Despite this success, its affront to our common sense view of the world is so sharp that, even if we can use it to describe with great accuracy the result of any given experiment, it is difficult to feel that we really understand quantum theory. Consider what two Nobel Laureates have said about quantum theory: "Anyone who is not shocked by quantum theory has not understood it" (Neils Bohr) and "I think I can safely say that nobody understands quantum mechanics" (Richard Feynman). The question of what quantum theory is really saying about the "fabric of reality" has challenged some of the greatest thinkers in physics and philosophy since the theory was developed in the 1920s. This profound inquiry into the foundations of quantum theory continues unabated to this day.

**Quantum Weirdness**

The heart of quantum weirdness lies in what is known as the *superposition principle*. Suppose we have one ball that is hidden in one of two boxes. Even if we don’t know which box it is in, we are inclined to believe it is actually in one of the two boxes, while nothing is in the other box. However, if instead of a ball we have a very microscopic object like an atom, it would be wrong, in general, to suppose that the atom was actually in one box and not the other. In quantum theory, the atom can behave like it is, in some sense, in both boxes at once – a *superposition* of what would seem to be two mutually exclusive alternatives. This bizarre behaviour is *essential* to how nature works at very microscopic scales – it is tightly woven into the very fabric of reality.

What do we mean when we say that "the atom can behave as if it were in two places at once"? Consider the classic double-slit experiment in which a stream of identical particles – all with the same speed and direction – is directed at a barrier with two slits.

Click image to enlarge |
Double-slit apparatus showing the pattern of electron hits on the observing screen building up over time. |

The particles may be electrons, atoms, or even large molecules – it makes no difference. Some particles will be blocked by the barrier, while others will make it to the other side and hit a second, observing screen. We will also suppose that the intensity of the stream is very low, so there is only ever one particle at a time in the apparatus. This ensures that whatever strange behavior we may observe is associated with individual particles as opposed to two or more particles having some kind of influence on each other. The experimental results can be summarized as follows:

- The particles, arriving one by one, hit the observing screen at random locations. Even though they all start in exactly the same "state," exactly where any one will hit cannot be predicted in advance. There is true randomness in nature, more profound than the randomness in rolling a die.
- Further, as more and more particles arrive, a distinct pattern of hits emerges – particles tend to hit more often in some places than others. This pattern tells us the
*probability*of a given particle hitting at a given location.

It turns out that this probability pattern can be *calculated* very precisely in several mathematically equivalent ways, for example:

A) One way is to forget about particles and consider instead imaginary waves passing through the apparatus. A given wave front will then *pass through both slits at the same time*, and two waves will emerge on the other side, one from each slit. As they travel towards the observing screen, these two waves will spread out, overlap, and interfere with each other – like water waves crisscrossing on a lake, resulting in an interference pattern at the screen: the waves will be more intense at some locations than others. By properly choosing the distance between the wave crests (the *wavelength* of our waves), this wave interference pattern can be made to exactly match our particle probability pattern.

B) Another way is to try to understand the experiment strictly in terms of particles passing through the apparatus. After all, it is particles that are entering the apparatus and particles appearing at the observing screen. In this case, the mathematics tells us that, in getting to any given point on the observing screen, each individual particle *exists in two paths at once*, one going through the left slit, the other going through the right slit. The probability the particle will actually hit near the point in question can then be calculated based on certain numbers associated with the two paths, and we arrive at the same particle probability pattern.

The mathematics involved here is very simple, but all interpretations of what it is suggesting about the nature of the universe involve a fundamentally strange idea of one form or another. In cases (A) and (B) above, this strangeness appears in the idea that each individual particle, in passing through the apparatus, somehow has knowledge of both slits: we have either our imaginary wave associated with the particle, or the particle itself, passing through *both* slits at once.

To see this more clearly, observe that with both slits open there are places on the screen where particles never hit (between the dark bands in the figure). Yet further experiments reveal that the particles have no problem hitting these places when they are forced to go through only one slit (when the other slit is temporarily blocked). **In other words, there are places on the screen that particles can hit when the left slit alone is open and when the right slit alone is open, but will never hit when**

*both***slits are open**. If we assume that any given particle really passes through just one slit (right or left), how can it "know" if the other slit (left or right) is open or not, and so "know" whether or not it is "allowed" to hit between the dark bands? Somehow the particle is behaving as if it can be in two places at once, left

**and**right slits. Returning to our atom and the two boxes, we have a similar situation: in the everyday world we would expect "atom in box 1"

**or**"atom in box 2." In the quantum world, however, we can, and usually do, have "atom in box 1"

**and**"atom in box 2."

Another way to say this is as follows. The central question in ordinary (non-quantum) physics can be characterized as: given that I know the initial position and velocity (speed and direction) of a baseball, what is its subsequent trajectory? In quantum physics, the type of question is entirely different: given that I saw a particle *here* and *now*, what is the *probability* I will see it *there* and *then*? Moreover, calculating this probability involves bizarre ideas of one form or another, such as: in getting from here to there, the particle exists simultaneously in all possible paths, including ones with a stopover at the Moon! In recent decades, scientists have begun to apply this quantum weirdness to the development of new and powerful technologies such as quantum cryptography and quantum computing – see **quantum information**.

**Entanglement**

If we have more than one particle, quantum superposition can result in an even stranger phenomenon called *quantum entanglement*. Two particles, say electrons, in an "entangled state" exhibit a very mysterious type of connection, or "correlation," between them. If one is disturbed in any way, the other is instantly affected – even if they are widely separated in space (e.g., one electron could be on the Earth and the other on Mars). The meaning of the word "affected" as used here is quite subtle. Entanglement is not strong enough to allow us to send information instantaneously, i.e., faster than the speed of light (hence there are no violations of Einstein’s theory of relativity), but entanglement is strong enough to have some truly fascinating, measurable consequences (a fact which Einstein was not comfortable with, and referred to as "spooky action at a distance"). The interplay here between the relativity and quantum theories is profound and fascinating. For example, one can ask questions like, "If one of an entangled pair of particles falls into a black hole, and the other flies outwards where we can see it, can the latter particle (or many such particles) be used to extract information about what has earlier fallen into the black hole, or even how the black hole was originally formed?"

To better appreciate the weirdness of quantum entanglement, let’s consider a simple thought experiment. Suppose we flip a coin and, without looking at it, cut it in half (so as to separate the two faces of the coin), hide each half in a sealed box, give one box to Alice and one box to Bob, and let Alice travel to Venus, and Bob to Mars. When Alice opens her box she will find either the heads *or* tails half of the coin, and Bob will find the opposite. There is nothing surprising about this.

Click image to enlarge |
Two electrons in the entangled state: up/up and down/down [more]. Figure courtesy of Boris Blinov, University of Washington. |

But now instead of a coin, with its two faces, suppose we have two electrons. It is easy to prepare the two electrons in two opposite states, one "spin up" and the other "spin down" (analogous to heads and tails), and conduct a similar experiment. The difference is that in the quantum world, the two cases – A) spin up in Alice's box and spin down in Bob’s box, and B) spin down in Alice’s box and spin up in Bob's box – can be made to exist *simultaneously*. Instead of the usual A **or** B, we can have A **and** B, according to the interpretation of quantum theory we discussed above. Before she looks, Alice's box contains an electron that is neither definitely spin up nor definitely spin down. It is in an *indefinite* state that can only be described by treating the electrons in the two boxes as being part of a single system – they cannot be described separately. The situation is similar for the electron in Bob's box.

If Alice now looks in her box, she forces nature to choose one or the other definite state, A or B, and nature will choose *randomly*. Suppose nature chooses state A (spin up for Alice, spin down for Bob). The remarkable thing is that this choice has an effect *simultaneously* in both boxes, no matter how far apart they are. The moment Alice looks in her box, she causes not only her electron to become definitely spin up, but also Bob's electron (in his still sealed box) to become definitely spin down. The act of Alice looking at her electron instantaneously affects Bob’s electron, regardless of the distance between them. This appears to be dangerously close to violating Einstein's speed of light principle! But because Alice has no control over which of the two definite states her electron will assume (nature chooses randomly), the process cannot be used to send information instantaneously, and so strictly speaking there is no violation of Einstein's speed limit. Nevertheless, it is certainly weird!

Besides posing deep and fascinating questions about the nature of reality, quantum entanglement has important applications in quantum cryptography. It also makes possible the transport of very delicate quantum information (e.g., the quantum state of the electrons in an atom - see figure) from one location to another in a process called "quantum teleportation," with important applications in quantum computing. Both of these applications are discussed further in **quantum information**.

Click image to enlarge |
A quantum teleportation machine which transfers the quantum state of one calcium atom to another. [More], Photo by C. Lackner, courtesy Universität Innsbruck. |

**Interpreting the Quantum World**

What are we to make of this strange quantum world? As intimated earlier, while the mathematics of quantum theory is well understood, it has led to many different interpretations of the nature of "reality."

Returning to our atom in a superposition of existing in box 1 **and** box 2, when we "look" into the boxes (e.g. by shining a light inside and looking for light scattered by an atom) we will always find a single atom in box 1 **or** box 2, never both, since there is only one atom. But what actually constitutes making a measurement, such as this one? Is there some physical interaction by which the measurement device forces a quantum system to yield a definite result (a strong version of what is called the "Copenhagen interpretation," and the interpretation underlying our discussion in this article)? Or is the definiteness an illusion – are both measuring device and quantum particle part of a larger quantum system in which all possible outcomes of the measurements are realized? That is, for every result obtained, are there myriads of copies of the measuring devices in "parallel realities," obtaining all possible results (the "many-worlds interpretation")? Or is the unpredictability itself an illusion, and is quantum theory built on some hidden foundation which itself follows a predictable evolution ("Bohmian mechanics")?

The answers to such questions about the foundations of quantum theory become essential in the context of several fundamental questions that have wide-ranging consequences. For instance, because the very early universe should be describable as a quantum system, quantum foundations questions become important in understanding the origin of our universe, that is, quantum **cosmology**. In addition, a better understanding of the foundations might help us with one of quantum theory’s great unsolved problems: how to incorporate gravity into its framework, and arrive at a theory of **quantum gravity**.

To learn more about quantum foundations at Perimeter Institute and the researchers, please click **here**.

## Perimeter Institute Resources

The following selection of Perimeter Institute multi-media presentations by leading scientists is particularly relevant to quantum foundations. Click on the link to read a full description of each talk and choose your viewing format.

- Einstein – Relativity and Beyond – John Moffat, Lee Smolin, John Stachel, Howard Burton (moderator) (basic)
- From Einstein to Quantum Information – Anton Zeilinger (basic)
- The Quantum and the Cosmos – Edward (Rocky) Kolb (basic)
- The Physics of Information: From Entanglement to Black Holes – Leonard Susskind, Sir Anthony Leggett, Christopher Fuchs, Seth Lloyd, Bob McDonald (host of CBC’s Quirks and Quarks) (intermediate)
- Are We Due for a New Revolution in Fundamental Physics? – Sir Roger Penrose (intermediate to advanced)
- Thoughts on the Future of Physics – Anthony Leggett (intermediate to advanced)

**Specially for Teachers and Students**

These multi-media talks by Perimeter Institute researchers and visiting scientists were presented to youth and educators during Perimeter Institute's ISSYP, EinsteinPlus or other occasions.

- The Strange Quantum: What does it mean and how can we use it? - Rob Spekkens (basic)
- Heisenberg's Uncertainty Principle - Jos Uffink (basic)

**Suggested External Resources**

- Special Report: Quantum World from the journal New Scientist (basic)
- Quantum physics news from ScienceDaily
- Double Slit Experiment. Description and video of an actual experiment done at Hitachi
- Al-Khalili, Jim.
**Quantum: A Guide for the Perplexed**. Weidenfeld & Nicolson, 2003. (basic) - Bell, John S.
**Speakable and Unspeakable in Quantum Mechanics**. Cambridge University Press, 1989. A classic collection of Bell’s scientific papers. (basic to advanced) - Gribbin, John.
**In Search of Schrödinger’s Cat: Quantum Physics and Reality**. Bantam, 1984. (basic) - Hey, Tony.
**The New Quantum Universe**. Cambridge University Press, 2003. (intermediate) - Polkinghorne, John.
**The Quantum World**. Princeton University Press, 1986.