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The Quantum Physics Sequence

26 Post author: Eliezer_Yudkowsky 11 June 2008 03:42AM

This is an inclusive guide to the series of posts on quantum mechanics that began on April 9th, 2008, including the digressions into related topics (such as the difference between Science and Bayesianism) and some of the preliminary reading.

You may also be interested in one of the less inclusive post guides, such as:

My current plan calls for the quantum physics series to eventually be turned into one or more e-books.

Preliminaries:

  • Probability is in the Mind:  If you are uncertain about a phenomenon, this is a fact about your state of mind, not a fact about the phenomenon itself.  There are mysterious questions but not mysterious answers.  The map is not the territory.
  • Reductionism:  We build models of the universe that have many different levels of description.  But so far as anyone has been able to determine, the universe itself has only the single level of fundamental physics - reality doesn't explicitly compute protons, only quarks.
  • Joy in the Merely Real:  If you can't take joy in things that turn out to be explicable, you're going to set yourself up for eternal disappointment.  Don't worry if quantum physics turns out to be normal.
  • Zombies! Zombies? and The Generalized Anti-Zombie Principle:  Don't try to put your consciousness or your personal identity outside physics.  Whatever makes you say "I think therefore I am", causes your lips to move; it is within the chains of cause and effect that produce our observed universe.
  • Belief in the Implied Invisible:  If a spaceship goes over the cosmological horizon relative to us, so that it can no longer communicate with us, should we believe that the spaceship instantly ceases to exist?

Basic Quantum Mechanics:

  • Quantum Explanations:  Quantum mechanics doesn't deserve its fearsome reputation.  If you tell people something is supposed to be mysterious, they won't understand it.  It's human intuitions that are "strange" or "weird"; physics itself is perfectly normal.  Talking about historical erroneous concepts like "particles" or "waves" is just asking to confuse people; present the real, unified quantum physics straight out.  The series will take a strictly realist perspective - quantum equations describe something that is real and out there.  Warning:  Although a large faction of physicists agrees with this, it is not universally accepted.  Stronger warning:  I am not even going to present non-realist viewpoints until later, because I think this is a major source of confusion.
  • Configurations and Amplitude:  A preliminary glimpse at the stuff reality is made of.  The classic split-photon experiment with half-silvered mirrors.  Alternative pathways the photon can take, can cancel each other out.  The mysterious measuring tool that tells us the relative squared moduli.
  • Joint Configurations:  The laws of physics are inherently over mathematical entities, configurations, that involve multiple particles.  A basic, ontologically existent entity, according to our current understanding of quantum mechanics, does not look like a photon - it looks like a configuration of the universe with "A photon here, a photon there."  Amplitude flows between these configurations can cancel or add; this gives us a way to detect which configurations are distinct.  It is an experimentally testable fact that "Photon 1 here, photon 2 there" is the same configuration as "Photon 2 here, photon 1 there".
  • Distinct Configurations:  Since configurations are over the combined state of all the elements in a system, adding a sensor that detects whether a particle went one way or the other, becomes a new element of the system that can make configurations "distinct" instead of "identical".  This confused the living daylights out of early quantum experimenters, because it meant that things behaved differently when they tried to "measure" them.  But it's not only measuring instruments that do the trick - any sensitive physical element will do - and the distinctness of configurations is a physical fact, not a fact about our knowledge.  There is no need to suppose that the universe cares what we think.
  • Where Philosophy Meets Science:  In retrospect, supposing that quantum physics had anything to do with consciousness was a big mistake.  Could philosophers have told the physicists so?  But we don't usually see philosophers sponsoring major advances in physics; why not?
  • Can You Prove Two Particles Are Identical?:  You wouldn't think that it would be possible to do an experiment that told you that two particles are completely identical - not just to the limit of experimental precision, but perfectly.  You could even give a precise-sounding philosophical argument for why it was not possible - but the argument would have a deeply buried assumption.  Quantum physics violates this deep assumption, making the experiment easy.
  • Classical Configuration Spaces:  How to visualize the state of a system of two 1-dimensional particles, as a single point in 2-dimensional space.  A preliminary step before moving into...
  • The Quantum Arena:  Instead of a system state being associated with a single point in a classical configuration space, the instantaneous real state of a quantum system is a complex amplitude distribution over a quantum configuration space.  What creates the illusion of "individual particles", like an electron caught in a trap, is a plaid distribution - one that happens to factor into the product of two parts.  It is the whole distribution that evolves when a quantum system evolves.  Individual configurations don't have physics; amplitude distributions have physics.  Quantum entanglement is the general case; quantum independence is the special case.
  • Feynman Paths:  Instead of thinking that a photon takes a single straight path through space, we can regard it as taking all possible paths through space, and adding the amplitudes for every possible path.  Nearly all the paths cancel out - unless we do clever quantum things, so that some paths add instead of canceling out.  Then we can make light do funny tricks for us, like reflecting off a mirror in such a way that the angle of incidence doesn't equal the angle of reflection.  But ordinarily, nearly all the paths except an extremely narrow band, cancel out - this is one of the keys to recovering the hallucination of classical physics.
  • No Individual Particles:  One of the chief ways to confuse yourself while thinking about quantum mechanics, is to think as if photons were little billiard balls bouncing around.  The appearance of little billiard balls is a special case of a deeper level on which there are only multiparticle configurations and amplitude flows.  It is easy to set up physical situations in which there exists no fact of the matter as to which electron was originally which.
  • Identity Isn't In Specific Atoms, Three Dialogues on Identity:  Given that there's no such thing as "the same atom", whether you are "the same person" from one time to another can't possibly depend on whether you're made out of the same atoms.
  • Decoherence:  A quantum system that factorizes can evolve into a system that doesn't factorize, destroying the illusion of independence.  But entangling a quantum system with its environment, can appear to destroy entanglements that are already present.  Entanglement with the environment can separate out the pieces of an amplitude distribution, preventing them from interacting with each other.  Decoherence is fundamentally symmetric in time, but appears asymmetric because of the second law of thermodynamics.
  • The So-Called Heisenberg Uncertainty Principle:  Unlike classical physics, in quantum physics it is not possible to separate out a particle's "position" from its "momentum".  The evolution of the amplitude distribution over time, involves things like taking the second derivative in space and multiplying by i to get the first derivative in time.  The end result of this time evolution rule is that blobs of particle-presence appear to race around in physical space.  The notion of "an exact particular momentum" or "an exact particular position" is not something that can physically happen, it is a tool for analyzing amplitude distributions by taking them apart into a sum of simpler waves.  This uses the assumption and fact of linearity: the evolution of the whole wavefunction seems to always be the additive sum of the evolution of its pieces.  Using this tool, we can see that if you take apart the same distribution into a sum of positions and a sum of momenta, they cannot both be sharply concentrated at the same time.  When you "observe" a particle's position, that is, decohere its positional distribution by making it interact with a sensor, you take its wave packet apart into two pieces; then the two pieces evolve differently.  The Heisenberg Principle definitely does not say that knowing about the particle, or consciously seeing it, will make the universe behave differently.
  • Which Basis Is More Fundamental?:  The position basis can be computed locally in the configuration space; the momentum basis is not local.  Why care about locality?  Because it is a very deep principle; reality itself seems to favor it in some way.
  • Where Physics Meets Experience:  Meet the Ebborians, who reproduce by fission.  The Ebborian brain is like a thick sheet of paper that splits down its thickness.  They frequently experience dividing into two minds, and can talk to their other selves.  It seems that their unified theory of physics is almost finished, and can answer every question, when one Ebborian asks:  When exactly does one Ebborian become two people?
  • Where Experience Confuses Physicists:  It then turns out that the entire planet of Ebbore is splitting along a fourth-dimensional thickness, duplicating all the people within it.  But why does the apparent chance of "ending up" in one of those worlds, equal the square of the fourth-dimensional thickness?  Many mysterious answers are proposed to this question, and one non-mysterious one.
  • On Being Decoherent:  When a sensor measures a particle whose amplitude distribution stretches over space - perhaps seeing if the particle is to the left or right of some dividing line - then the standard laws of quantum mechanics call for the sensor+particle system to evolve into a state of (particle left, sensor measures LEFT) + (particle right, sensor measures RIGHT).  But when we humans look at the sensor, it only seems to say "LEFT" or "RIGHT", never a mixture like "LIGFT".  This, of course, is because we ourselves are made of particles, and subject to the standard quantum laws that imply decoherence.  Under standard quantum laws, the final state is (particle left, sensor measures LEFT, human sees "LEFT") + (particle right, sensor measures RIGHT, human sees "RIGHT").
  • The Conscious Sorites Paradox:  Decoherence is implicit in quantum physics, not an extra law on top of it.  Asking exactly when "one world" splits into "two worlds" may be like asking when, if you keep removing grains of sand from a pile, it stops being a "heap".  Even if you're inside the world, there may not be a definite answer.  This puzzle does not arise only in quantum physics; the Ebborians could face it in a classical universe, or we could build sentient flat computers that split down their thickness.  Is this really a physicist's problem?
  • Decoherece is Pointless:  There is no exact point at which decoherence suddenly happens.  All of quantum mechanics is continuous and differentiable, and decoherent processes are no exception to this.
  • Decoherent Essences:  Decoherence is implicit within physics, not an extra law on top of it.  You can choose representations that make decoherence harder to see, just like you can choose representations that make apples harder to see, but exactly the same physical process still goes on; the apple doesn't disappear and neither does decoherence.  If you could make decoherence magically go away by choosing the right representation, we wouldn't need to shield quantum computers from the environment.
  • The Born Probabilities:  The last serious mysterious question left in quantum physics:  When a quantum world splits in two, why do we seem to have a greater probability of ending up in the larger blob, exactly proportional to the integral of the squared modulus?  It's an open problem, but non-mysterious answers have been proposed.  Try not to go funny in the head about it.
  • Decoherence as Projection:  Since quantum evolution is linear and unitary, decoherence can be seen as projecting a wavefunction onto orthogonal subspaces.  This can be neatly illustrated using polarized photons and the angle of the polarized sheet that will absorb or transmit them.
  • Entangled Photons:  Using our newly acquired understanding of photon polarizations, we see how to construct a quantum state of two photons in which, when you measure one of them, the person in the same world as you, will always find that the opposite photon has opposite quantum state.  This is not because any influence is transmitted; it is just decoherence that takes place in a very symmetrical way, as can readily be observed in our calculations.

Many Worlds:

(At this point in the sequence, most of the mathematical background has been built up, and we are ready to evaluate interpretations of quantum mechanics.)

  • Bell's Theorem: No EPR "Reality":  (Note:  This post was designed to be read as a stand-alone, if desired.)  Originally, the discoverers of quantum physics thought they had discovered an incomplete description of reality - that there was some deeper physical process they were missing, and this was why they couldn't predict exactly the results of quantum experiments.  The math of Bell's Theorem is surprisingly simple, and we walk through it.  Bell's Theorem rules out being able to locally predict a single, unique outcome of measurements - ruling out a way that Einstein, Podolsky, and Rosen once defined "reality".  This shows how deep implicit philosophical assumptions can go.  If worlds can split, so that there is no single unique outcome, then Bell's Theorem is no problem.  Bell's Theorem does, however, rule out the idea that quantum physics describes our partial knowledge of a deeper physical state that could locally produce single outcomes - any such description will be inconsistent.
  • Spooky Action at a Distance: The No-Communication Theorem:  As Einstein argued long ago, the quantum physics of his era - that is, the single-global-world interpretation of quantum physics, in which experiments have single unique random results - violates Special Relativity; it imposes a preferred space of simultaneity and requires a mysterious influence to be transmitted faster than light; which mysterious influence can never be used to transmit any useful information.  Getting rid of the single global world dispels this mystery and puts everything back to normal again.
  • Decoherence is Simple, Decoherence is Falsifiable and Testable:  (Note:  Designed to be standalone readable.)  An epistle to the physicists.  To probability theorists, words like "simple", "falsifiable", and "testable" have exact mathematical meanings, which are there for very strong reasons.  The (minority?) faction of physicists who say that many-worlds is "not falsifiable" or that it "violates Occam's Razor" or that it is "untestable", are committing the same kind of mathematical crime as non-physicists who invent their own theories of gravity that go as inverse-cube.  This is one of the reasons why I, a non-physicist, dared to talk about physics - because I saw (some!) physicists using probability theory in a way that was simply wrong.  Not just criticizable, but outright mathematically wrong:  2 + 2 = 3.
  • Quantum Non-Realism:  "Shut up and calculate" is the best approach you can take when none of your theories are very good.  But that is not the same as claiming that "Shut up!" actually is a theory of physics.  Saying "I don't know what these equations mean, but they seem to work" is a very different matter from saying:  "These equations definitely don't mean anything, they just work!"
  • Collapse Postulates:  Early physicists simply didn't think of the possibility of more than one world - it just didn't occur to them, even though it's the straightforward result of applying the quantum laws at all levels.  So they accidentally invented a completely and strictly unnecessary part of quantum theory to ensure there was only one world - a law of physics that says that parts of the wavefunction mysteriously and spontaneously disappear when decoherence prevents us from seeing them any more.  If such a law really existed, it would be the only non-linear, non-unitary, non-differentiable, non-local, non-CPT-symmetric, acausal, faster-than-light phenomenon in all of physics.
  • If Many-Worlds Had Come First:  If early physicists had never made the mistake, and thought immediately to apply the quantum laws at all levels to produce macroscopic decoherence, then "collapse postulates" would today seem like a completely crackpot theory.  In addition to their other problems, like FTL, the collapse postulate would be the only physical law that was informally specified - often in dualistic (mentalistic) terms - because it was the only fundamental law adopted without precise evidence to nail it down.  Here, we get a glimpse at that alternate Earth.
  • Many Worlds, One Best Guess:  Summarizes the arguments that nail down macroscopic decoherence, aka the "many-worlds interpretation".  Concludes that many-worlds wins outright given the current state of evidence.  The argument should have been over fifty years ago.  New physical evidence could reopen it, but we have no particular reason to expect this.
  • Living in Many Worlds:  The many worlds of quantum mechanics are not some strange, alien universe into which you have been thrust.  They are where you have always lived.  Egan's Law:  "It all adds up to normality."  Then why care about quantum physics at all?  Because there's still the question of what adds up to normality, and the answer to this question turns out to be, "Quantum physics."  If you're thinking of building any strange philosophies around many-worlds, you probably shouldn't - that's not what it's for.

Timeless Physics:

(Now we depart from what is nailed down in standard physics, and enter into more speculative realms - particularly Julian Barbour's Machian timeless physics.)

  • Mach's Principle: Anti-Epiphenomenal Physics:  Could you tell if the whole universe were shifted an inch to the left?  Could you tell if the whole universe was traveling left at ten miles per hour?  Could you tell if the whole universe was accelerating left at ten miles per hour?  Could you tell if the whole universe was rotating?
  • Relative Configuration Space:  Maybe the reason why we can't observe absolute speeds, absolute positions, absolute accelerations, or absolute rotations, is that particles don't have absolute positions - only positions relative to each other.  That is, maybe quantum physics takes place in a relative configuration space.
  • Timeless Physics:  What time is it?  How do you know?  The question "What time is it right now?" may make around as much sense as asking "Where is the universe?"  Not only that, our physics equations may not need a t in them!
  • Timeless Beauty:  To get rid of time you must reduce it to nontime.  In timeless physics, everything that exists is perfectly global or perfectly local.  The laws of physics are perfectly global; the configuration space is perfectly local.  Every fundamentally existent ontological entity has a unique identity and a unique value.  This beauty makes ugly theories much more visibly ugly; a collapse postulate becomes a visible scar on the perfection.
  • Timeless Causality:  Using the modern, Bayesian formulation of causality, we can define causality without talking about time - define it purely in terms of relations.  The river of time never flows, but it has a direction.
  • Timeless Identity:  How can you be the same person tomorrow as today, in the river that never flows, when not a drop of water is shared between one time and another?  Having used physics to completely trash all naive theories of identity, we reassemble a conception of persons and experiences from what is left.  With a surprising practical application...
  • Thou Art Physics:  If the laws of physics control everything we do, then how can our choices be meaningful?  Because you are physics.  You aren't competing with physics for control of the universe, you are within physics.  Anything you control is necessarily controlled by physics.
  • Timeless Control:  We throw away "time" but retain causality, and with it, the concepts "control" and "decide".  To talk of something as having been "always determined" is mixing up a timeless and a timeful conclusion, with paradoxical results.  When you take a perspective outside time, you have to be careful not to let your old, timeful intuitions run wild in the absence of their subject matter.

Rationality and Science:

(Okay, so it was many-worlds all along and collapse theories are silly.  Did first-half-of-20th-century physicists really screw up that badly?  How did they go wrong?  Why haven't modern physicists unanimously endorsed many-worlds, if the issue is that clear-cut?  What lessons can we learn from this whole debacle?)

  • The Failures of Eld Science:  A short story set in the same world as Initiation Ceremony.  Future physics students look back on the cautionary tale of quantum physics.
  • The Dilemma: Science or Bayes?:  The failure of first-half-of-20th-century-physics was not due to straying from the scientific method.  Science and rationality - that is, Science and Bayesianism - aren't the same thing, and sometimes they give different answers.
  • Science Doesn't Trust Your Rationality:  The reason Science doesn't always agree with the exact, Bayesian, rational answer, is that Science doesn't trust you to be rational.  It wants you to go out and gather overwhelming experimental evidence.
  • When Science Can't Help:  If you have an idea, Science tells you to test it experimentally.  If you spend 10 years testing the idea and the result comes out negative, Science slaps you on the back and says, "Better luck next time."  If you want to spend 10 years testing a hypothesis that will actually turn out to be right, you'll have to try to do the thing that Science doesn't trust you to do: think rationally, and figure out the answer before you get clubbed over the head with it.
  • Science Isn't Strict Enough:  Science lets you believe any damn stupid idea that hasn't been refuted by experiment.  Bayesianism says there is always an exactly rational degree of belief given your current evidence, and this does not shift a nanometer to the left or to the right depending on your whims.  Science is a social freedom - we let people test whatever hypotheses they like, because we don't trust the village elders to decide in advance - but you shouldn't confuse that with an individual standard of rationality.
  • Do Scientists Already Know This Stuff?:  No.  Maybe someday it will be part of standard scientific training, but for now, it's not, and the absence is visible.
  • No Safe Defense, Not Even Science:  Why am I trying to break your trust in Science?  Because you can't think and trust at the same time.  The social rules of Science are verbal rather than quantitative; it is possible to believe you are following them.  With Bayesianism, it is never possible to do an exact calculation and get the exact rational answer that you know exists.  You are visibly less than perfect, and so you will not be tempted to trust yourself.
  • Changing the Definition of Science:  Many of these ideas are surprisingly conventional, and being floated around by other thinkers.  I'm a good deal less of a lonely iconoclast than I seem; maybe it's just the way I talk.
  • Faster Than Science:  Is it really possible to arrive at the truth faster than Science does?  Not only is it possible, but the social process of science relies on scientists doing so - when they choose which hypotheses to test.  In many answer spaces it's not possible to find the true hypothesis by accident.  Science leaves it up to experiment to socially declare who was right, but if there weren't some people who could get it right in the absence of overwhelming experimental proof, science would be stuck.
  • Einstein's Speed:  Albert was unusually good at finding the right theory in the presence of only a small amount of experimental evidence.  Even more unusually, he admitted it - he claimed to know the theory was right, even in advance of the public proof.  It's possible to arrive at the truth by thinking great high-minded thoughts of the sort that Science does not trust you to think, but it's a lot harder than arriving at the truth in the presence of overwhelming evidence.
  • That Alien Message:  Einstein used evidence more efficiently than other physicists, but he was still extremely inefficient in an absolute sense.  If a huge team of cryptographers and physicists were examining a interstellar transmission, going over it bit by bit, we could deduce principles on the order of Galilean gravity just from seeing one or two frames of a picture.  As if the very first human to see an apple fall, had, on the instant, realized that its position went as the square of the time and that this implied constant acceleration.
  • My Childhood Role Model:  I looked up to the ideal of a Bayesian superintelligence, not Einstein.
  • Einstein's Superpowers:  There's an unfortunate tendency to talk as if Einstein had superpowers - as if, even before Einstein was famous, he had an inherent disposition to be Einstein - a potential as rare as his fame and as magical as his deeds.  Yet the way you acquire superpowers is not by being born with them, but by seeing, with a sudden shock, that they are perfectly normal.
  • Class Project:  From the world of Initiation Ceremony.  Brennan and the others are faced with their midterm exams.
  • Why Quantum?:  Why do a series on quantum mechanics?  Some of the many morals that are best illustrated by the tale of quantum mechanics and its misinterpretation.

Comments (22)

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Comment author: gordon_wrigley 11 June 2008 10:58:18AM 3 points [-]

I don't suppose you could spend a post or two explaining in your nice easy to understand way exactly what it is a quantum computer is supposed to do and how this might impact the NP problems.

Comment author: Vladimir_Golovin3 11 June 2008 12:20:34PM 6 points [-]

Eliezer -- this post goes straight to my Favorites. Giving concise, straightforward summaries to posts is a great idea.

My attention is very fragmented (thanks to my job), so when reading Quantum Arena, I completely missed the point of the post which you gave in your excellent summary:

"Instead of a system state being associated with a single point in a classical configuration space, the instantaneous real state of a quantum system is a complex amplitude distribution over a quantum configuration space."

This sentence, in fact, has told me a lot more than the entire post -- which, of course, I'm going to re-read now.

Please consider including such summaries / guides for every series of posts you write. It would be even better if you could include such summaries into a dependency graph like the one you posted here earlier -- for example, the summaries might display when a user hovers the mouse cursor over a graph node.

Comment author: Bill_Mill 11 June 2008 01:34:41PM 3 points [-]

Eliezer - will these e-books be edited by a professional editor, a friend, or just yourself?

Gordon - Scott Aaronson gave a wonderful explanation of quantum computing at his blog.

Comment author: Infotropism2 11 June 2008 02:02:10PM 1 point [-]

Question : money derived from those ebooks, goes it to the singularity institute ? In other words, is buying one of these equivalent to donating money to the institute ?

Comment author: Tom3 11 June 2008 02:06:13PM 1 point [-]

In the Timeless Physics section:

"The laws of physics are perfectly local; the configuration space is perfectly local."

Aren't the laws global?

Comment author: Michael_G.R. 11 June 2008 04:35:47PM 0 points [-]

Will the eBooks also be available as hard copies? I'm probably not alone in preferring to read long texts on paper, and printing them out isn't quite the same.

Comment author: Boris 11 June 2008 07:29:41PM 0 points [-]

Eliezer, thank you very much for all of these posts. I believe that this post is an excellent way of presenting them all in a reasonable sequence.

Comment author: Emil_Gilliam 12 June 2008 02:05:58AM 0 points [-]

I hope you can include this Tom the Dancing Bug cartoon in your e-book, as an example of what you're arguing against.

Comment author: Grif 02 August 2012 06:09:53AM 2 points [-]

Broken link. Here's a new one.

Comment author: David_Veksler 12 June 2008 03:34:56PM 0 points [-]
Comment author: Just_existing 16 January 2012 06:55:14PM *  4 points [-]

This is for everybody who can't wait on the upcoming e-book. I put the Basic quantum explanations in an e-book format myself, which you can download here: http://www.share-online.biz/dl/COXXQR5M6NJ0 The format is for the Amazon Kindle. I created it by copying the html-versions into Word, removing the comments, saving them as .pdf, and finally i created the e-book with callibre. The pictures are sligthly above the place where they are supposed be, apart from that everything should be fine.

Enjoy!

Comment author: Konkvistador 06 February 2012 09:49:23AM *  3 points [-]

This reminds me, it has been over three years since this was stated:

My current plan calls for the quantum physics series to eventually be turned into one or more e-books.

Considering this has not happened yet, I'm just wondering if there has been any word if this is still the plan.

Comment author: ashu_437 14 October 2013 12:27:51AM 0 points [-]

This link seems to no longer work. Can you please upload it somewhere else? Thanks.

Comment author: ete 17 October 2013 01:47:32AM *  0 points [-]

I've read all posts in the Basic Quantum Mechanics section, plus many of the links from it and a handful of others (working through the rest, I'm still only three days into this). Quantum mechanics is something I've had vague explanations of from education and discussions with educated people, but it seemed extremely complicated and confusing due to almost precisely the issues touched on in the normal way it's taught. Thank you for putting down the steps needed to walk me through rewriting my basic assumptions of reality to more accurately reflect how reality likely works, it's been very fun and interesting. I'm starting to feel like a native of the quantum universe, and.. it kinda makes sense. Definitely a whole lot more sense than my previous mangled understanding of probabilities and wave/particle duality. Having a base level reality which works very differently from high level phenomenon which feel more intuitive does not seem like a great surprise.

Anyway, one idea I've had which seems interesting to me, but I am not yet in knowledgeable to evaluate properly and would like thoughts on:

Would you, under the many worlds interpretation, be able to experimentally test whether a universe is infinite in time but not space?

I know that infinite time+finite space not a favored model for cosmology currently, but it's still interesting to me if quantum physics testably disproves a whole class of possible universes. And if by this (or similar) reasoning an infinite time/finite space universe is found to be incompatible with many worlds, finding evidence extremely strong evidence of an infinite time/finite space universe (highly unlikely as I understand it) would perhaps bring many worlds into question.

Possible line of reasoning:

  1. In a universe with finite space, there is a finite configuration space (finite amount of physical space, so finite possible universal states).
  2. Any particular blob of amplitude/branch/world will eventually evolve into a state of/near maximum entropy.
  3. Maximum entropy is not entirely stable even if no work can be extracted from it, so it is not a static point in configuration space.
  4. A non-static point in finite configuration space left to move for infinite time will eventually visit all possible arrangements of amplitude (configurations), infinite times. This includes Configuration A, which can be any possible point in configuration space.
  5. In both (particle left, sensor measures LEFT, human sees "LEFT") and (particle right, sensor measures RIGHT, human sees "RIGHT") blobs of amplitude, the universe evolves differently for a vast amount of time after the heat death of the universe, but given infinite time will at some point reach Configuration A with probability 1.
  6. Since both blobs of amplitude will, despite diverging for an unimaginable length of time, arrive at the same configuration as each other with probability 1, they are fully coherent allowing them to interact, and this is testable (and already falsified).

Points one, three, and four seems to me like the most likely weak link, but I'd be interested to know why this is not the case if it is indeed not the case. Perhaps at maximum-entropy each branch gets stuck in a unique infinite loop rather than visiting the rest of configuration space?

If the chain of reasoning holds and leads to the conclusions.. perhaps a stronger version of this argument could perhaps be constructed for a universe infinite in both time and space (depending on whether indefinitely expanding thermodynamic systems will reach all possible configurations given infinite time), though I'm already feeling somewhat out of my depth dealing with the weaker argument.

Comment author: paper-machine 17 October 2013 02:33:42AM *  0 points [-]

From a quick glance at your argument, it seems to me that quantum mechanics breaks down on the cosmological scale.

Comment author: ete 17 October 2013 03:20:23AM 1 point [-]

hm, from what I've been taking from the sequence quantum physics seems to apply fully at all levels, and the idea of it working differently/not applying is simply a matter of scale. For example an event causing a "split" affecting significantly macro objects almost entirely decohere, but not perfectly avoiding any kind of hard cutoff. Large systems definitely appear to work differently when you look at them on a large scale, but.. that appearance or classical hallucination is just an emergent property of underlying quantum effects.

Saying the quantum mechanics itself breaks down.. does not fit with the mental picture of reality I've taken from this, reality as entirely locally computable and with higher level effects based entirely on the base level substrate behavior. I'd like you to clarify what you mean by "break down", and preferably how reality would choose where to draw any line between scales where quantum mechanics does and does not break down?

I have read quantum physics has issues with gravity, perhaps that is what you're referring to? If so, I'd be interested in recommended further reading.

Comment author: paper-machine 17 October 2013 11:48:30AM 0 points [-]

from what I've been taking from the sequence quantum physics seems to apply fully at all levels, and the idea of it working differently/not applying is simply a matter of scale.

Nobody's resolved the fundamental problems between QM and general relativity (GR). EY comes close to claiming that MWI will do the trick, but it hasn't yet. At one point he even says that (paraphrasing) reality is a dream, and the dream satisfies special relativity -- at which point one has to ask why the dream doesn't satisfy general relativity.

Large systems definitely appear to work differently when you look at them on a large scale, but.. that appearance or classical hallucination is just an emergent property of underlying quantum effects.

See the previous note. Emergence is just another word for "magic."

Saying the quantum mechanics itself breaks down.. does not fit with the mental picture of reality I've taken from this, reality as entirely locally computable

This is an unfortunate side-effect of EY's tone in the QM sequence.

I'd like you to clarify what you mean by "break down", and preferably how reality would choose where to draw any line between scales where quantum mechanics does and does not break down?

The most evident problem in accepting both QM and SR simultaneously is that they substantially disagree on the value of the vacuum energy density.

Comment author: ete 17 October 2013 12:38:04PM *  1 point [-]

What I think you're saying, correct me if I'm wrong, is that there's a few big unknowns as to how QM applies to gravity or on cosmological scales, and because of this the answer to my chain of reasoning is "we just don't know"? That there's major unknowns is entirely reasonable/accurate, but.. I'm struggling to see exactly how the very real and important unknowns apply specifically to my reasoning.

Simply put: Where, in the line of reasoning, do you think the unknown of quantum gravity trips up the logic, and why?

It's seems quite possible that in discovering the answers behind the big unknowns we'll change some underlying assumptions and render my reasoning unworkable. But I don't see where in the line of reasoning not knowing vacuum energy density, or quantum gravity, causes a problem. And given that, it seems like working with the best available theory means applying certain aspects of QM at universal scale is not unreasonable, though we should expect we may need to update models once some big unknowns are resolved.

I think my use of emergence does not fall into the emergence/magic trap, since I am not attempting to explain anything about how large scale systems behave through emergence, my statement is purely that whatever the details of how macro systems work the large scale effects are caused by local physics being consistently applied and only appearing to work differently due to taking a larger view. Even though I used the word "emergence", my sentence can be reworded with my intended meaning if you swap it to "emerges from", which is specifically allowed by that post.

Also, you think my picture of reality as locally computable is "an unfortunate side-effect of EY's tone in the QM sequence"? If that's the case, do you dispute reality as locally computable? I'd be interested in sources which coherently argue for reality being non-locally computable.

Comment author: paper-machine 17 October 2013 02:50:14PM 1 point [-]

What I think you're saying, correct me if I'm wrong, is that there's a few big unknowns as to how QM applies to gravity or on cosmological scales, and because of this the answer to my chain of reasoning is "we just don't know"?

We do know -- QM predicts the wrong vacuum energy density by several orders of magnitude. We've measured this value empirically. Read the Baez link; he explains everything pretty clearly.

my sentence can be reworded with my intended meaning if you swap it to "emerges from", which is specifically allowed by that post.

The critical unanswered question is how "underlying quantum effects" generate the (observed) geometry of space-time. If there were a solution to that question, I'd take no issue with you saying it emerges from those quantum effects -- but we don't know if it's actually the other way around, that is, if it's actually relativistic effects on the microscale that generate quantum phenomena. Or if this is just the wrong question entirely, and that both are caused by a third thing.

That's how you fell into the emergence/magic trap.

EY has to spend a lot of time in the QM sequence insisting that QM is natural and fundamental to get over people's preconceptions of it as unnatural. However, that leads to people taking it as the unique baseline physical theory, which it is not.

Comment author: ete 17 October 2013 06:15:02PM 0 points [-]

Okay, I think I see where you're coming from better now. I have read that link, and at least feel like I conceptually understand some of the problems with applying quantum physics to the large scale. However, I'm still very curious as to exactly how the incompatibility in theories applies to this specific argument, and curious as to whether looking at a purely quantum universe (making the assumption that there is some way to derive relativistic experimental results from QM that we've missed, rather than that QM needs major changes) would give the results I'm describing, or whether I'm misunderstanding something about amplitude or thermodynamics in a heat death.

Hm, how to explain clearly.. It seems like what's being said is QM is at odds with observation (vacuum energy density) and at odds with our other best theory, relativity, (event horizon, thanks for chiming in shminux), so QM is wrong or incomplete in some way. I accept this as a likely conclusion, though I do not understand either theory deeply enough to be able to follow the arguments for inconsistency in full.

However, dismissing a thought experiment about a widely used theory with some possible implications (if I've not missed anything and have understood various things better than I'd guess I have, that chain of reasoning could show a certain interpretation (MW) is incompatible with finite space+infinite time, while a different interpretation (collapse) would not be), due to the underlying theory (QM) being wrong/incomplete for other reasons seems.. limiting. Even if the line of reasoning only holds meaning with the assumption that the universe is fundamentally quantum, local, and macro effects are all explainable in principle by the laws which govern the smallest parts, I'm interested in whether or not it holds.

I'm primarily trying to refine my mental model of how decoherence works with these thoughts, and an answer focused on whether in a quantum universe would, from our current understanding of quantum physics, do as I suppose (that is, in finite space+infinite time, it could never even slightly decohere due to probability 1 arriving at an identical configuration eventually), or have I made some error in my reasoning which can be explained and would allow me to improve my model of decoherence?

Comment author: shminux 17 October 2013 05:48:08PM 3 points [-]

To chime in as a person with grad-level training in the subject matter: there is a glaring tension between Quantum Field Theory and General Relativity in the low-energy macroscopic-size limit, which is very bad. How bad? Imagine "proving" that 1=2 in Peano arithmetic, something like that. The issue is the black hole: firewall or horizon? question. GR says that there is nothing locally special about crossing the event horizon (and must be applicable, since GR has been tested in this low-curvature regime), while QFT says that, after a while, the horizon becomes a high-energy incinerator (and must be applicable, since quantum entanglement has been tested in this low-energy regime). The best physics minds on the planet are at a loss to explain the problem. Last time something like that happened in physics, a completely new and unexpected theory eventually resulted. Odds are, we are in for a similar paradigm shift some day, hopefully soon.