*gedanken gadget*, is real in the sense that devices with the same characteristics have been built, although none of these take the actual shape of a chest of drawers. In fact, the devices built so far are way smaller in size. They are based not on drawers, but on photons or sub-microscopic particles.

While scaled-down, their behavior is exactly like that displayed by Albert's chest of drawers. A behavior predicted by the laws of quantum mechanics. So from a quantum theoretical point of view, the behavior of devices like Albert's chest is rather dull and unremarkable. Yet, for us human beings, whose view on reality is biased by sensory perceptions limited to classical physics situations, these devices are weird. For some of us they are weird beyond belief, for everyone else they are weird enough to force you to redefine your view on reality.

In this follow-up post we are going to dive deeper into these matters. You should be able to read and understand this blog post without any knowledge of quantum theory, and without reading the previous post on this subject. I will start by recapping the key features of Albert's drawers. Next, we will discuss some choices of worldview that are compatible with the existence of this remarkable piece of furniture. These are the possible choices that I could come up with. I am keen to hear which choice is yours. And maybe you can offer a choice not listed by me. Let's see where we get.

# Albert's Chest

Albert's chest, although most spooky when revealing its contents, appears rather unremarkable and featureless from the outside. Three rows, each consisting of three drawers, makes up this piece of furniture. Whenever Albert pulls open a drawer, he is presented with a number of socks. Once a drawer is open, Albert can not open just any remaining drawer. Each drawer opened blocks from opening all drawers not in the same row and all drawers not in the same column. This effectively restricts Albert, each morning when he inspects the chest in search for fresh socks, to the opening of three drawers configured in a horizontal row or in a vertical column. Only the next morning, after his housekeeper is done refilling the chest and resetting the drawers, can Albert again make a new choice of three drawers to open.

Initially, out of habit, Albert always opens a horizontal row of drawers. He does this without giving much thought to which of the three rows to open. After a few days, he starts noticing a pattern. Whichever row he opens, the three open drawers always contained a total even number of socks. Many days pass by, and Albert never discovers a row

*not*containing an even number. That makes sense: each row containing an even number of socks tells Albert that each morning the chest must be filled with an even number of socks. An observation comfortably compatible with the notion that socks come in pairs.

One morning, Albert decides to deviate from his fixed ritual, and opens a vertical column of drawers: the three leftmost drawers. Interestingly, this time he observes an odd number of socks distributed over the three opened drawers. The next day, he opens the same leftmost column of drawers, and again observed an odd number of socks. This raises Albert's interest. There must be a correlation between the leftmost drawers of the different rows. The next few mornings Albert checks the same column of drawers, and indeed each time observes an odd number of socks.

Albert gets curious about the other columns. What correlation will they reveal? The next day he opens the middle column. Again an odd number of socks. The next few days he again checks the middle column. Each time he observes an odd number of socks.

Albert is a clever guy, and he now realizes he can predict with certainty that the rightmost column of drawers must behave differently from the two columns already inspected. The rightmost drawers for sure must be correlated such that the socks in them add up to an even number. This is obvious as an odd number of socks in the rightmost drawers, added to the number of socks in the middle column (observed to be odd) and the leftmost column (also observed to be odd) would result in an odd total number of socks in the chest. A contradiction, as he had already observed, based on horizontal drawer openings, that the total number of socks in the chest is always even.

The next morning he eagerly opens the three rightmost drawers. To his astonishment he observes an odd number of socks.

The next few mornings he checks the same rightmost column. Each attempt reveals an odd number of socks. Albert realizes something must have gone wrong. Maybe his housekeeper coincidently changed from filling the chest with an even number of socks to filling it with an odd number of socks, just at the time he switched over from opening horizontal rows to vertical columns?The next morning Albert again opens a horizontal row. An even number of socks stares him in the face. He starts randomly switching between horizontal rows and vertical columns. Horizontal rows always deliver even numbers, vertical columns deliver odd numbers.

This drives Albert crazy. What is happening? What on earth can explain these observations? The results he is obtaining are logically impossible. "At any given morning if I would open three rows", Albert reasons, "I would end up with an even number of socks."

"But would I open three columns, I would end up with an odd number of socks."

"Yet in both cases I would have opened the same nine drawers. This is absolutely impossible!"

# Living With Albert's Chest

Being presented with Albert's chest, how do you incorporate its remarkable behavior in your views on physical reality? How would you put Albert at ease? I offer you five choices. What choice is yours? I don't claim completeness of the list. In case your choice isn't listed, I am most interested to hear the reasoning that allows you to live with Albert's chest.

**1) Deny Its Existence**

I will refer to this position as the 'Bill O'Reilly position'. This position is easy to maintain. Just tell these physicists to bugger of. You don't want to hear their crap and all that quantum nonsense. Quantum theory explaining this fantasy chest of drawers. C'mon, get real. And don't start again with your fairy tales how quantum theory has been tested to eleven decimal places, how it explains all of chemistry, and it has enabled my smartphone. If quantum theory was so damn capable, deliver me a hoover board!

Needless to say this position is not very popular with physicists. Yet to a sizable portion of human population this will be a comfortable position. If you don't take this position, you have to find an alternate position that allows you to explain to Albert his observations. No easy task!

**2) Accept Non-Local Socks**

This position, labelled the 'Deepak Chopra position', is popular in the pop-science literature. Much less so amongst physicists. To come to terms with Albert's chest of drawers, this position allows for non-locality effects, such as socks jumping instantaneously from one drawer into the other at the very moment you open a drawer. Great possibilities await us if this position is correct. "Beam me up, Scotty!"

Advocates of this position often use more nebulous terms to describe the magic that happens the very moment you open a drawer. You might hear phrases like "Sock potential crystalizes into socks when you open the drawer." Don't let this terminology fool you: something needs to happen faster than light (or should I say 'neutrino') speed, for you to always find the right (even or odd) number of socks in the drawer.

You guessed it, physicists are not very fond of superluminal effects and for them that pretty much rules out a 'Deepak Chopra position'.

**3) Embrace Precognition**

What if Albert's housekeeper can look in the future and predict if Albert will open a row or a column of drawers? With that knowledge she can prepare the drawers accordingly. This 'Nostradamus position' is ironclad. That is: provided everyone who ever operated a chest like Albert's has precognition capabilities and is keen on playing tricks on the opener of the drawers. Yet, none of the researchers who created and operated their own version of Albert's chest would keep a straight when you asked them if their experiments succeeded because of their own precognition capabilities. They would point out that even if they could predict future actions, they would be incapable of preparing their submicroscopic chest accordingly. Their quantum versions of Albert's chest operates by always preparing it in the same way.

Of all potential positions, this 'Nostradamus position' is probably the one least popular under physicists.

**4) Deny Free Will**

This 'Laplace position' starts from the assertion that both Albert as well as his housekeeper are sophisticated, yet deterministic machines. Many physicists will agree to this statement. 'Laplace position' advocates point out that the course of action of these machines is encoded in the big bang, and for reasons unknown to us, each time they prepare and subsequently open the chest, Albert's and his housekeeper's actions are correlated such that even rows and odd columns result.

This position takes the sting out of Albert's chest of drawers, but leaves unexplained why rows always come out as even, and columns as odd.

**5) Avoid The**

*"Would Have Happened If"*FallacyPictures made along the road not taken, don't exist. This summarizes the 'Bohr position' that forms a key element in the Copenhagen interpretation of quantum mechanics. It tells us that any reasoning that includes the outcomes of observations "that

*could*have been made

*if*things would have been different" is suspect. Such reasoning might be convenient in everyday life, it is fundamentally flawed when applied to systems in which quantum effects are prominent. For such systems, the assumption of a reality being associated with observations not made can not be maintained. Observations not made don't exist. Period.

This all may sound trivial, but most (if not all) sensible people would agree to the reasoning that if each row in Albert's chest of drawers always results in an even pair of socks, then the full drawer must always contain an even number of socks. Yet, according to the Bohr position this reasoning is fundamentally flawed, given that one can open only one row at a time. As soon as one rejects such reasoning, Albert's chest is no longer enigmatic.

# Excess Baggage

As mentioned above: I am interested to hear from you how you manage to live with Albert's chest of drawers. How would you explain to Albert the behavior of his chest of drawers? Have you taken up one of the five positions listed? Are you an O'Reilly, a Chopra, a Nostradamus, a Laplace, or a Bohr? Or did you identify your own unique position?

Let me offer you my view. A view that will not come as a surprise to you.

O'Reilly, Chopra and Nostradamus are 'not my thing'. Also the Laplace position does not provide a viable alternative to me, as it leaves too much to be explained. I see no other choice than to take up the 'Bohr position'. This position is sometimes referred to as an anti-realism position. However, such is a misnomer. The Bohr position does accept a reality, albeit a minimalistic reality that does not extend beyond observations made. This does not cause any problems, as nowhere in physics do we need an extended reality 'underneath the observations'. Assuming such a reality to be 'out there', creates excess baggage. Nature provides us with hard experimental evidence of its dislike for excess baggage. One piece of excess baggage, the luminiferous ether got eliminated from our worldview thanks to Einstein. Another piece of excess baggage, a reality underneath observations, got eliminated despite Einstein.

Nature economizes on her baggage. It has eliminated all elements of reality not strictly necessary, but at the same time has provided us with enough to chew on. Or, as Einstein would have put it:

*"Frugal is the Lord, but malicious He is not."*

What other excess baggage might we be carrying? What else should we let go to make progress in our understanding of the universe?