Re: [Phys-L] quantum measurement: observers, or not

[John Denker <jsd@av8n.com>]

On 3/25/19 4:49 AM, Antti Savinainen via Phys-l wrote:

> How should one think about "observer" in QM and relativity? 

Good question.  The short answer is, replace the "observer"
with something else, something that has the desired properties
but is simpler and easier to understand and free of undesired
properties.

> The term is widely used

Yes, alas.

> Or perhaps Mermin's lecture will clear it up.

Nope.

=======================

As for quantum measurement:  Two key properties we want are:
In the classical limit, a measurement should be
 a) unambiguous, and
 b) permanent.

If you have a measurement that you can tell to Wigner, and
Wigner can tell it to Wigner's friend, then clearly it is
classical.  The wavefunction has collapsed, which I take to
mean that all relevant wavefunctions have become un-entangled.
Another word for this is decoherence.

So the question arises, can we find a simpler way of obtaining
the key properties?  Something we understand, i.e. something
where we can write down a quantum-mechanical description of
*the measuring device itself*?

While we are at it, we might like to add a third key property:
 c) ideally, the measurement should not disturb thing being
  measured too much more than is required by the laws of physics.

For example, an ideal voltmeter should have a high input impedance.
Note: This is not always required;  for instance a bolometer
measures energy by absorbing it, with no pretense of leaving it
unchanged.

There are more details than I feel like explaining by email,
but the essential outline goes like this:
 a) you need /gain/ that you can get from an /amplifier/
 b) you need the /irreversibility/ that comes from /thermodynamics/

It turns out that there are amplifiers that can be understood down
to the last quantum-mechanical detail.  The poster child for this
is a playground swing, driven by /standing/ on it, standing up and
down at /twice/ the resonant frequency.  Any initial excitation
that is in phase with standing /up/ at the bottom of each half-cycle
gets amplified, because standing up does work against centrifugal
force, adding energy to the signal.  Meanwhile, any component that
is 90° out of phase gets actively de-amplified, since standing
/down/ at the middle of each half-cycle does negative work, sucking
energy out of the signal.  By amplifying the in-phase component and
de-amplifying the out-of-phase component, the amplifier:
 -- preserves area in phase space
 -- upholds the Heisenberg uncertainty principle
 -- upholds the second law of thermodynamics
 -- upholds Liouville's theorem
 -- upholds the optical brightness theorem
 -- upholds the unitarity of quantum mechanics
 ++ all of which are fundamentally the same thing.

You can easily build a table-top demonstration of such a thing.
I recommend it.  In the simplest case, you can lengthen and
shorten the pendulum by hand.  If you want to get fancy, you
can build a motorized version, which drives home the point
than an inanimate device can get the job done.

There are electronic versions of this:  The swing can become
an LC oscillator with a time-varying capacitance, 

The technical term for such a thing is "parametric amplifier".
The capacitance (or the length of the pendulum) is considered
a /parameter/ and you can achieve amplification by artfully
fiddling with the parameter.

Meanwhile, the poster child for a well-behaved thermodynamic
heat bath is mechanical waves on a semi-infinite string.  That
is to say, it starts "here" and goes off to infinity.  It has
infinite heat capacity;  that is, you can launch outbound waves
into the string and they run off and never come back.  It also
has thermal fluctuations, namely inbound waves, coming from
unpredictable far-distant properties of the initial condition.

  The fluctuation/dissipation theorem reduces to simply this:
  the impedance of the medium for inbound waves (fluctuations)
  is the same as the impedance for outbound waves (dissipation).

The electronic version of the heat bath is a 50 Ω transmission
line, or simply a 50 Ω resistor (and the heat sink to which it
is attached).

Rather then describing this in terms of plain old state vectors,
you are better off using /density matrices/.  You can see how
and where the wavefunction collapses.  For example, consider
this density matrix:

	[ ½  ½ ]
	[      ]
	[ ½  ½ ]

The particle has a 50% chance of being in the |up⟩ state and
a 50% chance of being in the |down⟩ state, but it does /not/
have 1 bit of entropy.  In fact it has zero entropy.  It is
a pure state.  The off-diagonal matrix elements tell you about
the correlations.  It is an entangled state.  It is a coherent
state.  It is a cat state (named after Schrödinger's cat).
Now it turns out that it doesn't take very much of a perturbation
to mess up the phase of the off-diagonal matrix elements.  You
soon get
	[ ½ -½ ]
	[      ]
	[-½  ½ ]

which is also a pure state.  Also you get lots of similar things
involving complex numbers.  When you take the ensemble average
over all phases, you get
	[ ½  0 ]
	[      ]
	[ 0  ½ ]

which is *not* a pure state.  It is classical.  It has one bit
of entropy.  Collapse has occurred.  Disentanglement has occurred.
Decoherence has occurred.  So this is how we make Wigner's friend
unnecessary:  We have produced a classical result, and we did not
need an anthropomorphic observer.  All we need is a good-enough
measuring device.  This is tremendous progress, because we can
*understand* the inner workings of the measuring device (whereas
nobody ever understood the inner workings of Wigner's friend).

    Tangential remark:  Planck invented QM as an outgrowth of
    /thermodynamics/ (not of classical canonical mechanics).
    This is not how we introduce the subject nowadays, and as
    always I am *not* suggesting that pedagogy should recapitulate
    phylogeny.  The point is simply that thermo and QM do play
    very nicely together.  AFAICT it is impossible to understand
    one without the other.

You can understand the measuring device in purely classical
terms.  That is:  Assume there is classical thermal noise in
the initial conditions of the dissipative element, at some
not-too-low temperature.  All the math works just fine.

For extra credit:  The QM version is 99.99% the same.  Just use a
much lower temperature, so that you are seeing quantum fluctuations
i.e. zero-point fluctuations rather than thermal fluctuations.  For
any single measuring device, the results are 100% the same.  This
is good enough for all practical purposes.

It gets slightly tricky if you hook multiple measuring devices to
the same signal.  Then, if you look closely enough, you can see
spooky correlations at a distance.  EPR.  Bell inequalities.  This
is a reminder:  Just when you thought you had quantum mechanics
entirely figured out, including the quantum measurement process,
you get reminded about this one dark corner of QM that is really
seriously weird.  Feynman once said that anybody who claims to
completely understand QM doesn't know what he's talking about.

HOWEVER, the point remains, you can get really, really close to
understanding the whole thing, measurements and all.  Having an
anthropomorphic observer is waaay more trouble than it is worth.
Instead, you are much better off using an amplifier and a heat
bath.  We know how to understand such things down to the last
detail.

There are some more-or-less understandable tutorials on the
subject, but I'm having trouble finding accessible copies.  I
can't spend any more time on this at the moment.  I will work
on it some more later.  If you want to see all the details in
a dense, not-very-tutorial format, there is always this:
  https://journals.aps.org/pra/abstract/10.1103/PhysRevA.29.1419
a copy of which is here:
  https://www.av8n.com/physics/refs/yurke-denker-1984-quantum-network.pdf

People have done experiments to show that you actually can
implement this sort of measuring device, and achieve a noise
floor (in one phase!) that is /below/ the zero-point fluctuations
in a black body.  It really is impressive to block the beam
with your and and observe that the noise reading goes /up/.
(At optical frequencies, your hand is effectively a zero-
temperature black body.)
  https://link.aps.org/doi/10.1103/PhysRevLett.60.764
a copy of which is here:
  https://www.av8n.com/physics/refs/yurke-vacuum-squeeze.pdf