From Hilbert Space to Dilbert Space


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From Eternity to Here: ....
physics, Feynman
gmcdavid
...The Quest for the Ultimate Theory of Time.

At the author's web site:

Why do we remember the past, but not the future? Why don't we meet people who grow younger as they age?Why do things, left by themselves, tend to become messier and more chaotic?
[...]
The arrow of time is easy to perceive, much harder to understand. Physicists appeal to the idea of entropy, the disorderliness of a system, which tends to increase according to the celebrated Second Law of Thermodynamics. But why was entropy ever small in the first place? That's a question that has been tackled by thinkers [...] all the way back to Lucretius in ancient Rome. But the answer remains elusive.

Roughly the first 3/4 of the book is quite standard physics, and a few related fields, e.g. information theory. The last few chapters, where the author, Sean Carroll, suggests a possible answer to the puzzle, are much more speculative, something he makes very clear.

To me the book was quite interesting. A few equations are displayed, but there is no actual use of mathematics. I have an M.S. in Applied Physics, so I cannot really say how a reader with no technical background would cope with it. Carroll goes through a lot of material, and the sheer quantity of it might be overwhelming. Unfortunately, that is just the way things are. Nobody is going to cope with this without the willingness to do some hard thinking. Carroll does include a lot of pop culture references that readers can relate to, although one of those may not be in any future edition of the book.

A couple interesting (to me) notes:

  1. The complexity of the universe is different from the entropy. Just after the Big Bang the universe was very simple--the same high energy subatomic soup every where. Right now the universe is very complicated: There are lots of galaxies, stars, planets, black holes, people, etc. However, the entropy of the universe has increased: The formation of all those objects is mostly due to gravitation, as matter coalesces together. This gravitational process increases the total entropy, more than offsetting the order in all the structure. Eventually all of this structure will fade away. Even black holes will decay by the Hawking process, leaving a very thin, cold, dark, and simple universe. So while the universe started in a simple state, evolved into a complex state, and will eventually decay into another simple state, the entropy is always increasing. See pages 199-201.



  2. Long ago, as an undergraduate at Carleton, one of my professors talked about the total energy of the universe. The gravitational potential energy V between two bodies decreases as they approach, because gravitation is attractive. For computational purposes we usally set V = 0 when the distance between them is infinite, and he argued that this is the natural thing to do. Then the gravitational energy is always negative. Assuming a finite universe, you can add up all the positive energy of mass, kinetic energy, etc. and then offset it by the negative gravitational energy. Professor Titus suggested the total energy of the universe would be zero. Carroll mentions in passing that you can prove this in general relativity. See p. 358.

    Now the universe appears to be infinite (this was not so clear back in 1972), so strictly speaking you cannot speak about its total energy. But the general concept still applies: Gravitational energy is still negative. Something can be created from nothing, if the something is offset by sufficient gravitational energy.


The whole book reminded me of what Sir Arthur Eddington wrote:

The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations—then so much the worse for Maxwell's equations. If it is found to be contradicted by observation—well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

On a lighter note, all of this talk about time and the universe also made me think of Severn Darden's
Metaphysics Lecture, which begins:

Now, why, you will ask me, have I chosen to speak on the Universe rather than some other topic. Well, it's very simple, heh. There isn't anything else!

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