AnthonyAguirre

How do you define "the universe"?

Actually a quite nice article. After also spending years as a professional physicist not understanding entropy, I finally decided that I was not necessarily the problem, and spent the last 5 years or so trying to understand it better by rewording the foundations with my research group. (I'm one of the papers the author cites is part of a series from our group developing "observational entropy" in order to do so.)

A lot of what makes this topic confusing is just that there are the two basic definitions — Gibbs (\sum p_i log l_i) and "Boltzmann" (log \Omega) — entropy, and they're really rather different. There's usually some confusing handwaving about how to relate them, but the fact is that in a closed system one of them (generally) rises and the other doesn't, and one of them depends on a coarse-graining into macrostates and the other doesn't.

The better way to relate them, I've come to believe, is to consider them both as limits of a more general entropy (the one we developed — first in fact written down in some form by von Neumann but for some reason not pursued much over the years.) There's a brief version here: https://link.springer.com/article/10.1007/s10701-021-00498-x.

This entropy has Gibbs and Bolztmann entropy as limits, is good in and out of equilibrium, is defined in quantum theory and with a very nice classical-quantum correspondence, and has been shown to reproduce thermodynamic entropy in both our papers and the elegant one by Strasberg and Winter: https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuan...

After all this work I finally feel that entropy makes sense to me, which it never quite did before — so I hope this is helpful to others.

p.s. If you're not convinced a new definition of entropy is called for, ask a set of working physicists what it would mean to say "the entropy of the universe is increasing." Since von Neumann entropy is conserved in a closed system (which the universe is if anything is), and there really is no definition of a quantum Boltzmann entropy (until observational entropy), the answers you'll get will be either a mush or a properly furrowed brows.

Probably better not to use the term "steady state" here (even if pretty appropriate) in that the "steady state" cosmological model is/was one that is exponentially expanding, with all physical observables statistically time-independent. It solves Olber's paradox due to the radiation redshift. That model was observationally incorrect, but actually has pretty much been reborn in "eternal inflation" in which the Universe as a whole is in a quasi-exponential state with local regions expanding sub-exponentially like our observable universe.

In either classic steady-state or eternal inflation case, energy conservation is not necessarily a problem: you can have vacuum energy that converts steadily into radiation, while being generated by the expansion.

For those who happen to like both geometric algebra and general relativity, my former student Joey Schindler wrote this quite beautiful paper extending geometric algebra to calculus on manifolds. https://arxiv.org/pdf/1911.07145.pdf

That was a fascinating read; thank you. Not every day that I learn about a whole new important multiverse!

A real challenge for prediction markets (with real-money stakes) will be to get sufficient liquidity on relatively small-ticket items outside of sports and politics.

For such items platforms like metaculus.com and Good Judgement seem more likely to provide more useful predictions, but without the ability to hedge against events that prediction markets have.

I discuss this in depth in this podcast: http://rationallyspeakingpodcast.org/show/rs-214-anthony-agu...

agreed! The starwisp paper is really very nice.

The plan calls for ultra-reflective coatings that are tuned to the wavelength of the laser. Apparently these exist, though I have not checked the numbers. In my class I abandoned laser propulsion quickly for just this reason (incinerated the target), but with these coatings it might work.

This is a pretty cool initiative — I looked into beamed propulsion a bit while teaching a course this past fall, and it seems to me that if we (or human technologies) are going to reach a star in our lifetimes, this is by far the most likely way. Still very challenging though.

For a quite detailed recent treatment of optical/IR propulsion see this paper by Philip Lubim:(http://www.deepspace.ucsb.edu/wp-content/uploads/2015/04/A-R...)

For a thorough, if somewhat outdated, treatment of the “starwisp” idea using microwaves rather than optical/IR lasers, see this paper: http://path-2.narod.ru/design/base_e/starwisp.pdf by Robert Forward.

To poll the success of this overall endeavor, as well as start to make predictions about which components will/won’t work, Metaculus is launching a series of questions —check it out if you have expertise or opinion: http://www.metaculus.com/questions/#/?order_by=-publish_time

This is a pretty cool initiative — I looked into beamed propulsion a bit while teaching a course this past fall, and it seems to me that if we (or human technologies) are going to reach a star in our lifetimes, this is by far the most likely way. Still very challenging though.

For a quite detailed recent treatment of optical/IR propulsion see: [this paper by Philip Lubin](http://www.deepspace.ucsb.edu/wp-content/uploads/2015/04/A-R...)

For a thorough, if somewhat outdated, treatment of the [“starwisp”](https://en.wikipedia.org/wiki/Starwisp) idea using microwaves rather than optical/IR lasers, see [this paper](http://path-2.narod.ru/design/base_e/starwisp.pdf) by Robert Forward.

To poll the success of this overall endeavor, as well as start to make predictions about which components will/won’t work, [Metaculus](http://www.metaculus.com/questions/#/?order_by=-publish_time) is launching a series of questions —check it out if you have expertise or opinion.