What is quantum entanglement? Part 4: relativity and entanglement

This is part 4 in a lengthy series of posts attempting to explain the idea of quantum entanglement to a non-physics audience.  Part 1 can be read here,  Part 2 can be read here, and Part 3 here

In the last post, we finally introduced the concept of quantum entanglement.  An example of an entangled state between two quantum particles is given by the decay of a spin-zero pion into a spin-1/2 positron and a spin-1/2 electron, as illustrated below.

This results in a combined quantum spin state for the electron and positron that may be written as:

We may read this as “the two spin-1/2 particles end up in a quantum state which is an equal superposition of the positron being spin-up and the electron being spin-down with the positron being spin-down and the electron being spin-up.”

This suggests that the electron and positron, when produced in the decay, might be considered to exist simultaneously in a state where the electron (-) is up and the positron (+) is down, and vice-versa — their fates are “entangled.”  When we measure the state of one of the particles, say the electron, it is 50% likely to “choose” the spin-up state and 50% likely to choose the spin-down state.  When it does, the positron, no matter how far away, must instantly take on the opposite spin state — at least according to the original Copenhagen interpretation of quantum physics. In short, after measurement, the combined state of the electron and positron is either:

But, note the use of the word “instantly.” Because angular momentum is conserved, if the electron is measured spin-down, the positron must be in a spin-up state.  This collapse of the wavefunction must happen as soon as the electron is measured, otherwise there would be the possibility of measuring the positron also in a spin-down state, which would violate angular momentum conservation.

This would seem to suggest that the electron must send a “message” to the positron, and this message arrives instantaneously, regardless of the distance between them.  However, according to Einstein’s special theory of relativity, nothing is supposed to be able to move faster than the vacuum speed of light.

This raises the question: does entanglement violate special relativity?  And, if it does, can we use it to communicate over vast distances at superluminal speeds?

As it turns out, the correct answer is “neither.”  Entanglement, when considered carefully in the context of the full quantum theory, turns out to be perfectly consistent with relativity.  But, as we will see, it is quite a theoretical adventure to come to that conclusion!

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What is quantum entanglement? Part 3: Entanglement, at last

This is part 3 in a lengthy series of posts attempting to explain the idea of quantum entanglement to a non-physics audience.  Part 1 can be read here, and Part 2 can be read here.

Here, in part 3, we will at long last introduce entanglement! But, before we do, we need to be sure we really understand what the wave properties of a quantum particle imply about its behavior.

So, by the late 1920s, physicists knew that discrete bits of matter — electrons, for example — sometimes act like a wave and sometimes act like a particle.  This seemingly contradictory nature is often referred to as wave-particle duality.  It was not immediately obvious how to interpret the wave properties of matter, but physicists finally settled on what is referred to as the “Copenhagen interpretation,” after the city in which it was more or less developed.  If we consider the motion of a single electron, the Copenhagen description of quantum behavior could be summarized as follows:

  • While freely propagating through space, the electron and all of its properties evolve as a wave.
  • The wave may be described as a “wave of possibilities”: the amplitude of the wave only describes the probability of the electron to be found in a certain position or configuration.
  • While evolving as a wave, the electron in general has no definite position or configuration — it is, roughly speaking, existing in all possible configurations simultaneously.  In Young’s double slit experiment, for instance, it is often said that the electron goes through both slits.
  • When a property of the electron is measured in an experiment, where the property must take on a definite value, the electron “chooses” an outcome, based on the wave probabilities mentioned above.  The wave “collapses” into that single outcome.  For instance, if we have a detector to measure the position of the electron, we will see that electron at a single definite location on the detector.
  • If the particle still is free to continue moving, the process repeats itself, the collapsed wave evolving again, usually resulting in a wave of many possible outcomes again.

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Posted in History of science, Physics | 12 Comments

Coming in 2018: Falling Felines and Fundamental Physics!

I’ve only been hinting at this revelation so far, but I am finally ready to let the cat out of the bag — almost literally!  I have signed a contract with Yale University Press to write my first popular science book, which I have tentatively titled “Falling Felines and Fundamental Physics!”

This book will combine physics and history to tell the surprisingly long story of scientists and engineers studying the remarkable ability of a cat to (almost) always land on its feet when it falls from a height. In other words, I will talk about images such as the famous one below, which was the first series of high-speed photographs taken of a falling cat, back in the 1890s.

Side view of a falling cat, by Marey. Images chronological from right to left, top to bottom.

Scientists and engineers have been fascinated by falling cats for a remarkably long time, stretching back at least as far as the 1850s and continuing to some extent even today.  The puzzle of “cat-turning,” as it was known in Victorian times, has played a noteworthy role in the history of photography, geophysics, robotics, and even space exploration.  Furthermore, the basic mechanism by which a cat rights itself while falling is connected to very profound mathematics related to the propagation of light, quantum physics, the motion of pendulums, and even parallel parking.

In telling the story, we will come across a number of famous physicists, such as James Clerk Maxwell, the father of electromagnetism, and see that cats — with their cat-turning — have caused all sorts of mischief over the years.  The book will contain many illustrations of cats in free-fall, as many photos have been taken over the years…

Series of images of a falling cat, taken by Magnus in 1922.

… and it will also include some images of my own cats, to help illustrate the physics without complicated mathematics!

Resident feline fluidity expert Cookie demonstrates the bendy-ness of cats.

My book, Falling Felines and Fundamental Physics, will take a light-hearted look at the history of the falling cat problem, and will at the same time use it to introduce fascinating and fun concepts in physics. The book is intended for anyone interested in physics, or cats, or both.  And it will include cat pictures!

I’m really excited to tell you this story! I’ve still got a lot of work to do, both writing and research, but the book is due to be finished in mid-2018, which means you will hopefully be able to read it in the second half of that year!

I will keep everyone updated on my progress!

(PS: haven’t forgotten the entanglement series of posts: was out of town for work this past week. Will return to it asap.)

Here, at the Dr. SkySkull Feline Angular Momentum lab, Sabrina and Sasha take a break from their researches.

Posted in Animals, History of science, Personal, Physics | 5 Comments

What is quantum entanglement? Part 2: Randomness and measurement

This is part 2 in a lengthy series of posts attempting to explain the idea of quantum entanglement to a non-physics audience.  Part 1 can be read here.

So, by the mid 1920s, physicists had made significant progress in developing the new quantum theory.  It had been shown that light and matter each possess a dual nature as waves and particles, and Schrödinger had derived a mathematical equation that accurately described how the wave part of matter evolves in space and time.

But it was not clear what, exactly, was doing the “waving” in a matter wave.   Water waves arise from the oscillation (waving) of water, sound waves arise from the oscillation of molecules in the air, but what is oscillating in a matter wave?  Or, to put it another way, what does such a wave represent?

We will try and answer this question by looking at how a matter wave manifests in an actual experiment.  It turns out that the best example for demonstrating the wave properties of matter is also the best example for demonstrating the wave properties of light: Young’s classic double slit experiment!  However, the double slit experiment was not done with electrons until decades after the foundation of quantum mechanics, so we must briefly step away from our historical discussion to investigate it.

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Posted in History of science, Physics | 9 Comments

What is Quantum Entanglement? Part 1: Waves and particles

If you follow science, or science fiction, to any degree, great or small, you’ve probably heard the term “quantum entanglement” before.  You may also have heard it referred to as “spooky action at a distance,” and understand that it somehow involves a weird connection between separated quantum particles that can “communicate,” in a sense, over long distances instantaneously.  You may have read that quantum entanglement is a key aspect in proposed technologies that could transform society, namely quantum cryptography and quantum computing.

But it is difficult for a non-physicist to learn more about quantum entanglement than this, because even understanding it in a non-technical sense requires a reasonably thorough knowledge of how quantum mechanics works.

In writing my recently-published textbook on Singular Optics, however, I had to write a summary of the relevant physics for a chapter on the quantum aspects of optical vortices. I realized that, with some modification, this summary could serve as an outline for a series of non-technical blog posts on the subject; so here we are!

It will take a bit of work to really get at the heart of the problem; in this first post, I attempt to outline the early history of quantum physics, which will be necessary to understand what quantum entanglement is, why it is important, and why it has caused so much mischief for nearly 100 years!

Small disclaimer: though I am a physicist, I am not an expert on the weirder aspects of quantum physics, which have many pitfalls in understanding for the unwary! There is the possibility that I may flub some of the subtle parts of the explanation. This post is, in fact, an exercise for me to test my understanding and ability to explain things. I will revise anything that I find is horribly wrong.

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Posted in History of science, Physics | 19 Comments

The Southern Reach trilogy, by Jeff VanderMeer

I’m not entirely sure why it took me three years to read Jeff VanderMeer’s Southern Reach trilogy.  One of his earlier novels, Finch, is on a very short list of “best books I’ve ever read.”  I suspect that I simply read the name “Southern Reach” and it somehow evoked images of the Southern United States in a weird way that didn’t appeal to me, and I just never got around to looking at the books.  Until, that is, I read the first description of the upcoming movie version of the first book, which instantly intrigued me.  Over the course of about 5 days, I read all three books of the trilogy.  They’re that good.

It is hard to find the right words to describe these novels.  Bewildering, intricate, confusing, surreal, thoughtful, haunting, poetic, horrific, terrifying, beautiful?  It is all these things, and more.

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Posted in Horror, Science fiction, Weird fiction | 1 Comment

Chills, by Mary SanGiovanni

I’ve been in a bit of a funk the past few weeks and haven’t been reading much.  What I needed to get myself back on track was a nice solid bit of horror fiction, and fortunately I had on hand the most recent novel by Mary SanGiovanni, Chills.

As is made clear from the cover image and the title, Chills centers on a danger that originates in the coldest weather.  A team of detectives and investigators race, in the midst of a blizzard, to solve a series of grisly murders and prevent future ones from occurring.  However, they soon learn that even worse things are happening, and that there are unnatural things in the whiteout…

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