
A flutter in time: Quantum mechanics is immune to the butterfly effect - helsinkiandrew
https://www.economist.com/science-and-technology/2020/08/15/quantum-mechanics-is-immune-to-the-butterfly-effect
======
dreamcompiler
I'm not surprised by this. The Butterfly Effect only applies to nonlinear
chaotic systems and at the quantum level everything is linear.
Nondeterministic, but linear.

You can easily build macro-scale nonlinear systems from micro-scale linear
quantum systems; a double pendulum for example.

I rather dislike that the word "chaotic" gets applied to all sorts of things.
It has a specific meaning, and it refers to nonlinear systems with sensitive
dependence to initial conditions. It does not imply some vague connotation of
"random."

Chaotic systems are nonlinear and thus theoretically deterministic but
practically unpredictable. Quantum systems are not even deterministic in
theory, but they're linear and thus they do not exhibit sensitive dependence
(the Butterfly Effect).

~~~
tbabb
Quantum mechanics is deterministic in most interpretations _except_
Copenhagen, which is losing favor.

~~~
klysm
Is there a term for deterministic but where there is ‘hidden’ state such that
it appears random?

~~~
ithkuil
Hidden variable theories don't satisfy the bell equation.

There are other interpretations that don't require hidden variables and yet
are fully deterministic. There is no free lunch though, so usually these
interpretations require you "lose" something else.

As a layperson, the one that I can make most sense of is the Everettian
interpretation (often called Many Worlds, although I personally find that a
source of confusion).

In the Everettian interpretation there is only a quantum state and the
observer is part of it. Thus the non-determinism and the wave function
collapse is just an illusion due to the fact that the observers themselves are
in a superposition state (which they are not aware of) and entangled with what
they observe.

~~~
guerrilla
> Hidden variable theories don't satisfy the bell equation.

No, _local_ hidden variable theories don't [1]. De Broglie–Bohm pilot wave
theory [2] is a non-local hidden variable theory.

[1].
[https://en.wikipedia.org/wiki/Quantum_nonlocality](https://en.wikipedia.org/wiki/Quantum_nonlocality)

[2].
[https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory](https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory)

[3].
[https://www.youtube.com/watch?v=RlXdsyctD50](https://www.youtube.com/watch?v=RlXdsyctD50)

~~~
ithkuil
Oh yes, pardon my sloppiness. I was focusing be contrast between determinism
an indeterminism and I was giving locality for granted.

The Everettian interpretation is fully local, where any non-locality is just
an illusion caused by observers observing correlations they cannot otherwise
explain if they insist on the impossibility of themselves being made of matter
itself being in superposition.

EDIT: it's understandably hard to throw away the first person pooling if view
and our innate feeling of self and identity. Fuethermor the mechanisms of
consciousness are poorly understood. I'd argue that what's making it hard to
make progress on understanding consciousness is entangled with what makes it
hard to accept the Everettian interpretation (which is the simplest
consequence of basic quantum mechanics, nothing is added )

------
matt123456789
1\. Researchers set the value of qubit X to zero

2\. They pressed rewind on all qubits

3\. They scrambled the value of qubit X

4\. They pressed “play”

5\. They checked the value of qubit X to see how close it was to zero. Turns
out it was very very close to zero.

This calls for an explanation of the recovery of the final value of qubit X
despite the destruction of its initial state during step 3. The article
proposes that the information necessary to recover the final value is encoded
in the qubits with which X is entangled.

I don’t know enough about QM to understand how the system is able to use this
information to “set” the qubit to the value that it “should” be. Do the
researchers’ actions influence the values of the qubits with which X is
entangled in such a way that the forward evolution results in a system where X
recovers its initial (final) value?

My background is in deep learning. If I look at the activations in the final
layer of a network, and want to achieve an output for a particular element, I
can set that element to the desired value and run the network backward to
reconstruct an input that would give that value. If I perturb that input
slightly, the network will produce a slightly different activation pattern. If
I take an adversarial approach, I can have what would appear to be an outsized
influence on the final layer activations. I wonder if such an adversarial
perturbation has a quantum analogue.

~~~
gus_massa
Following your numeration, I'll try to ELI25:

0) Let's assume they have 4 qbits. Then the system has 2^4 = 16 possibilities,
so the complete estate of the system is a complex vector of length 16

(v_0000, v_0001, v_0010, v_0011, ..., v_1110, v_1111)

such that

|v_0000|^2 + |v_0001|^2 + ... + |v_1110|^2 + |v_1111|^2 = 1

And |v_abcd|^2 is the probability that if you measure the value of all the
qbits you get the value a in the first one, b in the second one, c in the
third and d in the fourth. When you measure the value of all the bits, the
system "collapses" and randomly select one of the possibilities using this
probabilities. (Yes, it is weird.)

1) Let's assume that X is the first qbit. They made a system where the first
qbit is zero. This is means that the last 8 coefficient of the vector, i.e.
v_1000, ..., v_1111 are zero. So if you measure the system you always will get
a 0 in the first qbit.

They probably made an easier initial configuration, where one of the
coefficients is one and all the other are zero, but the important part is that
at least all the coefficients of the vector where the first qbit is 1 have the
value zero.

2) Letting the system evolve in time (without an intermediate measurement) is
equivalent of multiplying the vector of length 16 by an unitary matrix. The
coefficients of the matrix are determined by how you connect the quantum gates
or how your quantum system is made. The important part is that is unitary.

Reversing the time means multiplying by the inverse. If you make no
measurements, yo can go(simulate) back in time and return, and you get

v_new = U U^-1 v

so v_new = v

Here we must assume that the matrix U and U^-1 are not very diagonal or has
block, sparse, whatever. Let's assume that it is full or almost full and the
values of the vector are mixed thoughtfully by the matrix multiplication.

3) After going back in time, the state is w = U^-1 v. Then they measure one
qbit. Let´s assume that it is the last one. When you measure only one qbit,
you can get a 0 or a 1. Here you have to distinguish the coefficients where
the fourth qbit is 0 and the coefficients where the fourth qbit is 1.

The probability of getting 0 is related to the values of the coefficients
where the fourth qbit is 0

|w_0000|^2 + |w_0010|^2 + ... + |w_1100|^2 + |w_1110|^2

and the probability of getting 1 is

|w_0001|^2 + |w_0011|^2 + ... + |w_1101|^2 + |w_1111|^2

They sum 1, so it's a probability.

As a side effect of the measurement, if you get a 0, all the coefficients
where the fourth qbit is 1 get erased and only survive the coefficients where
the fourth qbit is 1. You have to multiply all of them so the sum is again 1.
But the important part is that half of the information is destroyed.

If the result of the measurement is 1, then the other half of the vector of
length 16 is erased. The important part is that in either case, half of the
vector is erased. You get a new vector w_half. :)

4) Now you return from your trip to the past. This is like multiplying the new
vector by U. So the result is

v_new = U w_half = U Msm w = U Msm U^-1 v

where Msm is the measurement operation.

Now v_new is not equal to the initial v, because the measurement in the past
is messing the calculation.

5) Now they measure the value of the first qbit in the new state. It is like
in 3. The probability of getting a 0 is

|v_new_0000|^2 + |v_new_0001|^2 + ... + |v_new_0110|^2 + |v_new_0111|^2

and the probability of getting 1 is

|v_new_1000|^2 + |v_new_1001|^2 + ... + |v_new_1110|^2 + |v_new_1111|^2

The result of the article is that in this last measurement there is a high
probability of getting a 0.

Note that if you apply this calculation to the initial states made in 1) you
get a 100% probability of getting a 0. So the idea is that the measurement in
the simulated past has not messed too much this value.

The important part is you can't use any unitary matrix U, it must be not very
sparse so U^-1 distribute the initial information in all the coefficients, and
when half of them are erased, you don't loose too much information.

------
gus_massa
The "butterfly effect" is only possible in some classic systems. For example
imagine that you put a drop of ink in a glass of water (with some sugar). If a
butterfly drinks some water, it will not change the final equilibrium state
where the ink is evenly distributed.

This prove that one particular quantum system does not have an important
butterfly effect, not that any quantum system does not have a butterfly
effect.

(Note that (as far as we know) reality is described by quantum mechanics. So
it they prove that any quantum system does not have a butterfly effect, then
the weather and all the other macroscopic systems do not have a butterfly
effect.)

~~~
hanoz
_> So it they prove that any quantum system does not have a butterfly effect,
then the weather and all the other macroscopic systems do not have a butterfly
effect._

You can build a chaotic system from non chaotic parts, so that doesn't follow
at all.

~~~
gus_massa
Completely agree. The problem is that they build _one_ small system that is
not chaotic. They didn't prove that _any_ quantum system is not chaotic as the
article try to present it.

------
kkylin
Looks like this is the paper:
[https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.12...](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.040605)

ArXiV: [https://arxiv.org/abs/2003.07267](https://arxiv.org/abs/2003.07267)

------
tasty_freeze
I've heard people claim that the mind cannot be strictly physical for there to
be free will, therefore free will must arise at the quantum level where there
are "free variables" that can interface to the strictly causal physical world.
Somehow these quantum events percolate up to the macro level to make manifest
that free will.

The butterfly effect only works when a physical system is on the knife's edge,
that it is prone to unstable/chaotic behavior. While it is conceivable that
these conditions could exist at times (all the way from quantum level to
saying "I'd like strawberry" vs "I'd like vanilla"), it seems unlikely to me
that those conditions happen frequently enough that one's free will can direct
the desired outcome consistently.

Secondly, the idea ignores the problem of how this free will "knows" which
quantum events to perturb such that their effects would cause the pachinko
machine of sub-atomic -> atomic -> molecular -> nervous system interactions to
achieve its intended outcome.

~~~
klysm
I think the notion of consciousness arising from quantum behavior is a kind of
‘god in the gaps’ fallacy
([https://rationalwiki.org/wiki/God_of_the_gaps](https://rationalwiki.org/wiki/God_of_the_gaps)).

~~~
oezi
I think parent didn't talk about consciousness, but free will/randomness
generated by the brain.

We already know that consciousness is lagging the decision processes in the
brain (we have decided to go for vanilla ice cream 30ms before we are
consciously aware).

It also seems obvious to me that the human brain can generate entropy somehow
(we can unpredictably go for chocolate ice cream). While I am sure that we
will be able to measure with sufficient accuracy any brain process that leads
to such decision while a decision is being taken, it seems that any suggestion
that we will be able know the outcome of the ice cream decision a time x prior
to presenting the choice (say 60 seconds) is impossible.

~~~
Vecr
I agree, but free will is not somehow being generated by that happening. In my
opinion, the sensation of "free will" is strong enough in most people to cause
them to defend it's objective existence, even though the evidence is doubtful.

------
kiki_jiki
Wouldn't this be simply because of the small number of variables compared to a
non-quantum scale system?

------
galaxyLogic
Because everything builds on behavior of elementary particles, which behave
randomly, everything more or less must behave randomly.

Because of things like laws of normal distribution when lots of randomly
behaving particles work together we have a way of predicting how the world
behaves. But we can never make 100% accurate predictions because at the bottom
there is randomness.

Butterfly effect amplifies the initial randomness, a small difference in the
random initial state can cause big differences in the end-state. But, there
even isn't any definite initial state. Therefore Butterfly Effect rules

This causes (in my view) the Arrow of Time. Because there are no definite
initial conditions there can not be any definite final conditions either.
Therefore it would be impossible to "reverse time" by following the equations
backwards from a given end-condition, because there are no definite end-
conditions.

Everything starts with a fuzzy quantum state of say momentum. Even when our
equations are deterministic because the initial condition is not knowable in
principle neither is the end-condition. And this must apply in the other
direction too, reversing the equations and starting from indefinite end-
condition we can not "reach back" to a definite "same" initial condition.
Therefore Time can not be reversed.

Now I am not a professional physicist, this is just my intuition. Based on the
above it seems intuitive to me why it is not a mystery that the Arrow of Time
can have only one direction.

~~~
ksaj
Besides the Thermodynamic Arrow of Time, there is also the Adaptive Arrow of
Time, which is effectively its reverse.

The theory of Natural Selection is an example of the Adaptive Arrow of Time,
since over time, variability in a population is minimized instead of
maximized, as the law of Thermodynamics would have it. That is to say, in
living things, randomness decreases disorder, at least for the time that a
thing is living or exhibiting life-like behaviours. Conway's Game of Life is
so named because of it.

Thermodynamics favours, among a set of probabilities, the most probable state.
Natural Selection, on the other hand, favours the improbable state. A purely
thermodynamic arrow of time would disallow increasing stability in
populations, and the entire concept of species.

There are other "arrows of time," but I don't know enough about them to
compare. My point is merely that thermodynamics explains only one of them. It
is a fascinating topic, and they are all probably related in some magical way
we are yet to understand.

~~~
galaxyLogic
It is fascinating. Are there any theories about why and how evolution is able
to work in the other direction than "time" in general?

~~~
ksaj
Here are two videos that explain it better than I ever could here:

[https://www.complexityexplorer.org/courses/103-origins-of-
li...](https://www.complexityexplorer.org/courses/103-origins-of-
life/segments/9707)

[https://www.complexityexplorer.org/courses/103-origins-of-
li...](https://www.complexityexplorer.org/courses/103-origins-of-
life/segments/9708)

Click on the Lectures tab if you are interested in Origins of Life. I took the
course, and fully recommend it. But only these two videos are specific to the
topic at hand. Some of the other materials overlap a little with quantum
subjects, but it's not really what the course is specifically about.

If you're interested in all the stuff you're hearing about COVID-19 with all
the vaccine trials etc, and what all this "spike" business is, you'll actually
understand it in depth if after going through the course in its entirety. And
you'll appreciate on a technical level why they keep hammering you to wash
your hands with _soap_. And as a side effect, you'll at least partially
understand how certain quantum calculations work.

If I sound like a fanboi, it's because I enjoyed the course greatly. Despite
it being so thorough, it is free. I donated, 'cos the world definitely needs
more courses like this.

------
dakial1
Maybe they thought they destroyed the information but it was still present
somewhere.

~~~
akvadrako
You can't destroy (or create) information in QM; a consequence of it being
linear.

------
ganzuul
This gives difficult to grasp answers about what time really is. If I
understood this right it implies that the present is a state of coherence, and
that the past and future diverges.

~~~
pmoriarty
This experiment merely "mimic the effect of evolving a quantum system
backwards in time".

Since this was a simulation there are no implications regarding time
whatsoever.

~~~
ganzuul
That doesn't seem right. Why would they simulate something with no relevance
to reality?

------
foxes
Quantum mechanics is unitary time evolution? Apart from measurement its all
linear, look at the Schroedinger equation... there's no chaotic dynamics. A
trivial result? Pity I cant read the rest of the article behind a paywall.

~~~
_Microft
Not that I could ever endorse such behaviour but have you tried calling on
Alexandra, patron saint of the paywalled scientist?

~~~
tzs
Would that work? This is an article for the general public in a weekly news
and opinion magazine. Isn’t that out of scope for the site you are hinting
about?

~~~
_Microft
Oops, I messed up. It would not help of course. My bad.

------
throw14082020
My heart fluttered as i thought this was another post about Flutter.

------
goldenkey
Mirror (non-paywall): [http://archive.is/SBBrp](http://archive.is/SBBrp)

