The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [116]
Figure 8.6 The Copenhagen approach to quantum mechanics envisions that when measured or observed, a particle’s probability wave instantaneously collapses at all but one location. The range of possible positions for the particle transforms into one definite outcome.
I understand full well if this explanation leaves you shaking your head. There’s no denying that quantum dogma sounds a lot like snake oil. I mean, along comes a theory that proposes a startling new picture of reality founded on waves of probability and then, in the very next breath, announces that the waves can’t be seen. Imagine Lucille claiming she’s a blonde—until someone looks, when she immediately transforms into a redhead. Why would physicists accept an approach that’s not only strange but that seems so downright slippery?
Fortunately, for all its mysterious and hidden features, quantum mechanics is testable. According to the Copenhagenists, the larger a probability wave is at a particular location, the greater the chance that when the wave collapses, its sole remaining spike—and hence the electron itself—will be situated there. That statement yields predictions. Run a given experiment over and over again, count how often you find the particle at various locations, and assess whether the frequencies you observe agree with the probabilities dictated by the probability wave. If the wave is 2.874 times as big here as it is there, do you find the particle here 2.874 times as often as you find it there? Predictions like these have been enormously successful. Wily as the quantum perspective may seem, it’s hard to argue with such phenomenal results.
But not impossible.
Which takes us to the third and most difficult question. The collapsing of probability waves upon measurement, Figure 8.6, is a centerpiece of the Copenhagen approach to quantum theory. The confluence of its successful predictions and Bohr’s forceful proselytizing led most physicists to accept it, but even polite prodding quickly reveals an uncomfortable feature. Schrödinger’s equation, the mathematical engine of quantum mechanics, dictates how the shape of a probability wave evolves in time. Give me an initial wave shape, say, that of Figure 8.5b, and I can use Schrödinger’s equation to draw a picture of what the wave will look like in a minute, or an hour, or at any other moment. But straightforward analysis of the equation reveals that the evolution depicted in Figure 8.6—the instantaneous collapse of a wave at all but one point, like a lone parishioner in a megachurch accidentally standing while everyone else kneels—can’t possibly emerge from Schrödinger’s math. Waves surely can have a needle-thin spiked shape; we’ll make ample use of some spiked waves shortly. But they can’t become spiked in the manner envisioned by the Copenhagen approach. The math simply doesn’t allow it. (We’ll see why in just a moment.)
Bohr advanced a heavyhanded remedy: evolve probability waves according to Schrödinger’s equation whenever you’re not looking or performing any kind of measurement. But when you do look, Bohr continued, you should throw Schrödinger’s equation aside and declare that your observation has caused the wave to collapse.
Now, not only is this prescription ungainly, not only is it arbitrary, not only does it lack a mathematical underpinning, it’s not even clear. For instance, it doesn’t precisely define “looking” or “measuring.” Must a human be involved? Or, as Einstein once asked, will a sidelong glance from a mouse suffice? How about a computer’s probe, or even a nudge from a bacterium or virus? Do these “measurements” cause probability waves to collapse? Bohr announced that he was drawing a line in the sand separating small things, such as atoms and their constituents, to which Schrödinger’s equation would apply, and big things, such as experimenters and their equipment, to which it wouldn’t. But he never said where exactly