This Magic Trick Has No Secrets
Ed: Oh great shaman, I’ve traveled far to the Himalayas to witness your magic trick.
Sh: Yes, I will show you it now. It consists of three tasks. You belong to the city – it would seem you people have short attention spans, so I will be quick. But first, take off your shoes.
Ed takes off his shoes and the shaman takes out two boxes. He proceeds to tie both the shoes together by their shoelaces, ensuring they don’t come apart.
Sh : Now wear this hood while I prepare this magic trick.
Ed obliges. After a while, he takes it off and sees the two boxes in from of him. His shoes are gone.
Sh: Your first task is to ask a question to figure out which box has both the shoes .
Ed (scratching head) : Umm, which box has both the shoes together?
The shaman opens the left box. It has both shoes tied together. He repeats this a few times – hooding and dehooding Ed between experiments. Results are as expected.
Ed: This does not seem to me a very impressive magic trick. You tied my shoes together and just shift it from box to box when my hood is on.
The shaman hoods him again. He unties the shoes and separates them into two.
Sh: Ok then the second task – ask a question to figure out which box has the right shoe and which the left.
Ed (getting flustered): This is ridic…okay which one has the left shoe and which one the right?
The shaman opens both the boxes to show him what’s inside each. Results are as expected.
Sh: We can repeat this a few times if you’re not convinced.
Ed (getting up): Oh I’m convinced all right. I’m convinced that this was a massive waste of time.
The shaman, nonplussed, hoods him again.
Sh: Now the third task. Please remove your hood and ask a question.
Ed: Which question should I ask?
Sh: My friend, now you know both questions, you must choose.
Ed: Ok, in which box are my shoes together?
The shaman opens both the boxes to show both the shoes in one of them, tied together, the other box as empty.
Ed (a bit puzzled): What if I’d chosen another question?
Sh: Why don’t you try?
Hooding and dehooding happens.
Ed: Which box has the left shoe and which the right?
The shaman opens both the boxes, showing that each shoe is now in one of each box, now untied.
Ed (befuddled): How did that happen? How did you know which question I was going to ask?
The shaman shakes his head.
Sh: I didn’t. Whichever question you choose to ask, is appropriately answered.
Perplexed, Ed tries this third experiment multiple times. Every time, he sees a result appropriate to the question he asked but inappropriate to the other question he could’ve asked.
Ed: Surely this is unreasonable. The shoes had to be either tied together or separated right before I asked the question? What’s the trick? Hidden assistant? Some hidden compartment in the box…
The shaman takes him inside a large cold refrigerated room. Inside is a photon beam, and two more boxes with holes, kept on top of each other.
Sh: Here’s an atom. Its wavefunction is simultaneously in both those two boxes. A veritable Schrodinger’s cat, if you will. Do you agree this is possible?
Ed (shivering): Obviously.
Sh: We now send a photon through the tiny holes in the top box. Were the atom in that box, the photon would bounce off the atom in a new direction. Were the atom in the bottom box, it would go straight through unchanged in direction. What do you think the photon would do?
Ed: Since the atom is simultaneously in both boxes, the photon does both the things. The atom’s wavefunction becomes entangled with that of the photon. The parts of the atom’s wavefunction in each box would no longer by themselves be in a superposition; they would have “collapsed.” I’ve done this in a lab a bazillion times. What point are you trying to make?
Sh: What happens next? If the photon does not interact with anything else, a tricky two-body interference experiment with this set of box pairs and photons could demonstrate that the atom was still simultaneously in both boxes — and that the photon had both bounced off the atom and gone through an empty box.
Ed: Well yes, but this doesn’t explain the magic trick. I’m not leaving until you tell me the secret behind it.
Sh: Do you not see – the result is dependent on what experiment you do! You could just look in one of the boxes, and find the atom in one of the boxes. Or do the interference experiment and find it in both. Despite your training as a physicist, do you still insist that a physical reality exists independent of your conscious observation of it?
Ed: But in this quantum experiment, the detector apparatus in interference experiment is doing the “observing“, not me. Any_thing_ could observe, there is no need for this consciousness mumbo-jumbo.
Sh: Ah, but that is too simple an explanation. A photon coming through one of the boxes does not observe whether or not the atom is in that box. It rather joins a superposition state with the atom. Say it moves towards a detector that’s built to fire if the atom is in the top box, and not fire if it’s in the bottom one. Should the photon hit the isolated detector, being a physical system, that detector just joins the atom-photon superposition state. The detector is simultaneously fired and unfired, and the atom is still simultaneously in both boxes. Should you get a second measuring apparatus, say your eyes, to observe the detector, it too would join the superposition, for the same reasons – and so on and so forth a causal chain would be formed – a giant superposition.
Ed: Yet, but when I look at the detector, I see a particular result, not a superposition.
Sh: Exactly, but how? John von Neumann showed that the mathematics of quantum mechanics allows the collapse of the wave function to be placed at any position in the causal chain from the measurement device to the “subjective perception” of the human observer. By definition, whatever is at the end of this causal chain must collapse the wavefunction. It should also be non-physical, not satisfying Schrodinger’s equations or any physical law, otherwise, it’d also be entangled in the superposition. Some call this “consciousness”, some call it Ātman, you may call it whatever you want. You may also not call it anything at all.
Ed: Ok, yes I agree, whether the atom is in superposition or not, depends on my choice of the experiment. What does my own free will specifically have to do with it? The choice of which experiment could be made by robot too. I can program a robot to take random decisions by say…flipping a coin if you will. Heads, it looks in the box; tails, it does the interference experiment.
Sh: Agreed, you could do that. Say we had thousand such box-pairs. And say it flipped this coin a thousand times for each pair. 550 times it got head, and so the atom stayed in one of the boxes in the pair. The other 450 times it got tails, so the atom stayed in the superposition. The result, you find, is puzzling – the coin’s landing is mysteriously connected to what is there in the respective box-pair set! The robot’s supposedly random choice will strangely always be the “right” choice. This would mean that there is some direct dynamic relationship between the coin landing and the observation made – you could then conclude that the coin landing is what causes the atom’s wavefunction to collapse!
Ed: Of course that is absurd – Bell’s theorem explicitly forbids that sort of causation. Causal relationships that travel at the speed of light, i.e. local causal relativity can never cause collapse of a wavefunction. Classical mechanics does not cause quantum phenomenon.
Sh: Very good! Now, unconvinced by the theory that the landing of the coin causes the wave-function to collapse, you replace the robot’s decision making with the only decision-making process you know has nothing to with what’s going in the box-pair. What is that?
Ed:My own free choice?
Sh: Yes! You would attach a button to the robot instructing it which experiment to do. You would direct it’s actions, it would not have any agency of its own. That brings you back into the causal chain.
Ed: So what you’re saying is the world is willed into existence by my observation of it? A tree doesn’t exist when I’m not looking at it?
Sh: If there was someway to isolate a tree from local causation, like we can do conveniently for the minuscule atom, then yes it would not exist as anything other than a probability wave. But a tree doesn’t exist so, and hence your brain perceives it as a series of particles in position and time. The reason we observe only states characterized by unique positions is that we humans are beings who can experience only position (and time). Speed, for instance, is just position at two different times.
Ed: So…it might be conceivable that there could be other beings could experience reality differently? Maybe even possibly directly experience the superposition states whose existence we can only infer. I need some water.
Sh: Perhaps. We can never know for sure. And it’s not just me saying it – von Neumann, Bohr, Bell, Wheeler, Wigner and a bunch of others. They and I may be wrong, but the facts are in front of you, and it is up to you to decide.
Ed: You are asking me to believe that your magic trick is explained by quantum mechanics. Surely there’s trickery involved. Your demonstration involved more than an expression of conscious intent. It required you to move your hands and open the boxes. Perhaps the mechanical opening of the box pairs, either sequentially or simultaneously, somehow physically untied and put the shoes wholly in a single box or spread them over two boxes.
Sh: Ah but no! This magic trick has no secrets. Nothing you have seen violates your laws of quantum physics. Quantum mechanics doesn’t have any restrictions on the size of the physical system. Our “technology” has merely enabled us to extend to larger objects what your Bohr of Copenhagen has taught you to accept with equanimity for the small.
Ed: I would like my shoes back, please.
The shaman looks at Ed, grinning. They go out of the room. Ed sits down to wear his shoes, bids farewell to the shaman and proceeds to leave.
THUD. Ed has collapsed, face first, flat on the ground. The shaman looks back.
Sh: Oh, those shoelaces…