Outer Limits of Reason (39 page)

•
A
corresponds to Ann's particle spinning up at 0°.

•
B
corresponds to Ann's particle spinning up at 45°.

•
C
corresponds to Ann's particle spinning up at 90°.

Combining these properties, we determine that

•
A
∧
 ~
C
corresponds to Ann's particle spinning up at 0° and spinning down at 90°.

•
A
∧
 ~
B
corresponds to Ann's particle spinning up at 0° and spinning down at 45°.

•
B
∧
 ~
C
corresponds to Ann's particle spinning up at 45° and spinning down at 90°.

By Heisenberg's uncertainty principle, it is impossible for Ann to measure the spin of her particles in these two different directions, so we are going to have to take into account that Bob's particles are spinning oppositely from Ann's particles. With this our propositions become

•
A
∧
 ~
C
corresponds to Ann's particle spinning up at 0° and Bob's particle spinning up at 90°.

•
A
∧
 ~
B
corresponds to Ann's particle spinning up at 0° and Bob's particle spinning up at 45°.

•
B
∧
 ~
C
corresponds to Ann's particle spinning up at 45° and Bob's particle spinning up at 90°.

Quantum mechanics makes probabilistic predictions concerning such measurements. It says that when the two angles are close to each other, the particles will probably spin opposite each other. That is, if Ann and Bob both measure spin at about 0°, then it is very probable that Ann will measure up and Bob will measure down or vice versa. Another way of saying this is that if they both measure close to 0°, it is very unlikely to find both spinning up. In contrast, when the two measurements are 90° apart, it is more likely that Ann and Bob will both measure up. Quantum mechanics tells us that the probability of having the same outcome of a measurement depends on the angle between the two measurements. If the angle is
φ
, then the probability of having them both up is

.

In our cases,

•
p
(
A∧
~
C
) is
,

•
p
(
A∧
~
B
) is
, and

•
p
(
B∧
~
C
) is
.

If this satisfies the logical and probabilistic laws that we derived, then we have

0.25 ≤ 0.0732 + 0.0732

and that is simply false!

 

What went wrong here? We showed that there is a basic conflict between the classical logic of three properties and quantum mechanics. How can this possibly happen? The answer is that we really cannot attach propositions about spin while they are in flight. They do not have fixed values then. Rather, the particles are spinning in a superposition of spinning both up and down. They only have fixed values after they are measured. Classical logic, which works so wonderfully with regular objects (like dollar bills in a box), does not apply here. More important than just showing that particles are in a superposition, Bell showed that the particles collapse from a superposition even though the particles are far away. When Ann does a measurement of her particle, Bob's particle collapses from its superposition to have the opposite spin of Ann's measured spin. This means that the usual notion of space that we have is wrong: measurements do affect distant objects.

When Bell formulated this inequality and proved his theorem he did not discuss experiments. He simply stated that this is what quantum mechanics predicted, and it is different from classical logic. A few years later, experimentalists like Alain Aspect and John Clauser confirmed the fact that the subatomic particles followed the laws of quantum mechanics as opposed to the laws of classical logic. Since then, many other experiments have been performed and have shown that Bell's results are not abstract mathematics but actually say something very important about the universe in which we live.

In essence, Bell's theorem is the ultimate expression of the Wholeness Postulate. It says that the outcomes of experiments depend on the whole experiment, including Ann's and Bob's measurements. In other words, we cannot just look at what Bob will measure or what Ann will measure. Rather, we have to consider what each will measure and where their particles came from. If the particles came from a single system with no spin, then the outcomes will take that into account.

There is still a way to believe in hidden variables and the fact that particles have spin properties even before they are measured. Rather than saying that the hidden variables keep track of three different spin values (for the three possible measurements that Ann can perform), we could say that the hidden variables keep track of the nine different measurements that Ann and Bob can possibly take. That is, Ann can perform three measurements and Bob can perform three measurements, which means that a total of nine different measurements can be performed on the two particles. If you assume that there are such hidden variables, then in fact the logical problems above go away. However, we are left with one very perplexing problem: How does Ann's particle know what measurements Bob will perform? After all, Bob could be across the universe. Such a theory is called a
nonlocal hidden-variable theory
. The very fact that such hidden variables need to take into account information that is very far away causes most physicists to disregard this possibility.

Regardless of the existence or nonexistence of nonlocal hidden variables, one thing remains certain: the notion of space where measurements do not affect distant objects is wrong. As we saw above, the EPR paper set up a dilemma. Either (a) the universe we live in is nonlocal, or (b) quantum mechanics is incomplete and contains nonlocal hidden variables. Either way, there are nonlocal effects.

 

One consequence of entanglement is to end the philosophical position of reductionism. This position says that if you want to understand some type of closed system, look at all the parts of the system. To understand how a radio works, one must take it apart and look at all of its components, because “the whole is the sum of its parts.” Reductionism is a fundamental supposition in all of science. Entanglement shows that there are no closed systems. Every part of a system can be entangled with other parts outside of the system. All different systems are interconnected and the whole universe is one system. One cannot understand a system without looking at the whole universe. That is, “the whole is
more than
just the sum of its parts.”

Once again, our defender of the sane, rational view of the world, Einstein, found it difficult to accept that distant points of our universe were so intimately connected. He derided entanglement as “spooky action at a distance.”
²³
But again, we must point out that many contemporary experiments show that Einstein was mistaken. The universe is a lot weirder than even he imagined.

The End of Time and Free Will: Quantum Eraser Experiments

We now know enough to describe some cutting-edge research called “quantum eraser experiments.” These experiments take the famous double-slit experiment and go much farther. Remember that in the double-slit experiment there will be a superposition of the photon and an interference pattern will be made. This will happen as long as we permit the photon to go through both slits. If we were somehow to measure which slit the photon went through, then, since we do not see things in a superposition, the photon would have to go through exactly one of the slits and there would be no interference. This is because we do not see superpositions; we can only see their effects.

What if there were a way of “seeing” which slit the photons passed through? Perhaps we can “tag” the photons when they pass through the slit so that we can later tell which tag they have and hence which slit they went through. In that case, there will not be a superposition and there will not be an interference pattern of the photons. In fact, we can do this: photons can be tagged by placing polarization filters next to each of the two slits, as in
figure 7.20
.

Notice that one filter is set horizontally and the other vertically. This will ensure that the photons that pass through different slits are tagged differently, so we can tell which slits they went through. Sure enough, when such an experiment is carried out, since there is information available that would tell us which slit the photon passed through, there will
not
be an interference pattern. The screen on the right will show light without interference.

There is an obvious question: When the photon leaves its source, does it go into a superposition or a position? We saw that if both slits are open and there is no way to tag the photons, then they go into a superstition. If, however, there is a way of tagging the photons, they do not go into a superposition and there is no interference. When the photons leave their source, how do they “know” if there is going to be a tagging device on the other side of the slits? After all, the filters can be far away from the source of the photons. And yet, somehow the photons “know” what to do. In terms of the Wholeness Postulate, this makes sense: the outcome of the experiment depends on whether there are tagging devices in the experiment.