Entries by John Baez

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…

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…