot waves) are ugly. They are not simple equations that give simple answers. Rather, they are equations that take into account many nonlocal phenomena. Even with this extradistant information, it is not easy to calculate what the outcomes will be. They are like some of the systems we met in
section 7.1
. Even though the laws are deterministic, they will not be much help in making anything predictable. That is, just because the particles know where to go does not mean we will be able to predict where they go.

Quantum Logic

The final school of thought that I will examine is quantum logic. These ideas were first formulated in a 1936 paper by Garrett Birkhoff (1911–1996) and John von Neumann (1903–1957).
³¹
Their aim was to modify the laws of logic so that they describe the quantum world. We all know the normal logical rules of living in the real world, but what are the logical rules of the quantum world?

Let us look at an example. Consider the following three propositions:

A
= Bob is a Democrat.

B
= Bob is young.

C
= Bob is rich.

We can combine these propositions to form

A
AND (
B
OR
C
).

This means that Bob is a Democrat and is either young or rich. We can also form the proposition

(
A
AND
B
) OR (
A
AND
C
).

This means that Bob is a young Democrat or Bob is a rich Democrat. If you read this carefully you will see that these are just two ways of saying the same thing. In symbols, we have that

A
AND (
B
OR
C
) = (
A
AND
B
) OR (
A
AND
C
).

This is an instance of the
distributive law
in logic. It says that AND distributes over the OR. Such instances are a basic fact of the universe, and we implicitly use this law every day of our life.

Now let us turn to the quantum world. Consider the following three propositions about the double-slit experiment:

X
= There was interference.

Y
= The photon went through the top slit.

Z
= The photon went through the bottom slit.

Combine these propositions to form

X
AND (
Y
OR
Z
)

which means that there was interference and the photon went through the top or bottom slit. In fact, it went through both slits. This is a true statement about the double-slit experiment. In contrast,

(
X
AND
Y
) OR (
X
AND
Z
)

means that there was interference and the photon went through the top slit (false), or there was interference and the photon went through the bottom slit (also false). This statement is false. In symbols, we conclude that

X
AND (
Y
OR
Z
) ≠ (
X
AND
Y
) OR (
X
AND
Z
)

So while the distributive law is true in the regular world of people, marbles, and Democrats, it fails in the quantum world of particles.

Researchers have gone on to look at many different aspects of the quantum world and examined it from the point of view of quantum logic. The positive side of quantum logic is the ability to make formal sense of the crazy subatomic world. After all, logic helps us navigate in the larger world; it would be nice to see logic help us in the subatomic world. The negative side is that quantum logic does not really make the weirdness go away. It simply begs the question: Why should we accept the strange rules of quantum logic? Why should the world follow rules that are different from the usual rules that we experience every day? If the quantum world follows quantum logic, then why should the real world follow classical logic? More questions remain.

Summing Up

All four of these interpretations of quantum mechanics are unsatisfactory. They each have negative aspects that make us uncomfortable and doubtful. It could very well be that none of the four interpretations (or any other available interpretation) is correct. It might be that in the future there will be another interpretation that will, in fact, give us the correct view. Or, we simply might never get the correct interpretation. Remember, there is nothing “out there” that ensures that the universe we live in is comprehensible.

At present, no scientific experiments can differentiate which of these schools of thought is correct. Every interpretation has its own way of looking at reality and predicting the results of quantum mechanics. A preference for a favorite interpretation basically depends on what type of properties you believe our universe has. If you believe that the universe is deterministic, then you will not follow the Copenhagen interpretation but rather the hidden-variable interpretation. If you cannot wrap your mind around the existence of billions and billions of different universes, then you must stay away from the multiverse interpretation. In contrast, if you blindly follow Occam's razor, then you might accept the multiverse interpretation with its simpler mathematics. All these different choices are essentially ideas that make you feel good about the universe you live in. Unless someone comes up with some experiment that can show one view to be correct and the others to be false, there is no scientific reason to choose any of them. For now, the correct interpretation of quantum mechanics is beyond science.

Unless you are doctrinaire and accept on faith one of the schools of thought, you have to join the rest of us wavering mortals and realize that the fundamental nature of our universe is simply beyond the limits of reason.

There are some researchers who would like to brush away this entire subject of interpreting quantum mechanics. They have a very pragmatic outlook and only care that the results on the measuring instruments are correct. These
instrumentalists
are only concerned that the equations work and make the correct predictions. They see no reason to pay any attention to
why
the equations work or what the underlying reality of the physical universe is. Their motto is “Shut up and calculate!” They believe that one should not waste time pondering what is going on “under the hood” and question whether a deeper reality even exists. To them, the underlying nature of the real world is either beyond us or is not worthy of thought. They think that the study of the interpretation of quantum mechanics is “only” metaphysics and hence should be thrown into the garbage heap of bad ideas.

David Deutsch has severely criticized such instrumentalists.
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He imagines some extraterrestrial race of supergeniuses giving the Earth an “oracle” or a “magic box” that tells what the outcomes would be for any possible experiment. That is, we humans input the experiment we want to perform into the oracle and it miraculously tells us what the outcome will be. It will make all the predictions we will ever want or need. This will satisfy the instrumentalists that tell us to shut up and calculate. They would no longer need to calculate. They can simply play with their oracle toy. However, this would be extremely unsatisfying for most human beings. We do not want to know the outcome of an experiment in advance. We want to understand why the universe works the way it does. We want an explanation as to why particles do what particles do. Most people are not satisfied with just knowing the results of an experiment. In fact, Deutsch says that we already have such a magic oracle: the universe we live in. It tells us the outcomes of all the experiments we can perform. But that is not enough. We invent mental models of how and why the universe works the way it works.

While I sympathize with the instrumentalist view that the proper interpretation of quantum mechanics is, at present, essentially unanswerable, and I would defend their constitutional right to ignore these questions, I nevertheless do not like their moral stance denying the basic human tendency to speculate about the world around us. Human beings should continue to try to understand our universe.

While quantum mechanics is a real science and we use its predictions every time we turn on a radio or a microwave oven, we nevertheless cannot truly understand why it works the way it works. Even though the laws of quantum mechanics describe and control most of the physical universe, we still have a hard time making it understandable. This forces us to ask several questions: Why do we find it so hard to understand quantum mechanics? Will we ever get used to the strangeness of quantum reality? What does it say about the relationship between our mind and the world we live in if we cannot make a mental model of this weirdness? As a partial answer to some of these questions, we must come to accept that the weirdness of quantum mechanics does not make it false. After all, we grew up in a world without superposition and so we should expect that our mind will consider superposition strange. We also came to experience the world with locality and so it stands to reason that the nonlocality of quantum mechanics should not make sense. Similarly, other strange aspects of quantum mechanics are beyond our comprehension. We must accept that our mind is not the be-all and end-all of the way the universe should work. Many years before the problems of interpreting quantum mechanics became apparent, David Hume asked, “What peculiar privilege has this little agitation of the brain which we call thought, that we must thus make it the model of the whole universe?”
³³
The universe works the way it works and we must adjust to it because it will not adjust to us.

I conclude with the words of Niels Bohr, the father of quantum mechanics. He wrote that some of the notions of quantum mechanics demand “a radical revision of our attitude as regards physical reality.”
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Indeed!

7.3  Relativity Theory

Albert Einstein's theory of relativity has some of the most beautiful ideas in all of science. Most of the ideas can be described with simple thought experiments that are easy to comprehend. Even though they are easy, they have revolutionized our understanding of the world around us.

It is not my aim to actually cover the details of relativity theory. I merely want to discuss the ways that relativity theory has reshaped our view of the universe. For that, we can ignore the equations and concentrate on some of the thought experiments with some helpful diagrams.