Amar Vutha

Quantum computers, quantum cryptography and quantum (insert name here) are often in the news these days. Articles about them inevitably refer to entanglement, a property of quantum physics that makes all these magical devices possible.

Einstein called entanglement “spooky action at a distance,” a name that has stuck and become increasingly popular. Beyond just building better quantum computers, understanding and harnessing entanglement is also useful in other ways.

For example, it can be used to make more accurate measurements of gravitational waves, and to better understand the properties of exotic materials. It also subtly shows up in other places: I have been studying how atoms bumping into each other become entangled, to understand how this affects the accuracy of atomic clocks.

But what is entanglement? Is there some way to understand this “spooky” phenomenon? I will try to explain it by bringing together two notions from physics: conservation laws and quantum superpositions.

Conservation laws

Conservation laws are some of the deepest and most pervasive concepts in all of physics. The law of conservation of energy states that the total amount of energy in an isolated system remains fixed (although it can be converted from electrical energy to mechanical energy to heat, and so on). This law underlies the workings of all of our machines, whether they are steam engines or electric cars. Conservation laws are a kind of accounting statement: You can exchange bits of energy around, but the total amount has to stay the same.

Conservation of momentum (momentum being mass times velocity) is the reason why, when two ice skaters with different masses push off from each other, the lighter one moves away faster than the heavier. This law also underlies the famous dictum that “every action has an equal and opposite reaction.” Conservation of angular momentum is why – going back to ice skaters again – a whirling figure skater can spin faster by drawing her arms closer to her body.

France’s Gabriella Papadakis and Guillaume Cizeron demonstrate the effects of conservation laws during the 2019 ISU European Figure Skating Championships in Belarus (photo by Shutterstock)

These conservation laws have been experimentally verified to work across an extraordinary range of scales in the universe, from black holes in distant galaxies all the way down to the tiniest spinning electrons.

Quantum addition

Picture yourself on a nice hike through the woods. You come to a fork in the trail, but you find yourself struggling to decide whether to go left or right. The path to the left looks dark and gloomy but is reputed to lead to some nice views, while the one to the right looks sunny but steep. You finally decide to go right, wistfully wondering about the road not taken. In a quantum world, you could have chosen both.

For systems described by quantum mechanics (that is, things that are sufficiently well isolated from heat and external disturbances), the rules are more interesting. Like a spinning top, an electron for example can be in a state where it spins clockwise, or in another state where it spins anticlockwise. Unlike a spinning top though, it can also be in a state that is [clockwise spinning] + [anticlockwise spinning].

The states of quantum systems can be added together and subtracted from each other. Mathematically, the rules for combining quantum states can be described in the same way as the rules for adding and subtracting vectors. The word for such a combination of quantum states is a superposition. This is really what is behind strange quantum effects that you may have heard about, such as the double-slit experiment, or particle-wave duality.

PBS Studios: The Double-Slit Experiment

Say you decide to force an electron in the [clockwise spinning] + [anticlockwise spinning] superposition state to yield a definite answer. Then the electron randomly ends up either in the [clockwise spinning] state or in the [anticlockwise spinning] state. The odds of one outcome versus the other are easy to calculate (with a good physics book at hand). The intrinsic randomness of this process may bother you if your worldview requires the universe to behave in a completely predictable way, but … c'est la (experimentally tested) vie.

Conservation laws and quantum mechanics

Let’s put these two ideas together now, and apply the law of conservation of energy to a pair of quantum particles.

Imagine a pair of quantum particles (say atoms) that start off with a total of 100 units of energy. You and your friend separate the pair, taking one each. You find that yours has 40 units of energy. Using the law of conservation of energy, you deduce that the one your friend has must have 60 units of energy. As soon as you know the energy of your atom, you immediately also know the energy of your friend’s atom. You would know this even if your friend never revealed any information to you. And you would know this even if your friend was off on the other side of the galaxy at the time you measured the energy of your atom. Nothing spooky about it (once you realize this is just correlation, not causation).

But the quantum states of a pair of atoms can be more interesting. The energy of the pair can be partitioned in many possible ways (consistent with energy conservation, of course). The combined state of the pair of atoms can be in a superposition, for example: [your atom: 60 units; friend’s atom: 40 units] + [your atom: 70 units; friend’s atom: 30 units].

This is an entangled state of the two atoms. Neither your atom, nor your friend’s, has a definite energy in this superposition. Nevertheless, the properties of the two atoms are correlated because of conservation of energy: Their energies always add up to 100 units.

For example, if you measure your atom and find it in a state with 70 units of energy, you can be certain that your friend’s atom has 30 units of energy. You would know this even if your friend never revealed any information to you. And thanks to energy conservation, you would know this even if your friend was off on the other side of the galaxy.

Nothing spooky about it.

Amar Vutha is an assistant professor of physics at the University of Toronto.

This article is republished from The Conversation under a Creative Commons license. Read the original article.

Could machine learning mean the end of understanding in science?

noreen.rasbach — Fri, 03 Aug 2018 14:28:57 +0000

Could machine learning mean the end of understanding in science?

noreen.rasbach Fri, 08/03/2018 - 10:28

Cutline

(photo by Shutterstock)

Amar Vutha

Artificial Intelligence

Faculty of Arts & Science

Physics

Subheadline

The Conversation with ��˾��ֱ��'s Amar Vutha

Much to the chagrin of summer party planners, weather is a notoriously chaotic system. Small changes in precipitation, temperature, humidity, wind speed or direction, etc. can balloon into an entirely new set of conditions within a few days. That’s why weather forecasts become unreliable more than about seven days into the future – and why picnics need backup plans.

But what if we could understand a chaotic system well enough to predict how it would behave far into the future?

In January this year, scientists did just that. They used machine learning to accurately predict the outcome of a chaotic system over a much longer duration than had been thought possible. And the machine did that just by observing the system’s dynamics, without any knowledge of the underlying equations.

Awe, fear and excitement

We’ve recently become accustomed to artificial intelligence’s (AI) dazzling displays of ability.

Last year, a program called AlphaZero taught itself the rules of chess from scratch in about a day, and then went on to beat the world’s best chess-playing programs. It also taught itself the game of Go from scratch and bettered the previous silicon champion, the algorithm AlphaGo Zero, which had itself mastered the game by trial and error after having been fed the rules.

The behaviour of Earth’s atmosphere is a classic example of chaos theory (photo by Shutterstock)

Many of these algorithms begin with a blank slate of blissful ignorance, and rapidly build up their “knowledge” by observing a process or playing against themselves, improving at every step, thousands of steps each second. Their abilities have variously inspired feelings of awe, fear and excitement, and we often hear these days about what havoc they may wreak upon humanity.

My concern here is simpler: I want to understand what AI means for the future of “understanding” in science.

If you predict it perfectly, do you understand it?

Most scientists would probably agree that prediction and understanding are not the same thing. The reason lies in the origin myth of physics – and arguably, that of modern science as a whole.

For more than a millennium, the story goes, people used methods handed down by the Greco-Roman mathematician Ptolemy to predict how the planets moved across the sky.

Ptolemy didn’t know anything about the theory of gravity or even that the sun was at the centre of the solar system. His methods involved arcane computations using circles within circles within circles. While they predicted planetary motion rather well, there was no understanding of why these methods worked, and why planets ought to follow such complicated rules.

Then came Copernicus, Galileo, Kepler and Newton.

Newton discovered the fundamental differential equations that govern the motion of every planet. The same differential equations could be used to describe every planet in the solar system.

This was clearly good, because now we understood why planets move.

Solving differential equations turned out to be a more efficient way to predict planetary motion compared to Ptolemy’s algorithm. Perhaps more importantly, though, our trust in this method allowed us to discover new unseen planets based on a unifying principle – the Law of Universal Gravitation – that works on rockets and falling apples and moons and galaxies.

The Milky Way Galaxy, which contains our solar system (photo by Shutterstock)

This basic template – finding a set of equations that describe a unifying principle – has been used successfully in physics again and again. This is how we figured out the Standard Model, the culmination of half a century of particle physics, which accurately describes the underlying structure of every atom, nucleus or particle. It is how we are trying to understand high-temperature superconductivity, dark matter and quantum computers. (The unreasonable effectiveness of this method has inspired questions about why the universe seems to be so delightfully amenable to a mathematical description.)

In all of science, arguably, the notion of understanding something always refers back to this template: If you can boil a complicated phenomenon down to a simple set of principles, then you have understood it.

Stubborn exceptions

However there are annoying exceptions that spoil this beautiful narrative. Turbulence – one of the reasons why weather prediction is difficult – is a notable example from physics. The vast majority of problems from biology, with their intricate structures within structures, also stubbornly refuse to give up simple unifying principles.

While there is no doubt that atoms and chemistry, and therefore simple principles, underlie these systems, describing them using universally valid equations appears to be a rather inefficient way to generate useful predictions.

In the meantime, it is becoming evident that these problems will easily yield to machine-learning methods.

AI might help identify new drugs to treat antibiotic resistant bacterial like Klebsiella, which causes about 10 per cent of all hospital-acquired infections in the United States (photo by NIH)

Just as the ancient Greeks sought answers from the mystical Oracle of Delphi, we may soon have to seek answers to many of science’s most difficult questions by appealing to AI oracles.

Such AI oracles are already guiding self-driving cars and stock market investments, and will soon predict which drugs will be effective against a bacterium – and what the weather will look like two weeks ahead.

They will make these predictions much better than we ever could have, and they will do it without recourse to our mathematical models and equations.

It is not inconceivable that, armed with data from billions of collisions at the Large Hadron Collider, they might do a better job at predicting the outcome of a particle physics experiment than even physicists’ beloved Standard Model!

As with the inscrutable utterances of the priestesses of Delphi, our AI oracles are also unlikely to be able to explain why they predict what they do. Their outputs will be based on many microseconds of what might be called “experience.” They resemble that caricature of an uneducated farmer who can perfectly predict which way the weather will turn, based on experience and a gut feeling.

Science without understanding?

The implications of machine intelligence, for the process of doing science and for the philosophy of science, could be immense.

For example, in the face of increasingly flawless predictions, albeit obtained by methods that no human can understand, can we continue to deny that machines have better knowledge?

If prediction is in fact the primary goal of science, how should we modify the scientific method, the algorithm that for centuries has allowed us to identify errors and correct them?

If we give up on understanding, is there a point to pursuing scientific knowledge as we know it?

I don’t have the answers. But unless we can articulate why science is about more than the ability to make good predictions, scientists might also soon find that a “trained AI could do their job.”

Amar Vutha is an assistant professor of physics at the University of Toronto.

This article was originally published on The Conversation. Read the original article.