News stories out today about a new result in quantum mechanics. You probably know that sometimes electrons and other tiny things act like particles, and sometimes they act like waves. Equations have been developed to describe this puzzling phenomenon. You may also have heard about the uncertainty principle, which sets an absolute limit on how precisely we can know the position and velocity of a sub-atomic particle. In the new work, physicists have shown that the equations describing these two things are actually the same; mathematically, "wave-particle duality" is just another way of saying "uncertainty principle," and vice-versa.
The mathematics we use to describe the physical world is full of these congruences. To mention just one famous example, if you formulate Einstein's general relativity in five dimensions you get Maxwell's equations for electromagnetism. It's rather encouraging, really. It makes me more confident that the math corresponds in a deep way to the nature of the world.
As to why that should be,who can say?
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"As to why that should be, who can say?"
Is the universe neatly ordered, or do we simply attribute "order" to the universe because that is our only way of conceiving of things? Math and physics clearly work and are seemingly universal and immutable. But at the same time, could we even measure or otherwise grapple with phenomena which exist outside of our systems of conception and ordering?
As one of my favorite comic strips by Randal Munroe puts it:
"I don't understand how my brain works. But my brain is what I rely on to understand how things work."
"Is that a problem?"
"I'm not sure how to tell."
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