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Q is for Quantum

Page 9

by Terry Rudolph


  Both options also provide a natural explanation of the two-PETE-boxes conundrum: The ball begins in a real state where it is definitely white; it evolves (via the action of the PETE box) to a real state where it is definitely [W,B]; it then evolves via a second PETE box back to a real state where it is white again; and so on.

  Although the details are beyond this book, the main thing to know is that this evolution follows a nice and precise wandering trajectory through the real states (much like the trajectory of a flipped coin through its own series of real states depicted earlier). We can calculate very precisely how one misty state changes into another and that one into yet another as time progresses. In fact this nice type of meandering through the mist occurs for any of the boxes we have encountered, as well as many others we have not. It is all very calm and pleasant.

  Until, that is, a human (such as me and I hope you) leaps in and observes the ball.

  If misty states are real, should we collapse in confusion?

  When we observe the ball, we only ever see it black or white. This means, for example, if the ball is actually in a real state corresponding to a mist such as [W,B], it must immediately “jump” into a different real state for which the ball is definitely black or white, according to what was observed:

  It is difficult to convey how repulsive most physicists find such “jumping.” In fact physicists usually use the term “collapse” which sounds more negative. Both words, when they correspond to familiar processes in our everyday lives (such as a building collapsing or a frog jumping), refer to something which is sudden, perhaps very fast, but which is still continuous. By continuous, I mean the building’s fall or the frog’s leap might initially appear to be completely instantaneous, but if you filmed it and then slowed the film right down, you would be able to see all the intermediate stages between the beginning and the end of the jump/collapse process.

  We saw a continuous type of evolution through the real states of a coin when I sketched how the real state changes from the time you flip it until the time it lands. If our present laws of physics are correct, however, once you make an observation the misty states necessarily collapse absolutely instantaneously and completely discontinuously. There is no time lag, and there are no intermediate states. The laws essentially demand this for self-consistency, so it is not even a case of us being able to hope that “maybe it just happens so fast we haven’t been able to see it in slow-motion yet.”

  There is no precedent for something like this in even the most sudden physical processes we ever encounter in other areas of our experience—or, for that matter, in all non-misty physics.

  To make matters worse, the laws demand that the collapse only ever happens when an observer, such as you or I, looks at the color of the ball. As we considered in Part I, we might employ a wide variety of different techniques to try to observe the ball’s color in different ways, some more gentle than others. The collapse process doesn’t care about the method we use to interact with the ball, it just happens as soon as that method is strong enough to tell us the ball’s color, and it doesn’t happen at all otherwise.

  Does it then matter in this situation whether or not we actually observe the color? What if we use some kind of unintelligent observing device to probe the ball between the boxes, but we do not look at the color recorded on the device? What we have done is create a really large misty state. The mist representing the ball is now entangled with the mist representing the stuff making up the device. It is this entanglement which causes the “disturbance” to the ball which is responsible for the fact it no longer always falls from the second PETE box the same color it entered the first. However, the actual collapse, the laws claim, only happens when you, the observer, look at this large misty state, either indirectly by reading the device or more directly just looking at the ball. Then the ball mist collapses into “black” or “white” and the observation-device mist collapses into a “black” or “white” reading.

  Why should observers be so important? Why should the widely different physical mechanisms they use to interact with the ball make no difference to the final real state the ball ends up in, or how that process occurs?

  And if you thought all that was bad enough, consider what happens when we extend our considerations to misty states of two or more balls. Consider the five-ball entangled (generalized Bella) misty state:

  If all misty states are real, then in some large set of all the real states of five balls, there sits this particular state. What happens when we observe one of the balls? At that point we collapse all of the balls to either the state where they are all black, or the state where they are all white—that is, to a completely different real state. None of the balls are left in a misty state, because if one of them is white they all are. That is more disconcerting than the single ball collapse, because the balls in this state can all be in completely different spatial locations.

  This means that (again, only if the misty states are real) it is possible in one spatial location to instantaneously change the real state of the world, in another location, arbitrarily far away. Imagine a giant misty state of many balls, spread throughout the universe. Is it really plausible that one person on one little planet orbiting an insignificant star is instantaneously changing the real state of a part of the universe arbitrarily far away?

  Faced with all this ugliness surrounding collapse, proponents of the notion that misty states are real have for the most part tried to modify our current physical laws by either (i) trying to find a more physically appealing model of collapse (one where it is proper dynamical process and doesn’t need observers); or (ii) trying to find a way to use the misty states as real states, but to completely remove collapse from the picture.

  Option (i) is difficult to make compatible with both current and near-future high precision experiments, as well as consistent with other aspects of physical laws (such as not being able to send messages faster than light), which we hold quite dearly. But there are some models which work (at least for the ball type of experiments we have considered; making them work for all experiments we can presently do is more tricky), and which soon will be experimentally ruled in or out.

  Option (ii) is more subtle—it typically involves thinking about the absolutely giant misty state that makes up everything in the universe including the observers of the balls, and denying that this giant misty state ever collapses. The challenge then is to extract an explanation of how the very small pieces of that giant mist that comprise you and me experience a world where we can talk about little mists of one and two balls, little mists that give random outcomes when we observe them; a world where the assumption of collapse works so well. (This is often called “the measurement problem.”) The most studied option along these lines has been to assume that the giant mist actually describes many different universes, and when you observe the misty state of a single ball there are actually two copies of you created, one that lives in a universe where the ball you observe is white and one where it is black:

  It is a dramatically different view of all of physical reality.

  A completely different option is to discard the idea that misty states are real, and we now turn to understanding this possibility.

  Currency collapse, mental collapse

  Imagine you have prepared a coin and flipped it, and you believe that its real state is equally likely to be in the heads region as the tails region of real coin states, as depicted previously. You describe the coin with the appropriate rocky state. Now, before you look at it yourself, a friend you trust tells you “Hey, that coin is heads.” At that point you immediately and instantaneously “collapse” your knowledge about the coin. Here is a to-scale diagram of you undergoing mental collapse:

  Acquiring information has caused you to change your mind about both the appropriate rocky state and the appropriate distribution over the set of real variables of the coin, because now you know for sure that the coin shows heads.

  Such “collapse via updating one�
��s knowledge” is clearly not a physical process as far as the coin is concerned—something changed in your mind, but the coin doesn’t care what happens in your mind. It is also clearly something that happens instantaneously; you do not slowly and continuously change the state you assign to the coin. The collapse will occur whenever you gain the appropriate information, and it doesn’t matter what physical mechanism you use to acquire that information—if it can provide the requisite information, you collapse; if not, you don’t. These are all features shared by the collapse of a misty state, but here they are not at all strange.

  These similarities motivate the question: Is it plausible that misty states are also features of our knowledge, rather than real states of the world?

  However, there is a very simple dissimilarity between coin collapse and misty state collapse. Collapse of the misty state is accompanied by some tangible disturbance to the experiment, because the output of the second PETE box depends on whether or not you observe the ball after the first PETE box (and cause the collapse).

  Because observing the ball involves interacting with it somehow (shining light off it, smelling it, licking it—whatever) it is not ridiculous to conclude: “Collapse happens in my head, which is where misty states live. There is, however, some new fundamental principle of physics which ensures that to probe a system strongly enough to be able to collapse my misty state of knowledge, I must use concrete physical interactions that cause a random disturbance to the real states of that system, whatever they may be.” The nice thing about this proposal is that it is completely non-committal about what the “actual real states” of a ball are. I gave in Part I a silly version of such an explanation when I imagined the balls could have hidden stickers on them which PETE boxes manipulate.

  However, the proponent of “misty states = real states” counters with: “Why bother thinking about these hidden real states at all? Just let the real state be the misty state and that is the physical thing disturbed by observation.”

  This in turn stimulates the counterpoint—even if you accept the weird behavior of such a supposedly real physical state when it is disturbed, why can a PETE box see the real states without disturbing them, but we cannot see them at all? What is the principle which decides which devices do or do not cause such disturbance?

  Well, comes the rejoinder, something enters the top of the second PETE box, since something falls out the bottom, and when we finally observe that something, it always looks like a colored ball. If the physical property of that something is not that it is “really in the misty state” while it is in transit, then why can’t you tell me what actually is the real state of that thing about which the mist represents only your knowledge?

  Into such back and forth charges no less a person than Albert Einstein, with a brilliant argument (what more do you expect?) that most people understand incompletely. You, I hope, will not be one of them.

  Einstein throws himself in completely

  Einstein presented an argument to prove that, even if we have no idea what the real states of a ball are, there exist real states in the overlap region of at least two misty states—that is, real states for which there is not a unique corresponding misty state. If a misty state was a physical property of a ball then we would be able to look at the real state and know what the “value of the mist” was (by definition of the real states). Einstein claims to prove there is an overlap between the real states corresponding to two or more misty states, and thus he concludes the “value of the mist” cannot be “on the paper”—it is not a physical property, it is not part of the “real physical state” of a ball.

  Einstein’s argument is built upon a demonstration that a subjective choice by one person (a.k.a. Alice), arbitrarily far away from a ball held in a storage box by another person (Bob), can collapse Bob’s ball to different sets of misty states:

  In particular, one of Alice’s choices leads Bob’s ball to end up in either misty state 1 or 2, while a different choice causes it to end up in either misty state 3 or 4; and all four misty states are different from each other. (Saying they are different means an experiment can be performed for which each misty state predicts a different set of probabilities for concrete observations, not just that they look different as a diagram.)

  Alice’s measurement, Einstein’s argument goes, does not affect Bob’s real state. Since she does change the misty states it can be in (at her whim), any given real state must correspond to at least two distinct misty states. More precisely, assuming that (i) a real state of Bob’s ball exists, and (ii) the real state of Bob’s ball cannot depend on what Alice does arbitrarily far away, Einstein concludes: there are many different misty states corresponding to a single real state of the ball.

  For a concrete example, imagine we start with two balls prepared in the entangled mist [WW,WB,BW] that we encountered in Part II. We give one ball to Alice and one to Bob (Einstein called them A and B; he wasn’t a very imaginative guy), who then move far apart from each other.

  Alice now chooses between two different experiments to perform. Much like when she was winning your gold, she can choose either to observe her ball directly, or to first pass it through a PETE box before observing it.

  In the case where she does nothing first, just observes her ball, she collapses both balls like this:

  Her other choice is to first pass her ball through a PETE box and then observe it. In doing so she collapses the state of Bob’s ball like this:

  Alice’s free choice of measurement—her choice to use the PETE box or not—made far away from Bob, can collapse his ball to either being in one of the states [W,B] or W, or to being in one of the pair of states [W,W,B] or B.

  For our particular example Einstein would say that since some of the time Alice collapses Bob’s ball to [W,W,B], it must be the case that some of the time the real state of Bob’s ball corresponds to [W,W,B], but it must also correspond to one (or both) of either W or [W,B]—the state it would have collapsed to had she done the other measurement. For Einstein’s argument it doesn’t particularly matter which of these two possibilities [W,W,B] overlaps with.

  In terms of our schematic diagrams, Einstein’s conclusion that at least some misty states correspond to overlapping sets of real states, perhaps something like this:

  That is enough to prove the misty states are not themselves real.

  It is possible to include arbitrarily more misty states in the argument by letting Alice do many more choices of measurements. The final conclusion is that for any given real state of Bob’s ball, there are actually arbitrarily many misty states.

  Einstein called all this “incompleteness” of the misty state description. He uses the term incompleteness (I surmise) because the real state was, by definition, meant to capture all and everything about the physical properties of the ball, and the misty states clearly do not do that if there exist real states in an overlap region of two misty states. But the confusing thing is that we (and he) could also claim the misty states are incomplete if they happened to be just one amongst many physical properties. That is, the “many real states per misty state” option, discussed previously as a more conservative claim about reality of the mist, is also a view in which the misty states are incomplete. Einstein gave other arguments for this very different type of incompleteness, but I’m going to skip them—if I teach you everything there is to know about this topic then you won’t be able to make a career as a philosopher, should you so wish, because everything will be clear to you. If you accept the argument of Einstein’s just given then whether there are additional underlying physical properties comprising the real states, or whether the mist is the only thing that is real, is moot—the misty states cannot be real at all.

  Note in passing that Einstein does not give a sausage (his words) about what Bob does or doesn’t measure, or what he can or cannot infer about the properties of his ball. And neither should you—it is irrelevant to this particular argument.

  The existence of real states in the over
lap region of two misty states would provide a nice explanation of the following: while there is an experiment for which the probabilities of the various outcomes are all different according to whether we drop into it a ball prepared in W or [W,B] or [W,W,B], that experiment never lets determine for sure which particular misty state the ball originated in. (This is obvious if we just observe the color, since seeing the ball is white we cannot for sure distinguish the three options, but it actually remains true no matter what experiment we do). If misty states are real, this is somewhat strange—why are we prevented from knowing something that nature knows? However, if we accept Einstein’s conclusion, then the reason we cannot always for sure determine whether a ball was prepared in W or [W,B] or [W,W,B] is because sometimes the real state of the ball itself is ambiguous about the matter—that is, in an overlap region compatible with all three of these. By hypothesis, what we mean by the real state is anything and everything that can affect the outcome of an experiment. Thus if the real state itself does not uniquely determine the misty state, neither can any experiment we do. Our inability to distinguish different misty states with certainty is then no more surprising than the fact we cannot always tell for sure, just by seeing a coin with heads facing upwards, whether the person who flipped that coin assigned it the rocky state or the rocky state .

  Questioning Einstein’s two assumptions

 

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