It is common knowledge that no information can travel faster than light. Einstein’s Special Relativity has become so ingrained in the minds of the public that contrary suggestions are often met with ridicule. However, both mathematics and experimentation have confirmed the existence of a phenomenon that seems to ridicule Einstein: quantum entanglement.

Electron Spin

In each of the electron clouds around the nucleus (orbitals) described previously, a maximum of two electrons can exist—i.e., with a probability of residing in a position that cannot be pinpointed exactly. Each electron in an orbital must have the opposite spin (denoted “up” or “down”) of its counterpart. The idea of electron spin is not conducive of physical rotation but rather the direction of the magnetic dipole moment of the electron. Elements with several unpaired electrons (and thus the dominance of one dipole direction) include iron and cobalt, rendering them magnetic in nature.

For any two electrons with a high probability of occupying a specific orbital, the Uncertainty Principle precludes knowledge of their position and momentum; however, knowledge of one electron’s spin immediately deduces knowledge of the other, implied by the Pauli Exclusion Principle.

Entanglement at a Distance

Now imagine a pair of distinct electrons not bound to any particular nucleus. By applying radiation to the electrons simultaneously (e.g., shooting them with a single laser beam), their spins are rendered into a superposition. As long as there is no external observer present during the application of radiation and subsequent separation of the electrons, each particle exists in a probabilistic spin of “up” and “down” simultaneously.

Through electrostatic repulsion and other separation techniques, the electrons are separated a substantial distance, far greater than the radius of any atom. Still having not read the states (spins) of the electrons, an experimenter applies more radiation to one of the electrons and notices that the other electron exhibits the exact same behavior, regardless of its separation distance. The two electrons are thus entangled: effects on one instantaneously induce effects on the other.

The experimenter proceeds to measure the spin of one electron, collapsing the superposition described by the electron’s wavefunction. Remarkably, the Pauli Exclusion Principle dictating opposite spins in a pair holds for entangled particles not bound by an orbital, so knowledge of one electron’s spin immediately conveys knowledge of the other’s. It is as if the information is conveyed at an infinite rate—id est, faster than light.

Implications

Time Travel

While quantum entanglement may threaten the veracity of a component of Einstein’s Special Relativity, his equations do acknowledge faster-than-light travel as a means of traveling backwards through time, due primarily to the idea of the speed of light defining “the present.” Special Relativity also states, however, that attaining a speed equal to or greater than that of light would require infinite energy, for mass approaches infinity as velocity converges to the speed of light. Despite the experimental veracity of information seemingly traveling faster than light, “information” is abstract and massless, so energy remains conserved. Another challenge to the “time travel” idea is that entanglement seems to apply only to subatomic particles, and even electrons are sensitive to separation (only massless photons exhibit perfect entanglement).

Teleportation

Faster-than-light travel into the past is contingent upon instantaneous travel over distance—i.e., teleportation. Researchers have been studying quantum teleportation to address the aforementioned objection regarding macroscopic objects’ inability to entangle. To achieve direct teleportation with an object—e.g., a human being—one must somehow entangle every subatomic particle comprising the object with an exact pattern of particles in the desired location such that the object exhibits a superposition that probabilistically upon observation collapses into the desired “point B” position—i.e., every particle must individually collapse into the wanted position and manifest itself as a component of the object itself. Not only is such an aggregate probability beyond any human conception; it is not entirely clear how the particles would become entangled in the first place. Purpose is defeated if the particles must be relatively close during the actual process (e.g., applying radiation simultaneously).

Quantum Computing

In contrast with the ideas above, quantum computing is certainly feasible and has been practically (albeit primitively) realized. A traditional computer incorporates low and high electrical signals (bits) to convey information in processing and storing. Computing speed and power is limited by the distance between different components and the relatively low speed of electrons through the circuits.

Qubits (quantum bits), on the other hand, allow instantaneous communication among circuit components and networks due to selective entanglement. The precise ramifications of such instantaneous communication will be discussed in the next post.

Refinement of the Bohr Model of the Atom

Neils Bohr’s model of the atom as a set of electrons “orbiting” the nucleus held for little over a decade after he first proposed it in 1913. The main premise behind the model was the existence of discrete energy levels occupied by electrons; energy is emitted when electrons “step down,” or move closer to the nucleus, and energy is absorbed when electrons move farther away from it.

Despite conforming to experimentation with hydrogen, the Bohr model broke down for heavier elements such as lithium, beryllium, and oxygen. With a larger and more attractive nucleus, electrons in motion should emit energy to the extent of their collapse into the positively charged nucleus. Additionally, electron positions were found to be more complex than can be described by mere spherical orbits. It seemed as if an observer could never know with certainty where the electron is. Enter physicists Erwin Schrödinger (Austria) and Werner Heisenberg (Germany).

Electron Superposition

In in 1926, Schrödinger shocked even Einstein with a new atomic model has remained the standard for over 90 years yet defies all conventional knowledge about the nature of “reality.” Schrödinger postulated that discrete energy levels did indeed surround the nucleus, but that they took the form of electron “clouds” (known as orbitals) where electrons have a certain probability of being observed. In other words, an electron does not have an absolute position able to be characterized by spacetime coordinates; it is instead in a probabilistic superposition described by the electron’s wavefunction. Only when the electron is observed (which will be shortly demonstrated as a farce) does it theoretically collapse into a definite position in space.

To the less scientifically adept, the concept of superposition is best analogized with Schrödinger’s seemingly bizarre but entirely plausible thought experiment: Schrödinger’s Cat.

The premise of the experiment involves a cat inside a closed box—i.e., not visible to any observer. There is a vial of poison that, if broken, kills the cat. Whether or not the vial breaks is governed by radioactive decay—a process based solely on probability, perhaps manifested as a Geiger Counter triggering a hammer. The question for an oblivious outsider is, ‘Is the cat dead or alive?’ One cannot settle on one configuration or the other because it is governed by uncertain, probabilistic laws, the results of which have not yet been observed. Schrödinger reasoned that the only logical conclusion is that the cat is both dead and alive, existing in a precarious superposition of life and death, before one opens the box to observe whether or not the Geiger counter has been triggered, whereby the superposition collapses into a single, deterministic state.

It was previously mentioned that such determinism with respect to electrons was a “farce.” Schrödinger and a number of other quantum physicists theorized that it was impossible to know the precise position and momentum (product of mass and velocity) of an electron simultaneously. The more certain one became about the position, the less certain he became about the momentum, and vice versa. Werner Heisenberg quantified this with his Uncertainty Principle, which implies that knowing the position of an electron within 1 Angstrom (10^-10 m) offsets certainty of its speed by nearly 600,000 m/s. Even motion, as it was discovered, is probabilistic.

As exemplified in the image above, an electron—having nonzero mass—has properties of both a particle and a wave. From the previous post, it was maintained that such a duality also holds for light. Because of the duality, both light and electrons exhibit quantum superposition, with knowledge of position and momentum never certain. However, the superposition phenomenon is not limited to the realm of massless and near-zero mass components of nature: it is exhibited by everything.

De Broglie Wavelengths and the Fall of Determinism

In 1924, French physicist Louis de Broglie published his PhD thesis in which he postulated the quantification of an electron’s wavelength according to the following relationship:

That is, the wavelength of an electron is inversely proportional to its momentum (h is Planck’s constant). After a pair of experiments confirmed de Broglie’s hypothesis, it was wondered, ‘If an electron exhibits de Broglie wavelength (and thus quantum superposition), then why can’t all matter be associated with a wavelength?’ In fact, the de Broglie wavelength is applicable to everything: protons, baseballs, people, planets, stars, etc.

At rest, a person has zero momentum and thus an infinite de Broglie wavelength, meaning that he acts only as a particle and exhibits no quantum superposition—i.e., his position is absolute. However, when he has nonzero momentum (say, when he is running), he has a finite wavelength and thus possesses properties of both a wave and a particle. At this state, it is impossible to know the runner’s exact position and velocity simultaneously. In fact, when the runner is not being observed with the senses of another conscious being, he exists in a superposition of residing everywhere in spacetime and being both dead and alive! Only when he is observed does the superposition collapse into a quasi-definite position (“quasi” because of the uncertainty principle).

Of course, because of the enormous mass of the runner (and all macroscopic objects) compared with an electron (9.11 x 10^-31 kg), the probabilities associated with his wavefunction are almost entirely skewed toward what we would expect. That is, it would take trillions upon trillions of times longer than the lifespan of the universe for the runner’s superposition to collapse such that he instantaneously tunnels to another planet, but it is entirely possible and has been warranted by experimentation.

Regarding his instantaneous teleportation to another planet, one may wonder how this would hold under Einstein’s special relativity, which sets the speed limit of the universe at 3 x 10^8 m/s, the speed of light. As we shall see in the next post, quantum mechanics may indeed threaten to overthrow relativity theory, which is what prompted Einstein to deride quantum mechanics, specifically quantum entanglement, as “spooky action-at-a-distance” and (rightfully so) at odds with all conceptions of nature.