The boil does a bunch of things, extracting and isomerisation of compounds from the hops, reactions involving the proteins and sugars that contribute to the flavour and colour, sterilising the wort, inactivating the malt enzymes, evaporation of volatile compounds, increasing acidity, and the coagulation of proteins. Despite all this, you don't
have to boil at all, in which case you've made a
raw ale which, by all accounts, can be a great beer. I've made good beer with 45 and 90 minutes boils, and as cheapbrew's link show, you could do a 30 minutes boil and make a beer indistinguishable from a beer with a 60 minute boil.
The hot break coagulates the proteins so that they can drop out of solution. This is because the proteins molecules unfold, revealing their 'sticky' innards, and they stick to one another and aggregate into clumps big enough for gravity to pull them down. The question of when it happens splits opinion, as this thread and others show, but the question misses the point. You can't point to one moment in time and say 'the hot break has happened'. There are loads of different proteins in unboiled wort and they all behave differently, and the range of behaviours can be understood by looking at how proteins respond to temperature in things you might be familiar with outside of brewing:
Some have already unfolded and aggregated in the mash. Indeed, proteins can even unfold and bind to one another at body temperature, and this is important in the aetiology of diseases such as Altzheimers.
Some will unfold but not bind to one another, which is just as well because they are important for head retention and body. Think of the protein collagen, you can simmer a chicken carcass for three hours and end up with a stock that sets in the fridge, because the unfolded collagen sets to form gelatin.
Some will not even unfold. These tend to be proteins that form fibers and have structural roles, like the keratin in your hair and fingernails. Boil away, these things aren't going to change their structure.
Ultimately, however, most proteins have evolved to be stable within the temperature range that the organism experiences and not much more than that, so most of them unfold and aggregate almost immediately. Scrambled eggs is basically a dish of unfolded aggregated protein, so that gives you an idea of the temperature and time it takes for this to happen. In the boil, just like with eggs, short cooking times and high agitation give smaller clumps (agitation with a fork for eggs, with a rolling boil for wort), while longer cooking times and low agitation gives bigger clumps. Most of the hot break material has already formed during the first 15 minutes, and this is all you really need. You might not be able to
see the break material, the classic "billowing clouds" just under the surface of the wort, because the aggregates are smaller, but they are there and they are big enough to be pulled down by gravity one the wort is chilled. After a 90 minute boil, all of the proteins with a molecular weight > 100,000 will drop out, and about half with MW < 5000 will drop out. Sure, longer boils get more protein out. You will get more protein dropping out of a six hour boil than a three hour boil, but you get diminishing returns - after the first 15 minutes, you are basically done.
