How physicists solved the problem of infinity?
During the mid 20th century, physicists were grappling with a perplexing puzzle. It seemed that every time they applied equations to explain fundamental properties we see and experience around us — like the mass of a particle or what happens when two particles interact with each other — they always got the same answer: infinity.
But this wasn’t a result at all. It was mathematics’ way of telling them that they were doing something wrong. Here, professor of physics and mathematics at Columbia University and co-founder of the World Science Festival, Brian Greene, reveals the story of how physicists ultimately tackled the puzzle of infinity.
You can learn more fascinating science at this year’s 10th annual World Science Festival in NYC taking place from May 30-June 4. Following is a transcript of the video:
Infinity is a way that nature, kind of, grabs you by the lapel and slaps you in the face and says, “You were doing something that doesn’t make any sense.”
So, one of the big problems that afflicted quantum mechanics is that when scientists started to do calculations with the structure, they found an answer that would pop out of the mathematics and did not make any sense.
The answer was infinity.
Almost any question that you asked, if you did the calculations, you know, “How does at a mass of a particle change?”,“How do these two particles slam into each other?”
The answer was infinite.
And infinite doesn’t mean big. So people realized that we had to find a way to deal with these infinities. Kind of get rid of them. During, I guess, it was the ’50s and ’60s, a group of scientists came up with a way of thinking about it, to got rid of the infinities.
And in essence, what they found is we were taking our equations a little too seriously.
We were pushing our equations to arbitrarily short distances. Arbitrarily high energy, where they, probably, don’t actually apply.
So what people realized is that if you cut off the equations, be more modest in how you apply them you can naturally get rid of the infinities and, in a way, still have a predictive theory.
So this is the subject of normalization in quantum field theory and that was a breakthrough that allowed us get things like the Standard Model of particle physics, which predicted the Higgs bosom that was discovered in 2012, by the Large Hadron Collider.
This is a structure, a mathematical structure that can make predictions for the properties of particles that agrees with observations to ten decimal places.
So this is, in many ways, the shining wonder of theoretical physics and without normalization, getting rid of the infinities — the structure would not fly.