Another interesting item that came out the Scott Aaronson thread mentioned in last post was a question to Scott about David Tong’s views on “physics laws can’t be simulated on a computer.”.
It turns out that there an unsolved puzzle that doesn’t allow the Standard Model to be simulated on a computer. I’ll let Tong explain it:
The difficulty lies with electrons, quarks and other particles of matter, called fermions. Strangely, if you rotate a fermion by 360 degrees, you do not find the same object that you started with. Instead you have to turn a fermion by 720 degrees to get back to the same object. Fermions resist being put on a lattice. In the 1980s Holger Bech Nielsen of the Niels Bohr Institute in Copenhagen and Masao Ninomiya, now at the Okayama Institute for Quantum Physics in Japan, proved a celebrated theorem that it is impossible to discretize the simplest kind of fermion.
https://www.scientificamerican.com/article/is-quantum-reality-analog-after-all/
Scott mostly dismissed the problem at first as a technical matter, but then later found the topic intriguing and one he might later post on. He still thinks its a technical; matter however, if it isn’t just technical it would mean:
“Reality is ultimately analog rather than digital. In this view, the world is a true continuum”.
Prasanna who posed the original question provided a video link. While I’m not a fan of videos, I found this one particularly interesting. The core explanation begins around 24 minutes, but there is a lot leading up to it, some of which I will need to listen to again. By the way, some of the question at the end are also really interesting.
The answer to whether we are living in a matric would be “no” if reality is analog. More correctly, it should be said we would not be living in a digital simulation.
A couple of things that caught my attention even though they are probably well-known to many.
Protons are an emergent phenomena. They emerge actually from thousands of quarks, but there happens to be small difference in the types of quarks and that number is usually what people use when they talk about the number of quarks in a proton.
Photons and gravitons are both massless. This allows them to travel at the speed of light. Odd isn’t it that the particle of gravity itself has no mass? Also, so interesting that gravity and the speed of light both have such prominent roles in Relativity. Is there some deeper connection?
The way he described reductionism made it seem to me that it might be better called “constructionism”. We can derive larger things with smaller things (although even that is practically impossible in most cases), but we can’t go the other way. We can’t look at the big things and derive the small things.A corollary is effects of the smaller things wash out as things get bigger. This is usually stated in the context of quantum fluctuations, but it might be more universally true. For example, we can derive biochemistry from chemistry but we can’t derive chemistry from biochemistry.