PART ONE: Making Sense of Quantum Randomness

Abstract

This paper is in three parts. In this Part One, the randomness displayed by quantum objects is explored. The notion of quantumhood in then introduced. It refers to a kind of “wave wholeness” of elementary particles that, most significantly, turns out to be necessary to sustain nature’s consistency. When this quantumhood is in danger of being lost, a wave collapse, or quantum jump, is in order.

Wavy lumps and random jumps

Subatomic or elementary particles are the tiniest specks of matter known today. They make up everything there is, be it atoms, ordinary objects, living organisms, and all the way up to planets, stars and galaxies. These particles are nothing like classical point particles. They’d rather be called “wavicles” on account, as we’ll see, of their surprising but well-established wave-particle nature. Quantum mechanics is the science which deals with them. According to it, subatomic particles behave as lumps most of the time and as jumps occasionally. Here I use the word “jump” as an umbrella word for the discontinuous events that take place in the microworld of quantum objects. These jumps are random and last virtually no time. We can describe lumps and jumps as follows:

  • Lumps are wave-like and deterministic. They are somewhat fuzzy and can be thought of as bundles of waves huddled together. These waves interfere mutually if and only if they belong to the same lump. They propagate in space in a smooth and relativistic way. In the theory, lumps are known as wave packets, wave functions and even state vectors.
  • Jumps, or leaps, are wave-less and random. They are sudden and discontinuous events. When they kick in, the quantum waves vanish and are said to collapse. A prime example is when a quantum measurement is carried out. They also arise in a wide range of microscopic events that share the same core features.

Lumps and jumps are worlds apart. They behave in many opposite ways, even when they relate to the same “wavicle” or subatomic particle. This is weird! Can we explain this lump-jump duality? I believe so, as this paper will hopefully show. It is important to note at the outset that a jump brings an elementary particle from an initial state that is fuzzy and smeared-out, to a final one that is always sharp and well defined. In other words, a jump typically shrinks a lump to a pinprick size. This being so, a lump or an elementary particle puts on a point particle appearance right after a jump. Because of this, the lump-jump duality comes across as a wave-particle duality. Another important consequence of this “fuzziness-sharpness duality” is that jumps need to be random. We’ll soon figure that out.

Consistency and the principle of quantumhood

As far as we can tell, nature is consistent. It complies with the acknowledged rules of logic. Indeed, nature’s consistency in the microworld rests heavily on quantum wholeness. Quantum wholeness, or quantumhood for short, is an all-or-nothing affair whereby we may find, say, 4 or 19 electrons, but never 2.28 or 17.165 of them. It relates to the wholeness of lumps and hence, to that of elementary particles: quantumhood means wholeness or fullness of elementary particles. Somewhat surprisingly, this wholeness is a matter of wave interference. It really is wave wholeness and it is utterly blind to spatial closeness. Concretely speaking, it means for example that if, with a half-silvered mirror, we split a photon into a reflected bit and a transmitted one that go their separate ways, this doesn’t, as such, run afoul of quantumhood – provided, that is, these (wavy) bits can still interfere mutually. To find out whether the mutual interference still holds its sway is easy. It suffices to bring the two bits together again by an appropriate setup, and watch how their interference plays out.
Why should nature bother about quantumhood? The answer hinges on a distinction between motion waves and substance waves. Ripples in water and sounds propagating through the air are examples of motion waves while quantum waves epitomize substance waves. The snag, with substance waves, is that when left to their own device, they can wreck nature’s consistency. This is due to their mutual interference, which is not a zero-sum game as far as they go (more on this and on motion and substance waves in Appendix 1B).

Since consistency is absolutely vital for nature, it has to be sustained everywhere and everywhen. This is the role of the principle of quantumhood, which oversees the way substance waves interfere. It manages it so that this interference doesn’t undermine nature’s consistency. This watertight principle is not about spatial closeness. It may allow a particle to be scattered into many shards that can be near or far, as long as these shards keep their ability to cross-interfere. This is the key. The principle of quantumhood only rules out independent bits of subatomic particles (these bits are independent if they cannot interfere mutually). This is why no one has ever found, say, independent pieces of electrons hanging out on their own. Whenever an electron is found, it is found whole. Even when it is scattered far and wide, it is still whole nonetheless. Recall that this wholeness is strictly a matter of wave interference within each lump. It is lump or wave wholeness, not spatial nearness.

The challenge of remaining whole: threats and jumps

The principle of quantumhood is ironcast. It brooks no transgression. At times however, remaining whole can be quite challenging for a lump. Then we’ll say that the principle of quantumhood is under threat as far as this lump, or elementary particle, is concerned. Such a situation is a quantum threat. To help gather how such a threat may arise and how nature may handle it, here is a short narrative:

Imagine that you’re about to cut a potato laying on a table in front of you, with a knife that can only be moved up and down but not sideways. The potato stretches on both sides of the knife, to its left and to its right, and therefore, cutting it is child’s play. There’s a catch however: the potato is a magic one and cannot be split. This is quantumhood-principle-for-magic-potatoes! Try as you may, it will remain uncut. What will happen instead is this. As you start chopping the magic tuber, it will suddenly shrink or “jump” to one side only – either to the right or to the left – of your threatening blade. In this squeezed-out new shape, in which the knife can only cut the air, the potato is no longer at risk. It is threat-free. This is exactly what its jump was meant and designed to achieve.

This little bit of a story provides a graphic insight into the ways of nature. It shows how nature might respond to a quantum threat. The potato was initially in a “fuzzy” state spread out on both sides of the knife. Because of this very fuzziness, the knife could cut it – a real threat was looming. Contrariwise, the potato’s final state, reduced or shrunk to one side only as it was, was accordingly “sharp”. It was also threat-free, since in this new setting, the knife was harmless as it could no longer split the tuber in two chunks. Similarly, an electron facing a quantum threat will suddenly jump. This jump or leap will also shrink or collapse it from a fuzzy (and hence threatened) initial state to a sharp (and hence threat-free) one.

Of course, this picturesque outline of how nature might handle the daunting challenge of a quantum threat is not to be taken at face value. It is merely symbolic. It gives no more than a rough and exploratory idea as to why, when a particle faces a quantum threat, a jump that will shrink the particle to a sharp final state is in order. This shape shifting trick, away from a fuzzy initial state, wipes the threat out. For example, an unstable system like a radioactive atom is under threat because of its fuzzy energy state and hence ill-defined energy level. Therefore, it will eventually jump, or decay, to a definite (or sharp) one.

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