## Saturday, February 6, 2010

### Best Physics equation ever

If you google "greatest equation ever", you may find many pages and discussions on this topic.
Usually Maxwell equations (which describe the electromagnetic field) are considered the "best" Physics equations ever. In mathematics, Euler's identity e^(ipi) + 1 = 0 has been voted as the most important equation.
Now, first of all it is hard to say what actually "best" means. Here I will define "best" not as the most beautiful, nor the most difficult to derive, nor the one which has given more practical results... I simply consider one of the equations that better represent the "state-of-art" in Physics.

Some days ago I was looking at this formula
T=\frac{1}{8\pi M}\,,

Which is the temperature of a Schwarzschild black hole (M being the black hole mass). I guess I have seen that formula thousand of times in the last year, and never though it was eligible as best physics formula ever... However there is a trick: the formula above is written in "God-given" units, the ones that theoretical physicists and lazy students like more.. In God-given units the speed of light c, Newton constant G, Boltzmann constant k and also Planck constant h, are set to unit.
Restoring more physical units, the same formula above reads
T=\frac{\hbar c^3}{8\pi G M k_b}\,.

And now it looks more appealing, doesn't it? This formula has inside nothing less than almost all the Physics we know. Of course Newton constant is there, after all black holes are gravitational objects... but also Planck constant is there, meaning that black hole temperature has something to do with quantum physics. Einstein's special relativity has its own place there, via the speed of light, c. Finally, we are talking about temperature, we also have Boltzmann constant, k.
Why is this formula so important? Well, for a technical point of view that is because it represents the fact that black holes are not "totally black", but instead they emit thermal radiation (called Hawking radiation, from the theoretical physicist Stephen Hawking who discovered that) with that temperature T.
But the very relevance of this formula lays in the fact that it contains both General Relativity (via c and G) and quantum physics (via h bar).... so it represents the bridge between these very different (?) worlds in Physics, which do not like talking to each others. But that is the topic for another post...

#### 1 comment:

1. I have a question:
let us take a black hole.........