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NancyLebovitz comments on Yet more "stupid" questions - Less Wrong Discussion
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Is conservation of matter a problem for the many worlds interpretation of quantum physics?
I don't believe I am explaining MWI instead of arguing against it... whatever has this site done to me? Anyway, grossly simplified, you can think of the matter as being conserved because the "total" mass is the sum of masses in all worlds weighted by the probability of each world. So, if you had, say, 1kg of matter before a "50/50 split", you still have 1kg = 0.5*1kg+0.5*1kg after. But, since each of the two of you after the split has no access to the other world, this 50% prior probability is 100% posterior probability.
Also note that there is no universal law of conservation of matter (or even energy) to begin with, not even in a single universe. It's just an approximation given certain assumptions, like time-independence of the laws describing the system of interest.
LOL @ your position. Agree on most.
Disagree on the conservation of energy though. Every interaction conserves energy (unless you know of time-dependent laws?). Though nothing alters it, we only experience worlds with a nontrivial distribution of energies (otherwise nothing would ever happen) (and this is true whether you use MWI or not)
I don't know enough of the underlying physics to conclusively comment one way or another, but it seems to me defining "total mass" as the integral of "local mass" over all worlds wrt the world probability measure implies that an object in one world might be able to mysteriously (wrt that world) gain mass by reducing its mass in some set of worlds with non-zero measure.
We don't actually see that in e.g. particle scattering, right?
Defining total energy as the integral of energy over space implies that an object in one part of space might be able to mysteriously gain energy by reducing energy in other parts of space.
Do we see this in the real world? How useful is the word "mysterious" here?
Ordinary energy conservation laws are local: they do not just state that total energy is conserved, but that any change in energy in a finite region of any size is balanced by a flux of energy over the boundary of that region. I don't think any such laws exist in "multi-world-space", which even accepting MWI is basically a metaphor, not a precise concept.
So are there mysterious fluxes that move energy from one part of space to another?
Umm, yes ? They're quite ubiquitous.
Those look more like boring, physical-law-abiding (non-mysterious) fluxes that move energy form one part of space to another.
Not mysterious ones, no - only the ordinary ones that Plasmon mentions.
"Mysterious" here means "via an otherwise unexplained-in-a-single-world mechanism."
There's no mysterious quantum motion for the same reason there's no mysterious energetic motion - because energy / mass / quantum amplitude has to come from somewhere to go somewhere, it requires an interaction to happen. An interaction like electromagnetism, or the strong force. You know, those ubiquitous, important, but extremely well-studied and only-somewhat-mysterious things. And once you study this thing and make it part of what you call "energy," what would otherwise be a mysterious appearance of energy just becomes "oh, the energy gets stored in the strong force." (From a pure quantum perspective at least. Gravity makes things too tricky for me)
The best way for a force to "hide" is for it to be super duper complicated. Like if there was some kind of extra law of gravity that only turned on when the planets of our solar system were aligned. But for whatever reason, the universe doesn't seem to have super complicated laws.
Is there any plausible argument for why our universe doesn't have super-complicated laws?
The only thing I can think of is that laws are somehow made from small components so that short laws are more likely than long laws.
Another possibility is that if some behavior of the universe is complicated, we don't call that a law, and we keep looking for something simpler-- though that doesn't explain why we keep finding simple laws.
"We looked, and we didn't find any super-complicated laws."
This would manifest as non-conservation of energy-momentum in scattering, and, as far as I know, nothing like that has been seen since neutrino was predicted by Pauli to remedy the apparent non-conservation of energy in radioactive decay. If we assume non-interacting worlds, then one should not expect to see such violations. Gravity might be an oddball, however, since different worlds are likely to have difference spacetime geometry and even topology potentially affecting each other. But this is highly speculative, as there is no adequate microscopic (quantum) gravity model out there. I have seen some wild speculations that dark energy or even dark matter could be a weak gravity-only remnant of the incomplete decoherence stopped at the Planck scale.
I don't see why differing spacetime geometries or topologies would impact other worlds. What makes gravity/geometry leak through when nothing else can?
Standard QFT is a fixed background spacetime theory, so if you have multiple non-interacting blobs of probability density in the same spacetime, they will all cooperatively curve it, hence the leakage. If you assert that the spacetime itself splits, you better provide a viable quantum gravity model to show how it happens.
Provide one? No. Call for one? Yes.
Sure, call for one. After acknowledging that in the standard QFT you get inter-world gravitational interaction by default....
In usual flat space QFT, you don't have gravity at all, so no!
Well, QFT can be also be safely done on a curved spacetime background, but you are right, you don't get dynamic gravitational effects from it. What I implicitly assumed is QFT+semiclassical GR, where one uses semiclassical probability-weighted stress-energy tensor as a source.
So I know you said you were simplifying, but what if the worlds interfere? You don't necessarily get the same amount of mass before "collapse" (that is, decoherence) and after, because you may have destructive interference beforehand which by construction you can't get afterwards.
As an aside, in amplitude analysis of three-body decays, it used to be the custom to give the "fit fractions" of the two-body isobar components, defined as the integral across the Dalitz plot of each resonance squared, divided by the integral of the total amplitude squared. Naturally this doesn't always add to 100%, in fact it usually doesn't, due to interference. So now we usually give the complex amplitude instead.
A) If they're able to interfere, you shouldn't have called them separate worlds in the first place.
B) That's not how interference works. The worlds are constructed to be orthogonal. Therefore, any negative interference in one place will be balanced by positive interference elsewhere, and so you don't end up with less or more than you started with. You don't even need to look at worlds to figure this out - time progression is unitary by the general form of the Schrodinger Equation and the real-valuedness of energy.
For a huge oversimplification:
The cosmos is a big list of world-states, of the form "electrons in positions [(12.3, -2.8, 1.0), (0.5, 7.9, 6.1), ...] and speeds [...] protons in positions...". To each state, a quantum amplitude is assigned.
The laws of physics describes how the quantum amplitude shifts between world states as time goes by (based on speed of particles and various basic interactions ....).
Conservation of matter says that for each world state, you can compute the amount of matter (and energy) inside, and it stays the same.
No. It's not that kind of many-ness.
No, at least not in a technical mathematical-physics sense. "Conservation of matter", in mathematical physics, translates to the Hamiltonian operator being conserved, and that happens in quantum physics and a fortiori in all its plausible philosophical interpretations. In concrete, operationalist terms, this implies that an observer measuring the energy of the system at different times (without disturbing it in other way in the meantime) will see the same energy. It doesn't imply anything about adding results of observations in different MWI branches (which is probably meaningless).
For example if you have an electron with a given energy and another variable that "branches", then observers in each branch will see it with the same energy it had originally, and this is all the formal mathematical meaning of "conservation" requires. The intuition that the two branches together have "more energy" that there was initially and this is a conservation problem is mixing pictorial images used to describe the process in words, with the technical meaning of terms.
The deeper (and truer) version of "conservation of matter" is conservation of energy. And energy is conserved in many worlds. In fact, that's one of the advantages of many worlds over objective collapse interpretations, because collapse doesn't conserve energy. You can think of it this way: in order for the math for energy conservation to work out, we need those extra worlds. If you remove them, the math doesn't work out.
Slightly more technical explanation: The Schrodinger equation (which fully governs the evolution of the wavefunction in MWI) has a particular property, called unitarity. If you have a system whose evolution is unitary and also invariant under time translation, then you can prove that energy is conserved in that system. In collapse interpretations, the smooth Schrodinger evolution is intermittently interrupted by a collapse process, and that makes the evolution as a whole non-unitary, which means the proof of energy conservation no longer goes through (and you can in fact show that energy isn't conserved).
This is quite misleading. Since collapse is experimentally compatible with "shut up and calculate", which is the minimal non-interpretation of QM, and it describes our world, where energy is mostly conserved, energy is also conserved in the collapse-based interpretations.
That's wrong, as far as I understand. The math works out perfectly. Objective collapse models have other issues (EPR-related), but conservation of energy is not one of them.
Links? I suspect that whatever you mean by energy conservation here is not the standard definition.
When isn't it? (This is another Stupid Question.)
One example is that in an expanding universe (like ours) total energy is not even defined. Also note that the dark energy component of whatever can possibly be defined as energy increases with time in an expanding universe. And if some day we manage to convert it into a usable energy source, we'll have something like a perpetuum mobile. A silly example: connect two receding galaxies to an electric motor in the middle with really long and strong ropes and use the relative pull to spin the motor.
What is conserved, however, according to general relativity, anyway, is the local stress-energy-momentum tensor field at each point in spacetime.
Read the first section of this paper. Conservation of energy absolutely is a problem for objective collapse theories.
The definition of conservation being employed in the paper is this: The probability distribution of the eigenvalues of a conserved quantity must remain constant. If this condition isn't satisfied, it's hard to see why one should consider the quantity conserved.
ETA: I can also give you a non-technical heuristic argument against conservation of energy during collapse. When a particle's position-space wavefunction collapses, its momentum-space wavefunction must spread out in accord with the uncertainty principle. In the aggregate, this corresponds to increase in the average squared momentum, which in turn corresponds to an increase in kinetic energy. So collapse produces an increase in energy out of nowhere.
I have skimmed through the paper, but I don't see any mention of how such a hypothetical violation can be detected experimentally.
Yeah, the paper I linked doesn't have anything on experimental detection of the violation. I offered it as support for my claim that the math for energy conservation doesn't work out in collapse interpretations. Do you agree that it shows that this claim is true? Anyway, here's a paper that does discuss experimental consequences.
Again, my point only applies to objective collapse theories, not instrumentalist theories that use collapse as a calculational device (like the original Copenhagen interpretation). The big difference between these two types of theories is that in the former there is a specified size threshold or interaction type which triggers collapse. Instrumentalist theories involve no such specification. This is why objective collapse theories are empirically distinct from MWI but instrumentalist theories are not.
... and is isomorphic to MWI...
Doesn't seem like it. You have an initial state which is some ensemble of energy eigenstates. You do measurements, and thereby lose some of them. Looks like energy went somewhere to me. Of course under non-ontological collapse you can say 'we're isomorphic to QM! Without interpretation!' but when you come across a statement 'we're conserving this quantity we just changed!', something needs interpretation here.
If your interpretation is that the other parts of the wavefunction are still out there and that's how it's still conserved... well... guess what you just did. If you have any other solutions, I'm willing to hear them -- but I think you've been using the MWI all along, you just don't admit it.
... or any other interpretation...
I guess our disagreement is whether "something needs interpretation here". I hold all models with the same consequences as isomorphic, with people being free to use what works best for them for a given problem. I also don't give any stock to Occam's razor arguments to argue for one of several mathematically equivalent approaches.
If you have any arguments why one of the many untestables is better than the rest, I'm willing to hear them -- but I think you've been using "shut-up-and-calculate" all along, you just don't admit it.
I totally do admit it. MWI just happens to be what I call it. You're the one who's been saying it's different.
Depends how you interpret it. If you say a new universe is created with every quantum decision, then you could argue that(though I've always treated conservation laws as being descriptive, not proscriptive - there's no operation which changes the net amount of mass-energy, so it's conserved, but that's not a philosophical requirement). But the treatment of many-worlds I see more commonly is that there's already an infinite number of worlds, and it's merely a newly-distinct world that is created with a quantum decision.
I can tell you the details, but they don't really matter.
MWI has not been experimentally disproven. It all adds up to normality. Whatever observations we've made involving energy conservation are predicted by MWI.