The EPR Tale for Deep Springs: 16 March 1998

The back story: In 1998 when I was teaching at Deep Springs I was asked to give a presentation at "Public Speaking". This is what I came up with...

"Given this opportunity of speaking to you about an aspect of my work or my interests I thought it would be best to try to give you one, elegant idea from physics. Well, one idea became two and, in fact, they grew into a story. Before beginning this story I'd like to mention that it is quite similar to a tale that I first heard from Yakir Aharonov.

Once there lived an evil (or good - I haven't figured out which) King who absolutely hated physics, physicists, even people who might one day think about physics. When such a poor, miserable soul entered his realm he would summarily clap them in chains and toss them in the deep dungeon. But the King was, along with many of his peers, a bit neurotic. He had a failing for good physicists. He also did not like being King so he devised a trial for anyone who had the slightest ability to model the natural world. If someone passed this test he promised he would (in probably the biggest mistake of his life) give away a son or daughter (as appropriate), make the winner king or queen and retreat to a monastery high the mountains on the edge of his realm. This is the story of the trial.

You are one of the unfortunate few people thinking about physics in this kingdom.

One day, with great trumpet fanfare QPS (for Quantum Postal Service) arrives with a package. You scramble down the stairs from your small room where you have been hiding all these years and find a package addressed to you, wrapped in beautiful, shimmering paper and tied with gold ribbon. The guards of QPS are waiting so you open it. Inside you find a simple box. It has doors on two sides and a note attached. Seeing that you have opened the package, the guards vanish into the crowd.

Once you are again up in your rooms, you find the directions. "A spring time present from the King!" Your heart sinks. "Is it rose or is it trillium? May your mind be not lost in delirium! Is it red or is it white? Please don't forget to write! Open one door at a time." You try a door. Sure enough, when you open the door on the top of the box, out of the murky blackness comes the sweet, not over-powering smell of wild rose. This is may be fun after all! Curious to see the color of the flower you try the door on bottom of the box. It won't open. Ah, open one door at a time! When the other one is closed the bottom door opens easily enough and, peering into the small hole you see the blush of red. Satisfied, you close the bottom door and turn the box over to smell the beautiful rose again. But to your horror it is the odor of trillium!!

Soon you discover a pattern. If you observe one aspect of the flower the other aspect, when you return to it, may be changed. You cannot be sure that there is a white trillium (quite rare) or a red rose or either of the other two possibilities.

After many rounds you find that if you smell the flower then you have a 50% chance to enjoy a rose smell and a 50% chance to recoil at the trillium smell. As long as you do not open the other door, the smell will stay the same. But you have no idea what color your flower is. If you decide to check on the color you find, again with a 50/50 chance, red or white. Thus once you find one aspect of the flower, you destroy your knowledge of the other. You can find exactly one half the knowledge you would expect of garden-variety flowers.

In fact you might call this a very simple flower. It has only two properties smell and color and only two choices rose-like or trillium- like and red or white. These flowers from the King have no shape, don't wilt, and certainly can not be admired from all angles. No, they are oddly censured. Perhaps they are a complex, rich structure hidden behind a dark vale. Perhaps they are just very simple flowers.

However, the king is well aware that simple flowers may not be the easiest flowers to understand.

Exhausted by your investigation of this curious flower you lay the box aside, relieved that it is no more than a curiosity. After dashing off a quick thank-you note to the King, you go back to studying the rate at which things accelerate down incline planes...

Not more than a week later, you receive a letter from your good friend and colleague, Lucy, in a distant city. She was visited by QPS as well. And she has the same sort of box as you! In the next day's post you find a letter from the King wishing you health and well-being and advising that you and your friend have a special pair of matched flowers. Whatever you find, your friend will find the opposite: If you smell trillium, she will smell rose. If you see red rose, she will see white trillium.

Being of somewhat a skeptical nature, you decide to test the King's claim. In a series of letters you and your friend work out a procedure. After synchronizing clocks with your friend, you make a measurement and send a letter to her describing which door to open and what she will find. She makes a measurement at the same time and writes you. If you observe a red flower, she observes a white flower. It works! Without in any way touching the distant box, given the King's information, you can predict with certainty what she will smell or see when she makes a measurement. Even so, the results of any one measurement are still random; you smell trillium half the time and rose half the time.

You even work out a system by which your friend makes a measurement just a fraction of a moment after you make yours. It still works! It doesn’t take any time for the flower to (apparently) know what to be!

Now life becomes feverish. Could you not make a system to transmit information from one city to another much faster than by QPS? But no, sadly you have no way of absolutely determining your own results (unless they are all the same!). It doesn't work. Oh well.

Your friend, though, points out, "Just as our boxes give half the information we expect," she writes, "our two boxes have half the information for a complete description of the whole system. For instance, there are four the possibilities rose-rose, rose- trillium, trillium-rose, and trillium-trillium. We know that our measurements will be opposite. So this correlation reduces the four outcomes to the two, rose-trillium and trillium-rose. How does your flower know to smell so that it is correlated with mine? And," she adds, "this happens arbitrarily fast!"

It is fashionable in your city to think of the world made of atoms - parts. All objects are divided into these small, indivisible, elementary parts or atoms. The properties of these parts are thought to be intrinsic; they do not depend on the history of the elementary parts nor the environment which they exist. An atom is `red' or it's not. Put another way, you might say "The real factual system [of your friend's flower] is independent of what is done with the system [of your flower] which is spatially separated from the former." (to paraphrase a paper by Einstein, Podolsky, and Rosen).

However, in your friend's city things seem quite different. She bombards you with questions, "What would it mean to have one flower in the universe? Could you tell if it was a rose or a trillium? How could this question have any meaning? In such a universe you would have nothing to compare it to." She suggests that the only way for a measurement to make any sense is in relation to something else. We know a rose smell only after smelling other roses. She writes that these especially simple flowers from the king make sense only when compared with themselves. "By smelling your flower you give a context for the smell of my flower," she writes. Groovy, holistic, but is it right?

You argue back and forth for many months. But the King will not wait. Clearly, with all this correspondence between you and your friend (all carried by QPS of course) the King is well aware of your activities. In a night-time raid, guards seize you, clap you in irons, confiscate all your inclined planes and water clocks, and toss you in the deep, dark dungeon.

You have one chance before you are executed. This is the trial. You must determine, precisely, the result of the King's observation of a box, both which door he opened and what the result was, from measurements before and after the King's. The King is kind and gives you a demonstration. He takes his box, assures you that you could do whatever measurement you want (including using another box) before his measurement. The King then simply opens one of the doors, notes the results, closes the door and hands the box to you. Of course, in the actual trial you do not see his measurement. Now it is up to you... "

Last modified 28 November 2022