### Brian Greene's Mulder and Scully Illustration Demonstrated Graphically

Fox is traveling in Paris and Dana is home in Washington D.C., when one day each receives a large package from an anonymous sender. The packages each contain 1000 small cubes, and on each cube are three small doors – one on each of three sides.

The cubes are numbered from 1 to 1000, and each of the doors is labeled A, B and C.

A letter is included in the package that explains that the cubes represent an alien technology that uses faster-than-light communications. It goes on to describe how the cubes work, as follows:

Behind each door on each cube is a light that will briefly flash either red or blue when the door is opened. Before any door has been opened on a particular cube, the colors that it will show have not been determined. The moment the first door is cracked

open on a specific cube, that cube randomly selects the colors it will show behind all of its doors, and at the same moment instantly transmits its decision to its corresponding cube in the other set, so that when any of that cubes doors are opened; they will show the same colors.

So, for example, say Fox is the first one to pick up cube #1, and he opens door A and sees a red light flash. What the letter is saying is that at the moment Fox opened the door, the cube randomly chose a set of colors to show behind its doors (say it picked red for A, blue for B, and red for C), and at the same instant transmitted this information to Dana’s cube #1 so that when she opens doors on that cube, she’ll also see the pattern red/blue/red for doors A, B and C.

Each numbered cube in Fox’s set is paired with the corresponding cube in Dana’s set. The first one to open one of the six doors in a pair initiates the random color selection, as described. Thereafter, the colors for that pair are set and unchanging.

The letter also explains that the cubes will self-destruct if tampered with, so Dana and Fox are unable to immediately test these claims by breaking open the cubes and inspecting their internal workings.

Now, as soon as Fox reads this letter, he calls Dana on the phone, full of excitement and wonder about this amazing “alien technology” that some anonymous benefactor has given them. But Dana is skeptical. “This is obviously a hoax”, she says, “and not a very good one at that. The bottom line is; the cubes will show the same colors behind corresponding doors on each cube, no matter what we do. Regardless which one of us picks up a particular cube first, the outcome will be that we’ll both see the same colors behind its doors."

"If you see red behind door A on some cube in your set, I’ll see red behind door A on the same cube in my set. How convenient that the cubes are set to self-destruct if we take them apart to investigate the letter's claims directly. For all we can tell, the cubes might just be wired up with Christmas lights, with each cube in my set wired identically as the corresponding cube in your set."

"There’s no alien technology here,” Dana concludes, “they’re just cubes wired up with lights, and somebody is trying to make fools of us.”

Fox is not ready to concede though, and gives it some thought. “You’re right,” he says. “The outcome is the same whether the letter is telling the truth, and the cubes behave as it describes, or you are right and the cubes are just wired up inside with red and blue lights. The key question is this: are the colors we see pre-determined, as with identically-wired Christmas lights, or are they not pre-determined, but chosen by the cubes at the instant one of a pair is first opened? Is there some test we can devise that could settle this?”

After considerable discussion, they realize there is such a test. Here’s what they do:

Fox and Dana both hang up the phone and proceed to open one of the three doors on each cube, in order, from 1 to 1000. For each cube they pick a door to open at random. As they do this, they record the cube number, the door they opened, and the color they saw. When they’re done, they each have a list that looks something like this:

Cube Door Color1 A red

2 C blue

3 A blue

4 B red

5 B blue

.

.

.

Then they get back on the phone and compare their lists. First they look at a few entries where they happened to pick the same door for the same cube number. In these cases, they verify that they both saw the same color behind the doors. This verifies that at least that part of the letter was accurate.

Next they compare colors straight across, cube-by-cube, regardless which door was opened. Fox has predicted that if the cubes are just hard-wired with lights, they will have seen the same color for the same cube less frequently than if the cubes behave as described in the letter.

*probability wave*that determines only the

*probability*that the particle will be found at any point in space, throughout the universe. Only at the instant a person measures a particle’s position does it assume a definite position.

*know*its position,

*By measuring it, you force it’s hand, so to speak – you*

**it doesn’t HAVE a position until you measure it!***make*it take on a position, for that instant.

*really does happen*when we look at things!

The graph appears predominantly red only because Excel draws the red line over the blue line. The black line at the center (sitting right around 66.6) is the “trend line” that Excel draws for both lines. This was not very encouraging.

Looking at that graph, it is clear, I think, that there really is a very slight, but discernable, difference in the outcomes. It amounts to only about 0.1% over the 10,000 tests, but there’s no doubt that the lines are not converging on the same number.

So what is the point of all this? My confidence in Greene’s presentation of the facts, and in the ideas about the nature of the universe that they imply, was shaken by my initial failed attempt to demonstrate them for myself. This second attempt, and the “cumulative average” graph above helps to reestablish my confidence, and with it my sense of wonder and fascination with those ideas.

## 3 Comments:

I read this whole thing thinking you were going to reach some fabulous conclusion about pre-destination vs. free will, but alas, you went all atypical on me!!! Intriguing article, though....

You will have to explain this time when get home. Something about the universe is in here. Love you. M>

Greene's example comes straight from another example, published many years earlier, by Mermin entitled "Is the Moon there when you don't look at it?" (see here: http://www.iafe.uba.ar/e2e/phys230/history/moon.pdf)

the colors are red and green in that example, and yes the result holds- but you need to do the math right. I have python code which you can see here: http://dl.dropbox.com/u/1813623/mermin.py

I think you can verify that it does actually work the way Greene and Mermin state.

Weird! :)

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