
Quantum theorem shakes foundations - robinhouston
http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392
======
ivan_ah
Very cool: <http://xxx.lanl.gov/abs/1111.3328>

Not sure if I understand all the assumptions. Here is the gist of it. The
debate is about the interpretation of quantum states |φ> (L2 norm unit vectors
in a complex vector space). Is |φ> something physical or is it simply a
outcome-probability-calculating method for predicting the quantum evolutions
and measurement outcomes.

View 1: |φ> is real.

View 2: |φ> is just a model of our knowledge of what is real + rules for
calculating prob outcomes.

Define the λ = { the physical state of a system }, i.e., that which //really//
exists in the world. The question is whether:

    
    
         λ = {|φ> and other stuff}               (1)
      or 
         λ = {other stuff not including |φ> }    (2)
    
    

If you have (2) then |φ> was really just some mathematical track-keeping and
calculation device -- it is not real: it is just something we use for
calculation. If (1) is true then the quantum state is part of the real world,
and in particular if quantum theory is complete, then λ = |φ>.

Point of view (2) says that the |φ> is not necessary to obtain the complete
physical state of the system.

The paper shows that point of view (2) is untenable.

Suppose only λs mattered for physics and (2) is true. Suppose further that a
single λ could correspond to two different quantum states |φ0> and |φ+>. Then
an apparatus that only knows λ would get "confused" sometimes and say that
impossible outcomes occurred. If you knew |φ>, you wouldn't get confused about
these outcomes. Therefore, they conclude that |φ> is a necessary part of the
physical description of the system.

|φ> is real.

~~~
grandalf
Interesting. So would it be correct to conclude that the paper just applies
logic to uncontroversial matters?

~~~
lisper
It's not "just logic", it's math, but yeah, pretty much.

~~~
grandalf
No intent to minimize the significance of logic. There is to little of it in
our world, often in spite of abundant facts.

------
newhouseb
Great timing with last night's Nova, Fabric of Time: Quantum Leap which covers
the context of this paper at a layman's level quite well (streamable for free
@ <http://www.pbs.org/wgbh/nova/>). It's a fantastic introduction to this sort
of material for the uninitiated, highly recommended.

~~~
spung
Thanks for this, enjoyed watching it this morning. I took the intro to Modern
Physics a few years back and this was a great refresher! So fascinating...

------
cygx
I didn't read the paper yet and it really might contain some valuable insights
into the nature of quantum mechanics (I'll take a look at it later today), but
I find this debate about whether the wave-function is a real object or not
hilarious: It completely fails to take into account that the wave function is
not defined on space-time, but rather on an abstract configuration space - it
confuses the mathematical model with physical reality.

The general problem with QM is that it's an algebraic and not a geometric
theory, ie you know the rules, but have no real concept about what they mean.
However, QM strongly resembles the Hamilton-Jacobi formulation of classical
mechanics, and the geometry of that is known (see eg
<http://arxiv.org/abs/math-ph/0604063> ).

The quantum numbers basically select a leaf of the foliation of our phase
space, and the wave function is some sort of probability distribution on that
(but not really ;)), which can be represented by a function on configuration
space (which is, in general, NOT space-time, in particular if multiple
particles are involved).

It's closest classical analogon is the action function S (or rather, its
differential dS), and you don't see many people arguing that dS is a real
object: it doesn't make a lot of sense to do so, and the same holds true for
the wave function.

~~~
cygx
I just read the paper. The authors actually make no claim about the reality of
the wave function, so disregard anything I said above (which is still true,
but not relevant).

However, they do claim to have disproven the statistical interpretation of QM.

This, however, is impossible: It can't be disproven from within QM, as all it
says is the following:

"We have no idea what happens when performing individual measurements.
However, let me tell you what you'll see when you repeat the experiment often
enough."

All the authors have shown is that their λ mechanism is flawed.

------
da-bacon
A very interesting paper (I used to work in quantum computing, so I think I
understand the paper pretty well after reading it a few times. Like most
foundations papers is deceptively short!)

The basic idea is fairly simple. From quantum states (the wave function) we
can determine probabilities of outcomes when these states are measured in
different manners. A major problem in quantum foundations is how to understand
these probabilities arise, i.e. where do these probabilities come from?

For example, it could be that the probabilities arise from our ignorance of
knowledge of the system (these are what people traditionally call hidden
variables.) Imagine a hard disk with a bunch of information on it. If you
don't know all of the bits on this hard disk, then your computer can act in
ways you can't explain because you don't know all of the bits. Each time you
setup your system and run a program you may get different results because that
extra information on the hard drive could be different, and so because you
don't know all of the information you will see probabilities of outcomes.
Mystery solved. Coming up with such a theory however currently always runs
into a problem with locality. But that's a story for a different comment
thread...

Here is what the authors ask. They say: well it could be that all of the
information that is specified in a quantum wave function is all that matters,
that is for each quantum state there is a one to one correspondence with a
configuration of the hidden information (they allow for extra information, but
that's basically irrelevant.) That is, literally, the quantum state is written
on your hard drive in all its glory detail, and each quantum state is
distinguished for any other quantum state. Contrary to this it could be that
the information overlaps in some way. That is for different quantum states,
some of the bits, say, will be in the same configuration. The authors then go
on to show that this later assumption isn't compatible with the predictions of
quantum theory (and show an experiment that can be done that will verify that
the later interpretation is not correct. If the experiment fails, then quantum
theory is wrong, and all hell will break lose. Assuming quantum theory holds,
this shows the second interpretation isn't viable.) Very neat.

There are a couple places where the argument seems a bit odd to me. For
example, it is really not clear to me why the measurement device in their
system has to depend on the portion of the information that is shared between
different prepared wave functions. If this information is ignored by the
measuring device, I don't see how their contradiction will arise. Of course it
self tells us something kind of interesting because it puts a limit on how
shared information is revealed to a measurement device (this seems almost
Kochen-Specker theorem like.)

~~~
sesqu
If I understood you correctly, the researchers show that a many-to-one
relationship between quantum representation and physical reality is untenable,
so the relationship must be one-to-one.

Isn't the conventional assumption that it's one-to-many? If so, this argument
isn't very interesting to me.

------
sage_joch
Out of curiosity, does this paper have any bearing on the many-worlds
interpretation of quantum physics?

~~~
lisper
Page 4:

"On a related, but more abstract note, the quantum state has the striking
property of being an exponentially complicated object. Specifically, the
number of real pa- rameters needed to specify a quantum state is exponen- tial
in the number of systems n."

This is an oblique way of saying that (quantum) reality consists of many
(classical) worlds.

~~~
hugh3
No it isn't, it's an explicit way of saying that the number of real parameters
needed to specify a quantum state is exponential in the number of systems.

~~~
lisper
Why do you think those are mutually exclusive? "the number of real parameters
needed to specify a quantum state is exponential in the number of systems" is
just a rewording of "the quantum state function is an exponentially
complicated object." But when you combine that statement with the main point
of the paper, namely, that this exponentially complicated object is physically
real, it is not unreasonable to infer that this physically real exponentially
complicated object comprises multiple copies of classical reality.

In fact, there are logically only three possibilities:

1\. The quantum wave function comprises zero classical realities, i.e. what we
call classical reality is not real but some kind of illusion. This is actually
a scientifically tenable point of view. See <http://arxiv.org/abs/quant-
ph/9605002>, particularly section VI.

2\. The quantum wave function comprises one classical reality, i.e.
Copenhagen. This is not any more a scientifically tenable point of view.

3\. The quantum wave function comprises multiple classical realities, i.e.
many-worlds is (are?) physically real.

Personally, I subscribe to option 1.

------
hasenj
From what I gather, quantum "particles" travel in a way that's wave-like, but
as soon as they interact with another quantum particle, the wave collapses
into a single point, and then starts traveling as a wave again starting from
the point of collapse. (or something along these lines).

This wave-like form is basically the "wave function"; it describes how the
quantum particle moves, and where we might find it.

If this is right, then I don't see anything "mysterious" in quantum
entanglement. If anything, quantum entanglement seems to be a proof that the
quantum-particle (aka wave function) has an internal state that can be known
without necessarily having to interact with it directly.

Somebody please throw some sense into me if I'm spewing non-sense.

~~~
SoftwareMaven
The problem is that the "collapse" (from wave to particle) occurs as a result
of somebody measuring. Google the double-slit experiment: when not measuring
individual photons, you get wave-like interference. When measuring individual
photons, you get particle behavior.

The conundrum is what is it about measuring that collapses the waveform? It is
quite a mystery, and, honestly, very exciting.

(btw, IANAP, but I love reading about it)

~~~
ivan_ah
> When measuring individual photons, you get particle behavior.

Actually, you get wave properties (interference) even with a single photon at
a time. This is why it is so fucked up...
[http://en.wikipedia.org/wiki/Double-
slit_experiment#Interfer...](http://en.wikipedia.org/wiki/Double-
slit_experiment#Interference_of_individual_particles)

~~~
Cushman
Not exactly. The collection of particles, even if you detect them one at a
time, displays an interference pattern. However, if you make an effort to
detect which slit each particle goes through, you see that each one behaves as
a particle, like you would expect, and the interference pattern vanishes.

And this is true whether you detect which slit it passes through before or
after its point of impact has been detected.

 _That's_ what's weird. A particle can be particle-like or wave-like, but not
both, and the thing that determines which it is is whether or not you _will_
look.

~~~
hasenj
It's not about humans looking at it. It's about collapsing the wave function.
The only to "look" at a particle is to make it interact with something
(trigger some chain reaction that ultimately sends a signal to one of your
senses, e.g. a photo multiplier). The moment it interacts with that thing, the
wave function collapses.

This part is not mysterious.

The mysterious part is, what in the world could be the thing that acts as a
wave function and then collapse to a single point when it interacts with
something else? What underlying reality does this hint at?

~~~
Anderkent
That part is not mysterious either - the collapse simply doesn't occur.

Say you have a photon in a superposition of state A and state B - think
position. If it is in state A it hits a detector, if it is in state B it does
not. If the detector is hit, it displays 'HIT' on its screen - otherwise it
does not. If 'HIT' is displayed, the researcher thinks photon was in state A,
otherwise the researcher thinks it is in state B.

The result of the experiment, without any wavefunction collapse, is a
superposition of two states of the entire system:

State 1: Photon is in A, Detector was Hit, Researcher thinks photon is in A

+

State 2: Photon is in state B, detector was not hit, researcher thinks photon
is in B.

As you can see, the fact that the researcher never sees a photon in a
superposition of states a+b (he doesn't ever see the detector both lit up and
not) is explained without any wavefunction collapse.

~~~
hasenj
> Say you have a photon in a superposition of state A and state B - think
> position.

Why are you assuming the particle has got to have a "position"?

The fact that a quantum particle can interfere with itself would be
experimental evidence that it doesn't in fact have a definite position.

------
Shengster
So does this imply that the universe is deterministic?

~~~
mdda
In some sense yes : If you know the starting conditions, one could just crank
it through to the outcomes (assuming the strongest form of their result).
OTOH, one can't measure everything, since you'd be collapsing wavefunctions
everywhere - changing the state of the universe as you go.

------
bglusman
OK, this might be a stupid/ignorant question, but what do they mean by "[it
seems very unlikely to be true that] if a quantum wavefunction were purely a
statistical tool, then even quantum states that are unconnected across space
and time would be able to communicate with each other."? Why is this less
likely than the alternative?

It reminded me of the single electron universe hypothesis by
Wheeler(<http://en.wikipedia.org/wiki/One-electron_universe>) and wonder if
anyone can speak to whether this changes perception on seriousness/testability
of that idea.

~~~
lisper
> Why is this less likely than the alternative?

Because the alternative is quantum mechanics. If unconnected states can
communicate, QM is wrong. QM is extremely unlikely to be wrong.

------
vest1
Question for the more knowable: Does this paper support/say-nothing/deny
anything about the view that the "particle-property" we're looking at is a
projection into the "space" we sense (at the moment) of a more complex entity
uniquely described by its wave-function?

------
ezyang
Is this about hidden-variable theories? I thought Bell's theorem already nuked
those...

~~~
redwood
afaik Bell's nuked local hidden variables, but not non-local, and also not
local in a deterministic universe

------
powertower
If you want to think about quantum state faster-than-light action-at-a-
distance spooky entanglement, look at it this way...

There are two gloves (a right and a left hand glove) and two lockboxes (box 1
and box 2).

Each lockbox contains one of the gloves. Someone other than you has placed the
golves in.

You open box #1 and discover that it contains the right hand glove. You now
know that box #2 contains the left hand glove (this is amazing to some).

The rational theory is that the states already existed before you looked into
either box.

The irrational theory is that neither of the states existed as "well-defined"
until after you looked into one of the boxes.

Quantum physics is just a way of abstracting the underlining reality. And it's
gone so far that it has completely de-materialized everything and replaces it
with math no one can understand.

Can anyone explain the proof to the irrational theory without more baseless
conjecture?

~~~
Anderkent
As many classical metaphors for quantum mechanics, your explanation is
intuitive, convincing, and demonstrably wrong.

There is simply no way to describe the underlying mechanisms of this world
using classical physics. However, since our brains are used to the classical
picture, the metaphors seem true at a glance.

------
ivan_ah
Very good explanation from an expert in the field:

[http://mattleifer.info/2011/11/20/can-the-quantum-state-
be-i...](http://mattleifer.info/2011/11/20/can-the-quantum-state-be-
interpreted-statistically/)

------
zwass
Does this break the non-determinism that makes quantum computing so efficient?

~~~
TeMPOraL
AFAIK It's not non-determinism that makes quantum computing efficient, it's
the ability to compute on superpositions, which effectively means computing
all outcomes at the same time.

~~~
zwass
Ah, right. I meant non-determinism in the sense of a non-deterministic
automaton that calculates all outcomes at the same time, not in the sense of
introducing randomness.

------
mindstab
So this is not a new idea, it's been around for decades, and just fallen in
and out of vogue. And now they present an [their] opinion piece on the topic.

I hardly think "shakes foundations" in the HN title and more of the same
hyperbole in the article is warranted

~~~
robinhouston
This article is about a new theorem that was uploaded to the preprint server
earlier this week[1], and the article quotes several quantum theorists who
describe this new result as important (or even ‘seismic’). On what basis do
you think it’s been around for decades?

1\. <http://arxiv.org/abs/1111.3328>

~~~
Jach
The actual formal theorem is new and great, but the general battle of
asserting the wave function's existence vs. non-existence (whatever either are
supposed to mean) vs. saying "I don't know tell me more about the wavefunction
and its experimental predictions working/failing" has been around for quite
some time. Here's a nice write-up of the ridiculousness of someone
definitively saying "I don't know why this works and therefore it doesn't
exist!" <http://lesswrong.com/lw/q5/quantum_nonrealism/>

------
protez
"The wavefunction is a real physical object after all, say researchers."

Mathematics is just a representation of reality, not the reality itself.

No single law in all scientific fields can state that the law itself is the
physical object, or a part of the Universe. One may assert that General
Relativity can explain lots of observations we can make about this universe.
However, even if the observations match the way the universe seems moving
100%, it doesn't indicate that the universe itself is GR. GR is just a
successful model of reality that can assert some important relationships among
macroscopic observations in this universe.

Assume that someone forged a ultimate theory that can integrate every possible
physical observation we can make about this universe. Even if that's the case,
he can't assert that "this universe IS the theory." It's merely the theory is
a successful model of reality, but not that reality is model itself.

No one can dare to claim that a set of mathematical description of observation
equals reality. No wavefunction can be a physical object. That's simply
idiotic.

~~~
wcoenen
Not everybody is convinced that reality deserves to be on a pedestal separate
from mathematics. Perhaps the only thing distinguishing our reality from
mathematical structures is _that we are part of it_. All mathematical
structures with self-aware substructures (such as ourselves) appear to be
"reality" from the point of view of its inhabitants.

<http://en.wikipedia.org/wiki/Ultimate_ensemble>

<http://en.wikipedia.org/wiki/Modal_realism>

~~~
protez
Presented in the criticism sections of your mentioned Wikipedia articles,
Gödel's incompleteness theorem is there as a strong rejection to mathematics =
reality argument. No mathematics is self-contained, which means it's
incomplete to describe the totality of reality.

We shouldn't forget that mathematics is an invention of mortal human beings.
For the dwellers in quantum space, the mathematical fundamental might be
totally different from our one.

