It took me 10 years to understand entropy

Not a physicist either, and I don't claim to understand entropy that well either but maybe it would help to consider that entropy may not be a universal variable of systems in the universe.

I think you should rather consider it as a mathematical construct that applies to some systems where the microscopic quantities are well defined, and where the 'averaging' that we can observe is also well defined. So if you look at thermodynamics, entropy is well defined, but you may be totally right, that what we call "microscopic states" in a gas can be broken down further in elementary particles, that may or may not behave in quantic ways, and what not, and counting the micro-states considering the elementary particles is a whole different game.

But it doesn't really matter. What matters is that at the scale we're at and with the microscopic/macroscopic relation that's defined, entropy works. The calculations that give some numbers to entropy show that it looks like entropy cannot decrease. They call it a universal principle of thermodynamics, because there is nothing (to my understanding), that explains it microscopically.

And it works for a variety of situation in physics, such that it seems that it's a universal property of nature. But it's mostly mathematical. It seems to say that "given a system we know everything about, there is no way to go to a system that has some unknown things to us".

Anyways. I mostly wrote this to see if I could articulate it to myself, hopefully it helps you as well.

Perhaps it's actually correct, but our intuitions about ridiculously long periods of time aren't good. Note that heat death is in ~10¹⁰⁰ years, whereas this Boltzman body would take ~10^(10⁶⁹) years. That second time period is literally incomprehensible. So we think, of course a fully formed human body wouldn't appear; in practice, that's not how it actually works; the fact that it appears possible is at best a mathematical artifact, not reality. But we're talking about a timescale that's not just longer than the age of the universe, or than the total lifespan of the universe, not just orders of magnitude longer than those times, but on a completely different scale. Given that, I think we need to toss out those intuitions.

As to the author's last question of whether such a thing even makes sense at all given those time scales, I don't see why not. After all, once the universe reaches heat death, as far as we know nothing from the outside is going to come along and garbage collect it, so why couldn't it last for an arbitrary/infinite number of years? And compared to that, ~10^(10⁶⁹) years, or ~10^(10^(10⁵⁶)) years, or whatever, is nothing.

> no one really knows what mass is. We only know that mass bends space-time curve, hence gravity.

Mass is much better understood by its role in inertia. Basically mass is the amount of energy you need to exchange with a thing to change its current speed. This observation works from Newtonian mechanics to QM and GR as well.

Now, why do things have mass? The famous E=mc² explains this for most things: they have mass because something inside them has potential or kinetic energy. This works all the way down to the atomic level - the mass of a proton for example is almost entirely explained by the potential energy of the quarks being held together in a small volume; the total mass of the quarks themselves is only a small fraction of that. Now, the mass of the elementary particles is somewhat more complicated, but the Standard Model does have explanations for those - symmetry breaking for fermions, and the Higgs mechanism for the massive bosons.

The next mystery is: why is inertial mass equal to gravitational mass? GR has essentially explained this, by showing that acceleration is equivalent to gravitational attraction depending on your frame of reference.

So overall, I'm not sure what Brian Greene means by that - mass is at least as well understood as other basic properties of particles (charge, spin, color charge).

This lecture by Leonard Susskind explains most of these things about mass in a way I found easy to follow:

https://www.youtube.com/watch?v=JqNg819PiZY

> The only thing I don't get is how physicists get around the discrete and finite restriction.

Actually, they don't! When you start doing the math about states in a quantum sense (i.e. statistical mechanics), the basic premise is that the available range of states _is_ discrete. Particles are quantized - so they can only possess certain allowable discrete energy levels. The broader laws of thermodynamics fall out of that and appear to be continuous as you scale up to the macro world across a huge number of microstates.

Then it maybe depends on what you meant by "the 2nd law of thermodynamics".