Outer Limits of Reason (38 page)

Eugene Wigner (1902–1995) took the Schrödinger cat experiment one step further to get to the heart of quantum mechanics. This experiment has become known as
Wigner's friend.
Imagine Wigner setting up the experiment and placing a live cat in the box. He then closes the box and walks out of the room. Rather than opening the box himself, Wigner has a friend open the box. Before it is opened, we have that the radioactive material is in a superposition, the poison is in a superposition, and the cat is in a superposition. Question: When the friend opens the box, is he also in a superposition of seeing the cat alive and seeing him dead? No human being has ever reported being in a superposition. Does the superposition only collapse when Wigner learns the result, or earlier when the friend learns the result? The obvious answer is that the friend is not in a superposition. Rather, the whole system collapses when the friend looks at it. The one thing that the friend has that no other physical object has is consciousness. Wigner uses this to show that a superposition collapses when any conscious being observes it. Wigner takes this as proof that the only thing in the world that can collapse a superposition to a position is human consciousness. Human beings only observe positions, not superpositions, so it must be something about consciousness. What is it about consciousness that brings about this collapse of a superposition to a position?

This role of consciousness brings to light a criticism of a school of philosophy called
materialism
. A materialist basically believes that this world contains physical objects and spaces between physical objects. And that is it! Most of the laws of physics can be seen from this perspective. A materialist believes that even human beings are simple creatures made out of atoms and molecules that simply follow the laws of physics. Quantum mechanics places simple materialism in jeopardy by highlighting a new entity in the universe called consciousness. This consciousness is not made of physical objects and yet it affects how the universe works. Consciousness causes a superposition to collapse to a position. No longer are there only physical objects and spaces between them. Scientists and materialists must incorporate consciousness into their worldview.

The End of Locality: Entanglement

Another counterintuitive aspect of quantum mechanics is
entanglement
. This concept shows that the whole universe is more interconnected than previously believed.

We first need to learn more about spin. There are important physical laws called
conservation laws
that state that certain measures in a system stay the same. Conservation of energy means that the amount of energy in a system does not change. That is, energy cannot disappear or come out of nowhere. There are also conservation of momentum and conservation of mass/energy. Quantum mechanics shows that there is a conservation-of-spin law. This means that throughout an experiment the amount of spin of all the subatomic particles must remain the same.

What happens when a particle does not have any spin and decays into two particles that do have spin? These two particles will each be spinning both positively and negatively in a superposition. Since there is a conservation- of-spin law, if one particle was measured to have positive spin (or right-handed spin) then in order to maintain the no-spin status of the whole system, the other particle must have negative spin (or left-handed spin). The two possibilities are depicted in
figure 7.19
.

Which of the two scenarios in
figure 7.19
actually occurs? Does the left one spin positively and the right one negatively, or the other way? The answer is that each of the two particles is in a superposition of spinning both ways. Only when one of the particles is measured does it randomly collapse into a particular spin direction. And here is the amazing part: the instant one of the particles collapses one way, the other must collapse the exact opposite way. This is true even if the two particles are light-years apart. That is, in order for the universe to maintain conservation of spin, measuring one particle's spin will collapse the other particle's spin across the universe. Although these two particles are far away, they are entangled with each other. How can this happen?

With the help of two younger colleagues—Boris Podolsky (1896–1966) and Nathan Rosen (1909–1995)—Einstein wrote one of the first papers about entanglement in 1935. It was titled “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” and came to be known as “EPR.” The goal of the paper was to show that there is something missing in the world of quantum mechanics. Einstein imagined two particles with spin flying apart from a no-spin particle source.
¹⁷
Let us envision that the particles are sent across the universe to Ann and Bob, who are going to measure different properties of the particles. Ann measures the spin of her particle at a particular direction. If she finds that her particle is spinning up, she automatically knows that Bob's particle must be spinning down in that direction. On the other hand, if Ann finds her particle is spinning down, she knows that Bob's particle is spinning up.

There is something seriously wrong here. In all of the previously known physics, objects affect other objects that are close by. One object pushes another object or one object affects another object through gravity or some other force. The main idea is that one object has to be near or local to another object in order to affect it. This fact about physics is called
locality
. However, entanglement shows that by Ann measuring her particle, Bob's particle far, far away instantly collapses its superposition of spins. How can Ann measuring her particle affect another particle across the universe? Rather than being local, entanglement shows that quantum mechanics seems to be
nonlocal
. Measurement of one particle instantly affects particles that are not nearby.
¹⁸

Researchers like to compare quantum entanglement to a similar thought experiment. Imagine someone taking a dollar bill and ripping it in half. The experimenter places the two halves in two different sealed boxes without revealing which half went into which box. One box is given to Ann and the other is sent to Bob, who takes his box to Alpha Centauri, the closest star to our galaxy. It is a mere 2.565 × 10
¹³
miles away. Once Bob is on Alpha Centauri, Ann opens her box. If she sees the left side of the dollar she immediately knows that Bob has the right side. On the other hand, if Ann has the right side of the dollar she knows that Bob has the left side. So Ann gained information about something millions of miles away and gained this information instantaneously. There seems nothing mysterious about this. One can say that the properties of the torn dollar bill traveled with it from Earth to Alpha Centauri. Can we say the same about the particles?

Einstein, Podolsky, and Rosen concluded that there are two possibilities in the case of the spinning particles. Either (a) there is some mysterious, nonlocal interaction that is different from any other branch of physics that explains how Bob's particle is affected by Ann's measuring her particle. If this was true, our naive notion of space where distant objects and measurements are independent of each other is wrong. Or (b) something similar to what is going on with the dollar bill is happening with the particles. In other words, the particles are not in a superposition. When they split up at the source they have fixed spin values. That is, the particles have their spin values when they leave their source, and when Ann measures her particle she finds out what her particle's spin values are and instantly knows Bob's values as well.

The EPR paper discounted possibility (a) since Einstein and his colleagues could not imagine that physics could work in such a strange manner.
¹⁹
Rather, they preferred to accept possibility (b) as the correct view. In that case, we must ask what is missing in quantum mechanics. Why could quantum mechanics not tell what spin a particle is in prior to measuring it? Einstein and his associates postulated that there must be
hidden variables
that stay with the particles from the time they leave their sources until the time they hit the measuring devices. These hidden variables are like the split dollar bill. They ensure that properties of the particles have a fixed value. Until physicists learn more about such hidden variables, Einstein and his coauthors insisted that quantum mechanics is incomplete and waiting to be finished.

 

That's the way the physics world remained for almost thirty years, until the brilliant Irish physicist John Stewart Bell (1928–1990) showed that, in fact, option (b) is wrong and only option (a) is possible. In 1964, Bell published a paper, “On the Einstein-Podolsky-Rosen Paradox,” which famously showed that no regular hidden variables can explain away the mysteries of quantum entanglement. This result—which came to be known as
Bell's theorem
or
Bell's inequality
—demonstrated that superposition is a fact of the universe
²⁰
and that our notion of space needs to be adjusted.

The intuition behind Bell's theorem
²¹
is that if we assume that there are hidden variables and that these hidden variables describe the properties of particles, they must satisfy some regular logical truths. In particular, if we allow Ann and Bob to each measure the spin of their particles in three different specified directions, then these spin properties must satisfy certain logical truths. Bell describes what these logical properties are and then shows that they are not satisfied by the quantum mechanics of spin. He concludes that the particles did not have these properties while traveling from the source to the observers. They are in a superposition before measurement.

To understand Bell's theorem
²²
we are going to need to step away from the quantum world for a minute and discuss a little classical logic. Consider an object with three different properties that the object can have, call them
A
,
B
, and
C
. For example, look at a person and ask whether they are

•
A
, male or ~
A
, female,

•
B
, Democrat or ~
B
, Republican, and

•
C
, young or ~
C
, old.

Consider a person who is both male and old (
A
 ∧ ~ 
C
). He is either a Democrat or a Republican (
B
 ∨ ~ 
B
). If he is Republican then he is a male and a Republican (
A
 ∧ ~ 
B
). Otherwise, if he is a Democrat he is old and a Democrat (
B
 ∧ ~ 
C
). We have just proved the following simple property:

If you are male and old, then you are either a male Republican or an old Democrat.

In symbols, this is represented as

(
A∧
~
C
) → [(
A∧
~
B
) ∨ (
B∧
~
C
)].

This logical rule is true for any three properties. We can prove this either by examining a truth table for this logical formula and seeing that it is a tautology, or simply by considering
A, B,
and
C
. If
A
and ~
C
are true, then either
B
is true or ~
B
is true. If ~
B
is true, then we have
A
and ~
B
. In contrast, if
B
is true, then we have that
B
and ~
C
are true.

An implication (→) about two properties tells us something about the probability of such properties happening. If
Q
→
R
, then the probability that
Q
is true is less than the probability that
R
is true. In symbols we write this as
p
(
Q
) ≤
p
(
R
). For example, it is a logical fact that if it is raining, then there are clouds in the sky. From this we conclude that the probability of a rainy day is less than or equal to the probability of a cloudy day.

Returning to our logical law about
A, B
, and
C
, we have that

p
(
A
∧
~
C
) ≤
p
(
A
∧
~
B
) +
p
(
B
∧
~
C
).

That is, the probability that
A
∧
~
C
is true is less than or equal to the probability that
A
∧
~
B
is true plus the probability that
B
∧
~
C
is true.

That is enough classical logic. Let us return now to our particles. Consider two particles that are entangled and sent to Ann and Bob. Both experimenters can measure the spin of the particles in one of three different angles. These three directions are going to correspond to the three properties of particles
A, B,
and
C.
In particular: