Stirring Coffee with My Thumb

Recently I was listening to the song The Frozen Logger, which my father Steve often sang when I was growing up. When I got to the line "at a million degrees below zero" though, the physicist part of my brain butted in to point out that the lowest the temperature can get is absolute zero, or -459.67 °F. Could he have been talking about wind chill? We can rearrange the equation for wind chill to give the velocity required to get from a given true temperature to -1 million °F:

Even at absolute zero, the wind speed would need to be 100 trillion times light speed, which is just not how anything works. A temperature this low is far outside the realm of possibility, but I'm not one to make a fuss over poetic license.

As I was thinking about this though, I started wondering about the other direction: Is there a maximum temperature allowed by physics? One way to think about temperature is the average speed of the molecules in a substance. Using the Maxwell distribution, we can find the temperature associated with an average speed:

Plugging in c for the velocity and the mass of hydrogen, we get a maximum temperature of 7.7 x 10^12 °F. Like the above, this has it's own set of problems: The v in the equation above is the average speed, but the particles all need to stay in (roughly) one place. That means rapidly changing direction, which would require enormous forces. In any case the speed distribution above was derived without considering relativity, so we can't actually apply it to speeds this fast.

I decided to see what possibilities the larger physics community had come up with for maximum temperatures, and I found this article polling some experts. Most of those arguments go back to the early universe, since the Big Bang model of the universe posits that all energy started at a point and has been expanding and cooling since. That concept leads to Planck units, which are combinations of the constants that go into the four fundamental forces in our universe. In the earliest stages of the universe, these forces are believed to have been unified into a single force, but we don't have a model for that yet (the elusive "Unified Field Theory"). The Planck units represent the scale for different quantities at which our understanding begins to break down. For temperature, this is 1.4 x 10^32 K – Converting this to °F doesn't make much difference, since it's still 20 orders of magnitude larger than our previous estimate.

One thing I find really interesting about physics is how well a model can work in one regime, but the same model gives bonkers predictions on a different scale. It's strange to have islands of complete understanding surrounded by seas of uncertainty.