
The Trouble with Many Worlds - lisper
http://blog.rongarret.info/2019/07/the-trouble-with-many-worlds.html
======
Diggsey
The many-worlds interpretation is a good way to reason about quantum mechanics
(certainly better than giving some special status to the experimenter), but
it's meaningless to ask whether those other worlds really exist or not, not
just because it's un-falsifiable, but also because if one defines "existence"
to include alternate worlds, then every possible state of the world exists. If
everything exists, then it's no longer a useful property to talk about.

One can replace many-worlds with an idea similar to relativity: you can only
make statements about the universe from the perspective of a particle within
that universe. Things entangled with that particle are "real", and one can
make statements about them, things not entangled with that particle are not
real.

When dealing with composite observers like ourselves, it's possible for a
particle to be entangled with only part of the observer. Since entanglement
propagates quickly, this is only a temporary inconvenience, but there are
certainly some metaphysical questions to answer about that interim state.

~~~
tim333
>it's meaningless to ask whether those other worlds really exist or not

Dunno - if you think of something like the two slit experiment whether the
worlds where the particle goes through slit one or where it goes through slit
two exist or not seems to have experimental results as they produce an
interference pattern.

You can also ask about more complicated situations and whether the other
worlds exist may not be meaningless if they have an effect on event
probabilities in ours, if only a small one.

~~~
Diggsey
In the many worlds interpretation, as soon as a world has "split"/"the wave of
differentiation has hit"/"particles have been entangled"/"whatever terminology
you want to use" from the observer, it has _zero_ impact on any future
results, not just a small impact. Until that split happens, we're just talking
about our own world. It's never possible to observe any evidence for more than
one world, that follows from the way we define what a "world" is.

Many-worlds does not try to explain why particles have a wave function, it
only tries to explain the source of the apparent randomness in the way that
wave function collapses, whilst removing the need for experimenters to be in
some way "special" and immune from quantum effects.

~~~
n4r9
Is that really true? In principle, if many worlds is the case then you could
have a super machine enact a powerful unitary transformation which transforms
the state of the observer such that there is interference between the two
copies of the observer.

------
orbifold
Something that never made sense to me is why people think of Quantum Mechanics
(the non-relativistic classical one) as fundamental. While some of its
principles certainly are, clearly QFT (quantum field theory) is fundamental.
From the perspective of quantum field theory there really is no observer just
different field that couple to each other. Something like a measurement can in
principle be described by a complicated interaction of fields (think of
shining light at a double slit). The big mistery is I would rather say why the
path-integral formulation of QFT (of which the principle of least action is
the classical limit) agrees so well with reality.

~~~
krastanov
There are a couple of reasons (you alluded to them when you said some of the
principles of QM are indeed as fundamental as QFT):

\- My favorite one is that in terms of computational complexity, the QM and
QFT are equivalent. A computational machine based on the rules of QM can
simulate QFT efficiently.

\- How does QFT describe the following situation: you have a particle created
at location x that then propagates and passes through a double slit setup
where you might selectively close one of the slits at any time (i.e. you
measure the particle's location). Any challenges of interpretation present in
QM are still present in the QFT formalism (but mathematically, both do predict
the evolution of the system correctly).

\- While my QFT experience is limited, I have the impression that the tools
for dealing withixed states it has are less developed than the ones in QM.
Given that due to the previous reasons QFT does not give much new insight to
the topic of measurements, it is reasonable to stick to the simpler (but
equivalent in our parameter regime) theory of QM and it's more sophisticated
mixed-state toolkit.

~~~
orbifold
\- Regarding your first point, I'm pretty sure this is untrue without further
qualifications (which I understand that you don't mention because this a forum
and not a scientific setting). In any case any such mapping would most likely
be NP hard (assuming your quantum computer has q-bits that can only interact
according to some graph, I would expect this to reduce to a graph isomorphism
problem).

\- You would deal with that by writing down a path integral (see for example
Feynman's PhD thesis) (btw. particle creation is not possible in non-
relativistic QM). The tricky thing is that of course "closing the slit" is a
very tricky thing to model in a path integral, but the situations "slit
closed" and "slit open" are rather straightforward. In any case even without
any computation what is clear from the path integral perspective is that
nothing mysterious is going on: You are supposed to sum over all possible
histories of the particle passing through the slit and hitting the screen,
weighted by e^iS. If there is some temporal variability in the position of the
slit, this just results in a huge complication in the integral to be carried
out (if you model closing the slit by a time dependent potential let's say).
The path integral is fundamentally a very good way of thinking about this,
because it generalises to much more complicated settings (gauge theory etc.),
whereas there really is nothing fundamental about measuring, you just happen
to drastically and in a temporally complicated way change the background your
quantum fields are propagating in.

\- On the contrary, basically QFT is the only way to deal with mixed states in
a principled way. For scattering you typically start out with the assumption
that things are in pure states at t=-infty and t=+infty, but in between the
whole point of introducing quantum fields is to keep track of how things are
spatially (plus gauge degrees of freedom etc.) "mixed". To be more specific QM
is just a D=1,0 QFT, with 1 time dimension and (zero-dimensional) points as
spatial dimensions. A mixed state rho is nothing more than a general quantum
field on these discrete points.

~~~
krastanov
On point 1: I did not get your argument about NP hardness and equivalence to
graph isomorphism. On the contrary, algorithms for efficiently simulating non-
trivial QFTs on a non-relativistic quantum computers exist:
[https://arxiv.org/abs/1111.3633](https://arxiv.org/abs/1111.3633)

Point 2: If "there is nothing fundamental about measuring" in the QFT case, I
do not see what is so special about the QM case (you just take a partial trace
over the "environment"). I (admittedly with humility as I am not as well
versed in QFT) really do not see how your answer is any different from this
(and I do not see how the path integral gives you anything new __for this
particular problem __, albeit being a beautiful formalism).

Point 3: QM has developed a lot of tools to deal with Marcovian and Non-
marcovian non-unitary dynamics (the whole zoo of master equations available in
it). Of course QFT can deal with density matrices if QM already can do that,
but the sophistication of the toolkit used for that purpose in QM seems yet
unsurpassed to me. And to your last point about creation of particles: Second
quantization is already available in non-relativistic QM, so there is nothing
weird about an a^dagger*b Hamiltonian in QM (I use it all the time for cavity-
qubit interactions) - so, yes, you can not deal with the creation of arbitrary
particles in QM, but you can still easily work with some restricted modes of a
field, without involving QFT.

~~~
orbifold
Regarding point 1: I should say that I'm not an expert in Quantum Computing,
but reading the referenced paper leaves me unconvinced that such an algorithm
exists in general. In the paper they show that they can simulate phi^4
efficiently and with arbitrary small discretisation error. My point regarding
the graph isomorphism in this case is as follows: In order to carry out the
discretisation, they employ a d-dimensional lattice and additionally introduce
a discrete number of Q-bits per lattice site. Then they require to be able to
evolve the state according to some time dependent hamiltonian (with
interactions adiabatically switched on and off). All proposed realistic
quantum computers only allow for a limited operator set of primitive
operations, dictated by the physical geometry of the implementation (1d
lattice of atoms in a trap etc.). My point was that more likely than not you
will always be able to come up with theories for which a mapping respecting
these physical constraints is hard (you won't easily be able to simulate a 3d
lattice with multiple q-bits per lattice site on a 2-d lattice of q-bits).
Also the article has to restrict itself to the case of massive particles and
as you know lattice simulation of fermions is also a problem.

Point 2 & 3: You are right of course, ultimately this is a question of what
techniques are useful. My comment was mostly aimed at the situation where
people start to discuss the philosophy of QM. There I find that QFT clarifies
the situation more than any philosophical elaboration on "measurement" and
things like that do.

------
ThePhysicist
I find this article rather hand-wavy. I mean, we have a very good
understanding of the measurement process in quantum mechanics through
experiments performed e.g. by Haroche's and Siddiqi's groups, which
demonstrate that quantum measurements are continuous, deterministic processes.
Irreversibility and the transition of a quantum state to a "classical" state
can be explained very well using entanglement and decoherence, which originate
from the coupling of the measured system with a very large, external quantum
system. With this approach, no magical wave-function collapse or breaking of
time reversal symmetry is required to explain the observed collapse of quantum
oscillations after measurement.

The interpretations of quantum mechanics that rely on wave-function collapse
need to provide a plausible mechanism for how the irreversibility within the
measurement process comes about, as a collapsed wave function is no longer
time-reversible (i.e. if we would flip the sign of the Hamiltonian we would
not be able to go back to a previous state as the wave function was
irreversibly changed during the measurement) and I haven't seen any physically
plausible attempt at this so far. So personally I still favor the many-worlds
hypothesis, if only because it doesn't require invoking a so-far unknown
process that destroys reversibility during quantum evolution.

~~~
fsh
What do you mean by measurements being deterministic? In Haroche's cavity-QED
experiments the outcome of each individual measurement is fundamentally random
and cannot be predicted. Quantum mechanics (regardless of which interpretation
one choses) only gives a probability distribution for the outcome of many
measurements.

~~~
ThePhysicist
Quantum measurements are not discontinuous, instantaneous processes but rather
determined by the continous evolution of the joint Hamiltonian comprising the
system being measured and the measurement system. You can perform partial
measurements of a quantum state and even exert feedback on the quantum system
to keep it at a given state (so-called quantum feedback). The outcome of a
given measurement is only random because we are part of the measurement system
and become entangled with it, which in combination with decoherence - due to
the near-infinite number of degrees of freedom in the measurement system -
leads to our experience of "quantum jumps". All of this can be explained with
the Schrödinger equation alone, without the need to invoke the principle of
wave-function collapse.

I don't like theories that require such a wave-function collapse mechanism in
order to get rid off all the extra "worlds" because they would require a
physically plausible mechanism that governs this collapse and the breaking of
time-reversal symmetry that it creates. It is also hard to think about a
scaling mechanism that would govern the wave-function collapse: If we imagine
that we will one day be able to build large quantum computers with many
millions or even billions of quantum bits we will be able to couple e.g. a
single qubit to the computer and perform a pseudo-random (but entirely
deterministic) range of operations on the other qubits. Should we assume that
at some point the wavefunction of the single qubit that is coupled to the many
other qubits will collapse? In that case we should not be able to reverse the
qubit to its initial state by reversing all operations performed on the other
qubits. At which scale should this happen then? If we could eventually scale
up the quantum computer to comprise a near infinite amount of qubits in such a
way that it's able to run a simulation of a toy universe with a conscious
observer in it, would that be enough to induce wave-function collapse (even if
we can still reverse the deterministic gate sequence at any time)? In such a
case, for each qubit state there would also be a version of the observer, each
seeing a different "collapsed" wave-function of the qubit. However, we could
still reverse the gate sequence of the computer at some point and bring it
back to its original state, uncollapsing the wavefunction of the qubit in the
process. Now, we would of course also reverse the state of the observer(s) to
their/its initial one. The question is, can we restore the state of the single
qubit to an uncollapsed quantum state while keeping the state of the observers
untouched? And if we could do it, what would it mean for the observer(s), will
we collapse their wave function in the process? Given infinitely precise
control over our quantum computer we should actually be able to do it since
the evolution of the quantum system is still deterministic. The more
interesting question is if this reversal of the single qubit state will
automatically lead to a collapse of the two observer(s) back to a single one
as well (here I'm not sure but this should be calculable).

In any case the conscious observer in our quantum computer would have no way
(as far as I can think of) to determine whether it lives in a many-worlds
quantum universe or one where wave functions collapse. We, on the other hand,
would know that its a many-worlds quantum universe because we just execute a
reversible, deterministic gate-sequence on the computer.

Sorry for rambling, my point is that it's a very metaphysical and (mostly)
irrelevant question for most physicists, and it's unlikely that we will really
come up with a way of deciding this question as we are part of the system that
we are trying to investigate. Answering the questions for a quantum world that
we simulate in a powerful computer might be possible, but it won't tell us
much about our own universe. I personally just prefer the many-worlds
hypothesis since it seems more elegant and simple and does not require coming
up with a new mechanism for destroying time-reversal symmetric in quantum
mechanics.

~~~
kgwgk
> All of this can be explained with the Schrödinger equation alone, without
> the need to invoke the principle of wave-function collapse.

But you need to invoke the principle of "we are part of the measurement system
and become entangled with it, which in combination with decoherence leads to
our experience of "quantum jumps"" which is not that much easier to understand
and you still have to introduce the Born rule somehow if you want to predict
probabilities.

The questions in your comment may be good questions, but the MWI doesn't
really answer them either.

------
spindle
As someone who's read a lot of work on the philosophy of quantum mechanics, I
want to say that this piece is VERY well written. (And I wasn't the person who
posted it to HN.)

~~~
lisper
Thank you! (I'm the author and the poster.)

~~~
je_bailey
My apologies if I get this wrong. Is this stating that the many possibilities
are all coexisting and that our brain is acting as a filter to provide a view
of possibilities that we define as ourselves?

~~~
lisper
That depends on what you mean by "this". If by "this" you mean MWI (the
Multiple Worlds Interpretation of quantum mechanics) then:

> Is this stating that the many possibilities are all coexisting

Yes.

> and that our brain is acting as a filter to provide a view of possibilities
> that we define as ourselves?

No, your brain is not "acting as a filter". There are multiple "your brains"
all "coexisting" in multiple universes (which MWI-ers call "the multiverse"),
none of which can ever communicate with each other.

------
xdarnold
Your objections seem to me to arise straightforwardly from a disconnect over
the definition of "you". Taking DW's position, and your axiom of unique self,
I can resolve the issue by saying something like:

Knowing that you can never be certain which branch you will end up in, bet on
the outcome that maximizes the liklihood that you will end up in a branch you
favor. Your bet, of course, will follow the form of the Born rule.

~~~
jeremyjh
Please explain the disconnect. In MW, there are many future "you" (or "I"),
all of which will exist. The fact that they do not share information with each
other doesn't change the fact that they are all you (or I). There isn't a
single branch you "end up" in, you are in all of them.

~~~
xdarnold
Your choice of the future here is arbitrary - we could just as easily say that
there are many past and present "you" in the multiverse. This assumes a
definition closer to DD/DW's than the author's.

The author seems to assert that his experience of self is incongruous with
this definition of your identity. As a historical fact, "you've" always either
chosen chocolate or vanilla, not both. The other branches aren't in fact you,
any longer.

------
millstone
Armchair physicist here, and yet:

> The probabilistic predictions of quantum theory are conventionally obtained
> from a special probabilistic axiom. But that is unnecessary because all the
> practical consequences of such predictions follow from the remaining, non-
> probabilistic, axioms of quantum theory, together with the non-probabilistic
> part of classical decision theory.

Well this seems crazy! We can drop the Born rule axiom, because you (a game
theorist) will make the same decisions whether the universe is deterministic
or probabilistic?

The difference is crucial, right? A PRNG requires hidden state: exfiltrate the
state and predict all future results. But there is no room in the wavefunction
+ Schrödinger equation for such state: you either augment it (Bohmian
mechanics) or accept the essential probabilistic nature.

Probabilistic predictions cannot be obtained from deterministic axioms, just
like PRNGs cannot produce true randomness.

How does Deutsch resolve this?

~~~
lisper
Deutsch is a many-worlder so he would say there is nothing to resolve because
there is no randomness. Everything in the time-evolution of the multiverse is
deterministic.

~~~
BoiledCabbage
Could I ask a question? As you are clearly someone with a deep knowledge QM.

Why is Bohmian mechanics so frequently dismissed? It's such a straight forward
premise - there is an actually physical guiding wave and everything else falls
out "normally". Instead pages are written about MWI and hypothetical agents
optimizing their overall decision in universes they'll never see. And
undefinable concepts of trillions of universes splitting simultaneously. And
I'm not trying to be snarky at all, as I feel what you wrote above is one of
the best presentations od the topic I've seen.

To be perfectly frank QM is starting to scare me about physics. To a layman
which I am, Bohmian mechanics is so simple and straightforward it's almost
"obviously right". The macroscopic analogy of Farady waves is almost a nail in
the coffin (to a layman). Allow for non-locality of guiding waves, just like
ripples on a lake and everything else is deterministic and matches all
scientific observations. Events have probability for the same reason the
weather has probability: because we can't measure with the sensitivity
required to account for the complexity of the system and the difference in
initial conditions.

And yet, I've never seen any write up against Bohmian. I've never seen anyone
with deep knowledge on the subject discuss why Bohmian isn't the best
interpretation. It's just dismissed as an "also-ran". What scares me is 20
years from now something will emerge making it clear that Bohmian is the
"correct" interpretation. And then the question in my mind will be, "what took
it so long to even be seriously considered?". It would be proof to me that
physicis is being shifted from investigating and following up on the best
explanation for data to instead becoming "lawyers" trying to find data to
support their favorite pre-decided argument (ie their favorite QM
interpretation).

Now all of that said, there is a reason why laymen don't make meaningful
contributions to a field. Their are deeper complexities that make their
intuitions wrong. But why are these flaws in Bohmian never discussed?

Would you mind taking even a few sentences to write up "what's wrong with
Bohmian" that would make the infinitely more complex MWI a more likely
candidate? I'm lost.

[1] -
[http://www.tcm.phy.cam.ac.uk/~mdt26/tti_talks/deBB_10/bush_t...](http://www.tcm.phy.cam.ac.uk/~mdt26/tti_talks/deBB_10/bush_tti2010.pdf)

~~~
lisper
The best place to find the answer to this question that I know of it David Z.
Albert's excellent book, "Quantum Mechanics and Experience." But the short
answer to your question is that Bohmian mechanics has two problems:

1\. In order to account for the outcome of Bell-type experiments on entangled
particles it has to assign a temporal ordering to space-like separated events.
The technical term for this is that you have to choose a "preferred foliation
of space-time". There has to be a preferred reference frame. But you can never
actually know what the preferred reference frame actually _is_.

2\. Yes, particles "have positions", but you can never actually know what
those position are (which is why I put "have positions" in scare quotes). This
is where all the quantum randomness hides in Bohmian mechanics. It's all "pre-
computed" in the infinite precision of a particle's position, but that
position is necessarily hidden from observation. I call this an IPU, an
Invisible Pink Unicorn. It's exactly the same thing as universe-weights in MWI
-- a set of numbers that are part of the theory but rendered immune from
observation not by practical limitations on technology, but by the theory
itself.

This is the fundamental problem with _all_ attempts to make quantum mechanics
look deterministic. The simple fact of the matter is that it's not
deterministic, so any attempt to make it look deterministic that makes the
same predictions as QM has to hide the randomness somewhere. Bohm hides it in
particle positions, and MWI hides it in universe weights. But it doesn't
matter what you _call_ the place in the theory where you've hidden the
randomness. What matters is that there is a place in the theory where you've
hidden the randomness, where it must forever remain hidden from the prying
eyes of experiment. So the claims that both Bohm and MWI make of being
deterministic are misleading at best.

~~~
hackinthebochs
>but that position is necessarily hidden from observation. I call this an IPU,
an Invisible Pink Unicorn.

But why expect that all state of the universe be open to observation? This
seems counter-intuitive to me. It seems far more reasonable that there
necessarily are facts about an implementation that no supervening system can
determine from within that system. For example, there are facts about a
physical computer that no software running on that computer could deduce. So
the fact that a QM theory posits state that is in principle off-limits to
observation doesn't seem like a reductio, but the expected case.

~~~
lisper
That's a good point, but remember, this is about rhetoric, not physics. The
question is not whether hidden state exists (it clearly does) but what kind of
_story_ you want to tell about it. If you find it enlightening to think about
hidden state as position, and you don't mind accepting all of the difficulties
that entails (like having to choose a preferred foliation), then by all means
go for it. But that is very different from saying that this story is actually
_true_. The only reason to prefer Bohm over a similar story that ascribes the
randomness to a literal invisible pink unicorn making decisions about
experimental outcomes is aesthetics.

------
bcgraham
Anyone else read Neal Stephenson’s _Anathem_? It drew heavily from Deutsch, so
it’s not totally surprising, but this argument seems pretty close to “Did you
read _Anathem_? Because _Anathem_.”

------
Taniwha
This has got me thinking about MW and the speed of light .... a quantum event
occurs here and the universes split, that split propagates out at the speed of
light ... at roughly the 'same' time a quantum event happens at Alpha Centuri
... the universe splits there and that change propagates out at the speed of
light .... 2 years later half way in between the splitting universes meet -
what does that mean?

~~~
xdarnold
"Splitting" does not propagate, or happen with any locality - it's the wave
function of the entire universe doing the splitting, so there's nowhere for it
to propagate!

~~~
n4r9
It makes sense to talk about the split propagating. A subsystem which is
spatially located at a distance from the splitting event will not immediately
become involved in the superposition, but may do once information about the
event has traveled.

~~~
xdarnold
When we talk about MWI as the asker is trying to more fully understand, we are
explicitly not talking about subsystems. There's just the one big evolving
state (of the universe).

~~~
n4r9
That's true, but that global state of the universe can be written in terms of
its reduced states on spatial subsystems. From this perspective we can talk
meaningfully about propagating superpositions. For example, take a toy example
in one dimension with three spatial subsystems A, B and C representing
disjoint intervals arranged in order. Immediately after a splitting event the
combined wavefunction over all subsytems might be:

(psi_1 + psi_2)_A x phi_b x rho_C

(ignoring normalisation for convenience) then after a certain amount of time
it becomes

(psi_1 x phi_1 + psi_2 x phi_2)_AB x rho_C

and then eventually

(psi_1 x phi_1 x rho_1 + psi_2 x phi_2 x rho_2)_ABC .

Now, all of that is certainly happening within the realm of some joint
superstate, but it still makes sense to talk about how fast the split
propagates, surely?

~~~
xdarnold
All depends on the context. Does it make sense to talk about propagating
splitting in this context? Surely no - for three reasons:

1\. You're describing a time evolution _of the subsystems_, which isn't really
a thing in the MWI.

A many-worlder would say, instead, that the Universe has split a bunch more in
the interim. He would point to the time evolution of the state of the
Universe, and perhaps there have a discussion about how the inseparability of
particular subsystems has propagated over time. Put differently, the many-
worlder might say the correlations of these particular relative states with
one another propagated over time.

What you've done, Everett would call characterizing branches of the universal
state in a space-like locality.

2\. Split != superposition. Frequently, splitting in MWI is identified with
decoherence, so in that sense there is a self-consistent way to describe local
splitting - but then you'd really mean, when you referred to the splitting of
"an object" or "a system", that Universal splitting had occurred in such a way
as to cause the object to exist in some particular multiple new branches.

3\. None of this line of discussion helps the parent gain an understanding of
how MWI is importantly different from (and the same as) other interpretations
of QM. It's far too shallow to amount to any real expert insight and yet too
technical to amount to any real layperson insight.

What can a discussion on propagating splitting illuminate here? It seems to me
that it is a less than useful idea for the parent and readers like him/her,
and many-worlds is more clearly understood without it.

~~~
n4r9
> You're describing a time evolution _of the subsystems_

In my head I'm thinking about the time evolution of the global state, but
examining the reduced state over certain subsystems at specific points in
time.

> Split != superposition. Frequently, splitting in MWI is identified with
> decoherence

Decoherence is a superposition effect, is it not? Entanglement with the
environment, i.e. a superposition of system-environment states.

> then you'd really mean, when you referred to the splitting of "an object" or
> "a system", that Universal splitting had occurred in such a way as to cause
> the object to exist in some particular multiple new branches

Yes, this is what I mean.

> What can a discussion on propagating splitting illuminate here?

Tbh I think it's unlikely that the parent is still following but I'm
continuing for the selfish purpose of trying to better understand your point.
That said, I believe that considering my toy example of a global quantum state
in one dimension _would_ illuminate their question about superpositions
propagating from here and alpha centauri and meeting in the middle.

~~~
xdarnold
> Decoherence is a superposition effect, is it not? Entanglement with the
> environment, i.e. a superposition of system-environment states.

The point I'm trying to make is that "splitting", while sometimes identified
with decoherence, isn't superposition (or any other well defined traditional
QM phenomenon). It's a term peculiar to MWI and it importantly has no clear
canonical technical definition. It generally refers to something just
considered abstractly: the branching of a single _universe_ into multiple. If
you use "split" and "entanglement" or "superposition" or any other QM term
interchangeably, you are bound to invite misunderstanding.

> ...illuminate their question about superpositions propagating...

Agreed... if that was their question. But their question didn't reference
superposition at all, it was about a split propagating:

> ...a quantum event occurs here and the universes split, that split
> propagates out at the speed of light...

Which is why I responded as I did. It is understandably confusing to wonder
what it means for propagating split universes to meet years later, if you
start talking about splits in this way. Propagating superposed particles? Much
easier to make sense of.

~~~
n4r9
Thank you for bearing with me for so long. I think I understand the point of
contention, i.e. that "split" is a slightly nebulous term which depends not
only on splitting but somehow on there being a negligible likelihood of future
interference between branches. In this context I agree it doesn't make sense
to speak of a split being spatially localised.

------
mannykannot
The idea of branch-counting seems untenable when we consider irrational
probabilities (which they are, of course, overwhelmingly likely to be),though
I think it would be begging the question to say, on that basis alone, that
branch-counting is the wrong way to look at it. I think the example used to
motivate branch indifference would be more persuasive if it used irrational
probabilities.

~~~
lisper
> it would be begging the question to say, on that basis alone, that branch-
> counting is the wrong way to look at it.

Exactly right.

> I think the example used to motivate branch indifference would be more
> persuasive if it used irrational probabilities.

What matters actually is not the probabilities but the branch
weights/amplitudes (because you have to square those to get the
probabilities). And those _are_ irrational if the probabilities are 2/3-1/3.

~~~
mannykannot
I take your point about the amplitudes not being rational, but in the examples
of branch counting that I have seen, including this particular example, the
counting is being done from the probabilities, not the 'raw' amplitudes.

------
mlthoughts2018
I did not like this article. I think the author incorrectly has some idea that
many worlds asserts the multiverse undertakes a real “splitting” activity when
observing the outcome of an experiment.

It does not. Rather all the different branches have always already existed all
the time, and you merely observe what branch “you” are on.

When you see the outcome of an experiment, it doesn’t mean “you branched” as
if the branches wouldn’t have existed if you hadn’t done the experiment.

It only means your brain got knowledge about which subset of all possible
universes you happen to be in.

The probabilities in quantum outcomes, like all probabilities, are about
subjective degrees of belief, as in they are about the state of a mind and not
objective attributes of nature.

~~~
lisper
> all the different branches have always already existed all the time

How many branches are there?

The answer is: there's no way to know because what constitutes "a branch" is
not well-defined. So saying that "all the different branches have always
already existed all the time" is meaningless because the phrase "all the
different branches" is meaningless.

> The probabilities in quantum outcomes, like all probabilities, are about
> subjective degrees of belief

No, they aren't. When you listen to a geiger counter, the number of clicks it
produces is an objective fact, completely independent of any sentient being's
beliefs. It is also random.

~~~
mlthoughts2018
There would have to be an uncountably infinite number, and the surface of
branches would be smooth, likely differentiable, because many experiments can
have outcome spaces of uncountably infinite cardinality.

> “No, they aren't. When you listen to a geiger counter, the number of clicks
> it produces is an objective fact, completely independent of any sentient
> being's beliefs. It is also random.”

You are simply incorrect about this. Did the Geiger counter click or did you
hallucinate or did the counter misfire or did your friend replace it with a
joke Geiger counter that always clicks or did a cosmic ray hit the circuitry
at just the right moment etc.

The probabilities around these things are about your subjective state of
knowledge, always.

~~~
lisper
> Did the Geiger counter click or did you hallucinate or did the counter
> misfire, etc.

Doesn't matter. What matters is that objective observers listening to the
counter independently will all _agree_ on how many clicks it made in a given
period of time. It is this _agreement_ that needs explaining. One possible
explanation is that the counter did, in point of physical fact, click that
many times. In fact, that seems like a very _plausible_ explanation for the
agreement to most people. That plausibility doesn't necessarily make it
_correct_ , but it does mean that you cannot dismiss it as "simply incorrect."
If I hallucinated the clicks, why then do I agree with all the other
observers, including inanimate ones like electronic counters? Are we all
experiencing the same hallucination? If the counter "misfired" then why do
geiger counters give the _appearance_ of producing random clicks in response
to radiation?

~~~
mlthoughts2018
Huh? If the counter is broken, you’ll all agree on the wrong number, because
of your mistaken brain state (believing the counter to be functioning
correctly). You may use a lot of italics, but the statement doesn’t add up to
anything.

~~~
lisper
> If the counter is broken, you’ll all agree on the wrong number

In what way will this number be "wrong"?

------
vkaku
I love the post. As time passed, I've come to think of our Universe
differently.

When I was out of school and Physics was cool: The Universe existed, created
me, I observe, things change.

When I am older and all the things are being unravelled: I existed, I begin to
observe, The Universe around me changes.

I am not on drugs, it's how I approach our world today.

------
beders
What has the human brain to do with anything? This whole thing is
philosophical at best. Physics is real whether we observe it or not. I think
we settled on that one. Using subjective experience in trying to explain
physical systems is bonkers.

~~~
fsh
On the contrary, decades of experiments violating Bell's inequality have shown
that the statement "Physics is real whether we observe it or not" can only be
true if we abandon locality. Non-local interpretations of QM, such as Bohmian
mechanics, are however incompatible with the Standard Model which is by far
the most accurately tested theory in physics.

~~~
kmm
There is no incompatibility between orthodox quantum mechanics and Bohmian
mechanics, the latter makes exactly the same predictions as the former. As
does any other interpretation of quantum mechanics. That's why they're called
interpretations, they're ways of ascribing an ontology to or making sense of
the mathematical models that are known to work so well to make experimental
predictions. They're not supposed to be competing theories.

There is nothing inconsistent or inherently problematic about abandoning
locality, quantum mechanics has some intrinsically non-local components
anyway. It speaks in favor of Bohmian mechanics that it explicitly describes
this non-locality and isolates it.

~~~
fsh
The point is that non-relativistic quantum mechanics and therefore also
Bohmian mechanics are wrong. They cannot even describe hydrogen atoms
correctly! Solving this issue required developing relativistic quantum field
theories. So far nobody managed to create a convincing relativistic version of
Bohmian mechnics.

------
tbabb
Using decision theory to explain quantum mechanics seems like a huge mistake
for a very simple reason: It confuses "ought" for "is". Decision theory makes
statements about what one _should_ do if one _wants_ a certain outcome. As the
author points out, what statements are we making about what we want? We are
free to decide that dividing ourselves and dividing an outcome are not
equivalent. But really the whole idea should look silly long before we come up
with such a specific counterexample: the laws of physics have no dependency on
the wants of human beings, in fact the wants of human beings are fully
dependent on the workings of physics (humans being physical systems), so an
explanation of physics in terms of statements about wants should appear
absurdly circular.

There does not need to be an agent optimizing outcomes in order for the
predictions of quantum mechanics to be correct. There doesn't need to be
agents _at all_ , since the laws of physics worked just fine in the billions
of years before there were people. This seems a bit like dressing up the
problematic Copenhagen notion of a privileged "observer" in different clothes.

I have never understood what is left to be explained in many worlds, and maybe
someone with deeper understanding can explain it: what is the problem with
simply saying that the squared amplitude gives the fraction of the
wavefunction that has evolved from the initial state into the final state?
What need is there to bring probability into the physics? If we are accepting
the initial wavefunction state as a premise x, and we associate each
configuration in the final state y with an experience we might have, then
isn't asking the "probability" of experiencing y given x, in a Bayesian sort
of way, naturally, emergently the same thing as asking the fraction of [the
wavefunction that evolved from all the configurations associated with x] which
is associated with y? What is missing and what is the dispute?

Last, what is this talk of "splitting"? I thought it was true that the
wavefunction is "incompressible", in that if some measurable that becomes more
confined, there is always some other measurable that becomes correspondingly
less confined? That is to say, if there is some axis in state space which
splits (distinguishes) universes by narrowing possibilities, there must always
be some other axis that merges (confuses) universes by widening possibilities?
That is to say, if ever you know more about what universe you are in, you must
know less (along some orthogonal axis) about what universe you came from? I.e.
for every "branch" there is a "merge".

------
leiroigh
It appears that a similar issue crops up in the interpretation of classical
mechanics.

That is, suppose we have our laws of classical mechanics. Hence, we have a
nice way of propagating states along time. Now we want to understand
thermodynamics and the arrow of time. Maths tell us that, if we slice-and-dice
microstates and macrostates in a certain way, then thermodynamics is correct.
In a certain way means "any non-crazy way with respect to Liouville measure"
and the entire thing only holds "for sufficiently chaotic/ergodic systems".

We observe (empirically / subjectively) that thermodynamics holds, and we have
an arrow of time. In order to explain this observation, we need an additional
axiom:

(A) The universe looks like it has Liouville-random but phantastically low-
entropy initial state in the far past. Liouville-random means something like
"absolutely continuous wrt Liouville-measure".

We could split that into

(A1) Thermodynamics makes sense. The universe cares about Liouville-measure.
(A2) With respect to Liouville-measure, we have a low-entropy state at some
point in time (hence we can define "past (noun): In the time-direction of the
designated point in time with low entropy").

In the overwhelming majority of such universes (classic trajectories),
observers see things that are compatible with both thermodynamics and an arrow
of time (and there is a possibility for conscious overservers to evolve).

Mathematically, there are many ways of measuring phase-space volume, in a way
that is invariant under time-evolution. Assuming ergodicity/chaoticity/mixing,
there is only a single such way that has bounded density function with respect
to "ordinary n-dim volume" (SRB-measure), and all these converge to Liouville.
But it would have been mathematically conceivable to take the same evolution
equations, and use a different measure that is supported on weird subsets of
low fractal dimension, and end up with different thermodynamics. Hence, we
need an extra axiom to separate observed reality from mathematical
possibility, and single out Liouville / ordinary volume.

Nobody takes issue with accepting this axiom. So why do people have issues
with accepting the Born rule as an axiom?

It is clear that we must add axioms to the evolution equations to explain that
we care about squared-amplitude and that we have an arrow of time. Sure, you
can try to prove theorems showing that alternatives to the Born rule are
crazy-weird, and make the axiom weaker ("if we care about anything at all, and
the thing we care about is not batshit insane then the Born rule holds"). For
example, MWI tries to replace copenhagen "if humans do experiments, use
squared-amplitude" with axiom "the universe cares about squared-amplitudes in
a non-crazy way" plus pseudo-theorem "human-scale experiments can be
approximated by Born rule". Certainly more elegant, because the universe
doesn't need to care about squishy emergent approximate concepts like "humans"
anymore. But it is the same axiom in the end, modulo some plausible not-quite-
proven maths for the pseudo-theorem.

Not-quite-proven even in the classical case: Formally proving unique
ergodicity / chaoticity / fast mixing is far beyond us for almost all non-
trivial systems. Just like e.g. complexity theory (we don't even have a formal
proof of P!=NP, so the name of the game is "mathematical plausibility" that is
spot-checked by tiny little theorems).

~~~
lisper
> why do people have issues with accepting the Born rule as an axiom

Because it offends people's intuitions about what must be happening behind the
scenes to make it true. Thermodynamics is mathematically complicated, but
intuitively very straightforward: you've got a bunch of billiard balls
bouncing around. People can visualize that. QM is fundamentally different. For
starters, the wave function operates in configuration space rather than
physical space, and is not always separable (which is what produces entangled
states). Furthermore, in classical mechanics, the limitation on knowing the
complete state of a system is merely technological. If we had accurate enough
measuring equipment the state of any system could be known in principle. In QM
this is no longer true. QM makes the true state of a system inaccessible even
in principle.

BTW, with respect to the arrow time, you might enjoy this:

[http://blog.rongarret.info/2014/10/parallel-universes-and-
ar...](http://blog.rongarret.info/2014/10/parallel-universes-and-arrow-of-
time.html)

~~~
leiroigh
Yeah, QM offends my aesthetic sensibilities as well. I cannot but shake my
head in disgust at creation.

But it does not get better by attempting to derive the Born rule. Of all
things to get offended by, why do people single out the Born rule? For
example, non-locality (e.g. Aharanov-Bohm) is imo much easier to understand
and already disqualifies reality from "believable theory-building". I
genuinely don't get it.

Re your link: I don't understand why the linked post talks about QM at all.
The arrow of time is a perfectly classical phenomenon; phrasing it in terms of
QM only helps us understand the formalism of QM if we already understood the
classical arrow of time. Or am I misunderstanding something?

~~~
lisper
> it does not get better by attempting to derive the Born rule.

Well, it _would_ get better if you actually _could_ derive the Born rule
without begging the question. But you can't so it doesn't.

> Of all things to get offended by, why do people single out the Born rule?

I guess you'd have to ask someone who was actually offended by it.

> am I misunderstanding something?

Yes, I think so. The arrow of time is _not_ a purely classical phenomenon.
Perhaps it _could_ be, i.e. if we were living in a purely classical universe
there might still be an arrow of time, but this is a moot point because we are
not living in a classical universe, so classical thermodynamics is not what
creates the arrow of time in our universe. It's more fundamental than that. It
_impossible_ to extract a classical universe from quantum dynamics without
establishing an arrow of time in the process.

~~~
leiroigh
Ah, ok, with "purely classical phenomenon" I meant "the classical limit h->0
also exhibits an arrow of time; observing the arrow of time and thermodynamics
is not enough to distinguish between a classical and quantum universe".
Therefore we gain no additional understanding of the phenomenon by looking at
QM; at most, we gain understanding of the mathematical framework of QM by
seeing how its formalism describes the classical arrow of time.

The arrow of time is a phenomenon that is robust under changes of underlying
theory; may as well discuss the simplest models that exhibit it, and these are
classical. Just like you would explain chaos with simple models first, e.g.
horseshoe, Lorentz, 3-body, before going into highly specific 1000 dimensional
systems.

edit: "Deriving the Born rule". An insightful "derivation" would be a pseudo-
theorem "if you want QM to limit to classical mechanics + Liouville Axiom,
then you must adopt the Born rule". But afaik this has been mostly done, so
there is nothing to explain anymore?

~~~
lisper
> the classical limit h->0 also exhibits an arrow of time

That is certainly true empirically. But it is much more difficult to explain
_why_ this happens in classical terms without begging the question -- you
can't just invoke the second law of thermodynamics here. You have to _derive_
the second law from Newtonian mechanics. That is an unsolved problem.

~~~
leiroigh
No, deriving the second law from Newton+Liouville is easy (in the form of
"mathematically plausible pseudo-theorem", that's late 19th century physics).
If you don't adopt Liouville measure as axiom, then it is impossible by (more
modern) counter-example: Thermodynamics looks different if you pre-suppose
that god cares about weird measures; and it is unavoidable if you pre-suppose
that god cares about Liouville measure.

~~~
lisper
OK... but this seems to me simply like trading one assumption for another. Is
there any reason why adopting the Liouville measure as axiom is any less
arbitrary than just adopting the second law directly?

~~~
leiroigh
Of course it is trading one assumption for another.

It basically comes down to "absent other specifications, one state is as
probable as another". As good Bayesians, we should reject this sentence: We
always, always need a prior; and if the prior is too crazy (e.g. has zero
probability mass on the correct hypothesis), then no amount of observation
will ever help us.

Since we deal with a continuous system, this is also a nonsensical sentence on
purely mathematical grounds: It could be "absent other specifications, one
state has as large probability density as any other, measured relative to
Liouville". An easy calculation shows that this state of affair (thermodynamic
equilibrium) is preserved by the flow. Furthermore, "If any state has as large
probability density as any other, measured to a small (absolutely continuous)
distortion of Liouville, and you wait long enough, then it all evens out to
Liouville", i.e. small distortions decay (mixing).

Large distortions do not need to decay. For example, you could single out one
specific crazy periodic trajectory (there are many crazy periodic
trajectories, but the set of crazy trajectories has small ordinary phase-
space-volume), and our large distortion is "I am somewhere on this specific
periodic trajectory". If we start on the periodic trajectory, then we stay on
it; hence, this state of affairs is preserved as well.

In order to separate the two, we need an axiom, like "Liouville is a good
prior". The equations of motion don't tell us that the first corresponds
better to reality than the second! This is an empirical observation.

Now start with Liouville, but prescribe that our initial data are in a
specific low-entropy macro-state. This means that we cut out some non-crazy
region of phase space and say "start anywhere here, but then count all states
as same probability". Then the second law holds (this is pseudo-theorem).

If we initially started with our crazy measure (concentrated on a single
periodic trajectory), then the second law fails / is vacuous. If we permitted
to cut out a crazy region of phase space, then it would also fail (crazy
region: Take a sane region R0 at time T0 and a sane region R1 at time T1, and
our crazy region consists of all points in R0 that will end up in R1 after
time T1-T0. All these points will end up in R1, so no second law for you).

This general program is as strong as it gets, and all the "non-crazy" caveats
are imo much less arbitrary than just adopting the second law directly. Of
course this opens a giant can of worms: What exactly does non-crazy measure
mean? What is a non-crazy way of slicing-and-dicing phase space into macro-
states? For which systems of physical thermodynamic interest can we formally
prove chaoticity / fast mixing?

Ok, I actually know the answer to the last question: Almost none. But I also
know the answer to "for which such systems of interest does anyone seriously
doubt that we have chaoticity / mixing": Almost none.

~~~
lisper
> Of course it is trading one assumption for another.

Why "of course"? If would only be "of course" if it were _impossible_ to
derive the second law from Newton's laws. AFAIK that hasn't been proven
impossible.

But I think you may have misinterpreted my objection. It's not that I object
to substituting one axiom for another _in general_. That can often represent
progress. For example: before Einstein, it was observed that inertial mass and
gravitational mass were very close to each other, lending considerable weight
to the reasonableness of assuming that they were in fact the same. It turns
out that you don't have to assume this. There's another set of axioms that
allow you to prove this, and these axioms are "better" because they provide a
much larger scope of explanatory power for the same axiomatic price.

By way of contrast, Turing machines and the lambda calculus are "the same" in
some deep sense that makes it silly to argue about which one is "the right
model" of computation.

It's not clear to me whether adopting Liouville really represents progress a
la relativity, or whether it's arguing potato-potahto a la Turing vs Church.

BTW, it just occurred to me that there is a fundamental difference between the
thermodynamic and quantum arrows of time: the thermodynamic arrow of time is
reversible in a non-isolated system. The quantum arrow is not.

------
mdemare
My rule of thumb with regard to objections to Many Worlds is that if the
article discusses consciousness, or brains, in any way, it’s not about Many
Worlds, but about consciousness, or brains, and I will stop reading it at
once.

~~~
EForEndeavour
Your comment enticed me to actually read the first few paragraphs of the
article, skim the rest, and ctrl+f for "conscious" and "brain". In my humble
opinion, your rule has raised a false positive here. The post is extremely
well written and sourced, weaving a story straight from highly technical
research papers. I'd suggest judging this article by itself, not a string-
matching filter.

Besides, isn't discussion of brains and consciousness perfectly relevant in
the context of QM, given the requirement for rigorous definitions of
observation, observers, etc.?

~~~
mdemare
Following your suggestion, I’ve read it now in its entirety and I’m
considering adding “subjective experience” to my axiom, but that might be too
aggressive.

~~~
lisper
It is the nature of subjective experience that is the source of all the
trouble with interpreting QM. If you ignore subjective experience, there is no
problem at all: the universe is quantum, and that's all there is to it.

But most people want to know why, if the universe is quantum, does it present
such a convincing illusion of being classical.

------
defterGoose
The whole "waves of differentiation" idea is quite an interesting one and
certainly seems to me to be an almost physical description of philosophical
concepts like free will and determinism. Perhaps these waves themselves
interfering are what gives rise to what we consider consciousness, since what
we experience subjectively is changing at every moment. Maybe the only reason
we are able to "think" at all and remain "coherent" and "self-subjective" in
our own brains is that these waves create images of the past on all their
neighboring matter that have a continuous time-evolution. There certainly (to
my mind at least) seems to be an element of randomness to thought that feels
quicker and less coherent than could be easily explained even by a large-ish
number of neurons with a comparable but larger number of interconnections.

I dunno, it seems a little overly-philosophical but surely there are
meaningful connections to be made between physical reality and the transience
of subjective experience.

