Not that I'm necessarily complaining since I enjoyed your previous review, but how could you have just finished it now?
Good review, but it would be easier to read if you added some commas and changed some existing commas to semicolons.
For John's reference, the wikipedia article on the comma splice might help.
Also, consider reading while paying attention to your breath. Chopping apart sentences which cannot be completed in a single breath may improve readability. A more complete theory along those lines was linked on LW long ago; my cursory search failed to turn it up.
Taken as a whole Everett's multiverse, where all things happen, probability is not a useful concept and everything is deterministic. However for observers like us trapped in a single branch of the multiverse, observers who do not have access to the entire wave function and all the information it contains but only a small sliver of it, probability is the best we can do.
I am unable to imagine an interpretation of this paragraph that makes it true.
Probability would be necessary for belief formation even if reality consisted of only a single world. More generally, the usefulness of probability to belief formation does not depend on any particular features or properties of the reality the belief-forming agent (or collection of agents, e.g., the people having this conversation) happens to find itself in (except for the trivial consideration that some realities cannot contain belief-forming agents).
Also, I am extremely skeptical that literally all things happen in the Everettian multiverse. For example, I would be extremely surprised if there exists or will ever exist a branch in which the law of the conservation of momentum is violated. The principle of charity demands that I assume that the OP (johnclark) knows that, but I have been in enough conversations on LW about many worlds to have strong evidence that some of the readers will take "all things happen" literally.
Clarification of parent:
I consider it true that probability is in the mind and that when taken as a whole, reality does not contain probabilities. In that sense, John Clark's statement, "Taken as a whole Everett's multiverse . . . probability is not a useful concept and everything is deterministic," is true. What I am extremely skeptical of is whether that truth depends somehow on the fact that our reality consists of branches that are constantly splitting or depends somehow on that fact that Schroedinger's equation applies to our reality.
Some of the laws of physics could change from universe to universe, but there must be some laws that remain invariant across the entire multiverse because without rules it would behave chaotically and if the multiverse behaved that way so would all the universes in it, including ours. However there is order in our universe, but what is fundamental and what is not? I think we probably all agree that purely mathematical things like pi or e would remain constant in all universes, but consider some of the physical things that might change:
The Planck constant. The speed of light. The gravitational (big G) constant. The mass of the electron, proton, and neutron. The electrical charge on the proton and electron. The inverse square law of gravity and electromagnetism. The conservation of Mass-energy, momentum, angular momentum, spin and electrical charge.The relative strength of the 4 forces of nature. The number of large dimensions in a universe. The Hubble constant. The ratio of baryonic matter to dark matter and dark energy.
It seems to me that the speed of light and Planck's constant may be more fundamental than other "constants" and the basic structure of the laws of physics may be more fundamental than the constants they use. But I could be wrong, perhaps the things that always remain the same are none of the above and we haven't even discovered them yet.
John K Clark
Some of the laws of physics could change from universe to universe
I will assume that by "universe" here you mean "Everett branch".
I agree that they could (with low probability), just as they could slowly change over time or be different billions of light years away. This is a possibility because our reality has a property that physicists call locality. What I object to is the belief, which more than a handful of LW and SL4 participants hold, that there is something about many worlds (or about quantum mechanics for that matter) that increases the probability of stuff like that happening above what it would be if our reality had this locality property but no Everett branching.
should increase the probability we assign to stuff like that happening.
There is also the
I understand that some of the laws of physics could change from universe to universe, but there must be some laws that remain invariant across the entire multiverse because without rules it would behave chaotically and if the multiverse behaved that way so would all the universes in it, including ours. However there is order in our universe, but what is fundamental and what is not? I think we probably all agree that purely mathematical things like pi or e would remain constant in all universes, but consider some of the physical things that might change:
The Planck constant.
The speed of light.
The gravitational (big G) constant.
The mass of the electron, proton, and neutron.
The electrical charge on the proton and electron.
The inverse square law of gravity and electromagnetism.
The conservation of Mass-energy, momentum, angular momentum, spin and electrical charge.
The relative strength of the 4 forces of nature.
The number of large dimensions in a universe.
The Hubble constant.
The ratio of baryonic matter to dark matter and dark energy.
It seems to me that the speed of light and Planck's constant may be more fundamental than other "constants" and the basic structure of the laws of physics may be more fundamental than the constants they use. But I could be wrong, perhaps the things that always remain the same are none of the above and we haven't even discovered them yet.
John K Clark
Some of the laws of physics could change from universe to universe, but there must be some laws that remain invariant across the entire multiverse because without rules it would behave chaotically and if the multiverse behaved that way so would all the universes in it, including ours. However there is order in our universe, but what is fundamental and what is not? I think we probably all agree that purely mathematical things like pi or e would remain constant in all universes, but consider some of the physical things that might change:
The Planck constant.
The speed of light.
The gravitational (big G) constant.
The mass of the electron, proton, and neutron.
The electrical charge on the proton and electron.
The inverse square law of gravity and electromagnetism.
The conservation of Mass-energy, momentum, angular momentum, spin and electrical charge.
The relative strength of the 4 forces of nature.
The number of large dimensions in a universe.
The Hubble constant.
The ratio of baryonic matter to dark matter and dark energy.
It seems to me that the speed of light and Planck's constant may be more fundamental than other "constants" and the basic structure of the laws of physics may be more fundamental than the constants they use. But I could be wrong, perhaps the things that always remain the same are none of the above and we haven't even discovered them yet.
John K Clark
I enjoyed the review; but there's one comment I believe to be in error.
...Byrne does not make it clear if this means they are as numerous as the number of points on a line, or as numerous as an even larger infinite set like the set of all possible clock faces...
I'm pretty sure that the set of all possible clock faces has the same cardinality as the set of points in a line (see space-filling curve).
What's even meant by a "clock face" in this context?
(BTW, note that you don't need a space filling curve to show that R has the same cardinality as R x R; what's surprising about a space filling curve is that it's additionally continuous.)
Good point. I just assumed that "clock face" meant something isomorphic to the unit square.
(I prefer linking space-filling curves as opposed to just the bare statement because space-filling curves are constructive.)
I just assumed that "clock face" meant something isomorphic to the unit square.
Like, what, a subspace of R^2 homeomorphic to it? OK, yeah, so only continuum-many.
(I prefer linking space-filling curves as opposed to just the bare statement because space-filling curves are constructive.)
Yeah I guess there isn't anything obvious to link to that shows how to do R x R constructively the direct way, huh?
When I read the anecdote about how Peano was inspired to give an explicit construction because Cantor's original proof didn't, I decided to not bother looking up info on Cantor's proof.
ETA: Re-reading my own link, I find that I misremembered what inspired Peano to search for space-filling curves -- he was looking specifically for continuous mappings, and my link was more specific than necessary, just as you pointed out in your first reply to me in this thread.
Huh, did Cantor do it by well-ordering or something? I wouldn't know. In any case it's pretty easy to explicitly put 2^N x 2^N in bijection with 2^N, because the former is just 2^(2N), and 2N is in bijection with N. What this cashes out to is, if you have two elements of 2^N, and want to make one that encodes them both, you just interleave them. Note also this works for any 2^S when you have an explicit bijection between S and 2S. If you want it for R all you need is an explicit bijection between R and 2^N. It's a more general consequence of well-ordering that S x S is of the same cardinality as S for any infinite S, and that is necessarily nonconstructive, but for "practical" infinite sets (by which I basically mean ℶ_n for n finite) many bijections can be made explicitly that would in general require choice.
No. Each clock face has the same cardinality as the points of a line, but the set of possible clock faces (which I take to mean something like "ways of colouring a disc", where how many colours you're allowed doesn't really matter) has the same cardinality as the set of ways of colouring a line, or equivalently the set of subsets of the line, in other words 2^continuum.
Voted down for starting off with "no" before it was established what what was being talked about. This all depends on what he meant by "clock face". Until that's clear it's simply impossible to say.
I'd been going to reply and say "butbutbutbut the only possible interpretation of 'clock face' that would make the cardinality not be 2^c would be that 'clock face' means 'pair of clock-hand positions', and that's just ridiculous" ... and then I looked at the rest of the thread and saw that that was apparently what JKC meant. My apologies.
EDITED to add: er, and actually there are perfectly reasonable interpretations that make the cardinality only the same as that of R, such as anything that can be described completely by a finite set of simple closed curves, or an RGB colouring where the colour at each point is a continuous function of position. So: total fail. Sorry again.
Great post; I had only really about Everett's work on MWI.
Some typos:
talking about many worlds as a interpretation
Linus Pauling credited Evert by name
Please burn be and DON'T FILE ME
Does a copy of this letter exist?
Everett as a freshman devised a logical proof against the existence of God.
I also enjoyed the book immensely and would commend it to anyone interested in the foundations of QM. Everett called his theory 'relative state' though he did not object to others calling it 'many worlds'. In E's theory there is one world, the wave function. We macroscopic beings are in a 'slice' of that world.
E's theory solves a lot of problems: derives the Born probability rule and removes the need to postulate it, explains Schrodinger's cat and Wigner's friend, fits perfectly with decoherence, allows partial measurements, removes the need to postulate a classical measurement apparatus, works with relarivistic QFT and QCD, has no spooky action at a distance, is deterministic at a fundamental level, and has no ill defined 'collapse'. Not bad.
The price is to give away the intuition that 'this' version of me is the only 'real' one. Just as we gave away the intuition that the earth is not moving post Copernicus.
The sociology is also interesting - Bohr was totally dominant and crushed the Everett heresy. John Wheeler, Everett's supervisor, was utterly cowed by Bohr.
Everett's model does not even explain simple state transitions. let alone anything more interesting, like radioactive decay.
Having read his thesis I think it does. Why not?
Edit: original thesis not thesis. There were two versions, a longer version with more proofs and detail and a shorter version ordered by Bohr which is sadly truncated and watered down.
How many worlds are created when an atom emits a photon when going from an excited state to the ground state?
The issue is not whether the number of worlds in finite or infinite, but when the worlds come into existence. When do you think it happens?
This is one of those "unask that question grasshopper!" situations.
There is according to Everett, just one world, consisting of the wave function.
As macroscopic beings we experience a projection of that wave function onto a lower dimensional space. One can think of one projection as one 'world' but really there is just one world. You have to read the whole thing unfortunately to really see it.
As quantum measurements occur the projections 'split'. This creates the illusion of indeterminacy because we only see part of the world.
I've just finished this book and its one of the most enjoyable things I've read in a long time. Being a staple of science fiction and the only interpretation of quantum mechanics to enter the popular imagination it's a little surprising that "The Many Worlds of Hugh Everett" by Peter Byrne is the first biography of the originator of that amazing idea. Everett certainly had an interesting life, he was a libertarian and a libertine, became a cold warrior who with his top secret clearance was comfortable with the idea of megadeath, became wealthy by started one of the first successful software companies until alcoholism drove him and his company into the ground. Everett died of heart failure in 1982 at the age of 51, he was legally drunk at the time. He requested that his body be cremated and his ashes thrown into the garbage. And so he was.
Byrne had an advantage other potential biographers did not, the cooperation of his son Mark, a successful rock musician and composer whose music has been featured in such big budget movies as American Beauty, Hellboy, Yes Man, all three of the Shrek movies and many others. Mark gave Byrne full access to his garage which was full of his father's papers that nobody had looked at in decades.
Everett was an atheist all his life, after his death Paul Davies, who got 1,000,000 pounds for winning the Templeton religion prize, said that if true Many Worlds destroyed the anthropic argument for the existence of God. Everett would have been delighted. Nevertheless Everett ended up going to Catholic University of America near Washington DC. Although Byrne doesn't tell us exactly what was in it, Everett as a freshman devised a logical proof against the existence of God. Apparently it was good enough that one of his pious professors became very upset and depressed with "ontological horror" when he read it. Everett liked the professor and felt so guilty he decided not to use it on a person of faith again. This story is very atypical of the man, most of the time Everett seems to care little for the feelings of others and although quite brilliant wasn't exactly lovable.
Everett wasn't the only one dissatisfied with the Copenhagen Interpretation which insisted the measuring device had to be outside the wave function, but he was unlike other dissidents such as Bohm or Cramer in that Everett saw no need to add new terms to Schrodinger's Equation and thought the equation meant exactly what it said. The only reason those extra terms were added was to try to rescue the single universe idea, and there was no experimental justification for that. Everett was unique in thinking that quantum mechanics gave a description of nature that was literally true.
John Wheeler, Everett's thesis adviser, made him cut out about half the stuff in his original 137 page thesis and tone down the language so it didn't sound like he thought all those other universes were equally real when in fact he did. For example, Wheeler didn't like the word "split" and was especially uncomfortable with talk of conscious observers splitting, most seriously he made him remove the entire chapter on information and probability which today many consider the best part of the work. His long thesis was not published until 1973, if that version had been published in 1957 instead of the truncated Bowdlerized version things would have been different; plenty of people would still have disagreed but he would not have been ignored for as long as he was.
Byrne writes of Everett's views: "the splitting of observers share an identity because they stem from a common ancestor, but they also embark on different fates in different universes. They experience different lifespans, dissimilar events (such as a nuclear war perhaps) and at some point are no longer the same person, even though they share certain memory records." Everett says that when a observer splits it is meaningless to ask "which of the final observers corresponds to the initial one since each possess the total memory of the first" he says it is as foolish as asking which amoeba is the original after it splits into two. Wheeler made him remove all such talk of amoebas from his published short thesis.
Byrne says Everett did not think there were just an astronomically large number of other universes but rather an infinite number of them, not only that he thought there were a non-denumerable infinite number of other worlds. This means that the number of them was larger than the infinite set of integers, but Byrne does not make it clear if this means they are as numerous as the number of points on a line, or as numerous as an even larger infinite set like the set of all possible clock faces, or maybe an even larger infinity than that where easy to understand examples of that sort of mega-infinite magnitude are hard to come by. Neill Graham tried to reformulate the theory so you'd only need a countably infinite number of branches and Everett at first liked the idea but later rejected it and concluded you couldn't derive probability by counting universes. Eventually even Graham seems to have agreed and abandoned the idea that the number of universes was so small you could count them.
Taken as a whole Everett's multiverse, where all things happen, probability is not a useful concept and everything is deterministic. However for observers like us trapped in a single branch of the multiverse, observers who do not have access to the entire wave function and all the information it contains but only a small sliver of it, probability is the best we can do. That probability we see is not part of the thing itself but is just a subjective measure of our ignorance.
Infinity can cause problems in figuring out probability but Everett said his theory could calculate what the probability any event could be observed in any branch of the multiverse, and it turns out to be the Born Rule (discovered by Max Born, grandfather of Olivia Newton John) which means the probability of finding a particle at a point is the squaring of the amplitude of the Schrodinger Wave function at that point. The Born Rule has been shown experimentally to be true but the Copenhagen Interpretation just postulates it, Everett said he could derive it from his theory it "emerges naturally as a measure of probability for observers confined to a single branch (like our branch)". He proved the mathematical consistency of this idea by adding up all the probabilities in all the branches of the event happening and getting exactly 100%. Dieter Zeh said Everett may not have rigorously derived the Born Rule but did justify it and showed it "as being the only reasonable choice for a probability measure if objective reality is represented by the universal wave function [Schrodinger's wave equation]". Rigorous proof or not that's more than any other quantum interpretation has managed to do.
Everett wrote to his friend Max Jammer:
"None of these physicists had grasped what I consider to be the major accomplishment of the theory- the "rigorous" deduction of the probability interpretation of Quantum Mechanics from wave mechanics alone. This deduction is just as "rigorous" as any deductions of classical statistical mechanics. [...] What is unique about the choice of measure and why it is forced upon one is that in both cases it is the only measure that satisfies the law of conservation of probability through the equations of motion. Thus logically in both classical statistical mechanics and in quantum mechanics, the only possible statistical statements depend upon the existence of a unique measure which obeys this conservation principle."
Nevertheless some complained that Everett did not use enough rigor in his derivation. David Deutsch has helped close that rigor gap. He showed that the number of Everett-worlds after a branching is proportional to the conventional probability density. He then used Game Theory to show that all these are all equally likely to be observed. Everett would likely have been delighted as he used Game Theory extensively in his other life as a cold warrior. Professor Deutsch gave one of the best quotations in the entire book, talking about many worlds as a interpretation of Quantum Mechanics "is like talking about dinosaurs as an interpretation of the fossil record".
Everett was disappointed at the poor reception his doctoral dissertation received and never published anything on quantum mechanics again for the rest of his life; instead he became a Dr. Strangelove type character making computer nuclear war games and doing grim operational research for the pentagon about armageddon. He was one of the first to point out that any defense against intercontinental ballistic missiles would be ineffectual and building an anti-balistic missile system could not be justified except for "political or psychological grounds". Byrne makes the case that Everett was the first one to convince high military leaders through mathematics and no nonsense non sentimental reasoning that a nuclear war could not be won, "after an attack by either superpower on the other, the majority of the attacked population that survived the initial blasts would be sterilized and gradually succumb to leukemia. Livestock would die quickly and survivors would be forced to rely on eating grains potatoes and vegetables. Unfortunately the produce would be seething with radioactive Strontium 90 which seeps into human bone marrow and causes cancer". Linus Pauling credited Evert by name and quoted from his pessimistic report in his Nobel acceptance speech for receiving the 1962 Nobel Peace prize.
Despite his knowledge of the horrors of a nuclear war Everett, like most of his fellow cold warrior colleagues in the 50's and 60's, thought the probability of it happening was very high and would probably happen very soon. Byrne speculates in a footnote that Everett may have privately used anthropic reasoning and thought that the fact we live in a world where such a war has not happened (at least not yet) was more confirmation that his Many Worlds idea was right. Incidentally this is one of those rare books where the footnotes are almost as much fun to read as the main text.
Hugh's daughter Liz Everett killed herself a few years after her father's death, in her suicide note she said "Funeral requests: I prefer no church stuff. Please burn be and DON'T FILE ME. Please sprinkle me in some nice body of water or the garbage, maybe that way I'll end up in the correct parallel universe to meet up with Daddy". And so she was.
John K Clark