That is how are measurements physically proceeded (in
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Introduction to quantum physics: states, correlations and measurements
There is no physical law that say whether and when the state of
systems happen to be measured (observed), but for all practical
terms of how things appears, there is a condition specifying the
time when the hypothesis that measurement happened starts to be
"possible" (but not necessary). This condition is decoherence.
Other needed page :
Entropy in information theory
and statistical physics
Decoherence is NOT an interpretation, but it is an effective (though
only emergent) physical property that can be deduced from quantum
theory disregarding the choice of interpretation.
Its precise definition is :
A system S is said to have decohered with respect to a possible
measurement M, if there will be no more difference on the
probabilities of any future possible measurement of S, whether or
not the wave-function of S is assumed to be now already collapsed
with respect to M. Therefore in all practical terms, the
indetermination of the state of the system has been collapsed from a
quantum indetermination to a classical one, to be represented by an
element of the (n-1)-simplex (rather than the quantum n-states
shape) whose ends have irreversibly become clearly distinguishable
by measurements, at the expense of any other direction of
In other words, a decoherence is NOT a spontaneous collapse, but it
is the description of the circumstances where the question whether a
collapse happened or not, becomes unverifiable, so that the "already
collapsed" hypothesis becomes compatible with the predictions of
quantum theory on future measurement results (while a collapse
before decoherence would violate the predictions of quantum theory
on future measurements).
However, this property of decoherence is an emergent property that
only makes sense as a limit property of large systems instead of
elementary ones, because it depends on which future measurements can
remain possible or not in practice, and this is a fuzzy condition.
It is not exactly an internal change, but an external irreversible
loss of future opportunities to make measurements capable of
deducing the past characters of the system expressed by components
of the wave-function that an hypothetical present collapse would
In practice, decoherence happens as soon as (but not only if) a
measurement has been "physically processed", in the sense that we
have a macroscopic delivery of the measured result, that is, when
the information of the result is "out of the box" with many copies
of this information escaping in the environment, for example by
radiation or gravitation, so that it cannot be anymore securely
hidden by any further operation.
Let us now explain how the laws of quantum physics
allow measurements to be proceeded, finally reducing quantum
states into classical probabilistic states at a macroscopic level.
The interaction of a 2-states system we want to observe
with a measurement apparatus, will end up to produce correlated
states of the system with the apparatus.
We described above the sphere of correlated states between (↑,↓
) and (↓,↑).
By just rotating one spin, we get a similar sphere of
correlated states between (↓,↓ ) and (↑,↑), (and similarly to
adapt to the chosen direction of measurement).
Assuming that the measurement apparatus was initially in a known
pure state, the sphere of initial states of the system, will evolve
into such a sphere of correlations, with ↓ evolving into (↓,↓ ), and
↑ into (↑,↑) (where one component represents the state of the
measurement apparatus, and the other represents the state of the
system after measurement).
This would operate the complete observation of the system that would
collapse it into the perceived state... if we could observe the
state of the measurement apparatus.
So, how to do it ? The advantage of the measurement apparatus, will
be that it will let its state appear macroscopically, which means
that it will will make many copies of its state in the same
way. Such copies are faithful for copying the wanted
classical bit of information: whatever the state we can have in
the sphere of states between (↓,↓ ) and (↑,↑), if ever the first
component is measured in the intended direction (↑ or ↓), then
the possible result ↑ for one copy will collapse the other copy to ↑
too, while the other possible result ↓ on one copy will
collapse the other copy to ↓ too. And their respective
probabilities properly reflect the wanted observation.
Moreover, the mere fact of losing one of the copies away in the
environment, suffices to collapse the sphere of possible initial
states, by projecting it (orthogonally) onto its diameter, which
represents the segment of classical probabilistic states between
the 2 possible results we wanted to measure.
The cases of weak measurements, can be obtained by some other ways
of mapping the sphere of the object's initial state, into a
correlated state with the measurement apparatus. This is completed
by the same exact copying procedure for the obtained bit of
information as in the exact case.
Debunking some errors on decoherence, irreversibility and interpretations of quantum physics
As I explored the debates on the interpretations of quantum physics,
I went through the preprint "Why Current Interpretations
of Quantum Mechanics are Deficient" and others by the same
Tammaro). Unfortunately, I found the arguments of this article
to be not valid, but the expression of his naive misinterpretations
of the topics. I wrote him the below but he did not reply.
Other people also reacted to this article:
Here is a copy of my reply to his articles (replacing "you" by
"him"), which I consider interesting to publish for pedagogical
reasons, as these remarks may help other students learning about
decoherence and the measurement problem, who may be tempted with the
He wrote, after equation (4):
"For current technologies it would be very difficult indeed to
observe interference with a (near) macroscopic device.
Fundamentally speaking, however, equation (3) does permit the
observation of interference. Hence we cannot disregard the
superposition in a fundamental description, as future
technologies may bring it within experimental grasp. "
His misunderstanding here is his assumption that a clear
"fundamental" separation exists between what is "fundamental" and
what is only "for current technologies". By definition, a
measurement is a measurement if the measuring device is macroscopic,
that is, it is made of a very large number of atoms. But, roughly
speaking, the difficulty to "reverse" the measurement that was made
so as to measure the interference, is (something like) exponentially
difficult with respect to the size of the device, and also as time
passes and decoherence happens.
Formally, the "measurement of the interference" is a measurement
that does not commute with the initial measurement, so that it is a
logical contradiction to claim that both happened. More precisely,
this means that his hypothetical "future technologies to measure the
interference" are actually undoing the first measurement, which
means that this first measurement has to be understood as never
having taken place at all.
However, the thing is that, while this "undoing" of the measurement
does not seem "fundamentally impossible" when looking at the
fundamental equations, it quickly turns out to be completely
impossible by any conceivable technologies when he puts the problem
in context. And the obstacle is the same that explains the time
arrow of thermodynamics, that is the irreversibility of entropy
A naive idea in trying to reverse the measurement process (or the
entropy creation process) at an elementary level, would be to
"bounce it back", by a sort of "mirror". This is strictly impossible
because, depending on how "try to make it":
- Reversing the state to let further natural evolution bring it
backwards ? This reversion would have to be an antilinear
which is fundamentally impossible since all evolution has to be
- Keeping the state as such but changing the sign of the Hamiltonian
so as to reverse the evolution ? We can change the potential energy
function in different ways but we cannot change the sign of the
kinetic energy function.
The only remaining "solution" is to completely isolate the system
and "wait a long time" until its natural evolution comes back to a
configuration making the wanted new measurement practically possible
again. But this is impossible in practice for the following reasons:
One is that we need to use huge supercomputers in order to predict
exactly how long we need to make this very long wait before making
the new measurement that can successfully measure the thing we
wanted to measure.
The other reason is that the isolation of the system has to remain
perfect during this very long wait. And the average needed time of
wait is an exponential function of the size (number of atoms...) of
the isolated system. But in practice, totally isolating a big system
for a very long time is completely impossible because there are too
many interactions with the environment, which makes bigger and
bigger the size of the total system (including the affected
environment) where the information is dispersed and that we would
have to isolate again for an even much longer time.
These interactions can be : any thermic contact ; any exchange of a
photon by thermic radiation ; and finally, any exchange of a
graviton, which we obviously cannot bounce back to remain confined
inside the limits of the system, by whatever "mirror for gravitons"
we may wish to think about.
This irreversibility can be compared to the event of falling into a
black hole : the horizon after which nothing can come back is not
locally well-defined, however from a global viewpoint the fall is
After this he wrote
"Can we know if the observed pointer reading accurately
represents the “system value” or was it perturbed (perhaps even
strongly) by the environment? Clearly, one cannot know
without an appeal to another measuring apparatus, for which the
same difficulty may arise"
To be short : yes we can know it, and for this we do not need to
appeal to another measuring apparatus. We know it because the laws
of physics are such that the risks of perturbations are
insignificant when applied to the shape of the first measuring
apparatus, which has been precisely designed as to be robust in this
way, otherwise it would not be considered a measuring apparatus at
"It is obvious to every experimentalist that there is a great
difficulty in building a device which acts on a system to
produce perfect (or even near perfect) correlation between
states without introducing uncontrollable phase shifts"
Phase shifts do not matter here.
What matters is that |κi|=|ki|.
The phase is irrelevant because it has to be understood as the phase
of the state of the environment. Not only the phase of this state is
irrelevant but the whole state of the environment is irrelevant: it
plays no role on the resulting perception of the device by the
observer because it is traced out. In other words, what matters is
that the evolution by interaction with the environment, commutes
with the wanted observable. This is all what we need to know and
this is what we have, provided that the known laws of physics apply
to the well-designed apparatus.
With his analogy of the boat and the wave, the point is that the
boat is much bigger than the waves: the correct analogy is that we
have a 100-meters long boat reflecting centimeter-size waves. Even
if we have only one boat and a thousand waves, the waves will be
reflected by the boat in a way that depends on the position and
orientation of the boat, but these position and orientation will not
be significantly affected by the waves, but can be reliably measured
again by new waves, to be clearly distinguished from completely
different positions and orientations of the boat.
After this I directly skipped to his section about the Bohm
interpretation. There again he has a misunderstanding : while the
"position of the electron" appears fixed in an hydrogen atom, this
does not constitute a dipole because in the Bohm interpretation, the
diplole is not defined by the "position" of the charge but by
quantum properties of its guiding wave, so that the effective
predictions remain identical to those of orthodox quantum mechanics.
Now in the section on "consistent histories". Again his criticism is
wrong. Because he refers maybe to an expression of "consistent
histories" that did not make use of decoherence.
"the set of histories such that the particle has a well
defined position x0 at t0
forms a realm. In a like manner, one may show that the set of
histories such that the particle has a well defined momentum p0
at t0 also forms a realm."
No, they are not valid realms because they do not satisfy the
condition of decoherence. To satisfy the condition of decoherence, a
realm has to correspond to a physical evolution that includes a
measurement process of the considered observables, in other words,
happens in a context where decoherence makes the observable
accessible in a classical rather than quantum manner.
Any two decoherent realms will then be compatible in the sense that
their observables commute, unlike the examples he gave.
"Let us demonstrate that the probability for a given
realm is necessary for consistency and argue that it is an
obvious quantity to be deduced from experiment"
There are 2 possibilities: either the system is closed and the
experimenter does not measure anything in between. Then the realm is
only a choice of interpretation of what happens, no matter what
Or the experimenter makes some measurements in between, but these
very acts of physical measurements are themself disturbing and
changing the course of evolution, forcing the inclusion of his
observables in the realm of evolution of what happens (now in the
presence of these measurements), thus cannot constitute any measure
of adequacy of a realm describing what would happen in the absence
of these measurements.
"Firstly, the consistent histories formalism deems
that it must follow a particular history (in some realm).
Secondly, there is nothing outside the system to enact realm
selection. It is straightforward to see that there are only two
ways to guarantee the consistency of these two statements"
No. He imagines a problem where there is absolutely no problem.
Because the situation is exactly the same as in the following
"This vector has particular values of its coordinates (in some
coordinates system). But there is nothing outside the vector to
decide the selection of the coordinates system".
There is no a paradox here. At least not mathematically. Hum ok
there is a metaphysical dimension here that makes things different,
but empirically if we don't include a conscious observer in the
system but only look at the end result or in the many-worlds
interpretation, there would be no problem.
A good reason why the state of the environment cannot be measured is
that it is very quickly lost as entropy.
The answer most often cited is that of environmental ignorance.
Namely, the environment is not measured or the experimenter
lacks control over the environment.
The mention of “measurement” or “ignorance” in an argument for
the trace procedure is unacceptable."
"the assumption of unitary evolution of closed systems is
incompatible with any nonunitary evolution whatever"
The adjective "unitary", and the question whether an evolution is
unitary or not, does not make sense in the absolute but only
relatively to the Hilbert space of the system that he is
considering. The problem, what makes the evolution non-unitary, is
that we are not considering the same system along the way, so that
the evolution is not taking place inside a fixed Hilbert space.
First we consider a system (or measurement apparatus), then we
introduce the environment, then the system interacts with the
environment, then the environment leaves and we consider the state
of the system separately from the environment.
" It is evident that a realistic environment has a
Hilbert space with a large number of dimensions; however,
insight can be had by considering much simplified models."
Precisely not : by his oversimplification he loses the necessary
concepts to understand how things happen, and this is one of the
causes creating the troubles he complains of.
"In particular, we have introduced an environment whose
approximate base may be taken to be..."
The initial state of the environment is not a pure state but a very
mixed state made of an astronomical number of components (according
to its entropy). Among these components he can find the ej
"Of particular note is that the initial environment state
cannot involve a superposition of (...), because such an initial
superposition immediately spoils the interpretation of (6),"
Not even : (6) remains true (with different final states of the
environment) when replacing ϵin by ϵj.
Then I looked at his other article : "Structural Instability and
Quantum Lying in the Many-worlds (Relative State) Interpretation" I
only had a very short look at his article, but my guess (unless he
has anything deeper that how it seems) is that this is simply a
naive mistake he is making: while "theoretically possible", these
"quantum liar states" are effectively impossible for thermodynamic
reasons, that is, for the exact same reason that it is impossible
for thermodynamically irreversible processes to be reversed.
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interpretation problem of quantum physics
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