Quantum Field Theory (QFT) unifies quantum mechanics and special relativity, treating particles as excitations of fundamental fields that permeate space. For example, photons are ripples in the electromagnetic field. QFT provides the framework for the Standard Model, explaining fundamental forces and particle interactions.
The public has a distorted view of science, because children are taught in school that science is a collection of firmly established truths. In fact, science is not a collection of truths. It is a continuing exploration of mysteries.
- Freeman Dyson
Collapse of the Wave Function: When an observation is made, the superposition collapses into a single state. For example, the electron that was in multiple locations will "choose" one position once measured. ✍️
Entropy is one of those formulas that many of us learn, swallow whole, and even use regularly without really understanding.
(E.g., where does that “log” come from? Are there other possible formulas?)
Yet there's an intuitive & almost inevitable way to arrive at this expression.
The Golden Ratio (ϕ) is a mathematical constant approximately equal to 1.618, often called the "divine proportion."
It appears in nature, from the spirals of sunflower seeds to the structure of galaxies, and has been used in art and architecture, including the Parthenon and Da Vinci's "Vitruvian Man." ✍️
numerous times when I ventured the opinion that the US will never elect a woman president my listeners would scold me, sometimes angrily. "how can you say that!"
but I think that it is the truth, not a very cheering truth, yet a truth nonetheless. between swaggering-macho & old-timey Christian notions of a "woman's place"--a woman hasn't a chance here as women do in other countries.
all candidates have flaws but only the woman candidate must struggle against a flaw that is her very identity in the US.
Lab was absolutely buzzing meeting the incredible Dr. Katalin Karikó @kkariko! 👩🔬 Ellie Petty got to share her work and soak up some wisdom from the legend herself. Truly inspiring for us all 🌟
Thing 4. Use some damn visuals.
It is often said that “a picture is not a proof.”
Many mathematicians are paranoid about drawing specific examples, because they may betray the general meaning.
Folks: it. will. help. your. students.
Useful but often neglected picture: taking the Fourier series of a function is really no different from projecting a vector onto a basis:
-Your function is a vector
-You have a basis of sines and cosines
-The inner product of two functions just replaces a sum with an integral
It is the honor of a lifetime to join @kamalaharris in this campaign.
I’m all in.
Vice President Harris is showing us the politics of what’s possible. It reminds me a bit of the first day of school.
So, let’s get this done, folks! Join us. https://t.co/tqOVsw2OLM