by Demand:
No two snowflakes are exactly alike.
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A recent post in the r/replies subreddit questioned the age-old veracity of it, asking how it could be that “no two snowflakes can really be alike” — a reference to the claim that no two snowflakes are exactly alike:
What does science say about this oft-performed truth? In short, that scale matters when making claims about how similar two objects might be.
At the visual level, with expensive laboratory equipment, you can create snowflakes that look quite identical. At the molecular level, the chance of two snowflakes being identical is so astronomically low that it is considered impossible.
How Are Snowflakes Formed?
On his website, Kenneth G. Libbrecht, Chair of the Physics department at the California Institute of Technology and known snowflakes photographer, which explains that small changes in the microenvironment around a snowflake within a cloud affect its form. That’s because these changes force the snowflake to switch between two different crystallizations processes — faceting and branching.
Faceting, the simpler of the two processes, produces six-sided prisms thanks to the atomic structure of the frozen water molecules. The formation of these hexagonal prisms gives the snowflakes the famous six-sided symmetry.
Simple hexagonal prisms produced by faceting. Credit: snowflakes.com.
Branching produces the chaotic features that extend away from the growing hexagonal prisms; branching occurs because the corners of those prisms attract crystallized water vapor faster than the flat surfaces:
A basic example of branching. Credit: snowflakes.com.
The repeated transition between these two methods of crystal growth ultimately determines the characteristics of a snowflake, Libbrecht explains:
As it falls through the clouds, the crystal adjusts to ever-changing temperatures and humidity, and each change causes the arms to grow slightly differently. The exact shape of the final snow crystal is determined by the precise path it took through the clouds. But all six armies took the same path, so they all had the same changes at the same time.
Sing Two Snowflakes look Like Each Other?
Using preciselycontrolled temperature and humidity conditions in his Caltech lab, Libbrecht has created many “designed snowflakes” and can even control the final shape to some extent.
Leibrich said by email that he describes these similar flakes as “identical twins” because, like human twins, “Obviously they’re quite similar in appearance, but they’re not *exactly* identical.” Although it looks qualitatively similar, that similarity breaks down when you start looking at a smaller and smaller scale. Libbrecht said:
Visually, under the microscope, you could say they are essentially identical. But if you look at the molecular level, they are far from identical. So if you want to talk about equal snowflakes, you have to define exactly what you mean by equal.
It is therefore imagined that there are two snowflakes appearance identical, but that is far from identical at the molecular level. The concept of two snowflakes being “the same,” therefore, depends on how the term is defined.
What is going on at the Molecular Level?
At the molecular level, the probability of two snowflakes being created alike is mathematically impossible given the effectively infinite number of ways to create a snowflake, Liebrich told us:
The number of possible ways to arrange the branches and side branches is far, far, far greater than even the total number of snowflakes that have ever fallen on Earth.
In addition to the possibility that two microenvironments would grow completely identical for two snowflakes to grow outside the laboratory, the chemical building blocks that make up the snowflake are unlikely to be 100 percent identical either. That is because nature contains a small fraction of oxygen and hydrogen isotopes that are slightly heavier than the most common form. It is impossible to demonstrate that the anomalous water molecules that make up these heavier atoms could be in the same place in two different flakes and it is not unreasonable to assume.
What Does It Even Mean To Be Equal?
The question of whether two objects can be literally identical is one that has a rich history in both philosophy and theoretical physics. Many philosophers believe that the question of identical snowflakes is pointless, because no two objects – even atoms – can be truly alike.
This claim is common called “Leibniz’s Law” and it was lively discussion a philosophical question, in various forms, for centuries. Although the concept would apply to anything considered to be an object, snowflakes provide an attractive way to demonstrate the implausibility of unidentifiable objects because, despite being all made of water molecules, each snowflake produces a alone intricate and complex patterns.
A visual resemblance between snowflakes can only be achieved superficially under highly controlled laboratory conditions. So we classify the claim that no two snowflakes are exactly alike.
Sources:
Forrest, Peter. “The Identity of the Indiscernibles.” The Stanford Encyclopedia of Philosophy. Winter 2016.
Libbrecht, Kenneth G. “Snowflake Science” Snowflakes.com. Accessed 18 December 2017.
Libbrecht, Kenneth G. “An Experimental Apparatus for Observing the Formation of Deterministic Structure in Plate-on-Pedestal Ice Crystal Growth.” Snowflakes.com. Accessed 18 December 2017.
Caltech.edu. “The Feynman Lectures Ch. 4: Identical Particles” Accessed 18 December 2017.
Saunders, Simon. Leibniz’s physics and principles Symmetry in Physics: Philosophical Reflections. 2003.
