Exploring Quantum Mysteries

Many scientists, including Einstein, thought there must be something wrong with quantum mechanics, particularly because of its probabilistic nature. As Einstein put it, “God does not play dice.” He thought that quantum mechanics was a useful theory, but that eventually someone would figure out a better theory—better in the sense of getting the right predictions but doing away with the probability part.

Let’s now unpack the terms “deterministic” and “local.” By “deterministic,” we mean the common sense notion that an object like a photon or an electron always has a definite value of its properties such as linear polarization direction or spin orientation and that those properties determine (no probability involved) how the object interacts with measurement devices (or with anything else for that matter). We may not know what the property value is until we measure it, but it is, in some sense, really there.

As we have seen with entangled states such as the two-qubit spin-$½$ state

$$|ψ⟩ = \frac{1}{\sqrt{2}} (|↑↑⟩ + |↓↓⟩),$$

when I observe the orientation of the spin of one of the qubits, I might get $↑$. Then when Alice measures the orientation of the other qubit’s spin, she will get $↑$. Such states are often called Bell states because of their use in illustrating Bell’s theorem.

The “realistic” or “deterministic” account is that the two qubits both had those spin orientations before the measurements; all we did was to observe what is already there. Those qubit properties determine how the qubit interacts with the measurement device and which light gets lit. The lights appear to be red or green randomly only because we don’t know which set of properties is launched each time the source emits the qubits. I prefer to use the term deterministic account because “real,” “reality,” and “realism” are philosophically loaded terms; it would take us a whole other book to dig into the meaning of those words.

Now let’s talk about “local.” Local means that the outcome of the measurements depends only on the specific measurement device, its settings, and the properties of the entity the device interacts with. The results do not depend on what is going on at the other measurement device, at the source, at Simone’s Café, or on some exoplanet on the other side of the galaxy. There are two parts to that requirement. One is practical: We have to be sure we exclude effects such as the vibrations of the table on which the equipment is set up, “hidden” signals that might travel through the electrical power lines, and so on. We might also worry about whether choosing the measurement device settings affects the source or somehow affects the measurement devices themselves from a distance. We can even arrange to choose the device settings so they go into place after the source has emitted the entities. That rules out the possibility that the measurement device settings influence what the source sends out.

All those kinds of “hidden signal” effects can be ruled out by having the detectors far enough apart so that no signal can travel from one to the other during the time interval between when Alice’s measurement device carries out its measurement and when my measurement device does its measurement. It is easy to make sure there is not enough time for a hidden signal to travel from one detector to another since all signals have an upper speed limit: $≈ 3 × 108\text{m/s}$. This is the speed of light and the speed of gravitational waves and, as far as we know, it is nature’s fundamental speed limit. So, if we make sure that the detectors are far enough apart that a signal can’t get from one to the other between two measurements, then we can rule out that kind of influence.

Having done all of this, the actual measurements agree with the quantum predictions, not the hidden signals’ deterministic prediction. The bottom line of this argument is that having a local, deterministic model, although it may conform both to our intuition about how systems interact (the deterministic part) and to our knowledge about the limits of sending signals from one part of the world to another, does not conform to the way the world works.

Bell’s theorem generalizes this argument for different measurement setups and different questions about the correlations among the measurement results. In all cases for which experiments have been carried out, the experimental results agree with the predictions of quantum mechanics. The conclusion is that these experiments rule out any reasonable local, deterministic alternative to quantum mechanics.