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shminux comments on Open thread, August 5-11, 2013 - Less Wrong Discussion
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Yeah, sorry, that was uncalled for.
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).
Yes, with all of those states.
They must be, since they result in different macroscopic effects (from the forensic time-of-death measurement).
Yes, but in this case they are not.
Not at all. In the diffraction experiment you don't distinguish between different paths, you sum over them.
No, you measure the time pretty accurately, so wrong-tme states do not contribute.
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.
Yes it will. But a different time in different "worlds". Way too many of them.
The first few responses here boil down to the last response:
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, 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.
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.
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.)
Any links?
Indeed, the underlying equations are the same whether you aesthetically prefer MWI or not.
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?
Spacetime is not saturated with decoherence events.
Inference gap.
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.
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?
That's right, but it doesn't add up to what you said about spacetime being saturated with 'world-branching' events.
While the decay wave is propagating, for instance, nothing's decohering. It's only when it reaches the critically unstable system of the detector that that happens.
There is no single moment like that. if the distance from the atom to the detector is r and we prepare the atom at time 0, the interaction between the atom/field states and the detector states (i.e. decoherence) starts at the time c/r and continues on.
Depends on your framework, but it will actually start even earlier than that in a general QFT. The expectation <phi(r,t),phi(0)> will be non-zero for all times t. I suppose the physical interpretation is something like a local-fluctuation trips the detector.
Of course, commutators will be non-zero as locality requires.
I see that my short, simple answer didn't really explain this, so I'll try the longer version.
Under a collapse interpretation, when is it OK to collapse things and treat them probabilistically? When the quantum phenomena have become entangled with something with enough degrees of freedom that you're never going to get coherent superposition back out (it's decohered) (if you do it earlier than this, you lose the coherent superpositions and you get two one-slit patterns added to each other and that's all wrong)
This is also the same criterion for when you consider worlds to diverge in MWI. Therefore, in a two-slit experiment you don't have two worlds, one for each slit. They're still one world. Unless of course they got entangled with something messy, in which case that caused a divergence.
Now... once it hits the messy thing (for simplicity let's say it's the detector), you're looking at a thermally large number of worlds, and the weights of these worlds is precisely given by the conservation of squared amplitude, a.k.a. the Born Rule.
I take it that it bothers you that scattering events producing a thermally large number of worlds is the norm rather than the exception? Quantum mechanics occurs in Fock space, which is unimaginably, ridiculously huge, as I'm sure you're well aware. The wavefunction is like a gas escaping from a bottle into outer space. And the gas escapes over and over again, because each 'outer space' is just another a bottle to escape from by scattering.
Or is what's bugging you that MWI is usually presented as creating less than a thermally large number of worlds? That's a weakness of common explanations, sure. Examples may replace 10^(mole) with 2 for simplicity's sake.
I think we are in agreement here that interacting with the detector initially creates a messy entangled object. If one believes Zurek, it then decoheres/relaxes into a superposition of eigenstates through einselection, while bleeding away all other states into the "environment". Zurek seems to be understandably silent on whether a single eigenstate survives (collapse) or they all do (MWI).
What I was pointing out with the spontaneous emission example is that there are no discrete eigenstates there, thus all possible emission times and directions are on an equal footing. If you are OK with this being described as MWI, I have no problem with that. I have not seen it described this way, however. In fact, I do not recall seeing any treatment of spontaneous emission in the MWI context. I wonder why.
Another, unrelated issue I have not seen addressed by MWI (or objective collapse) is how in the straight EPR experiment on a singlet and two aligned detectors one necessarily gets opposite spin measurements, even though each spacelike-separated interaction produces "two worlds", up and down. Apparently these 2x2 worlds somehow turn into just 2 worlds (updown and downup), with the other two (upup and downdown) magically discarded to preserve the angular momentum conservation. But I suppose this is a discussion for another day.
Peculiar. That was one of the first examples I ever encountered. Not the first two, but it was one of the earlier ones. It was emphasized that there is a colossal number of 'worlds' coming out of this sort of event, and the two-way splits in the previous examples were just simplest-possible cases.
How can you cut a pizza twice and get only two slices? By running the pizza cutter over the same line again. Same deal here. By applying the same test to the two entangled particles, they get the same results. Or do you mean, how can MWI keep track of the information storage aspects of quantum mechanics? Well, we live in Fock space.