
Atomic Spins Evade Heisenberg Uncertainty Principle - okket
https://www.scientificamerican.com/article/atomic-spins-evade-heisenberg-uncertainty-principle/
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photon-torpedo
Clickbait headline, I'd say. The experiment fully agrees with known quantum
mechanics. (Nevertheless, it is an impressive technical achievement.)

The authors of the original Nature article say that "spins obey non-Heisenberg
uncertainty relations", which is true if "Heisenberg uncertainty relation" is
(narrowly) defined as the uncertainty relation for position and momentum,
Δx⋅Δp ≥ ħ/2\. But since spins don't have position and momentum, they are not
expected to observe this uncertainty relation anyway. The more general
uncertainty relation for any two observables A and B reads ΔA⋅ΔB ≥ |⟨[A,B]⟩|/2
(where [A,B]=AB-BA is the commutator, and ⟨⟩ is the expectation value) and for
spins which have three components Sx, Sy, Sz the commutator is [Sx,Sy]=iħSz
etc, therefore the uncertainty relation for two spin components reads ΔSx⋅ΔSy
≥ ħ/2⋅|⟨Sz⟩|, hence it does not seem so surprising that it can be made rather
small if the expectation value of the third spin component can be made small.

Edit: typo

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monktastic1
Also: "This is because to measure its position you have to disturb its
momentum...". Another article in the long, illustrious tradition of mis-
explaining HUP as being due to measurement "disturbing" some property or the
other.

~~~
jeffwass
"Another article in the long, illustrious tradition of mis-explaining HUP as
being due to measurement "disturbing" some property or the other."

Disagree, it's a perfectly reasonable explanation of what's happening.

'Measuring' the system is really 'operating' on it. A quantum operation puts
the system into one of the operators eigenstates, and also yields the
eigenvalue as the measurement itself.

Two non-commuting operators, A and B, will have different eigenstates.
Applying operator A on the system puts the system into some eigenstate _a_ ,
which will be some linear combination of the eigenstates _b_ , of operator B.

So yes, operating on the system with operator A will put the system into a
superposition of _b_ states. If the system was in a well-defined _b_
eigenstate previously, it's not anymore. It was 'disturbed' by the
'measurement' done by operator A.

Position and momentum operators are examples of non-commuting operators. So
are the 'spin' operators that measure angular momentum along different axes.

~~~
pif
> it's a perfectly reasonable explanation of what's happening.

It's not false, but it's not entirely true. The uncertainty principle doesn't
state that you can't _measure_ p and q with arbitrary precision. It states
that you cannot _imagine_ them with arbitrary precision. It's like the double
slit experiment: when you measure which slit is traversed, interference
patterns disappear; but, when you don't measure, you cannot even _think_ that
the photon is passing through one slit instead of the other.

~~~
jeffwass
I don't follow your comment on imagining the measurements.

Uncertainty Principle refers to the arbitrary precision of two operators. You
can measure each operator individually to arbitrary precision. In theory, that
is.

If the two operators commute you can get theoretical arbitrary precision on
both measurements together. Since their commutator is zero.

If they don't commute, the product of standard deviations of each measurement
operator is restricted to no less than half the expectation value of their
commutator. (photon-torpedo's comment at the top of this thread gives a better
summary).

~~~
pif
It's not "imagining the measurements".

The UP is not only: "You can't know position and momentum together." It
rather: "Position and measurement _cannot be defined_ together."

In classical mechanics, you can imagine a particle being at a certain position
with a certain momentum. In quantum mechanics, you cannot.

~~~
jeffwass
Sorry, I have no idea what you're trying to convey in the first two
paragraphs.

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mathw
The article's introduction explains the uncertainty principle as the observer
effect, where the process of measurement changes a system. Which it's not,
quantum uncertainty is a fundamental consequence of the underlying physics, it
has nothing to do with influence from the measurement process.

And that's about as far as I understand it. The whole thing seems intended to
make my primitive brain hurt. But any experiment which starts off by cooling
things down to "a few microkelvin" definitely has my appreciation.

~~~
parenthephobia
> Quantum uncertainty is a fundamental consequence of the underlying physics,
> it has nothing to do with influence from the measurement process.

If you can prove that, your Nobel prize awaits. :)

The truth is that nobody knows why there is quantum uncertainty. The common
belief is that the uncertainty is "real", but non-local hidden variable
theories have not been proven to be impossible.

(In a recent survey of physicists, 47% favoured explicitly real uncertainty -
[https://arxiv.org/pdf/1612.00676.pdf](https://arxiv.org/pdf/1612.00676.pdf))

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randomaxes
This is a technique called squeezing, it in no way violates our fundamental
understanding of physics. Heisenberg uncertainty is generally: 1/2ћ ≤ ΔxΔp. If
you measure something in a way that you have complete uncertainty in the
quantity p then you can have arbitrarily fine resolution in x.

It's interesting, but squeezing is a common technique, and this headline
misrepresents the importance of this experiment.

~~~
jessriedel
It's not just the headline. Sentences like this are false:

> ...measure the spin precession rate much more accurately than previously
> thought possible.

since no one thought different.

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tbrownaw
Heh. Ask only what you want to know, _and nothing more_.

Good for QM because it gives you a sink to dump uncertainty, good for hiring
because it helps you not get sued, good for avoiding miscommunications in
general, ......

~~~
mikekchar
In a related way, I often talk about the Heisenberg Uncertainty Principle of
Metrics. The more you measure with the intent of adjusting the process, the
more people intentionally and unintentionally drive their behaviour based on
the metric. So it's a real skill to minimise measurement so that you are able
to control the areas you need to control without creating incentives for
people to do bizarre things in areas you didn't think about. It always drives
me crazy when managers start measuring things "just in case I want to use the
information in the future". It pretty much guarantees unpredictable behaviour
of the workers.

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philipov
This reminds me of a recent observation by (I think) some Princeton ethical
philosopher, that any theory of human behavior becomes invalid once it becomes
known by a significant proportion of the population, because people's behavior
anticipates expectations of their behavior.

~~~
kordless
This is simply thinking about thinking, which is allowed (at least in Zen) as
long as one doesn't think about thinking about thinking. In other words,
holding irrational beliefs and spreading those beliefs in a viral way, either
in the population, or inside one's own head, creates suffering if there is no
means to end holding the irrational beliefs.

