## Struggles with the Continuum: Spacetime Conclusion

We’ve been looking at how the continuum nature of spacetime poses problems for our favorite theories of physics — problems with infinities. Last time we saw a great example: general relativity predicts the existence of singularities, like black holes and the Big Bang. I explained exactly what these singularities really are. They’re not points…

## Struggles with the Continuum: General Relativity

Combining electromagnetism with relativity and quantum mechanics led to QED. Last time we saw the immense struggles with the continuum this caused. But combining gravity with relativity led Einstein to something equally remarkable: general relativity. In general relativity, infinities coming from the continuum nature of spacetime are deeply connected to its most dramatic successful…

## Interview with Mathematical Physicist John Baez Part 2

Read part 1 of this interview. Tell us about your experience with past projects like “This Week’s Finds in Mathematical Physics”. I was hired by U.C. Riverside back in 1989. I was lonely and bored, since Lisa was back on the other coast. So, I spent a lot of evenings on the computer. We had…

## Interview with a Mathematical Physicist: John Baez Part 1

We are proud to introduce you to Mathematical Physicist and PF member John Baez! Give us some background on yourself. I’m interested in all kinds of mathematics and physics, so I call myself a mathematical physicist. But I’m a math professor at the University of California in Riverside. I’ve taught here since 1989. My wife Lisa…

## Struggles with the Continuum – Freeman Dyson and QED

Last time I sketched how physicists use quantum electrodynamics, or ‘QED’, to compute answers to physics problems as power series in the fine structure constant, which is $$\alpha = \frac{1}{4 \pi \epsilon_0} \frac{e^2}{\hbar c} \approx \frac{1}{137.036} .$$ I concluded with a famous example: the magnetic moment of the electron. With a truly…

## Struggles with the Continuum: Quantum Electrodynamics

Quantum field theory is the best method we have for describing particles and forces in a way that takes both quantum mechanics and special relativity into account. It makes many wonderfully accurate predictions. And yet, it has embroiled physics in some remarkable problems: struggles with infinities! I want to sketch some of the…

## Struggles with the Continuum – Relativity and Quantum

In this series, we’re looking at mathematical problems that arise in physics due to treating spacetime as a continuum—basically, problems with infinities. In Part 1 we looked at classical point particles interacting gravitationally. We saw they could convert an infinite amount of potential energy into kinetic energy in a finite time! Then we switched…

## Struggles With the Continuum: Point Particles and the Electromagnetic Field

In these posts, we’re seeing how our favorite theories of physics deal with the idea that space and time are a continuum, with points described as lists of real numbers. We’re not asking if this idea is true: there’s no clinching evidence to answer that question, so it’s too easy to let one’s philosophical…

## Struggles With The Continuum: Quantum Mechanics of Charged Particles

Last time we saw that nobody yet knows if Newtonian gravity, applied to point particles, truly succeeds in predicting the future. To be precise: for four or more particles, nobody has proved that almost all initial conditions give a well-defined solution for all times! The problem is related to the continuum nature of space:…

## Struggles With the Continuum: Is Spacetime Really a Continuum?

Is spacetime really a continuum?  That is, can points of spacetime really be described—at least locally—by lists of four real numbers ##(t,x,y,z)##? Or is this description, though immensely successful so far, just an approximation that breaks down at short distances? Rather than trying to answer this hard question, let’s look back at the struggles…