You're looking at Less Wrong's discussion board. This includes all posts, including those that haven't been promoted to the front page yet. For more information, see About Less Wrong.

Luke_A_Somers comments on Open thread, August 5-11, 2013 - Less Wrong Discussion

3 Post author: David_Gerard 05 August 2013 06:50AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Article Navigation

Comments (307)

CC Licenced

Comments (307)

Sort By: Best

Show:

You are viewing a single comment's thread. Show more comments above.

Comment author: Luke_A_Somers 07 August 2013 02:59:37PM * 0 points [-]

I wouldn't call Everett 'Anthropic' per se. I consider it an application of the Generalized Anti-Zombie Principle: Here you've got this structure that acts like it's sapient†. Therefore, it is.

As for BM formally specifying how the reality fluid works... need I point out this this is 100% entirely backwards, being made of burdensome details?

Would you say that acknowledging the Born probabilities themselves 'comes out of the blue', since they aren't derived from the Schrödinger equation?

The Schrödinger Equation establishes linearity, thus directly allowing us to split any arbitrary wavefunction however we please. Already we can run many worlds side-by-side. The SE's dynamics lead to decoherence, which makes MWI have branching. It's all just noticing the structure that's already in the system.

Edited to add †: by 'acts like' I mean 'has the causal structure for it to be'

Comment author: EHeller 11 August 2013 01:13:00AM * 0 points [-]

The Schrödinger Equation establishes linearity, thus directly allowing us to split any arbitrary wavefunction however we please.

But many of the more-general lagrangians of particle physics are non-linear, in general there should be higher order, non-linear corrections. So Schrödinger is a single-particle/linearized approximation. What does this do for your view of many worlds? When we try to extend many worlds naively to QFTs we run into all sorts of weird problems (much of the universal wavefunction's amplitude doesn't have well defined particle number,etc). Shouldn't we expect the 'proper' interpretation to generalize nicely to the full QFT framework?

Comment author: tut 11 August 2013 08:16:58AM 1 point [-]

Shouldn't we expect the 'proper' interpretation to generalize nicely to the full QFT framework?

Or rather, the proper interpretation should work in the full QFT framework, and may or may not work for ordinary QM.

Comment author: Luke_A_Somers 12 August 2013 02:02:28PM * 0 points [-]

What are you talking about? I've only taken one course in quantum field theory, but I've never heard of anything where quantum mechanics was not linear. Can you give me a citation? It seems to me that failure of linearity would either be irrelevant (superlinear case, low amplitudes) or so dominant that any linearity would be utterly irrelevant and the Born Probabilities wouldn't even be a good approximation.

Also, by 'the Schrodinger equation' I didn't mean the special form which is the fixed-particle Hamiltonian with pp/2m kinetic energy - I meant the general form -

i hbar (d/dt) Psi = Hamiltonian Psi

Note that the Dirac Equation is a special case of this general form of the Schrodinger Equation. MWI, 'naive' or not, has no trouble with variations in particle number.

Comment author: RobbBB 07 August 2013 09:32:41PM * 0 points [-]

I wouldn't call Everett 'Anthropic' per se.

I'm not sure what you mean by 'anthropic per se'. Everett (MW) explains apparent quantum indeterminism anthropically, via indexical ignorance; our knowledge of the system as a whole is complete, but we don't know where we in the system are at this moment. De Broglie (HV) explains apparent quantum indeterminism via factual ignorance; our knowledge of the system's physical makeup is incomplete, and that alone creates the appearance of randomness. Von Neumann (OC) explains apparent quantum indeterminism realistically; the world just is indeterministic.

The SE's dynamics lead to decoherence, which makes MWI have branching. It's all just noticing the structure that's already in the system.

This is either a very implausible answer, or an answer to a different question than the one I asked. Historically, the Born Probabilities are derived directly from experimental data, not from the theorized dynamics. The difficulty of extracting the one from the other, of turning this into a single unified and predictive theory, just is the 'Measurement' Problem. Bohm is taking two distinct models and reifying mechanisms for each to produce an all-encompassing theory; maybe that's useless or premature, but it's clearly not a non sequitur, because the evidence for a genuine wave/particle dichotomy just is the evidence that makes scientists allow probabilistic digressions from the Schrödinger equation.

MW is not a finished theory until we see how it actually unifies the two, though I agree there are at least interesting and suggestive first steps in that direction. BM's costs are obvious and clear and formalized, which is its main virtue. Our ability to compare those costs to other theories' is limited so long as it's the only finished product under evaluation, because it's easy to look simple when you choose to only try to explain some of the data.

Comment author: Luke_A_Somers 07 August 2013 10:44:41PM 1 point [-]

I see what you mean now about anthropism. Yes, ignorance is subjective. Incidentally, this is how it used to be back before quantum ever came up.

This is either a very implausible answer, or an answer to a different question than the one I asked. Historically, the Born Probabilities are derived directly from experimental data, not from the theorized dynamics

Historically, Born was way before Everett and even longer before decoherence, so that's not exactly a shocker. Even in Born's time it was understood that subspaces had only one way of adding up to 1 in a way that respects probability identities - I'd bet dollars to donuts that that was how he got the rule in the first place, rather than doing a freaking curve fit to experimental data. What was missing at the time was any way to figure out what the wavefunction was, between doing its wavefunctiony thing and collapse.

Decoherence explains what collapse is made of. With it around, accepting the claim 'The Schrödinger Equation is the only rule of dynamics; collapse is illusory and subjective', which is basically all there is to MWI, requires much less bullet-biting than before it was introduced. There is still some, but those bullets are much chewier for me than any alternate rules of dynamics.

(incidentally, IIRC, Shminux, you hold the above quote but not MWI, which I find utterly baffling - if you want to explain the difference or correct me on your position, go ahead)

maybe that's useless or premature, but it's clearly not a non sequitur

Good thing I never said it was.

Comment author: EHeller 11 August 2013 01:42:35AM 0 points [-]

Decoherence explains what collapse is made of. With it around, accepting the claim 'The Schrödinger Equation is the only rule of dynamics; collapse is illusory and subjective', which is basically all there is to MWI

Well, you still need a host of ideas about how to actually interpret a diagonal density matrix. Because you don't have Born probabilities as a postulate, you have this structure but no method for connecting it back to lab-measured values.

While it seems straightforward, its because many-world's advocates are doing slight of hand. They use probabilities to build a theory (because lab experiments appear to be only describable probabilistically), and later they kick away that ladder but they want to keep all the structure that comes with it (density matrices,etc).

I know of many good expositions that start with the probabilities and use that to develop the form of the Schroedinger equation from Galilean relativity and cluster decomposition (Ballentine, parts of Weinberg).

I don't know any good expositions that go the other way. There are reasons that Deutsch, Wallace,etc have spent so much time trying to develop Born probabilities in a many world's context- because its an important problem.

Comment author: Luke_A_Somers 12 August 2013 02:10:27PM * 1 point [-]

Hold on a moment. What ladder is being kicked away here?

We've got observed probabilities. They're the experimental results, the basis of the theory. The theory then explains this in terms of indexical ignorance (thanks, RobbBB). I don't see a kicked ladder. Not every observed phenomenon needs a special law of nature to make it so.

Instead of specially postulating the Born Probabilities, elevating them to the status of a law of nature, we use it to label parts of the universe in much the same way as we notice, say, hydrogen or iron atoms - 'oh, look, there's that thing again'. In this case, it's the way that sometimes, components of the wavefunction propagate such that different segments won't be interfering with each other coherently (or in any sane basis, at all).

Also, about density matrices - what's the problem? We're still allowed to not know things and have subjective probabilities, even in MWI. Nothing in it suggests otherwise.

Comment author: shminux comment score below threshold [+] (24 children)

Comment author: Luke_A_Somers 07 August 2013 06:30:04PM * 1 point [-]

Regurgitating the teacher's password is a matter of mental process, and you have nowhere near the required level of evidence to make that judgement here.

As for radioactive decay, I'm not clear what you require of MWI here. The un-decayed state has amplitude which gradually diminishes, leaking into other states. When you look in a cat box, you become entangled with it.

If the states resulting from death at different times are distinguishable, then you can go ahead and distinguish them, and there's your answer (or, if it could be done in principle but we're not clever enough, then the answer is 'I don't know', but for reasons that don't really have bearing on the question).

Where it really gets interesting is if the states resulting from cat-death are quantum-identical. Then it's exactly like asking, in a diffraction-grating experiment, 'Which slit did the photon go through?'. The answer is either 'mu', or 'all of them', depending on your taste in rejecting questions. The final result is the weighted sum of all of the possible times of death, and no one of them is correct.

Note that for this identical case to apply, nothing inside the box gets to be able to tell the time (see note), which pretty much rules out its being an actual cat.

So... If you find Schrödinger's cat dead, then it will have had a (reasonably) definite time of death, which you can determine only limited by your forensic skills.

Note: The issue is that of cramming time-differentiating states into one final state. The only way you can remove information like that is to put it somewhere else. If you have a common state that the cat falls into from a variety of others, then the radiation from the cat's decays into this common state encodes this information. It will be lost to entropy, but that just falls under the aegis of 'we're not clever enough to get it back out' again, and isn't philosophically interesting.

Comment author: shminux 07 August 2013 07:33:02PM * 2 points [-]

Regurgitating the teacher's password is a matter of mental process, and you have nowhere near the required level of evidence to make that judgement here.

Yeah, sorry, that was uncalled for.

The un-decayed state has amplitude which gradually diminishes, leaking into other states.

Right. And each of those uncountably many (well, finitely many for a finite cutoff or countably many for a finite box) states corresponds to a different time of death (modulo states with have the same time of death but different emitted particle momenta).

When you look in a cat box, you become entangled with it.

Yes, with all of those states.

If the states resulting from death are distinguishable at different times

They must be, since they result in different macroscopic effects (from the forensic time-of-death measurement).

Where it really gets interesting is if the states resulting from cat-death are literally, quantum-identical.

Yes, but in this case they are not.

Then it's exactly like asking, in a diffraction-grating experiment, 'Which slit did the photon go through?'.

Not at all. In the diffraction experiment you don't distinguish between different paths, you sum over them.

The final result is the sum of all of the possible times of death, and no one of them is correct.

No, you measure the time pretty accurately, so wrong-tme states do not contribute.

Note that for this latter case to apply, nothing inside the box gets to be able to tell the time (cramming time-differentiating states into one final state would violate Liouville's theorem or some quantum equivalent, the name of which slips my mind), which pretty much rules out its being an actual cat.

Not quite. If the cat does not interact with the rest of the world, the cat is a superposition of all possible decay states. (I am avoiding the objective collapse models here.) It's pretty actual, except for having to be at near 0 K to avoid leaking information about its states via thermal radiation.

So... If you find Schrödinger's cat dead, then it will have had a (reasonably) definite time of death, which you can determine only limited by your forensic skills.

Yes it will. But a different time in different "worlds". Way too many of them.

Comment author: Luke_A_Somers 07 August 2013 10:19:08PM * 0 points [-]

The first few responses here boil down to the last response:

But a different time in different "worlds". Way too many of them.

Why is it too many? I don't understand what the problem is here. When you'd collapse the wavefunction, you're often tossing out 99.9999% of said wavefunction. In MWI or not, that's roughly splitting the world into 1 million parts and keeping one. The question is the disposition of the others.

Where it really gets interesting is if the states resulting from cat-death are literally, quantum-identical.

Yes, but in this case they are not.

Well, yes, because it's a freaking cat. I had already dealt with the realistic case and was attempting to do something with the other one by explicitly invoking the premise even if it is absurd. The following pair of quote-responses (responding to the lines with 'diffraction' and 'sum of all the possible') was utterly unnecessary because they were in a conditional 'if A then B', and you had denied A.

Of course, one could decline to use a cat and substitute a system which can maintain coherence, in which case the premise is not at all absurd. This was rather what I was getting at, but I'd hoped that your ability to sphere the cow was strong enough to give a cat coherence.

Comment author: shminux 07 August 2013 11:16:50PM * -1 points [-]

Why is it too many? I don't understand what the problem is here. When you'd collapse the wavefunction, you're often tossing out 99.9999% of said wavefunction. In MWI or not, that's roughly splitting the world into 1 million parts and keeping one. The question is the disposition of the others.

Well, if you are OK with the world branching infinitely many ways every infinitesimally small time interval in every infinitesimally small volume of space, then I guess you can count it as "the disposition". This is not, however, the way MWI is usually presented.

Comment author: So8res 08 August 2013 03:48:55PM * 1 point [-]

On the contrary, I've found that MWI is "usually presented" as continuous branching happening continuously over time and space. And (the argument goes) you can't argue against it on the grounds of parsimony any more than you can argue against atoms or stars on the grounds of parsimony. (There are other valid criticisms, to be sure, but breaking parsimony is not one of them.)

Comment author: shminux 08 August 2013 05:31:28PM * -1 points [-]

On the contrary, I've found that MWI is "usually presented" as continuous branching happening continuously over time and space.

Any links?

And (the argument goes) you can't argue against it on the grounds of parsimony

Indeed, the underlying equations are the same whether you aesthetically prefer MWI or not.

Comment author: So8res 08 August 2013 06:15:25PM 1 point [-]

Sure. Here's one. LW's own quantum physics sequence discusses systems undergoing continuously branching evolution. Even non-MWI books are fairly explicit pointing out that the wavefunction is continuous but we'll study discrete examples to get a feel for things (IIRC).

In fact, I don't think I've ever seen an MWI claim outside of scifi that postulates discrete worlds. I concede that some of the wording in layman explanations might be confusing, but even simplifications like "all worlds exist" or "all quantum possibilities are taken" implies continuous branching.

It seems to me like continuous branching is the default, not the exception. Do you have any non-fiction examples of MWI being presented as a theory with discretely branching worlds?

Comment author: Luke_A_Somers 08 August 2013 03:38:26PM 1 point [-]

Spacetime is not saturated with decoherence events.

Comment author: shminux 08 August 2013 05:32:33PM -1 points [-]

Inference gap.

Comment author: Luke_A_Somers 09 August 2013 08:14:28PM 2 points [-]

Roughly speaking: if you're working in an interpretation with collapse (whether objective or not), and it's too early to collapse a wavefunction, then MWI says that all those components you were declining to collapse are still in the same world.

So, since you don't go around collapsing the wavefunction into infinite variety of outcomes at every event of spacetime, MWI doesn't call for that much branching.

Comment author: shminux 09 August 2013 11:28:47PM -1 points [-]

Roughly speaking: if you're working in an interpretation with collapse (whether objective or not), and it's too early to collapse a wavefunction

I don't understand what "too early to collapse a wavefunction" means and how it is related to decoherence.

For example, suppose we take a freshly prepared atom in an excited state (it is simpler than radioactive decay). QFT says that its state evolves into a state in the Fock space which is a

ground states of the atom+excited states of the EM vacuum (a photon).

I mean "+" here loosely, to denote that it's a linear combination of the product states with different momenta. The phase space of the photon includes all possible directions of momentum as well as anything else not constrained by the conservation laws. The original excited state of the atom is still there, as well as the original ground state of the EM field, but it's basically lost in the phase space of all possible states.

Suppose there is also a detector surrounding the atom, which is sensitive to this photon (we'll include the observer looking at the detector in the detector to avoid the Wigner's friend discussion). Once the excitation of the field propagates far enough to reach the detector, the total state is evolved into

ground states of the atom + excited states of the detector.

So now the wave function of the original microscopic quantum system has "collapsed", as far as the detector is concerned. ("decohered" is a better term, with less ontological baggage). I hope this is pretty uncontroversial, except maybe to a Bohmian, to Penrose, or to a proponent of objective collapse, but that's a separate discussion.

So now we have at least as many worlds/branches as there were states in the Fock space. Some will differ by detection time, others by the photon direction, etc. The only thing limiting the number of branches are various cutoffs, like the detector size.

Am I missing anything here?

continue this thread »

Luke_A_Somers comments on Open thread, August 5-11, 2013 - Less Wrong Discussion

Article Navigation

Comments (307)

Nearest Meetups

Virtual Study Room

Recent Comments

Recent Posts

Recent Open Threads

Recent Rationality Diaries

Recent Wiki Edits

Top Contributors, 30 Days

Recent Karma Awards

Comments (307)

Top Contributors, 30 Days

You'll need to login or register to do that

(Don't worry, it only takes a few seconds)

Create

Login