Newton’s Cradle

“What do we know?”  We observe the world around us, but what do our sensory organs tell us?  Do they reveal an accurate representation of the world around us or, like Schröedinger’s cat, do our observations and pre-conceived expectations “force” the Universe into preferred states?  Perhaps, then, a better question becomes, “What can we know?”  These are themes we explore in Newton’s Cradle.

Around the turn of last century William Thomson, better known as Lord Kelvin, is purported to have said, “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement”.  This attribution is almost certainly apocryphal.  Although scientists have exhibited their fair share of hubris over the ages, it’s doubtful that even the most arrogant would go as far as to make this claim.  It is true, however, that there have been periods where science has held the belief that everything is knowable eventually.  That may seem like a more reasonable statement at first blush, but as science advanced, we learned the folly of this way of thinking as well.

It began around the 1920’s with the increasing theoretical and experimental evidence revealing that subatomic particles do not obey Newton’s Laws of motion, but rather the laws of quantum mechanics. The behavior of subatomic particles like electrons, protons, even photons isn’t deterministic, but rather swims within the river of probability.  Subatomic particle behavior is not governed by notions like “where they are” and “what they are doing”, but rather “where they most likely are” and “what they most probably are doing.”

An emergent physical law arising from the postulates of quantum mechanics–one that perfectly elucidates this point–is the Heisenberg Uncertainty Principle.  It tells us that we can measure accurately the position of an object like an electron, or its momentum, but not both.  In other words, you can either know accurately where something is or how fast it is moving–or you can know both poorly.

When confronted with implications of a quantum mechanical description of the subatomic universe Albert Einstein, oft regarded as the father of modern physics, refused to accept them and quipped, “God does not play dice.” (the actual quote was “…I, at any rate, am convinced that He does not throw dice.”). [1] He felt that such a description may accurately model what appears to be happening, but was a barrier to true understanding of the way the Universe operates.

While on the topic of barriers, colloquially the word tends to invoke impressions of sometime fixed and impenetrable.  A term that doesn’t generally come to mind is “microscopic”.  “Fixed”, “impenetrable”, and “microscopic” all describe a concept which may prove to be a frustrating barrier to our ultimate understanding of the Universe: the Planck Length. The Planck length is defined to be 1.616 x 10 ^-35 m, or a bit larger than a trillionth of a trillionth of a trillionth of a meter.  How can something so much smaller than human comprehension act as a barrier?

Scientists now believe that the Planck Length may represent a lower limit to our ability to probe the universe – that we may never be able to understand the behavior of anything smaller than this.  Most current cosmological models hold that, at its beginning, the entire Universe was condensed into a single dimensionless point.  Despite the small size of the Planck Length, the Universe in this state was far smaller still.  What initiated the Big Bang, and what happened as the Universe expanded from a mathematical singularity to the diameter of one Planck Length? The mystery behind the creation and early evolution of the universe may forever be just that, a mystery.

New and future mathematical techniques in String Theory and M-Theory may show that these barriers may simply be temporary roadblocks… but that still doesn’t mean that everything is knowable. Nature certainly isn’t 100% predictable.

One of the hallmarks of a successful scientific theory is that is can be used for prediction.  We learned that Earth spins on its axis; we can predict with a high degree of accuracy that the sun will rise tomorrow morning.  If you have a pendulum of a given length, you can accurately predict/calculate its period of oscillation.  If there is a full moon tonight, you can predict that there will be another in about 29 days.

Certain dynamical systems defy prediction, at least over long time scales, though.  Such systems are said to be chaotic.  Chaotic systems were recognized as early the 1600’s, but it really wasn’t until the 1970’s that Chaos Theory was a discipline in its own right. Contrary to common wisdom, chaos has nothing to do with “randomness” (the scientific term for random being “stochastic”).  A chaotic system, given the same starting point, will always end up at the same ending point.  Very tiny changes to those initial conditions may lead to dramatically different outcomes, though.  Well-known to many by now is the famous “Butterfly Effect” – the notion that a butterfly flapping its wings in Beijing one day can effect the weather in New York next week.

Some surprisingly simple systems can be chaotic.  Although the period of a pendulum swing is easily determined, and its position at any time easily calculated, a double pendulum – a second pendulum suspended from the mass at the end of the first – is chaotic.  We are surrounded by chaotic systems. Weather is chaotic.  The orbits of some of Saturn’s moons are chaotic, and even the orbits of all the planets in the Solar System lie on the edge of chaos. To make life more confusing, scientists are now starting to find evidence of chaos in quantum mechanical systems – a marriage of the probabilistic and unpredictable.

Related to chaotic systems are complex systems. While science has yet to come up with a single definition of a complex system, they usually consist of many parts–often interacting in simple ways–that exhibit unexpected behavior not predicted based upon the behavior of the individual parts.  Traffic represents a complex system.  So do insect colonies and animal swarms.  Many types of complex systems have all the hallmarks of chaotic systems, except that the individual interacting elements are capable of making choices. The character Ian Malcolm referred to Jurassic Park as a chaotic system but it was, more accurately, a complex system.

Quantum mechanics, chaos, and complex systems:  the story of Newton’s Cradle lies within these realms – the physics of the unpredictable and the unknowable. Behind the curtains around which science has never peered is where our story takes place.

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[1] It is ironic that Albert Einstein won the 1921 Nobel Prize for a quantum mechanical phenomena, the photoelectric effect.