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.

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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.

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About Paul Gordon 1368 Articles

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26 Comments

  1. There's no such thing as Infinity/infinite it's just a conceptual placeholder until we have more accurate means to measure something.

  2. Don't understand the confusion. Just look at infinity as an acceleration instead of a finite number. As in when a mass approaches the speed of light it's mass increase acceleration meets the terminal velocity resisted by space/time equalizing at 186,000 mps^2.

  3. unless youre a physicist this is a good push into studying a topic. nothing more.

    I would give it a 3/10, due to the fact – just like the pre 60's equation, this video took itself too seriously and didnt address the more fundamental aspects of the problem. That problem being what the fuck they did.

  4. Basically, by using unrealistic numbers in an equation, they set themselves up for 'infinity' and a few years later someone came by and said, hey why don't we use numbers that represent the real world… oh look no more infinity now and yay i've solved your problem, now go solve more realistic issues and not your imaginary world of numbers

  5. I have a theory about time travel and infinite worlds exists on a quantum level and this is why we have infinity. And we as human beings are just vibrations and time doesnt exist only vibrations, hence why time travel can be achieved ect. and time does not exist but a made up thing labeled by humans. For example, the numbers 0 – infinite is where we can time travel hence the start of creation "0" and the infinite "now|" and this is why dark matter exists because of negative numbers 0 -1 -2 ect, but its the opposite so we dont know it. like parrelel universes yes they exist but dont u think they have opposites? its the law of nature, light, darkness, positive, negative ect. P.S. I'm currently high af' 4/20

  6. What I understood from it was that infinity is not a real achievable number so instead they used a different value in its place sort of like rounding. Correct me if I'm wrong tho it's very interesting

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